Residual Strength and Fatigue Lifetime of ... - Solid Mechanics

Residual Strength and Fatigue Lifetime 

of Debond Damaged Sandwich Structures 

PhD Thesis 

Ramin Moslemian 

September 2011

Residual Strength and Fatigue Lifetime of 

Debond Damaged Sandwich Structures 

Ramin Moslemian 

TECHNICAL UNIVERSITY OF DENMARK 

DEPARTMENT OF MECHANICAL ENGINEEING 

SECTION OF COASTAL, MARITIME AND STRUCTURAL ENGINEERING 

SEPTEMBER 2011

Published in Denmark by 

Technical University of Denmark 

Copyright © Ramin Moslemian 2011 

All rights reserved 

Section of Coastal, Maritime and Structural Engineering 

Department of Mechanical Engineering 


Nils Koppels Alle, Building 403, DK-2800 Kgs. Lyngby, Denmark 

Phone +45 4525 1360, Telefax +45 4588 4325 

Email: info.skk@mek.dtu.dk 

WWW: http://www.mek.dtu.dk 

Publication Reference Data 

Moslemian, R. 

Residual Strength and Fatigue Lifetime of Debond Damaged 

Sandwich Structures 

PhD Thesis 

Technical University of Denmark, Section of Coastal, Maritime 

and Structural Engineering 

September 2011 

ISBN 978-87-90416-73-7 

Keywords: Fatigue, Fracture, Sandwich Structures, Composite 

Materials, Debonding

Preface 

This thesis is submitted as a partial fulfillment of the requirements for the Danish Ph.D. degree. 

The work was conducted at the Section of Coastal, Maritime and Structural Engineering, 

Department of Mechanical Engineering, Technical University of Denmark, during the period 

from January 2008 to September 2011. The project was supervised by Associate Professor 

Christian Berggreen, Professor Leif A. Carlsson, Senior Scientist Bent F. Sørensen and Senior 

Scientist Kim Branner. 

My sincere thanks go to Associated Professor Christian Berggreen for his supervision during the 

entire project, encouragement, and many illuminating discussions about different topics from 

practical matters regarding the experiments to theoretical discussions about fracture mechanics. 

His support and guidance is highly appreciated. Many thanks to Professor Leif A. Carlsson from 

Florida Atlantic University, for his insightful comments and constructive criticism. Special 

thanks go to Assistant Professor Amilcar Quispitupa at the Department of Mechanical 

Engineering, DTU for interesting discussions and priceless helps during the experiments. I am 

further grateful to Professor Jørgen Juncher Jensen, head of the Section of Coastal, Maritime and 

Structural Engineering, Department of Mechanical Engineering, DTU for facilitating a friendly 

trouble-free atmosphere at the working environment and to other colleagues at the Department as 

well. 

Part of this thesis was conducted abroad during seven months at the Department of Mechanical 

Engineering, University of Delaware, USA under the supervision of Professor Anette Karlsson. I 

would like to thank Anette for all her guidance, and for introducing the cycle jump technique to 

me which is the main foundation under the second part of this thesis. Very special thanks go to 

Professor Brian Hayman from Department of Mathematics, University of Oslo, Norway (earlier 

at Det Norske Veritas) for providing test specimens and precious discussions. Thanks to PhD 

candidate Marcello Manca and MSc student Sota Sugimoto for helping me with conducting 

fatigue experiments. 

Finally my very special thanks go to Leila for being there for me and her support during the last 

years of the study. 

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ii

Executive Summary 

Sandwich composites have been widely used in recent years for weight critical structures such as 

airplanes, wind turbine blades and high speed vessels because of superior stiffness/weight ratio 

compared to conventional metallic structures. Sandwich composites, composed of different 

materials with very different stiffness properties, are prone to different and peculiar damages. 

Face/core debonding is one of the most common damages sandwich composites can experience. 

A face/core debond may initiate due to different reasons such as problems during the 

manufacturing process or due to impact loading. Face/core debonding can be very critical for the 

structural performance as the basic sandwich principle is compromised due to absence of 

connection between the face and the core resulting in a lack of structural carrying capacity and 

integrity. 

A question that arises with all applications of sandwich composites is that of damage tolerance: 

how is the structural performance influenced by the presence of production defects or in-service 

damages? The aim of this thesis is to develop methodologies to answer this question. 

Traditionally costly and extensive experiments have been conducted for the assessment of 

damaged structure especially when they are exposed to cyclic loading. In this thesis as an 

alternative approach to reduce the cost and amount of experimental work, the main focus has 

been directed towards the development of numerical schemes replacing costly experiments. 

However to examine the accuracy and efficiency of the developed numerical schemes, they are 

all validated against experiments. 

The thesis is divided into two main parts. In the first part debonded sandwich columns and 

panels exposed to static loads are analyzed based on a fracture mechanics based numerical 

scheme. To validate the developed scheme, compression tests are conducted on debond damaged 

sandwich columns and panels. Furthermore, the face/core interface fracture toughness of the 

tested columns and panels are determined and applied in the finite element models to estimate 

failure loads. A good accuracy achieved in failure load estimations illustrates the efficiency of 

the developed scheme. However in some cases the simulations of the debonded sandwich panels 

show around 46% deviation in the determination of the failure loads compared to the 

experiments, indicating that the developed scheme should be used carefully. 

In the second part of the thesis fatigue lifetime of debond damaged sandwich composites is 

studied. To make the finite element simulation of fatigue crack growth practical, a cycle jump 

iii

method to accelerate the simulation is developed and incorporated in the fracture mechanics 

based numerical scheme developed in the first part of the thesis. It is shown that by utilizing the 

cycle jump method up to 99% of the computation time can be saved by eliminating the need for 

the simulation of every individual cycle. Using the developed numerical scheme, fatigue crack 

growth in the face/core interface of debonded sandwich X-joints and panels is simulated and 

compared with the conducted fatigue experiments. As inputs to the numerical scheme, crack 

growth rate relations for the interface of the analyzed sandwich X-joints and panels are 

determined at different mode-mixites. A good accuracy of the simulations compared to the 

fatigue experiments suggests that the developed accelerated fatigue crack growth scheme is a 

reliable tool for the damage assessment of debonded sandwich composites exposed to cyclic 

loading. 

iv


v

Synopsis 

Sandwich kompositter er i de seneste år ofte blevet brugt til vægt-kritiske strukturer såsom fly, 

vindmøllevinger og højhastigheds-skibe på grund af det overlegne stivhed/vægt-forhold i forhold 

til konventionelle metalliske strukturer. Sandwich-kompositter, sammensat af forskellige 

materialer med meget forskellige stivheds-egenskaber, er tilbøjelige til at få forskellige og 

varierende skadestyper. Skader i samlingen mellem dæklag og kerne er en af de mest 

almindelige skadestyper sandwich kompositter kan opleve. Skader i samlingen mellem dæklag 

og kerne kan initieres på grund af forskellige årsager, såsom problemer i fremstillingsprocessen 

eller belastningers indvirkningen på samlingen. Skader i samlingen mellem dæklag og kerne kan 

være meget afgørende for den strukturelle styrke, da det grundlæggende sandwich-princip er 

kompromitteret på grund af den manglende forbindelse mellem dæklag og kerne, hvilket 

resulterer i en mangel på strukturel bæreevne og integritet. 

Et spørgsmål der opstår ved alle anvendelser af sandwich-kompositter er skades-tolerance: 

Hvordan er den strukturelle integritet påvirket af tilstedeværelsen af produktionsfejl eller driftskader? 

Formålet med denne afhandling er at udvikle metoder til besvarelse af dette spørgsmål. 

Traditionelt er dyre og omfattende eksperimenter blevet udført for at vurdere den strukturelle 

integritet af beskadigede strukturer, især når disse udsættes for cyklisk belastning. I denne 

afhandling modeller, som et alternativ til at reducere omkostningerne og størrelsen af 

eksperimenter, præsenteret. Hovedvægten er lagt på udviklingen af numeriske simuleringsmodeller 

som kan erstatte eksperimenter, men for at undersøge nøjagtigheden og effektiviteten af 

de udviklede modeller er de alle valideret imod eksperimenter. 

Afhandlingen er opdelt i to hoveddele. I den første del analyseres sandwich søjler og paneler 

med skader udsat for statiske belastninger baseret på brudmekanisk numerisk modeller. For at 

validere de udviklede modeller, er der udført komprimerings-forsøg på beskadigede sandwichsøjler 

og paneler. Brudenergien for dæklag/kerne samlingen i de testede søjler og paneler er målt 

og derefter anvendt i finite element modeller til at estimere brudlasten. En god nøjagtighed ved 

beregningen af brudlasten tyder på, at de udviklede modeller er anvendelige. I vise tilfælde 

afviger simuleringerne af skadede sandwichpaneler dog med omkring 46% i forhold til 

vi

eksperimenterne. Dette ses som et tegn på, at i mere komplekse geometrier bør de udviklede 

modeller bruges med forsigtighed. 

I den anden del af afhandlingen er udmattelses-levetid af beskadigede sandwich kompositter 

undersøgt. For at gøre finite element simuleringen af udmattelses-revnevækst praktisk, er der 

udviklet en ”cycle jump” metode for at accelerere simuleringen. Denne er blevet indarbejdet i de 

i den første del af afhandlingen udviklede numeriske modeller. Det er vist, at ved at benytte 

”cycle jump” metoden kan op til 99% af beregnings-tiden spares, da behovet for simulering af 

hver enkelt cykel elimineres. Ved hjælp af de udviklede numeriske modeller er udmattelsesrevnevækst 

i dæklag/kerne samlingen for sandwich X-samlinger og paneler simuleret og derefter 

sammenlignet med de gennemførte udmattelses-eksperimenter. En god nøjagtighed i 

simuleringerne i forhold til udmattelses-eksperimenterne viser, at de udviklede accelererede 

udmattelses-revnevækst-modeller er et pålideligt værktøj ved skadesvurdering af sandwichkonstruktioner 

udsat for cykliske belastninger. 

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viii

Publications 

[P1] R. Moslemian, C. Berggreen, L. A. Carlsson and F. Aviles, “Failure Investigation of 

Debonded Sandwich Columns: An Experimental and Numerical Study”, Journal of 

Mechanics of Materials and Structures, Vol. 4, No. 7-8, 1469–1487 (2009). 

[P2] R. Moslemian, A. Karlsson and C. Berggreen, “Accelerated Fatigue Crack Growth 

Simulation in a Bimaterial Interface”, International Journal of Fatigue, Vol. 33(12), 

1526-1532 (2011). 

[P3] R. Moslemian, C. Berggreen, A. Quispitupa and B. Hayman, “Damage Tolerance of 

Uniformly Compression Loaded Debond Damaged Sandwich Panels - an Experimental 

and Numerical Study”, Journal of Sandwich Materials and Structures, Accepted. 

[P4] R. Moslemian and C. Berggreen, “Interface Fatigue Crack Propagation in Sandwich X- 

Joints”, International Journal of Fatigue, to be submitted. 

[P5] R. Moslemian, C. Berggreen, “Experimental and Numerical Investigation of Fatigue 

Crack Growth in Sandwich Panels”, International Journal of Fatigue, to be submitted. 

[P6] R. Moslemian, A. Karlsson and C. Berggreen, “Analysis of Face/Core Debond 

Propagation in Sandwich Panels Exposed to Cyclic Loading”, Engineering Fracture 

Mechanics, to be submitted. 

ix

Contents 

Preface 

Executive Summary 

Synopsis (in Danish) 

Publications 

Contents 

Symbols 

1. Introduction 1 

1.1 Background and Motivations ……………………………………………….. 1 

1.2 Thesis Overview ……………………………………………………………. 3 

1.3 Linear Elastic Fracture Mechanics …………………………………………. 5 

1.4 Linear Elastic Fracture Mechanics in the Interfaces ……………………….. 7 

1.5 Fatigue Crack Propagation in Sandwich Composites ……………………… 10 

2 Face/Core Debond Propagation in Sandwich Columns 16 

2.1 Background and Objectives ………………………………………………… 16 

2.2 Experimental Set-up ………………………………………………………... 17 

x 

i 

iii 

vi 

ix 

x 

xv

2.3 Experimental Results ……………………………………………………….. 19 

2.4 Characterization of Face/Core Interface Fracture Resistance ………………. 22 

2.5 Finite Element Model of the Debonded Columns ………………………….. 29 

2.6 Comparison of Numerical and Experimental Results ………………………. 31 

2.7 Conclusions …………………………………………………………………. 37 

3 Failure of Uniformly Compressed Debond Damaged Sandwich Panels 39 

3.1 Background …………………………………………………………………. 39 

3.2 Test Specimens ……………………………………………………………... 40 

3.3 Characterization of Face/Core Interface ……………………………………. 43 

3.4 Panel Tests ………………………………………………………………….. 49 

3.5 Panel Analysis ………………………………………………………………. 53 

3.6 Conclusion …………………………………………………………………. 60 

4 Fatigue Crack Growth Simulation in a Bimaterial Interface 63 

4.1 Background …………………………………………………………………. 63 

4.2 Cycle Jump Method ………………………………………………………… 65 

4.3 2D Face/Core Fatigue Crack Growth in Sandwich Beams ………………… 67 

4.4 3D Face/core fatigue crack growth in sandwich panels ……………………. 74 

4.5 Conclusion ………………………………………………………………… 85 

xi

5 Face/core Interface Fatigue Crack Propagation in Sandwich Structures 88 

5.1 Background …………………………………………………………………. 88 

5.2 Face/Core Fatigue Crack Growth in Sandwich X-Joints …………………… 90 

5.2.1 Experimental Study of the STT Specimens …………………………….. 91 

5.2.2 Fatigue Characterization of the Face/Core Interface …………………… 102 

5.2.3 Finite Element Modeling of the STT Specimen ……………………….. 110 

5.3 Fatigue Crack Growth in the Face/Core Interface of Sandwich Panels ……. 114 

5.3.1 Fatigue Experiments on Sandwich Panels ……………………………… 114 

5.3.2 Finite Element Modeling of the Debonded Panels ……………………... 120 

5.4 Conclusion …………………………………………………………………. 124 

6 Conclusions and Future Work 128 

6.1 Buckling Driven Face/Core Debond Propagation in Sandwich Structures … 128 

6.2 Fatigue Crack Growth in Bimaterial Interfaces …………………………….. 130 

6.3 Face/Core Interface Fatigue Crack Growth in Sandwich Structures ……….. 131 

6.4 Future Works ……………………………………………………………….. 133 

References 137 

A Additional Results from the Column Compression Tests 145 

A.1 Debonded Columns with H45 Core ……………………………………………. 145 

xii

A.2 Debonded Columns with H100 Core …………………………………………. 146 

A.3 Debonded Columns with H200 Core …………………………………………. 147 

A.4 Initial Imperfections in Debonded Columns …………………………………. 148 

A.5 Out-of-plane deflection of Debonded Columns ………………………………. 150 

B Additional Results from the Panel Compression Tests 155 

B.1 Load vs. In-plane Displacement Curves ………………………………………. 155 

B.2 Out-of-plane Deflection vs. Load Curves ……………………………………. 157 

B.3 Out-of-plane Deflection of the Debonded Panels ……………………………. 159 

C Additional Results from the Tests on the STT Specimens 163 

B.1 Axial Displacement vs. Force Curves from the Static Tests …………………. 163 

xiii


xiv

Symbols 

Roman Symbols 

A extensional stiffness 

a crack lenght 

B coupling stiffness 

Bct 

thickness of the CT specimen 

b width of the MMB specimen 

bs 

width of the steel specimen 

C1 

compliances of the first sub-beams in MMB specimen 

C2 

compliances of the second sub-beams in MMB specimen 

C3 

compliances of the third sub-beams in MMB specimen 

CMeasured measured compliance 

CMMB 

compliance of the MMB sandwich specimen 

Crig 

compliance of the MMB test rig 

Csteel 

compliance of the steel specimen 

c lever arm distance in the MMB test set-up 

D bending stiffness 

Ddenond bending stiffness of the debonded part of the MMB specimen 

Dintact 

bending stiffness of the intact part of the MMB specimen 

E Young’s modulus 

Ef 

Young’s modulus of the face sheet 

Ec 

Young’s modulus of the core 

Er 

Error in each cycle 

Est 

 

F 

Young’s modulus of steel 

overall average error 

Force 

G the energy release rate 

Gc 

facture toughness 

Gf 

shear modulus of the face sheet 

Gxz 

shear modulus of the core 

GMMB 

the energy release rate of the MMB specimen 

GIC 

interface fracture toughness under pure mode I 

GI 

mode I strain energy release rate 

GII 

mode II strain energy release rate 

mode III strain energy release rate 

GIII 

xv

H11 

bimaterial constant 

H22 

bimaterial constant 

h characteristic length 

hc 

core thickness 

hf 

face thickness 

K complex stress intensity factor 

KI 

mode I stress intensity factor 

KII 

mode II stress intensity factor 

k non-dimensional curve fitting parameter 

L length of the specimen 

M moment 

Njump 

number of jumped cycles 

Nref 

total number of cycles 

P load 

Pcr 

buckling load 

Pmax 

maximum fatigue load 

qy 

control parameter 

R computational efficiency ratio 

r radius 

Sij 

compliance matrix element 

S12 

discrete slope of the state variable increment between cycle one and two 

S23 

discrete slope of the state variable increment between cycle two and three 

Sjump 

estimated slope after a cycle jump 

T none-singular stress parallel to crack surface 

t time 

Ws 

required energy for creation of new surfaces 

x distance from crack tip 

y state variable 

yjump 

estimated state variable from the cycle jump analysis 

estimated state variable from the reference analysis 

yref 

Greek Symbols 

material mismatch parameter 

potential energy 

deflection 

ij 

Kronecker’s delta 

max 

maximum displacement 

x 

opening relative displacement of the crack flanks 

y 

sliding relative displacement of the crack flanks 

z 

out-of- plane relative displacement of the crack flanks 

tcyc 

time of each cycle 

tjump 

cycle jump time 

cycle jump time for state variable y 

ty,ump 

xvi

oscillatory index 

ratio between compliance matrix elements 

Poisson’s ratio 

elastic foundation modulus parameter 

stress 

ij 

cr 

wrinkling load 

angle 

finite width correction factor 

Mode-mixity phase 

load partitioning parameter 

xvii


xviii

Chapter 1 

Introduction 

1.1 Background and Motivation 

Because of a high stiffness and strength to weight ratio, sandwich structures have received 

increasing attention in a variety of weight critical structures like wind turbine blades, airplanes 

and ships. A sandwich structure comprises two strong and stiff face sheets separated by a light 

core. The face sheets carry applied in-plane and bending loads and the core resists shear loads. 

The three layers are typically glued together which forms additional glue layers in the sandwich. 

The sheet materials can be metalic or non-metalic. The matalic face sheets include steel, 

aluminium etc., whereas the non-metalic face sheets are normally the fibre reinforced composites 

(FRP). The main types of the core are the corrogated, the honeycomb, the balsa and the foam 

cores. The corrogated cores are to a great extent used in heavy industries like shipbuilding as 

well as packing industries. The honeycomb cores are more expensive and typically used in 

aeronaticall industries because of their superior performace compared to weight. The balsa and 

foam cores offer a good performance compared to price and are widely used in maritime 

strcutures and wind turbine blades. 

Because of being composed of very dissimilar materials, sandwich structures have peculiar 

damage modes (Zenkert, 1997): 

Face/core failure 

Core shear failure 

Face wrinkling 

Face/core debonding 

Global buckling 

Shear crimping 

Face dimpling 

Core indentation 

1

These peculiar damage modes often result in considering higher safety factors during a design 

process compared to similar metallic structures, which makes a detailed study of failure modes 

of sandwich structures essential if maximum structural efficiency is to be reached. Face/core 

debonding and its propagation are among the most critical damages a sandwich structures may 

experience, as structural integrity is closely linked to the adequacy of the bonding in the 

face/core interface in these structures. Debonds may emerge due to production defects, in-service 

overloading and local loads like impact, see Figure 1.1. A debond may be initiated directly in the 

face/core interface, in the core just below the resin-rich cells or in the face sheet (for composite 

face sheets). If a debond emerges in any of these locations, depending on the loading at the crack 

tip and toughness of other neighbouring layers, it may continue propagating in the original 

debond position or kink into the core, interface or face sheet, see Figure 1.2. Studies have shown 

that face/core debonding considerably reduces the load carrying capacity of sandwich structures 

(Nøkkentved et al., 2005, and Berggreen et al., 2005). A question that arises for debond 

damaged sandwich structures is that of damage tolerance: how is the structural performance 

influenced by the presence of debonding? The question of damage tolerance does not only apply 

to the design and optimisation of sandwich strcutures, but is also relevant to the residual strength 

and lifetime of already in service structures with minor or major damages. In recent years, a 

number of analytical and numerical studies have been conducted to predict the initiation and 

propagation of debonds in sandwich structures exposed to static loading, e.g. Kardomateas and 

Huang (2003), Sankar and Narayan (2001), Chen and Bai (2002) and Avilés and Carlsson 

(2007). Furthermore, experiments have been performed to determine the residual strength and 

identify the failure mechanisms of debonded sandwich structures, e.g. Avery and Sankar (2000), 

Vadakke and Carlsson (2004) and Xie and Vizzini (2005). 

Linear Elastic Fracture Mechanics (LEFM) has been extensively used to model debond initiation 

and propagation where the energy dissipation zone (fracture process zone) is relatively small 

compared to specimen dimensions, (Hutchinson and Suo, 1992). Furthermore, several studies 

have dealt with the determination of the fracture toughness of face/core interface in sandwich 

structures, e.g. Cantwell and Davies (1996), Li and Carlsson (1999) and Østergaard et al. (2007). 

In sandwich structures with composite face sheets the fracture process zone becomes large due to 

kinking of the crack into the composite face sheet and consequent fibre bridging which violates 

LEFM assumptions, see Figure 1.2. As an alternative to LEFM, cohesive zone modelling has 

been used in the literature, e.g. Lundsgaard-Larsen et al. (2008, 2010) and Østergaard et al. 

(2008) to model face/core debonding in the presence of fibre bridging. 

In few studies experiments have been conducted to some extent in order to examine the accuracy 

of the developed analysis methods in debonded sandwich structures e.g. see Berggreen et al. 

(2005), Jolma et al. (2007) and Aviles et al. (2006). However, despite all the proposed numerical 

and analytical methods, a comprehensive study of debond damaged sandwich structures, 

addressing systematically issues like debond propagation, characterisation of the fracture 

2

toughness of the interface at different mode-mixities and finally validation of these methods 

against experiments is still missing. 

Regarding the analysis of sandwich composites exposed to cyclic loading only a limited number 

of studies are found in the literature. Fatigue analyses of undamaged sandwich beams have been 

conducted by beam bending tests by Shenoi et al. (1995), Burman and Zenkert (1997), Kenny et 

al. (2002, 2005), Kulkarni et al. (2003) and Zenkert et al. (2011). The objective of these studies 

was to analyse the fatigue response of foam cores subjected to shear loading. In the case of 

debond damaged sandwich structures subjected to cyclic loading, fatigue experiments have been 

conducted by Shipsha et al. (1999, 2000, 2003) on debond damaged sandwich beams to 

determine stress-life S-N diagrams, crack growth rates and indentify fatigue crack growth 

mechanisms. Burman et al. (1997, 2000) also conducted four-point bending tests on debond 

damaged sandwich beams. However, all these studies have considered loading cases with pure 

mode I or II dominated loading at the crack tip and not a general mixed-mode condition. 

Figure 1.1: Debond in the structure of a ship after removal of the face sheet, from Berggreen 

(2005). 

Figure 1.2: Three different scenarios for face/core debond propagation. 

3

1.2 Overview of the Thesis 

In this thesis a step-by-step analysis approach has been adopted for the analysis of debonded 

sandwich structures exposed to static and cyclic loading. The thesis is divided into two main 

parts. The first part addresses debonded sandwich structures exposed to quasi-static loading. The 

analysis initially considers debonded sandwich columns and then further develops to geometries 

like debonded panels. The second part of this thesis addresses the failure of debond damaged 

sandwich structures exposed to fatigue loading. The thesis consists of six chapters as follows: 

1. Introduction 

2. Face/Core Debond Propagation in Sandwich Columns 

3. Failure of Uniformly Compressed Debond Damaged Sandwich Panels 

4. Fatigue Crack Growth Simulation in a Bimaterial Interface 

5. Face/core Interface Fatigue Crack Propagation in Sandwich Structures 

6. Conclusion and Future Work 

The first and the last chapters are introduction and final remarks and comments on future work. 

In Chapters 2 and 3 failure of debonded sandwich composites exposed to static loading is 

investigated. Chapter 2 contains an analysis of buckling driven crack propagation in foam cored 

sandwich columns with face/core debonds. LEFM and the finite element method are applied in 

order to analyse the behaviour of debonded sandwich columns with various PVC core materials 

and glass/epoxy face sheets. Associated compression tests are carried out to validate the 

numerical results. In Chapter 3 the numerical analysis method developed in Chapter 2 is 

extended further from column to panel level, and buckling driven debond propagation in 

sandwich panels with a circular debond is studied. Furthermore, the simulation results are 

validated against compression tests on debonded sandwich panels with various PVC and PMI 

core materials and debond diameters. In Chapters 4 and 5 the numerical tools which have been 

developed earlier to determine fracture parameters like the energy release rate and mode-mixity 

are utilised to simulate fatigue debond growth in sandwich composites. In Chapter 4 a numerical 

method is developed to overcome the obstacle of computational limitations. The method 

accelerates the simulation of fatigue crack growth by eliminating the need for simulation of all 

individual cycles. The acceleration method is verified by reference simulations of all individual 

cycles, at the end of the chapter. The developed numerical scheme is utilised to simulate 2D 

fatigue face/core debond growth in sandwich X-joints in Chapter 5. Additionally, the simulations 

are validated against fatigue tests conducted on the Sandwich Tear Test (STT) specimen 

representing an idealised sandwich X-joint. Finally, the developed numerical scheme is further 

extended from beam to panel level to simulate 3D fatigue debond growth in sandwich panels. 

Sandwich panels with circular debonds are tested under cyclic loading and the debond growth is 

monitored utilising a Digital Image Correlation (DIC) system. Consequently, the crack growth 

rate measured in the experiments is used to validate the developed numerical scheme. 

4

These numerical and experimental studies provide a better understanding of the behaviour of 

debond damaged sandwich composites under static or fatigue loading. Moreover, they develop 

reliable analysis tools for assessing the damage tolerance and fatigue lifetime of debonded 

sandwich composites. 

Since Linear Elastic Fracture Mechanics (LEFM) for the interfaces is the main theoretical 

foundation of this thesis, it will be presented in the next section of the Introduction. Finally, a 

brief history of fatigue analysis in sandwich composites will be presented in the last section of 

the Introduction. 

1.3 Linear Elastic Fracture Mechanics 

Griffith in 1920 established the foundations of fracture mechanics. He applied a stress analysis of 

an elliptical hole from Inglis (1913) to the unstable crack propagation problem. Based on the 

principle of energy conservation of thermodynamics, Griffith proposed the energy balance 

concept for fracture. According to Griffith’s theory, a crack may be formed or propagate if the 

potential energy change provided by strain energy and external forces, resulting from crack 

growth, is enough to overcome the surface energy and generate new surfaces. In 1948 Irwin 

extended Griffith’s concept to metals by including plastic energy dissipation at the crack tip. In 

1956 Irwin proposed the Griffith energy or energy release rate G as a measure of available 

energy for crack growth as 

 

 

where is the potential energy and dA is the crack area increment. According to Equation (1.1) 

the critical energy release rate Gc or fracture toughness can be defined as 

 

 

where Ws is the required energy for creation of new surfaces. 

Generally, a crack may experience three types of loading, see Figure 1.3. Mode I loading where 

the applied load tends to open the crack, mode II loading where the in-plane shear loading tends 

to slide one crack face against the other and mode III corresponding to the out-of-plane shear and 

sliding of the crack flanks. A crack may be loaded in any of these three modes or in a mixedmode 

combination of them. In 2D modelling of a crack problem, only the first two modes are 

typically used. 

5 

(1.1) 

(1.2)

Figure 1.3: Fracture modes, from Berggreen (2005). 

A stress singularity at the crack tip for a 2D problem, introduced by each mode of loading, can 

be defined in a polar coordinate system as 

 

 

 

where is Kronecker’s delta, T the non-singular stress parallel to the crack surface. r and are 

radius and angle in a polar coordinate system with origin at the crack tip. and 

are two functions defining the shape of the stress field, see Figure 1.4. KI and KII are the mode I 

and II stress intensity factors. If the definition of three crack tip loading modes is applied to the 

stress field, then the pure mode I stress field will be symmetric with respect to the crack line with 

and for =0, and the pure mode II is anti-symmetric with and 

for =0. Consequently, KI and KII can be defined as 

 

 

(1.4) 

Figure 1.4: Homogeneous near-crack tip definitions. 

The theory described above is known as homogeneous linear elastic fracture mechanics, which is 

applicable to the fracture of homogeneous solids where the plasticity at the crack tip is very 

small compared to the crack geometry. 

6 

r 

(1.3)

1.4 Linear Elastic Fracture Mechanics in Material 

Interfaces 

Linear elastic fracture mechanics (LEFM) addresses the fracture of solids in which the size of the 

zone dominated by non-linear inelastic deformations close to the crack tip is small compared to 

the crack length. When a crack propagates in homogeneous solids it mostly occurs in opening 

mode I loading. Even if there is an initial mixed-mode loading at the crack tip, the crack will 

eventually kink into a path with pure mode I loading. However, in an interface crack between 

two dissimilar materials this is not the case and the crack tip loading is a mixed-mode loading 

even if the global load is pure mode I. This is to due asymmetries of moduli and Poisson’s ratios 

along the interface, where both shear and normal stresses exist in the crack front (He and 

Hutchinson, 1989). A strong dependency of the fracture toughness and mode-mixity has been 

observed in different experimental investigations, e.g. Liechti and Chai (1992), making the 

mode-mixity phase angle an important parameter for the characterisation of interface cracks. 

Figure 1.5: Interface crack geometry. 

A general interface crack problem assumes that a crack is located between two orthotropic elastic 

materials denoted as #1 and #2, as shown in Figure 1.5. Two materials are joined along a straight 

interface and the crack tip is located at x=0. The displacement and stress fields close to the crack 

tip can be described according to Suo (1989): 

 

 

 

 

 

 

where y and x are the opening and sliding relative displacements of the crack flanks, and 

are normal and shear stresses. K is the complex stress intensity factor defined as 

(1.7) 

7 

(1.5) 

(1.6)

In Equations (1.5) and (1.6) H11, H22 and the oscillatory index are bimaterial constants 

determined from the elastic stiffnesses of material 1 and 2: 

 

 

where and n are non-dimensional orthotropic constants given in terms of the elements S11 and 

S22 of the compliance matrix: 

 

 

 

 

and The compliance elements for plane stress conditions are given by 

 

 

 

 

 

 

 

 

8 

(1.8) 

(1.9) 

(1.10) 

(1.11) 

(1.12) 

For the plane strain condition a correction to the compliance terms is given as 

 

 

where i and j are related to the x- and-y directions in the coordinate system shown in Figure 1.5. 

The oscillatory index, , in Equations (1.6) and (1.7) is given as 

(1.13) 

 

 

(1.14) 

 

where 

 

 

The complex stress intensity factor can be related to the strain energy release rate by (Suo, 

1989): 

 

 

The mode-mixity phase angle as suggested by Hutchinson and Suo (1992) can be defined as 

(1.15) 

(1.16)

(1.17) 

 

where h is the characteristic length of the crack problem chosen somewhat arbitrarily. The 

characteristic length is chosen as face sheet thickness throughout this thesis. The strain energy 

release rate and mode-mixity phase angle may also be derived in terms of the opening and 

sliding relative displacements of the crack flanks as 

 

 

 

 

 

 

 

9 

(1.18) 

(1.19) 

Equations (1.18) and (1.19) are only functions of relative opening and sliding displacements at 

the crack flanks and may conveniently be used in the finite element method for determination of 

the strain energy release rate and mode-mixity phase angle. However, in an interface both the 

strain energy release rate and the phase angle close to the crack tip behave in an oscillatory 

manner (Williams, 1959), see Figure 1.6. This oscillation is physically impossible since it 

calculates that the upper and lower surfaces of the crack will wrinkle and penetrate into each 

other close to the crack tip. It is shown that the extent of the oscillatory region is of the order of 

10 -6 of the crack length (Erdogan, 1963). England (1965) determined the distance from the crack 

tip, which after the first interpenetration occurs in the order of 10 -4 of the crack length. This 

mathematical error needs to be avoided for determination of realistic mode-mixity and strain 

energy release rate. 

Berggreen et al. (2005) compared different numerical methods for avoiding the mathematical 

oscillatory error, including the Virtual Crack Extension method (Parks, 1974, and Hellen, 1975) 

and the Virtual Crack Closure technique (Beuth, 1996). Furthermore, Berggreen (2005) 

developed the Crack Surface Displacement Extrapolation (CSDE) method for avoiding this 

imaginary oscillation. The CSDE method is schematically presented in Figure 1.6. The crack 

surface displacement extrapolation method exploits the observation that the variation of modemixity 

phase angle and energy release is linear in the K dominated region before the oscillation 

zone close to the crack tip. This linear variation may be used to extrapolate the mode-mixity 

phase angle and the energy release rate to the crack tip position and avoid the oscillatory part. 

The CSDE method is used throughout this thesis for determination of the mode-mixity phase 

angle and energy release rate.

Figure 1.6: Schematic illustration of the CSDE method. 

1.5 Fatigue Crack Propagation in Sandwich Structures 

Specimens with pre-cracks are normally used to study crack propagation rates for a given 

material. In these specimens one or more cracks are artificially created and by applying cyclic 

load the crack growth is measured. The Single Edge Notched Bending specimen (SENB) and the 

Compact Tension specimen (CT), as shown in Figure 1.7, are two standard specimen types used 

for measurement of mode I crack growth rate. 

Figure 1.7: The single edge notched bending specimen (SENB) and the compact tension 

specimen (CT). 

The resulting crack growth rate, da/dN, is usually plotted against the stress intensity factor K 

defined as Kmax-Kmin in a load cycle. 

10

Figure 1.8: Typical fatigue crack growth rate vs. K diagram. 

The crack growth rate diagram is divided into an initiation phase (I), a stable crack growth phase 

(II) and an unstable crack growth phase (III), as shown in Figure 1.8. The initial phase includes 

non-continuous fracture processes with a very low crack growth rate. The stress intensity factor 

range in this phase approaches the fatigue crack growth threshold, Kth. The linear intermediate 

phase is the most interesting phase due to the linear relation between the logarithm of the crack 

propagation rate and the logarithm of the stress intensity factor. This phase covers a large range 

of stress intensity factors and crack propagation in this phase is generally more stable than in the 

two other phases. The linear phase of the diagram, also named the Paris regime, can be written as 

 

 

where m is the slope of the linear phase and c is the crack growth rate for K=1. 

11 

(1.20) 

In phase III the crack grows fast and in an unstable manner. The effect of the loading ratio, 

R=Fmin/Fmax, on the crack growth rate is shown in Figure 1.8. It is seen for a given crack growth 

rate that the K value increases with increased loading ratio. The influence of the loading ratio is 

due to the fact that the crack growth is mainly determined by the maximum stress intensity factor 

value for each fatigue cycle, Kmax, and its proximity to the fracture toughness of the material, Kc. 

In homogeneous materials due to the fact that the crack only experiences opening mode I 

loading, the crack growth rate diagram is unique. On the contrary, in an interface due to the 

existence of mixed-mode loading at the crack tip and the resistance of other layers toward 

kinking of the crack, different crack growth rate relations exist for different mode-mixities.

The compact tension specimen (CT) is typically used to measure the fatigue crack growth rate in 

metals in the Paris regime (regime II) according to the test procedure specifications ASTM 

E647-93. The stress intensity factor of the CT specimen can be determined by 

 

 

 

(1.21) 

 

where Bct is thickness of the specimens and is a finite width correction factor, given by 

 

 

 

 

 

 

 

 

 

 

 

 

 

12 

 

 

 

 

 

 

(1.22) 

Burman et al. (1998) used the CT specimen with some dimensional modifications to extract both 

the mode I fracture toughness and the mode I crack growth rate of H100 PVC foam, see Figure 

1.9. 

Figure 1.9: Modified CT specimen, after Burman et al. (1998). 

The resulting crack growth rate data for H100 PVC foam was more scattered compared to typical 

fatigue crack growth rate diagrams, which can be attributed to the brittleness of the PVC foam 

material. Zenkert et al. (2008, 2010) also studied the fatigue response of various closed-cell foam 

materials under tension, compression and shear loading. 

In the case of an interface crack, the crack growth rate is a function of both the stress intensity 

factor and mode-mixity. There is no standard testing procedure for the measurement of face/core 

interface fatigue crack growth rate in sandwich structures. However, in recent years several precracked 

test specimens including the Cracked Sandwich Beam (CSB) (Carlsson et al., 1991), the

sandwich Double Cantilever Beam (DCB) (Prasad and Carlsson, 1994), the modified Tilted 

Sandwich Debond specimen (TSD) (Berggreen and Carlsson, 2010), the Single Cantilever Beam 

(SCB) (Cantwell and Davies, 1994, 1996), the Three-Point Sandwich Beam (TPSB) (Cantwell 

and co-authors, 1999, 2001), the sandwich DCB subjected to Uneven Bending Moment named 

DCB-UBM (Lundsgaard et al., 2008) and the sandwich Mixed Mode Bending (Quispitupa et al., 

2009) have been proposed for interface fracture toughness characterisation of sandwich 

structures. Many of these specimens can be applied to fatigue crack propagation testing as well, 

see Figure 1.10. 

Among these test specimens, Shipsha et al. (1999) used DCB and CSB specimens to measure 

face/core interface fatigue crack growth rates in foam cored sandwich beams under pure mode I 

and II loading. The disadvantage of utilising the CSB, DCB, TPSB and SCB specimens is the 

impossibility of mode-mixity variation for a fixed specimen geometry and material 

configuration. Utilising the CSB specimen, only mode II dominated crack growth rates and 

fracture toughness can be measured while with the DCB and TPSB only mode I dominant 

loading of the crack tip is possible. The TSD specimen may be used to measure the fracture 

toughness in a wide range of mode-mixities. However, since the mode-mixity is a function of 

crack length in this specimen, it is not directly suitable for standard interface fatigue 

characterisation at a specific mode-mixity. As to the DCB-UBM and MMB specimens, apart 

from being able to load the crack at different mode-mixities, the mode-mixity also remains 

constant as the crack grows, which makes these specimens ideal candidates for the measurement 

of interface fatigue crack growth rates. The DCB-UBM specimen has not been used for fatigue 

tests yet. However, Quispitupa et al. (2008) used the sandwich Mixed Mode Bending (MMB) 

specimen to measure face/core interface crack growth rates for a range of mode-mixities. The 

MMB test rig allows for adjustment of the mixed-mode ratio simply by changing the location of 

the support at point A, see Figure 1.10. The MMB test rig is used in this thesis to measure 

fracture toughness in Chapter 3 and crack growth rates in Chapter 5. In Chapter 2 as an 

alternative method, the TSD specimen is used to measure the face/core fracture toughness of the 

sandwich configurations. 

13

A 

Figure 1.10: CSB, DCB, TSD, DCB-UBM, SCB and MMB test specimens. 

14


15

Chapter 2 

Buckling Driven Face/Core Debond 

Propagation in Sandwich Columns 

2.1 Background and Objectives 

It is known that the bond between the face sheets and core is a potential weak link in a sandwich 

structure see e.g. Xie and Vizzini (2005) and Veedu and Carlsson (2005). In the case of in-plane 

loading, the behaviour of sandwich beams and columns containing imperfections or interfacial 

cracks has been investigated to a certain extent. Hohe and Becker (2001) conducted an analytical 

investigation to study the effect of intrinsic microscopic face/core debonds. Kardomateas and 

Huang (2003) studied buckling and postbuckling behaviour of debonded sandwich beams by a 

perturbation procedure based on non-linear beam equations. Sankar and Narayan (2001) studied 

the compressive behaviour of debonded sandwich columns by testing and numerical analysis. 

Most of their columns failed by buckling of the debonded face sheet. Vadakke and Carlsson 

(2004) similarly studied the compression failure of sandwich columns with a face/core debond. 

They investigated the effect of core density and debond length on the compressive strength of 

sandwich columns. Results of their experiments showed that failure occurred by buckling of the 

debonded face sheet, followed by rapid debond growth towards the ends of the specimen. They 

also showed that the compression strength of the sandwich columns decreases significantly with 

increasing debond size. Furthermore, columns with high-density cores experienced less strength 

reduction at any given debond size. Østergaard (2008) used a cohesive zone model for debonded 

columns and investigated the relation between global buckling behaviour and cohesive layer 

properties. The study showed that the compression strength reduction caused by a debond can be 

explained by two mechanisms: First from the interaction of local debond and global column 

buckling and secondly from the development of a damage zone at the debond crack tip. Only a 

few works have assessed in detail the determination of fracture parameters like energy release 

16

ate, phase angle and debond propagation load in debond damaged sandwich structures subjected 

to in-plane loading, and validated the results against experiments see e.g. Berggreen and 

Simonsen (2005) and Sallam and Simitses (1985). A good starting point for detailed fracture 

analysis of sandwich structures is specimens like columns and beams which can be modelled 

using the 2D finite element models which has not been thoroughly examined in the literature. 

In this chapter, as our starting point, failure of compression loaded sandwich columns with an 

implanted through-width face/core debond is examined. Compression tests were conducted on 

sandwich columns containing face/core debonds. The strains and out-of-plane displacements of 

the debonded region were monitored using Digital Image Correlation (DIC) technique. Finite 

element analysis and linear elastic fracture mechanics were employed to estimate the critical 

instability load and compression strength of the columns. Tilted Sandwich Debond (TSD) 

specimens were applied for determination of the fracture toughness of the interface in a modemixity 

similar to tested sandwich columns. Energy release rate and mode-mixity were 

determined and compared to fracture toughness data obtained from TSD tests, predicting 

propagation loads. Instability loads of the columns were determined from the out-of-plane 

displacements using the Southwell method. Results show that the finite element estimates of 

debond propagation and instability loads are in overall agreement with experimental results. The 

proximity of the debond propagation loads and the instability loads shows the importance of 

instability in connection with the debond propagation of sandwich columns. 

2.2 Experimental Setup 

Sandwich panels consisting of 2 mm thick plain-woven E-glass/epoxy face sheets over 50 mm 

thick Divinycell H45, H100 and H200 PVC foam cores were manufactured using vacuum 

assisted resin transfer molding and cured at room temperature. A face/core debond was defined 

by inserting strips of Teflon film, 30 m thick, between face and core in desired locations in the 

panels. The widths of the Teflon strip were 25.4, 38.1 and 50.8 mm. The width defines the length 

of the debond in the column specimens subsequently cut from the panels. It was observed that 

the single Teflon layer insert used to define the face/core debond did not perfectly release the 

bond between the face and core. To achieve a non-sticking, traction-free debond in the 

specimens, the debond was mechanically released by wedging knives with very thin blades (0.35 

and 0.43 mm thick). The width and length of the columns were 38 and 153 mm, respectively. 

Figure 2.1 shows a column specimen cut from a panel. A test rig was designed and manufactured 

for axial compression testing of the columns, see Figure 2.2 (a). The test rig includes four 25 mm 

diameter solid steel rods to maintain alignment of the upper and lower plates of the test rig 

during compressive loading. Linear bearings were attached to the upper plate to minimise 

friction. Steel clamps of a width of 80 mm were attached to the upper and lower plates of the 

fixture to clamp the columns. The test rig was inserted into an MTS 810 100 kN capacity servohydraulic 

universal testing machine, see Figure 2.2 (b). A 2 MPixel digital image correlation 

17

(DIC) measurement system (ARAMIS 2M) was used to monitor 3D surface displacements and 

surface strains during the experiments. Testing of the columns was conducted using ramp 

displacement control with a piston loading rate of 0.5 mm/min. A sample rate of one image per 

second was used in the DIC measurements. Three replicate tests were conducted for each 

specimen configuration. 

The material properties of the face sheets, assumed to be in-plane isotropic, were determined by 

tensile tests based on the ASTM standard D3039. The compression strength of the face sheets 

was measured on laminate specimens cut from the actual sandwich face sheet using the ASTM 

standard IITRI (D3410) test fixture. Core material properties were obtained from the 

manufacturer (DIAB, Divinycell H Technical Data, Labholm), see Table 2.1. Symbols E and G 

represent Young’s and shear moduli, Poisson’s ratio, max the compression strength of the core 

and the tensile and compression strengths of the face sheets. GIC is the mode I fracture toughness 

of the core material (Li and Carlsson, 1999). 

2.1: Face and core material properties from experiments conducted on samples from the face 

sheet and fracture toughness, from Li and Carlsson (1999). 

Material E (MPa) G (MPa) max (MPa) GIc (J/m 2 ) 

Face: E-glass/epoxy 10360 3816 0.31 168 (T)/ 95.4 (C) N/A 

Core: H45 50 15 0.33 0.6 (C) 150 

Core: H100 135 35 0.33 2 (C) 310 

Core: H200 240 85 0.33 4.8 (C) 625 

Figure 2.1: A column test specimen with H100 core and 38.1 mm debond. 

18

Figure 2.2: (a) Schematic representation of test fixture (b) actual test setup. 

2.3 Experimental Results 

Figure 2.3 shows typical load vs. axial displacement and load vs. out-of-plane displacement 

curves for columns with a 50.8 mm debond and H45, H100 and H200 cores. The out-of-plane 

deflection refers to the centre of the debond, for additional results see Apendix A. 

Load (kN) 

10 

8 

6 

4 

2 

0 

(a) 

H200 

H100 

H45 

(a) 

0 0.2 0.4 0.6 0.8 1 

Axial displacement (mm) 

Figure 2.3: (a) Load vs. axial displacement (b) out-of-plane deflection at the debond centre vs. 

load for columns with a debond length of 50.8 mm. 

Figure 2.3 (a) shows that the columns respond in a fairly linear fashion after the initial stiffening 

region until collapse. Figure 2.3 (b) shows that the out-of-plane deflection increases slowly with 

increasing load until the maximum load. It will later be shown that the point of maximum load 

19 

3 

Out-of-plane deflection 

(mm) 

2 

1 

0 

(b) 

H200 

H100 

H45 

(b) 

0 5 

Load (kN) 

10

corresponds to the onset of debond propagation. Figure 2.3 (b) shows that the critical 

propagation load increases as the core density is increased. Figure 2.4 shows DIC images of outof-plane 

displacement in a column with an H45 core and a 50.8 mm debond just before and after 

debond propagation. During the compression tests the DIC measurements furthermore revealed 

that opening of the debond was not perfectly symmetric, see Figure 2.4 (a). This can be 

attributed to a slight misalignment of the fibres in the face sheets and lack of perfectly uniform 

load introduction at the ends of the columns. Figure 2.5 shows DIC images of initial out-of-plane 

imperfection of two columns with H100 cores and 50.8 mm debonds, released using the thin 

(0.35 mm) and thicker (0.43 mm) blades, respectively. The inital imperfection amplitudes are 

approximately 0.25 and 0.51 mm. A Photron APX-RS high-speed camera was used to track the 

debond propagation at a frame rate of 1000 images per second. Figure 2.6 shows the debond 1 

ms before and right after the debond propagation. A slight opening of the debond is seen before 

propagation. Slight crack kinking into the core, resulting in the crack propagating just beneath 

the interface on the core side, was observed in most of the column specimens with H45 core. 

Some specimens with H100 core displayed this failure mode as well, see Figure 2.7. The fracture 

toughness of the H45 core (150 J/m 2 , see Table 2.1) is likely less than that of the face/core 

interface, which could explain the observed crack propagation path. A detailed kinking analysis, 

similar to what was presented in Li and Carlsson (1999), must be carried out to investigate this 

further. This is, however, out of the scope of this study. All columns with H200 core and 25.4 

mm debond failed by compression failure of the face sheet above the debond location, see Figure 

2.8. This can be explained by the proximity between the debond propagation load of the 

debonded face sheet and the compression failure load of the face sheet, which can be calculated 

from the compression strength and the cross section area of the face sheet, see Table 2.1. Face 

compression failure was also observed for one of the columns with H100 core and 25.4 mm 

debond length. The H200 column specimens with 38.1 and 50.8 mm debonds failed by debond 

propagation although kinking was not observed, thus, promoting crack propagation directly in 

the face/core glue interface. Moreover, the observed crack propagation rate was less for the H200 

specimens, indicating a tough interface. 

(a) (b) 

Figure 2.4: Debond opening (a) prior to propagation (b) after propagation for a column with 

H100 core and 50.8 mm debond length from DIC measurements. 

20

(a) (b) 

Figure 2.5: Initial imperfections in columns with H100 core and 50.8 mm debond where the 

debond was released using (a) a thin blade (0.35 mm) (b) a thicker blade (0.43 mm). 

Figure 2.6: High-speed images, which show the debond in a column with H45 core and 50.8 

mm debond length 1 ms before propagation and right after propagation has taken place. 

21

Figure 2.7: Crack kinking into the core in a column with H100 core and 25.4 mm debond. 

Figure 2.8: Face compression failure in a column with H200 core and 25.4 mm debond. 

2.4 Characterisation of Face/Core Interface Fracture 

Resistance 

The aim of this section is to determine the fracture toughness of the face/core interface in a 

mode-mixity identical to the one in the column specimens at the onset of crack propagation using 

22

the TSD specimen. The measured fracture toughness will be used in the next section to predict 

debond propagation load. The Tilted Sandwich Debond (TSD) specimen was introduced in 1999 

by Li and Carlsson for fracture testing of sandwich specimens. To achieve a range of modemixities 

at the crack tip the sandwich specimen is tilted so that the debonded face is subjected to 

an axial load, in addition to the normal load. A schematic representation of the conventional TSD 

specimen is given in Figure 2.9. 

Figure 2.9: Schematic illustration of the conventional TSD specimen. 

Stress intensity factors for the TSD specimens may be determined as follows (Hutchinson and 

Suo, 1992): 

 

 

 

 

 

 

where and KI and KII are mode I and II components of the stress intensity factor and hf 

is the face sheet thickness. F and M are edge force and moment applied to the loaded face sheet, 

respectively. is the oscillatory index given for isotropic materials in Equation (1.14). The 

mismatch parameter is given by 

23 

(2.1)

(2.2) 

where and for plane stress and plane strain, respectively. E and are 

Young’s modulus and Poisson’s ratio, respectively. Normal force and moment in the TSD 

specimen can be determined from the vertical force P and the tilt angle by 

(2.3) 

(2.4) 

For the reduced formulation where ==0 

 

 

 

 

 

 

 

Finally, the energy release rate can be calculated by 

 

 

 

 

 

Regarding the mode-mixity it was revealed that the mode-mixity for a conventional TSD 

specimen remains quite unaffected by the tilt angle (Li and Carlsson, 2001). Furthermore, it was 

discovered that the unreinforced TSD specimens display positive mode-mixity phase angles for 

tilt angles up to around 80 for all analysed PVC core materials, thus provoking the crack to kink 

into the core (Berggreen and Carlsson, 2010). To increase the range of achieved mode-mixities 

by the TSD specimen, two modified designs of the TSD specimen were proposed by Berggreen 

and Carlsson (2010). In the first modified design the upper face sheet of the TSD specimen is 

reinforced by a thick stiff steel plate to increase the stiffness of the loaded face sheet as shown in 

Figure 2.10. It was shown that by reinforcing the upper face sheet with a stiff steel plate the 

range of phase angles is expanded because of increasing shear loading and crack tip root rotation 

in the specimen. 

24 

(2.5) 

(2.6) 

(2.7)

Figure 2.10: Schematic presentation of the first modified TSD specimen. 

Further modifications were made by reducing the global shear deformation of the core by 

reinforcing the left edge of the TSD specimen by placing a metal block, see Figure 2.11. To 

avoid compression failure of the core at the right end of the reinforced TSD specimen due to 

rotation of the reinforced face sheet, a short link is pin-attached between the rigid base of the test 

rig and the centre of the steel reinforcement bar on both sides of the TSD specimen, see Figure 

2.11. 

Figure 2.11: Schematic presentation of the second modified TSD specimen. 

25

A modified version of the tilted sandwich debond (TSD) specimen, shown in Figure 2.10, was 

used to determine the fracture toughness of the interface. The determined fracture toughness will 

be used later to determine the crack propagation load in the column specimens applying the finite 

element method. Finite element analysis of the modified TSD specimen was carried out in order 

to determine the appropriate tilt angle to match the mode-mixity phase angles for the tested 

columns. A 2D finite element model with a highly refined mesh in the crack tip region, smallest 

element size of 3.33 m, was developed in the commercial code, ANSYS version 11, using 8node 

iso-parametric elements (PLANE82), see Figure 2.12. The energy release rate (G) and the 

mode-mixity phase angle () were determined from relative nodal pair displacements along the 

crack flanks obtained from the finite element analysis using the CSDE method outlined in the 

introduction. The characteristic length h is arbitrarily chosen as the face sheet thickness. 

Figure 2.12: Finite element model used in analysis of the modified TSD specimen with neartip 

mesh refinement. The smallest element size is 3.33 m. 

The mode-mixity phase angle of each column specimen was extracted at a load corresponding to 

the onset of debond propagation (from the experiments) using finite element modelling (to be 

presented later). The extracted phase angles were exploited in finite element models of the TSD 

specimens to determine the matching tilt angle at a crack length of 50 mm for specimens with 

H45 core and 63.5 mm for specimens with H100 and H200 cores. The face sheets were 1.5 mm 

thick, and the core thickness 25 mm. A 12.7 mm thick steel bar of the same width and length as 

the sandwich specimen (25.4 x 180 mm) was used to reinforce the loaded face sheet. The 

material properties of the face sheets and cores in the TSD specimens are identical to those of the 

columns specimens. The resulting specifications for the TSD specimen including the calibrated 

tilt angle are given in Table 2.2. 

Table 2.2: TSD specimen dimensions and tilt angles. 

Core Initial crack length (mm) Phase angle, deg Tilt angle (), deg 

H45 50 -24 

55 

H100 63.5 -29 

60 

H200 63.5 -37 

70 

TSD specimens of a length of 180 mm and a width of 25.4 mm were cut from panels prepared 

with one face sheet only. Figure 2.13 shows the TSD test setup with an H100 TSD specimen 

26

tilted 60. The bottom core surface of the specimen was bonded to a steel plate bolt connected to 

the test rig. Prior to bonding, the bonding surfaces were thoroughly sanded and cleaned with 

acetone to promote adhesion. Hysol EA-9309 aerospace epoxy paste adhesive was used for 

bonding. The steel bar contained a through-width hole near the end in order to allow pin load 

application. All tests were conducted at a rate of 1 mm/min, and three replicate specimens were 

tested. 

Figure 2.13: Modified TSD test setup. 

Figure 2.14 shows typical load vs. displacement curves for TSD specimens with H45, H100 and 

H200 foam cores. The load-displacement plots are fairly linear until the point of crack 

propagation, where the load suddenly drops. The load required to propagate the crack 

significantly increases as the core density is increased. Compared to conventional TSD 

specimens without steel reinforcement, see e.g. Li and Carlsson (2001), substantially larger loads 

are required to generate crack growth in the steel reinforced specimens, as a result of the large 

bending and shear stiffnesses of the steel reinforced upper face sheet. The crack propagation 

behaviour for the H45 specimens was rather unstable, with the crack suddenly growing 25-50 

mm at each crack increment, which allowed only about three crack increments before the crack 

reached more than 70% of the total specimen length, where the test was stopped. For the 

specimens with H45 foam core, the crack propagated beneath the face/core interface, on the core 

side, Figure 2.15 (a), which is consistent with the observations from the column tests and the 

27

previous observations of crack path behaviour for low-density foam cores, see e.g. Li and 

Carlsson (1999). For specimens with H100 core, unstable crack growth was more pronounced, 

with the crack growing about 50 mm at each increment, allowing only two crack increments 

before the crack reached 70% of the specimen length. For the H100 specimens the crack location 

was again beneath the face/core interface, however, now slightly closer to the face sheet, just 

below the resin-rich layer on the core side, see Figure 2.15 (b). The H200 specimens failed at 

considerably higher loads (> 4 kN) by sudden delamination between the plies of the upper face 

sheet, causing a large unstable crack, reaching almost to the end of the specimen at one crack 

increment, see Figure 2.15 (c). Given such an unstable crack growth behaviour with a few crack 

increments per specimen, the use of standard data reduction methods such as “compliance 

calibration” or “modified beam theory” becomes questionable for this test. Thus, the fracture 

toughness of the face/core interface was determined from finite element analysis of the TSD 

specimen with the critical load as input. The calculated fracture toughness values and phase 

angles are listed in Table 2.3. 

Load (kN) 

1.2 

0.8 

0.4 

ao=50.8 mm 

a1=67.2 mm 

a3=88.1 mm 

a4=121 mm 

0 

0 0.4 0.8 1.2 1 

Vertical displacement (mm) 

Load (kN) 

3 

2 

1 

0 

0 Vertical 1displacement 2 (mm) 

Figure 2.14: Load vs. vertical displacement diagram for TSD specimens: (a) H45, (b) H100 

and (c) H200. 

Table 2.3: Calculated phase angles and fracture toughnesses at measured fracture loads. 

TSD specimen Phase angle, deg Fracture toughness (J/m 2 ) 

H45 -24 

176±35 

H100 -29 672±69 

H200 -37 --- 

For the H200 specimens kinking of the crack into the face sheet occurred, so that the fracture 

toughness of the face/core interface could not be determined. Consequently, it was not possible 

to predict the face/core debond propagation load for the columns with H200 core. 

28 

ao=63.5 mm 

a1=124 mm 

a3=149 mm 

(a) (b) (c) 

Load (kN) 

5 

4 

3 

2 

1 

a o = 63.5 mm 

0 

0 1 2 

Vertical displacement (mm)

(a) (b) 

Figure 2.15: Crack propagation paths in TSD specimens: (a) H45 (b) H100 and (c) H200 

core. 

2.5 Finite Element Model of the Debonded Columns 

Finite element modelling of the column specimens was done in the commercial finite element 

code ANSYS version 11. Because of material, geometrical and loading symmetries, only the 

upper half-symmetry section of the column geometry was modelled, see Figure 2.16. The 

columns were assumed to contain an initial imperfection in the form of a half-wave eigen mode 

shape, determined from eigen buckling analysis. Overlapping of crack flanks was avoided by use 

29 

(c)

of contact elements (CONTACT173 and TARGET170), and displacement controlled 

geometrical non-linear analysis was conducted. To simulate the boundary conditions in the 

experimental setup, nodes on the top side of the columns, in contact with the top ending plate of 

the test rig, were displaced uniformly in the direction of loading. Furthermore, the nodes in 

contact with the lateral clamp surfaces were constrained to have zero lateral displacement. 

Symmetry boundary conditions were applied to the symmetry plane. Hence, displacements of the 

nodes on the symmetry plane were assumed to be zero in the loading direction, see Figure 2.16. 

Due to the need of a high mesh density at the crack front when performing the fracture 

mechanics analysis, a submodelling technique was developed, where displacements calculated 

on the cut boundaries of the global model with a coarse mesh were specified as boundary 

conditions for the submodel. Submodelling is based on St. Venant's principle, which states that if 

an actual distribution of forces is replaced by a statically equivalent system, the distributions of 

stresses and strains are altered only near the regions of load application. The approach assumes 

that the stress concentration around the crack tip is highly localised; therefore, if the boundaries 

of the submodel are sufficiently far away from the crack tip, reasonably accurate results may be 

obtained in the submodel. Interpolated displacement results at the cut boundaries in the global 

model were used as boundary conditions in the submodel at different load steps. A 20-node 

isoparametric element (solid 95) was used in the finite element model. The finite element model 

and submodel are shown in Figure 2.17. In the global model and the submodel, the size of the 

elements along the crack flanks near the crack tip is 0.2 and 0.01 mm, respectively. The energy 

release rate and the mode-mixity are determined on the basis of relative nodal pair displacements 

along the crack flanks obtained from the finite element analysis and the CSDE method as 

explained in the introduction. 

Figure 2.16: Applied boundary conditions in the finite element model of the columns. 

30

Figure 2.17: Finite element models. (a) Half-model showing the mesh in the global model. 

The smallest element size is 0.2 mm. (b) Submodel showing the refined mesh. The element size 

close to the crack tip is 10 m. 

2.6 Comparison of Numerical and Experimental Results 

Results from the experimental testing and numerical modelling presented above are compared. 

The focus is divided into three parts: The effect of imperfections on the instability behaviour, the 

through-width variation of energy release rate and mode-mixity and, finally, the influence of 

imperfections on the debond propagation. In order to examine the effect of initial imperfection 

on the instability behaviour of the specimens, columns with initial imperfection amplitudes of 

0.1, 0.2 and 0.4 mm were analysed numerically and compared with test results. The columns 

tested had in average an imperfection magnitude of 0.2 mm. Figure 2.18 shows the deformed 

shape of a debonded sandwich column with H100 core containing a 50.8 mm face/core debond 

and 0.2 mm initial imperfection amplitude. The imperfection resembles a half-sine wave with the 

maximum deflection at the centre, consistent with DIC measurements described above. Figure 

2.19 shows load vs. out-of-plane deflection for columns with H100 core and 25.4, 38.1 and 50.8 

mm debonds determined from numerical analysis at imperfection amplitudes of 0.1, 0.2 and 0.4 

mm and testing (two or three replicates are shown). The numerical and the test results show that 

31 

(a) 

(b)

the debond opening initially increases slowly with increasing load, but then increases rapidly as 

the maximum load is approached. At the maximum load, which corresponds to the onset of 

propagation, the load decreases due to the displacement controlled loading and debond 

propagation resulting in increased compliance, while the out-of-plane displacement of the 

debonded face rapidly increases. The load reduction is shown only for the experimental results, 

as only initiation of debond propagation is modelled numerically (no crack propagation 

algorithms are implemented in the finite element model). It is seen that the initial imperfection 

magnitude does not influence the out-of-plane deflection of the columns very much. A 

bifurcation instability of the debonded face sheet is not observed until the propagation point. 

Evidently, the presence of initial imperfection transforms the behaviour of the debonded face 

sheet into compression loading of a curved column. The failure load is found from fracture 

mechanics analysis, when the crack tip loading reaches the fracture toughness. Because of the 

imperfection present in the debonded face sheet, the critical instability load is extracted from 

both experimental and finite element results applying the Southwell method (Southwell, 1932). 

The Southwell method is a graphical method which estimates the instability load of imperfect 

structural columns. Southwell showed that the deflection, , at the centre of an imperfect 

column, loaded by a load P, is given by 

 

 

 

where Pcr is the instability load, and is proportional to the initial imperfection ( ). By plotting 

vs. /P, Pcr,, the instability load, can be determined by the slope of the line (the so-called 

Southwell plot method). 

Figure 2.18: Deformed shape of a column with H100 core containing a 50.8 mm face/core 

debond after local buckling of the debonded face sheet. 

32 

(2.8)

Out-of-plane displacement (mm) 

4 

3 

2 

1 

0 

Column1 

FEA, IMP=0.1 mm 



Debond= 25.4 mm 

0 4 8 12 16 

Load (kN) 


4 

3 

2 

1 

0 

(a) 

Figure 2.19: Finite element and experimental results for out-of-plane vs. load diagram for 

columns with H100 core and (a) 25.4 mm debond (b) 38.1 mm debond (c) 50.8 mm debond. 

The average initial imperfection magnitude in the tested columns is 0.2 mm. 

Numerical and experimental results are compared in terms of instability load values listed in 

Table 2.4. For the finite element analysis results, a 0.2 mm initial imperfection was selected, 

which is consistent with experimental values. From the results listed in Table 2.4, it is seen that 

experimental and numerical instability loads are in good agreement. Further, it is seen that the 

instability load drops significantly as the debond length increases, which is well-known for any 

buckling problem. 

33 


Column1 

Column2 

Column3 

FEA, IMP=0.1 

FEA, IMP=0.2 

FEA, IMP=0.4 


4 

3 

2 

1 

0 

Column1 

Column2 

Column3 

FEA, IMP=0.1 

FEA, IMP=0.2 

FEA, IMP=0.4 


0 2 4 6 8 10 

Load (kN) 

0 4 8 12 

(c) 

Load (kN) 

(b)

Table 2.4: Instability loads determined from Southwell plots applied to experimental and finite 

element results using 0.2 mm initial imperfection. 

Experiment Finite element analysis 

Debond length (mm) Debond length (mm) 

25.4 38.1 50.8 25.4 38.1 50.8 

Core Instability load (kN) Instability load (kN) 

H45 12.9±1.5 10.1±1.1 6.1±0.9 14.1 8.5 5.6 

H100 14.8±0.8 10.5±1.7 8.7±0.6 15.2 11.6 8.8 

H200 -- 13±1.2 8.5±0.3 -- 13.8 9 

Energy release rate and mode-mixity were determined across the width of the columns. 

Generally it is assumed that the edges of the columns are under plane stress and the interior is in 

plane strain. Thus, in the analysis of energy release rate and phase angle a plane stress 

formulation was adopted for nodes on the specimen edges and a plane strain formulation for the 

interior points. Figure 2.20 presents the distributions of energy release rate normalised with the 

interface fracture toughness, Gc, and phase angle across the width of a column with H45 core and 

50.8 mm debond. Similar results were obtained for columns with other core materials and 

debond lengths. Figure 2.20 shows the classical thumb-nail distribution of the energy release 

rate, normalised with the fracture toughness of the interface, increasing from the edges towards 

the centre of the specimen. The phase angle also displays a maximum in the interior. The 

magnitude of the phase angle, however, is minimum in the interior, which means that the loading 

in the centre is more mode I dominated than the edges. Based on the results shown in Figure 2.20 

the debond propagation is expected to initiate in the interior. Thus, in the debond propagation 

analysis, the plane strain formulation in the centre of the specimen was employed. 

G/Gc 

1.1 

1 

0.9 

0.8 

0.7 

0 0.2 0.4 0.6 0.8 1 

x/b 

(a) 

Figure 2.20: Distribution of energy release rate (a) and phase angle (b) across the column 

width for a column with H45 core and 50.8 mm debond. 

34 

Phase angle (deg) 

-21 

-22 

-23 

-24 

-25 

-26 

x/b 

0 0.2 0.4 0.6 0.8 1 

(b)

Figure 2.21 shows energy release rate and mode-mixity in terms of phase angle vs. load for 

columns with a 50.8 mm debond and H45, H100 and H200 cores. Figure 2.21 (a) shows that G 

increases significantly in a certain load regime which can be associated with the opening of the 

debond. The fracture toughness values shown in Figure 2.21 (a) were determined by the TSD 

tests, described in Section 4. The reduction of phase angle as the load increases, Figure 2.21 (b), 

shows that the crack tip loading becomes more shear dominated at high loads. 

G (J/m 2 ) 

1200 

800 

400 

0 

H45 

H100 

H200 

(-24º) H45 

(-29º) H100 

Gc(-29), H100 

G c(-24), H45 

0 3 6 9 12 

Load (kN) 

(a) 

Phase angle (deg.) 

Figure 2.21: (a) Energy release rate vs. load and (b) phase angle vs. load for columns with a 

50.8 mm debond and H45, H100 and H200 cores. 

In order to investigate the influence of the initial imperfection on G and , columns with H100 

core and 38.1 mm debond with three initial imperfection magnitudes (0.1, 0.2 and 0.5 mm) were 

analysed. Figure 2.22 shows G and vs. load for these columns. From Figure 2.22 (a) it is seen 

that G is not highly sensitive to the initial imperfection magnitude. The phase angle, Figure 2.22 

(b), is sensitive to the initial imperfection at small loads, but appears to converge to a value about 

-30 ° at higher loads, which indicates that the mode-mixity is less influenced by the initial 

imperfection at higher loads. 

The crack propagation load was estimated using fracture toughness data from the TSD tests. 

Energy release rate and mode-mixity in terms of phase angle were determined in the interior 

(centre) of the columns. Numerically predicted and experimentally determined propagation 

loads, which means the maximum load in the load vs. axial displacement diagrams (Figure 2.3 

(a)), for the debonded columns are listed in Table 2.5. 

35 

-18 

-22 

-26 

-30 

-34 

-38 

Load (kN) 

0 3 6 9 12 

(b) 

H45 

H100 

H200

G (J/m2) 

600 

400 

200 

0 

H100 

IMP=0.1mm 

IMP=0.2mm 

IMP=0.5mm 

(a) 

0 2 4 6 8 10 

Load (kN) 

Figure 2.22: (a) Energy release rate vs. load and (b) phase angle vs. load for a column with 

H100 core and 38.1 mm debond with different initial imperfection magnitudes. 

Table 2.5: Numerically predicted and experimentally measured debond propagation loads. 

Experiment Finite element analysis 

Debond length (mm) Debond length (mm) 

25.4 38.1 50.8 25.4 38.1 50.8 

Core Debond propagation load (kN) Debond propagation load (kN) 

H45 13.5±1 9.8±1.4 6.3±1.1 10.6 7.1 5.4 

H100 13.8±0.9 10±1.2 8±0.9 16.8 11.2 9.1 

H200 -- 12.3±1.7 8.1±1.2 -- -- -- 

The FEA predictions of debond propagation loads agree reasonably with the experimentally 

measured ones. It is clearly observed that the debond propagation load in the debonded columns 

decreases as the debond length increases. Furthermore, the propagation load increases with 

increased core density as a result of the increasing fracture resistance with core density. 

However, some inconsistencies are seen in the experimental results. For example the measured 

debond propagation loads for columns with H100 and H200 cores and 50.8 mm debond length 

are almost identical. These inconsistencies could be attributed to the local material distortions at 

the crack tip caused by the use of a blade to release the face/core debond and the resin-rich area 

at the tip of the insert film. The proximity of the debond propagation loads and the instability 

loads in Tables 2.4 and 2.5 show that the local instability load could be used as a measure of 

debonded column strength for this particular column case. This is, however, not a general 

conclusion valid for all debonded column cases where other failure mechanisms, such as 

compression failure, occur prior to local buckling instability. 

36 

Phase angle (deg.) 

-10 

-20 

-30 

-40 

0 2 4 

Load (kN) 

6 8 10 

(b) 

IMP=0.1mm 

IMP=0.2mm 

IMP=0.5mm 

H100

2.7 Conclusion 

The first step in a step by step analysis of debonded sandwich structures is to analyse simple 

structures like sandwich columns and beams. In this case the analysis is less complicated 

compared to the analysis of debonded sandwich panels because of the possibility of having a fine 

mesh at the crack tip and a more detailed analysis due to less complex geometry. The 

compressive failure mechanisms of foam cored sandwich columns containing a face/core debond 

were experimentally and numerically investigated in this chapter. Sandwich columns with 

glass/epoxy face sheets and H45, H100 and H200 PVC foam cores were tested in a specially 

designed test rig. 

Most of the tested columns failed by debond propagation at the face/core interface or just below 

the interface towards the column ends. Bifurcation type buckling instability of the debonded face 

sheet was not observed before the debond propagation was initiated. It is believed that the initial 

imperfections are mostly responsible for this behaviour, which is similar to compression of a 

curved beam. Slight crack kinking into the core, resulting in the crack propagating below the 

interface on the core side, was observed in most of the column specimens with H45 core and 

some columns with H100 core. All columns with H200 core and 25.4 mm debond failed by 

compression failure of the face sheet above the debond location, which can be attributed to the 

proximity between the debond propagation load of the debonded face sheet and the compression 

failure load of the face sheet. Face compression failure was also observed for one of the columns 

with H100 core and 25.4 mm debond length. 

Instability and crack propagation loads of the columns were predicted based on a geometrically 

non-linear finite element analysis and linear elastic fracture mechanics. Modified TSD specimens 

were tested in different tilt angles to measure the fracture toughness of the interface at the 

calculated mode-mixity phase angles for the column specimens associated with the debond 

propagation. Comparison of the measured out-of-plane deflection, instability, and debond 

propagation loads from experiments and finite element analyses showed fair agreement. For 

most of the investigated column specimens, it was shown that the instability and debond 

propagation loads are very reasonable estimates of the ultimate failure load, unless the other 

failure mechanisms occur prior to buckling instability. 

37


38

Chapter 3 

Failure of Uniformly Compressed Debond 

Damaged Sandwich Panels 

3.1 Background 

In the previous chapter a detailed analysis of face/core fracture in sandwich columns under 

compression was presented. A finite element model of the columns was developed and utilised to 

determine fracture parameters like the energy release rate and mode-mixity phase angle. In order 

to predict the crack propagation load, face/core interface fracture toughness of the columns was 

determined using the TSD specimen. Furthermore, the developed finite element model was 

validated against compression tests on debonded columns with different cores and debond 

lengths. The next step in studing the interface fracture of sandwich structures is to extend the 

analysis from simple geometries like beams and columns to geometries like panels. 

In recent years, efforts have been made to investigate the effect of face/core debonding on the 

residual strength of sandwich panels. Berggreen and co-authors (2005) in different studies 

investigated the failure of debonded sandwich panels loaded with non-uniform compressive and 

lateral pressure loading. They additionally proposed a new method for determining numerically 

the mode-mixity at the crack tip. Avilés and Carlsson (2007) focused on sandwich panels 

containing circular embedded debonds. They conducted uniform compression tests and finite 

element analysis to determine the residual strength of the damaged panels. Chen and Bai (2002) 

conducted finite element analysis to study the postbuckling behaviour of face/core debonded 

sandwich panels on the basis of the von Karman non-linearity assumption and the zigzag 

deformation theory combined with a debonding model and a multi-scalar damage model. Despite 

all the numerical and experimental studies, a comprehensive study of debond damaged sandwich 

panels, and analysis of issues like debond propagation, characterisation of the fracture toughness 

of the interface at different mode-mixities and finally validation of these methods against 

experiments is still missing. 

39

Hayman (2007) has described a damage assessment procedure for sandwich structures, which 

was originally developed for naval ships, but has potential for application to other structures with 

similar construction. The procedure exploits the fact that sandwich structures in ship’s hulls are 

to a large extent built up of a limited number of fairly large, flat panels that are supported at their 

edges. These panels are subjected primarily to local transverse pressure loadings and to in-plane 

loadings which are associated with global bending of the hull girder. Many cases of production 

defects and in-service damage initially involve a region of the panel that is small compared to the 

length and breadth of the panel. In such cases damage assessment requires use of a local strength 

reduction factor Rl, defined as the ratio between the far-field applied stress (or strain) causing 

failure in the presence of the damage to the corresponding value in the absence of the damage. 

The effect of the damage on the strength of both the panel and the structure as a whole may be 

determined from this local strength reduction factor Rl, which depends on the type and size of the 

damage, the material lay-up and the predominant stress state (tension, compression, shear) in the 

damage location. 

In this chapter, the above-mentioned damage assessment approach is adopted and strength 

reduction factors are determined for debond damaged sandwich panels under uniform 

compression loading, by a combination of finite element modelling and testing. Uniform 

compression tests were conducted on intact sandwich panels with three different types of core 

material (H130, H250 and PMI) and on similar panels with circular face/core debonds having 

three different diameters. The strains and out-of-plane displacements of the panel surface were 

monitored using the digital image correlation (DIC) technique. Mixed Mode Bending (MMB) 

tests were conducted to determine the fracture toughness of the interface of the panels for a full 

range of negative mode-mixities. Finite element analysis and linear elastic fracture mechanics 

were applied to determination of the critical buckling load and compression strength of the 

panels. Finally, the modelling approaches and failure criteria are discussed. 

Numerically determined crack propagation loads in most of the cases show fair agreement with 

experimental results, but in a few cases up to 45% deviation is seen between numerical and 

experimental results. This can mainly be ascribed to the large scatter in the measured interface 

fracture toughness and differing crack tip details. Tentative strength reduction curves are 

presented, but uncertainty concerning the intact strengths of the applied materials needs to be 

removed before these can be used with confidence. 

3.2 Test Specimens 

Uniform compression loading tests were conducted on intact sandwich panels and panels with a 

predefined debond. A total of 30 panels were manufactured, each 460 mm long and 380 mm 

wide. The face sheets were of glass-reinforced plastics (GFRP) consisting of Devold AMT noncrimp 

fabrics and two different types of vinylester resin with the following lay-ups: 

40

Type A: Three layers of DBLT-850 quadriaxial (0/90/+45/-45) glass with Dion 9102 

vinylester 

Type B: As type A but with Dion 9500 rubber-modified vinylester 

Type C: Three layers of DBL-800 triaxial (0/0/+45/-45) glass with Dion 9102 vinylester 

In addition, a layer of chopped strand mat (CSM) was placed between each face sheet and the 

sandwich core. The core materials were PVC (H130 and H250) and PMI (51-IG) foams. The 

thicknesses of the core and the face sheets were 30 mm and approximately 2 mm, respectively, 

see Figure 3.1. All panels were reinforced with wooden inserts at the top and bottom edges of the 

panel to avoid crushing of the core at the loaded edges. The panels were resin injection molded 

and cured with vacuum consolidation. Furthermore, the top and bottom edges of the panels were 

machined straight and parallel following the specimen manufacturing. 

Figure 3.1: Geometry of panel specimens and an image of a manufactured panel with a 

debond diameter of 200 mm. 

Debond defects with three diameters (100, 200 and 300 mm) were introduced during the 

manufacturing process by laying a circular piece of 0.025 mm thick Airtech release film on the 

core and sealing the edges with resin before lamination. However, after manufacturing of the 

panels it was observed that the face sheet was partially bonded to the core in the debonded area, 

probably due to small perforations of the release film. To release the partial adhesion, a small 

hole with a 2 mm diameter was drilled into the backside through the thickness of the panels and 

the debonded face sheet was pushed, using a thin metallic bar, to a point where all partial 

cohesions were eliminated. The panel test specimens are listed in Table 3.1. Fracture mechanical 

characterisation tests were performed in connection with the debond studies. For these tests, special 

sandwich beam specimens were manufactured with face sheet lay-ups of type A, B and C and cores 

of a thickness of 10 and 20 mm. 

41

Table 3.1: Panel test specimens. 

Lay-up type Core material Debond diameter (mm) No. of specimens 

100 2 

A H130 

200 

300 

2 

2 

Intact 3 

100 2 

B H250 

200 

300 

2 

2 

Intact 3 

100 3 

C PMI 51 IG 

200 

300 

3 

3 

Intact 3 

Each layer of DBLT-850 fabric contains approximately 835 g/m 2 glass reinforcement and each 

layer of DBL-800 has approximately 810 g/m 2 . Each face has in addition a 100 g/m 2 layer of 

chopped strand mat (CSM) placed against the core at the interface. Typical properties for the 

laminates are given in Table 3.2. 

Table 3.2: Face sheet material properties from experiments conducted on samples from the 

face sheet. 

Material property Type A/B Type C 

Elastic modulus, x-direction (GPa) 19.4 26.4 

Elastic modulus, y-direction (GPa) 19.4 11.7 

Elastic modulus, z-direction (GPa) 9.2 9.2 

Poisson’s ratio xy 0.316 0.514 

Poisson’s ratio xz 0.32 0.32 

Poisson’s ratio yz 0.32 0.32 

Shear modulus, xy (GPa) 7.4 7.4 

Shear modulus, xz (GPa) 3.0 3.0 

Shear modulus, yz (GPa) 3.0 3 

Tensile strength (MPa) 294/313 490 

Compression strength (MPa) 300/320 463 

These in-plane properties are based on tests performed on similar laminates, but without a CSM 

layer. These laminates had a 53.8% fibre volume ratio, resulting in a thickness of 0.61 mm or 

0.59 mm for each layer of DBLT-850 or DBL-800 reinforcement, respectively. The thicknesses per 

layer for the laminates in the tested panels were observed to be slightly higher than the calculated 

thicknesses. This appears to have been mainly due to the extra CSM layer. Burn-off tests performed 

on specimens taken from the face sheets indicated fibre volume contents between 51.5% and 55.3%, 

42

the lowest values being for the Type C (triaxial DBL-800) laminates. The core materials are 

Divinycell PVC foams of type H130 and H250, and Rohacell PMI foam of type 51-IG. The 

properties for the core materials, taken from the manufacturers’ data sheets, are given in Table 3.3. 

Core 

type 

Nominal density 

(kg/m 3 ) 

Table 3.3: Material properties of the cores. 

Compressive modulus 

(MPa) 

43 

Shear modulus 

(MPa) 

Compressive strength 

(MPa) 

H130 130 170 50 3 

H250 250 300 104 6.2 

PMI 52.1 70 19 0.9 

3.3 Characterisation of Face/Core Interface 

The interface fracture toughness characterisation of the foam cored sandwich specimens was 

performed using the Mixed Mode Bending (MMB) test rig and the MMB sandwich specimen 

(Quispitupa et al., 2009 and 2010), as shown in Figure 3.2. The MMB test rig was originally 

developed for mixed-mode fracture testing of monolithic composites (Reeder et al., 1990 and 

Ozdil et al., 2000) and has recently become an ASTM standard test method D6671-01. The 

MMB test rig allows adjustment of the mixed-mode ratio by changing the lever arm distance c as 

shown in Figure 3.2. Quispitupa et al. (2009) further developed the MMB test rig for fracture 

testing of sandwich structures. The standard MMB composite test specimen is a rectangular 

unidirectional beam specimen with a predefined delamination located at the midplane. In the 

MMB sandwich specimen the initial crack is located in the face/core interface at the top of the 

specimen, see Figure 3.2. The compliance of the MMB sandwich specimen is determined by 

(Quispitupa et al., 2009): 

 

 

 

 

 

 

 

 

where and P are the deflection of the loading point and the applied load, respectively, c is the 

lever arm distance, L the half-span length and is the load partitioning parameter at the left 

support (see Figure 3.2) given by 

3 

a 1 a 1 

 

3 D2 

k G f h f Gxzhc 

3 

3 

(3.2) 

a 1 a 1 a 1 a 1 

 

 

3 D k G h G h 3 D k G h 

2 

f 

f 

xz 

c 

1 

f 

f 

where the subscripts 1 and 2 refer to the face sheet and the core, respectively, a is the crack 

length, k is the shear correction factor, k=1.2, D2=D-B 2 /A, D1=1/(Efhf 3 /12), hf and hc are the face 

(3.1)

sheet and the core thickness, respectively, Gxz is the shear modulus of the core, Gf is the shear 

modulus of the face sheet and Ef and Ec are the face and core moduli. 

Figure 3.2: Mixed mode bending test rig for sandwich specimens. 

The A, B and D terms are the extensional, coupling and bending stiffnesses of any given 

laminated beam given by 

A E h E h 

f 

f 

c 

c 

Ec 

E f 

B hf 

hc 

2 

(3.4) 

1 3 2 

3 2 

D Efhf3hfhcEchc3hfhc 12 

(3.5) 

where K is the elastic foundation modulus 

Ec 

b 

K 

hc 

2 

C1, C2 and C3 are compliances of the subbeams defined as 

 

 

 

 

 

 

 

 

 

 

 

 

(3.8) 

 

 

 

Saddle 

 

 

 

P 

 

 

 

 

C 

L 

 

 

44 

L 

Hinge 

a 

(3.3) 

(3.6) 

(3.7) 

(3.9)

is the elastic foundation modulus parameter defined as 

 

3 

hf bE f 

3K 

and Ddebpnded and Dintact are the bending stiffness of the debonded and intact parts of the MMB 

specimen (Quispitupa et al., 2009): 

45 

(3.10) 

 

2 B 

D 

 

debonded 1 D 

A 

(3.11) 

3 3 

E f hf 

2 E f hf 

Echc 

Dintact 

hchf 

2 

6 12 

(3.12) 

The energy release rate can be expressed as 

(3.13) 

 

When the expressions for the compliance and the energy release rate are known, it is possible to 

determine the crack length at a given load and deflection and fracture toughness as the crack 

grows. However, to fully characterise the face/core interface the mode-mixity must be evaluated 

as well. Since there is no analytical expression for the interface mode-mixity, it is usually 

determined by use of the finite element method. For static characterisation, the fracture 

toughness of the interface can be determined by Equation (3.13) and the mode-mixity is 

evaluated using finite element modelling and the CSDE method as explained before. For fatigue 

characterisation of the interface, Equation (3.1) is used to determine the crack length from the 

compliance of the MMB specimens evaluated from the actual applied load and displacement of 

the test specimen. Fracture testing of the MMB specimens was performed at a cross-head rate of 

1 mm/min. Figure 3.3. shows typical load vs. displacement curves for representative loading 

conditions and specimens. In Figure 3.3 the point where the crack starts to propagate is marked 

with an open circle (“”). The load vs. displacement curves are fairly linear up to the point of 

crack propagation. It is seen that the load drops due to a change in the specimen stiffness as the 

crack propagates. The critical failure load was marked according to the ASTM D6671/D 6671M- 

06 recommendation (the load at which the compliance has increased by 5%) and complemented 

by visual inspection. These critical failure loads (Pc) were used in the determination of the 

face/core interface fracture toughness (Gc), according to the procedure outlined by Quispitupa et 

al., (2009).

Load (N) 

250 

200 

150 

100 

50 

0 

H130 Core 

=-28 

0 1 2 3 4 5 

Displacement (mm) 

Load (N) 

250 

200 

150 

100 

50 

H250 Core 

=-29 

0 

0 1 2 3 4 


Figure 3.3: Typical experimental load vs. displacement curves (“” indicates the onset of 

crack growth) for specimens with (a) H130 core (b) H250 core and (c) PMI core. 

Since the face/core interface toughness is strongly dependent on the mode-mixity at the crack tip, 

the mode-mixity was determined from finite element analysis of the MMB specimens for all 

loading conditions and materials tested in this study. A finite element model of the MMB 

specimen was developed in the commercial finite element code, ANSYS, using 4-node 

isoparametric elements (SOLID42), see Figure 3.4. Geometrically non-linear analysis of the 

MMB specimen was performed with displacement controlled loading. The mode-mixity phase 

angle () was determined from relative nodal pair displacements along the crack flanks obtained 

from the finite element analysis, applying the crack surface displacement extrapolation (CSDE) 

method presented in the Introduction of this thesis. The characteristic length h is arbitrarily 

chosen as the face sheet thickness in this study. 

Figure 3.4: Finite element model of the MMB sandwich specimen. The smallest element size is 

3.33 m. 

46 

Load (N) 

150 

100 

50 

0 

PMI Core 

=-20 

(a) (b) (c) 

0 0.5 1 1.5 2 2.5 

Displacement (mm)

Figure 3.5 shows the face/core debond fracture toughnesses vs. phase angle for specimens with 

H130, H250 and PMI 51 IG cores. The mechanical properties for these materials were listed in 

Tables 3.2 and 3.3. It should be noted that the DBL reinforcement in lay-up C was oriented with 

the 0º plies parallel to the load direction in the panel tests and transverse to the beams in the 

MMB fracture specimens, thus simulating the fibre orientation in the 3 and 9 o’clock positions 

along the circular debond in the panels. Figure 3.5 reveals that the face/core interface fracture 

toughness is strongly dependent on the mode-mixity at the crack tip for all sandwich composites 

examined herein, especially in mode II dominated loading, i.e. increased shear loading at the 

crack tip. However, this dependency is weak in mode I dominated loadings, i.e. low magnitudes 

of mode-mixity, where roughly constant fracture toughness is observed, see Figure 3.5. A 

phenomenological relationship between fracture toughness and mode-mixity proposed by 

Hutchinson and Suo (1992) is used to fit the experimental data by Equation (3.14). A fitted curve 

(by visual inspection) is represented by a continuous line in Figure 3.5, for the three sandwich 

composites being examined, i.e. specimens with H130, H250 and PMI cores. In addition, the 

upper and lower bounds are shown as dashed lines. A large scatter in the fracture toughness vs. 

phase angle results is observed, which is expected in sandwich composites due to different 

manufacturing defects and crack propagation paths at the face/core interface. 

2 

tan 

G 1 1k Gc IC 

(3.14) 

In Equation (3.14), GIC is the interface fracture toughness in pure mode I and k is a nondimensional 

curve fitting parameter. Here, since in mode I dominated loading, a roughly constant 

fracture toughness is observed, GIC is assumed to be the minimum fracture toughness value for 

the material being evaluated. Thus, when =0, Gc() = GIC. 

(a) (b) (c) 

Figure 3.5: Fracture toughness vs. phase angle results and curves for specimens with (a) 

H130 (b) H250 and (c) PMI cores. 

Based on the face/core debond fracture toughness vs. phase angle results shown in Figure 3.5, 

the parameters for Equation (3.14) are provided in Table 3.4 for each sandwich configuration. 

47

Table 3.4: Parameters in the face/core interface fracture toughness function, Equation (3.14). 

Core 

GIC (J/m 2 ) 

Average fit 

GIC (J/m 2 ) 

Lower bound 

GIC (J/m 2 ) 

Upper bound 

k 

H130 450 280 620 0.45 

H250 500 350 660 0.55 

PMI 115 80 150 0.55 

Figure 3.6 illustrates the typical crack path observed in the MMB specimens with PMI core. As it 

is seen, the crack grows below resin-rich cells in the core for all measured mode-mixities. 

Figure 3.6: Crack path for an MMB specimen with PMI core. 

For specimens with H130 core and mode-mixity phase angle of 0° >> -20°, the crack path was 

located below the face/core interface, see Figure 3.7. However, for the mode-mixity phase angle 

of -25° >> -65°, as shown in Figure 3.8, the crack path was in the actual face/core interface. As 

mentioned earlier, a toughening mechanism due to the increased negative mode-mixity is 

observed in this core material as well. This trend in the fracture toughness vs. mode-mixity was 

previously reported for other debonded sandwich materials tested at controlled mode-mixities, 

see Berggreen et al. (2005). 

Figure 3.7: Crack path for an MMB specimen with H130 core below the face/ core interface. 

48

Figure 3.8: Crack path for an MMB specimen with H130 core in the face/core interface. 

For specimens with H250 core, the crack propagated in the interface for all measured modemixities 

as shown in Figure 3.9. In these specimens the fracture toughness increased with 

increasing magnitude of the negative mode-mixity phase angle at the crack tip similar to the 

specimens with PMI and H130 cores. Additionally, it was observed that in longer crack lengths 

(4mm), fibre bridging started to emerge, which can be attributed to the CSM layer placed in the 

face/core interface during the manufacturing process of the MMB specimens. The fibre bridging 

enhances the fracture toughness by creating a large fracture process zone and, thus, the modemixity 

might lose its validity. Since the fracture experiments are focused on fracture initiation 

and not propagation, no analysis for fibre bridging is presented in this study. 

3.4 Panel Tests 

Figure 3.9: Crack path for an MMB specimen with H250 core. 

Figure 3.10 shows the test rig designed to introduce a uniform in-plane compressive load to the 

edges of either plane or singly curved sandwich panels. The test rig was inserted into a four- 

column Instron 8508 servo-hydraulic testing machine with a maximum capacity of 5 MN. 

However, a 1 kN Instron load cell was used for the tests to increase the accuracy of the load 

measurements. A 4 Mpix Digital Image Correlation (DIC) measurement system (ARAMIS 4M) 

49

was used to monitor 3D surface displacements and 2D surface strains continuously during the 

experiments. The DIC camera position and the test rig are seen in Figure 3.10. A ramp 

displacement controlled loading with a rate of 1 mm/min was applied in all tests. A sample rate 

of one image per second was used for the DIC measurements. The DIC system was used to 

measure the initial imperfection in the surface of the panels. Figure 3.11 shows the initial 

imperfection measurement for a panel with H130 core and a debond diameter of 200 mm. 

(a) (b) 

Figure 3.10: (a) Test rig and (b) test setup. 

Figure 3.11: Initial imperfection from DIC measurements in a panel with H130 core and a 

debond diameter of 200 mm. 

All debonded panels failed by propagation of the debond to the edges of the panels. Figure 3.12 

shows typical out-of-plane deflections of the debonded panels before and after debond 

propagation measured by the DIC system. Prior to debond propagation, a large debond opening 

can be seen corresponding to the buckling of the debonded face sheet. 

50

(a) (b) 

Figure 3.12: Out-of-plane deflection from DIC measurements of a panel with H130 core and 

a debond diameter of 100 mm (a) prior to propagation and (b) after propagation. 

Figure 3.13 shows typical load vs. axial displacement and load vs. out-of-plane displacement 

curves for panels with a 100 mm debond and H250, H130 and PMI cores, for additional results 

see Apendix B. The out-of-plane deflection refers to the centre of the debond. The debond 

opening initially increases very slowly with increasing load until a bifurcation load level 

corresponding to the local buckling of the debonded face sheet. After buckling the debond 

opening increases rapidly in the postbuckling regime approaching the debond propagation load 

level. At the onset of propagation, the load decreases due to the displacement controlled loading 

and debond propagation resulting in increased compliance, while the out-of-plane displacement 

of the debonded face rapidly increases. 

(a) (b) 

Figure 3.13: Typical (a) load vs. axial displacement and (b) load vs. out-of-plane displacement 

for panels with a debond diameter of 100 mm. 

All intact panels with H130 and H250 cores failed by compression failure of a face sheet close to 

the wooden inserts, see Figure 3.14 (a). This can be attributed to additional peeling stresses 

51

arising due to the junction between the insert and the core and to a slight unintentional mismatch 

between the core and the insert thicknesses, see Hayman et al. (2007). The intact panels with 

PMI core failed by a combination of shear crimping and global buckling, see Figures 3.14 (b) 

and 3.14 (c). Figure 3.15 shows the debond propagation load vs. the debond diameter, in each 

case the mean result for two or three specimen replicates is used. It appears that the debond 

propagation load decreases significantly with increasing debond diameter. 

Face sheet compression 

failure 

Figure 3.14: (a) Compression failure of a face sheet in an intact panel with H130 core (b) 

global bucking and (c) shear crimping of intact PMI panels. 

Failure load (kN) 

500 

400 

300 

200 

100 

0 

(a) 

Global buckling 

0 50 100 150 200 250 300 

Debond Diameter (mm) 

3.15: Measured propagation load vs. debond diameter. Measured failure loads for the intact 

panels can be identified for a debond diameter of 0 mm. 

The theoretical compressive failure loads for the intact panels, based on the material compressive 

strengths in Table 3.1, are shown in Table 3.4 together with the measured values. This table also 

shows the load at which wrinkling of the face sheets and shear crimping is predicted for each 

case. Wrinkling load of the face sheets is determined based on a formula proposed by Hoff et al. 

(1945): 

52 

(b) 

H130 

H250 

PMI 

Shear crimping 

(c)

(3.15) 

cr 

0. 5 3 E f EcGc 

where Ef and Ec are modulus of elasticity of the face sheets and core and Gc is the shear modulus 

of the core. It is seen that wrinkling is likely to have influenced the strength of the A panels and 

both wrinkling and crimping are likely to have influenced the strength of the C panels. The 

observed behaviour raises an important question concerning the value of intact strength that 

should be used in determining a local strength reduction factor Rl. Should this be based on the 

compressive strength of a laminate measured in tests on small laminate samples in which all 

types of buckling are prevented, or should it be based on the compressive strength actually 

observed for the tested panel? Most types of buckling are dependent on the size of the panel and 

its boundary conditions. Moreover, they are not affected by very local losses of stiffness. Thus, it 

seems appropriate to base Rl on the basic compressive strength of the laminate and rather 

perform separate checks of possible effects of buckling. An exception to this is local wrinkling of 

the face sheet, which is independent of panel size and boundary conditions and in practice may 

provide a modified material strength to replace the value measured in tests on small laminate 

samples. 

3.5: Measured and theoretical failure loads for intact panels. 

Lay-up Measured failure 

Theoretical failure loads (kN) 

type load (kN) Compressive failure Shear crimping Face sheet wrinkling 

A 325 448 642 409 

B 357 502 1335 663 

C 279 636 243 229 

3.5 Panel Analysis 

A 3D finite element model was developed in the commercial finite element code, ANSYS 

version 11, using 8-node isoparametric elements (SOLID45). Geometrically non-linear analysis 

of the debonded panels was performed with displacement controlled loading. The panels were 

assumed to contain an initial imperfection in the form of a half-sinusoidal wave as determined 

from eigenbuckling mode shapes. The magnitude of the initial imperfection is obtained from 

DIC measurement of the test specimens shown in Figure 3.11. Because of geometry and loading 

symmetry only a quarter of the panel was modelled. Symmetry boundary conditions were 

applied to the symmetry planes. Due to the need for a high mesh density at the crack tip when 

performing the fracture mechanics analysis, a submodelling technique was employed. The finite 

element model and submodel are shown in Figure 3.16. 

53

(a) 

Debonded face sheet 

Figure 3.16: Finite element model of a panel with a debond diameter of 100 mm. (a) 

Submodel min. element length 0.02mm (b) global mode min. element length 0.25 mm. 

Figure 3.17 shows load vs. out-of-plane deflection of the centre of the dobond for panels with 

200 mm debond and PMI, H130 and H250 cores determined from experiments and finite 

element analysis. In Figure 3.17 the point where the crack starts to propagate in the tested panels 

is marked with an open circle (“”). The load reduction at the onset of propagation is shown only 

for the experimental results, as only initiation of debond propagation is modelled numerically (no 

crack propagation algorithms are implemented in the finite element model). 

(a) (b) (c) 

3.17: Finite element and experimental results for out-of-plane displacement vs. load diagram 

for panels with 200 mm debond and (a) H130 (b) H250 and (c) PMI core. 

Experimental buckling load of the debonded panels and numerical buckling loads determined by 

linear eigenbuckling analysis as well as non-linear finite element analysis are given in Table 3.6. 

It is seen that the buckling loads of the panels with 100 mm debond diameter increase 

significantly with increasing core stiffness, but for the larger debonds the increase is smaller. The 

numerical and experimental buckling loads show fair agreement. 

54 

200 

200 

200 

200 

(b)

3.6: Numerical and experimental buckling loads. 

Buckling loads (kN) 

Core type Debond diameter (mm) 

Experiment Non-linear FE eigenbuckling FE 

H130 

100 

200 

106.5±4.5 

27±1 

100 

26 

94.5 

26.9 

300 15 12 12.9 

H250 

100 

200 

121±9 

24±1 

104 

28 

100 

28 

300 16 13 12.5 

PMI 

100 

200 

85.5±3.5 

28.5±3.5 

94 

28 

109 

33.8 

300 11.5±4.5 14 15.9 

In order to estimate the crack propagation load of the panels, the energy release rate and phase 

angle were determined along the debond front. The energy release rate (G) was determined from 

relative nodal pair displacements along the crack flanks obtained from the finite element 

analysis. The energy release rate and mode-mixity phase angle are given by Equation (1.18) and 

(1.19) in the Introduction of this thesis. h, which is the characteristic length of the crack problem, 

is chosen as the face sheet thickness. In Figure 3.18 the normalised energy release rate and phase 

angle with respect to the maximum determined energy release rate and phase angle along the 

debond front are plotted in polar diagrams for the H130 panels with 100 mm, 200 mm and 300 

mm debond diameter in a load level close to the experimental debond propagation load. 

Maximum energy release rate and minimum phase angle occur in the 0-degree debond front, 

implying the onset of debond propagation in this location, which is similar to experimental 

observations, see Figure 3.12. The same conclusion may be drawn for the panels with PMI and 

H250 core. 

90 

1 

120 

135 

0.8 

150 

0.6 

0.4 

165 

0.2 

180 

0 

105 

195 

210 

225 

240 

255 

75 60 

15 

0 

345 

330 

315 

300 

285 

120 

1 

90 

75 

60 

45 

30 

135 

150 

0.5 

45 

30 

105 

(a) (b) 

270 

270 

100 mm 200 mm 300 mm 

100 mm 200 mm 300 mm 

3.18:(a) Normalised energy release rate (G/Gmax) and (b) normalised phase angle (/max) 

for H130 panels with debond diameters of 100 mm, 200 mm and 300 mm. 

55 

165 

180 

195 

210 

225 

240 

255 

0 

-0.5 

15 

0 

345 

330 

315 

300 

285

Figure 3.19 shows the determined energy release rate vs. load curves for the panels with 100, 

200 and 300 mm diameter. The fracture toughness values shown in Figure 3.19 were determined 

from the MMB tests at a -20 phase angle, which is close to the numerically determined phase 

angle at the experimental debond propagation load, described previously. It appears that the 

energy release rate increases significantly at a load level which can be associated with the 

buckling of the debond. The horizontal line in the diagrams shows the average fracture toughness 

of the interface of the panels for the determined phase angle. The point where the fracture 

toughness line and energy release rate curve intersect eachother indicates the debond propagation 

load. 

(a) (b) (c) 

3.19: Energy release rate vs. load for panels with (a) PMI (b) H130 and (c) H250 core. 

Numerically predicted and experimentally determined propagation loads for the debonded panels 

are listed in Table 3.7. Due to large scatter in the measured interface fracture toughnesses, the 

crack propagation load was determined for a maximum, average and minimum measured 

fracture toughness level. It is seen that based on the average of the measured fracture 

toughnesses level, the FEA predictions are 7-46% higher than the experimental ones. For the 

minimum fracture toughness the deviation is between 3-33% and for the maximum 14-65%. This 

deviation may be partly due to differing crack tip details and crack growth mechanisms between 

the panels and the MMB specimens. The distortions in the debond crack tip are due to 

mechanical releasing of the debonds, making the debonds not perfectly circular, as well as some 

partial adhesions in the debonded area in the experiments as mentioned earlier, which are not 

taken into account in the finite element modelling. A further cause of inaccuracy in the 

predictions could be different debond growth mechanisms between the panels and the MMB 

fracture toughness characterisation tests. To investigate this issue some of the tested panels were 

cut, and debond propagation paths in the 0 debond front location where the debond starts to 

propagate were compared with the MMB specimens tested under mode I dominated loading. 

Figure 3.20 shows debond propagation paths in the panels and the MMB specimens. In the 

panels and the MMB specimens with H130 and PMI cores the debond kinks into the core and 

propagates beneath the face/core interface. However, in the panels and the MMB specimens with 

H250 core the debond propagates directly in the interface, which can be explained by the higher 

56

fracture toughness of the H250 core compared to H130 and PMI cores. Fibre bridging was 

observed after around 4-5 mm of crack propagation in the panels with H250 core. The similarity 

between the debond propagation paths in the MMB specimens and the panels refutes the role of 

the different propagation paths in the inaccuracy of the determined debond propagation loads. 

Table 3.7: Numerical and experimental debond propagation loads. 

Panel Debond diameter (mm) 

H130 

H250 

PMI 

57 

Debond propagation load (kN) 

Experiments FE (min./ave./max.) Ratio FE/exp. 

50 --- 270/304/324 --- 

100 162.5 168/186/202 1.03/1.14/1.24 

200 92.5 123/135/151 1.33/1.46/1.63 

300 80 102/116/132 1.27/1.45/1.65 

50 --- 314/328/341 --- 

100 166 193/205/214 1.16/1.23/1.29 

200 114.5 135/147/155 1.18/1.28/1.35 

300 105 114/123/129 1.08/1.17/1.23 

50 --- 181/186/193 --- 

100 108.3 112/116/124 1.03/1.07/1.14 

200 70.3 76/81/87 1.08/1.15/1.23 

300 49 63/66/72 1.28/1.34/1.47

H130 MMB H130 Panel 

H250 MMB 

Interface crack growth 

3.20: Debond propagation paths in MMB specimens and panels. 

In order to investigate the effect of initial imperfection magnitude on the behaviour of the panels, 

PMI panels with 100 mm debond and different initial imperfection magnitudes were analysed. 

Figures 3.21 (a) and 3.21 (b) show the energy release rate vs. load and phase angle vs. load 

curves for panels with different initial imperfection magnitudes. It is seen that the energy release 

rate is not sensitive to the initial imperfection magnitude. The phase angle, Figure 3.21 (b), is 

sensitive to the initial imperfection under small loads, but appears to converge to a value about 

0° under higher loads, indicating that the mode-mixity is less influenced by initial imperfection 

under higher loads. 

58 

H250 Panel 

PMI MMB PMI Panel 

Interface crack growth

(a) (b) 

3.21: (a) Energy release rate vs. load and (b) mode-mixity vs. load for panels with PMI core 

and 100 mm debond with different initial imperfection magnitudes. 

As mentioned previously, compiling a plot of strength reduction factor Rl against debond 

diameter presents some difficulty. However, Figure 3.22 shows a strength reduction factor based 

on the intact strength corresponding to compressive material failure as shown in Table 3.4, which 

is in turn based on the laminate compressive strengths presented in Table 3.1. The reduced 

strength values are based on the measured debond propagation loads, with the values for 50 mm 

debonds interpolated with the aid of the FE simulations. This figure is tentative in view of the 

uncertainties regarding the intact strengths and also the differences between test and analysis 

results reported above. 

3.22: Local strength reduction factors for panels with debonds. 

59


In this chapter the compressive failure of foam cored sandwich panels containing a face/core 

circular debond was experimentally and numerically investigated. Sandwich panels with 

glass/polyester face sheets and H130, H250 and PMI foam cores were tested in a specially 

designed test rig. All debonded panels failed by the propagation of the debond to the edges of the 

panels. All intact panels with H130 and H250 cores failed by the compressive failure of a face 

sheet very close to the wooden inserts, which can be attributed to additional peeling stresses 

arising due to the junction between the insert and the core and to a slight unintentional mismatch 

between the core and insert thicknesses. Intact panels with PMI core failed by a combination of 

shear crimping and global buckling. MMB characterisation tests were conducted to measure the 

fracture toughness of the face/core interface for a span of mode-mixity phase angles. Results 

showed increasing fracture toughness for increasing magnitude of the phase angle. A large 

scatter was observed in the fracture toughness results due to brittleness of the core material, 

different manufacturing defects and dissimilarity in crack propagation paths at the face/core 

interface. 

Instability and crack propagation loads of the panels were estimated based on geometrically nonlinear 

finite element analysis and linear elastic fracture mechanics. A numerical scheme similar 

to the one developed in Chapter 2, based on submodelling was used for the simulations. In some 

of the panels the FEA predictions are up to 46% higher than the experimental ones, which can be 

attributed to the large scatter in the measured fracture toughness using MMB fracture toughness 

results and differing crack tip details between the panels and the MMB specimens due to 

mechanical releasing of the debonded area. However, in most of the panels better agreement, up 

to 20% deviation, is observed between numerical and experimental results. To investigate the 

debond propagation path in the tested panels, some of the panels were cut and it was observed 

that the debond propagation path is similar between the panels and the MMB specimens. It was 

observed that in the panels and the MMB specimens with PMI core and panels with H130 core, 

the debond kinks into the core and propagates beneath the face/core interface. However, in the 

MMB specimens with H130 core two different crack growth paths were observed. In the H130 

MMB specimens with the mode-mixity phase angle of 0° >> -20° (similar to the panels), the 

crack path was located below the face/core interface. However, when the magnitude of the 

mode-mixity phase angle was increased to -25° >> -65°, the crack path was directly in the 

face/core interface. In the panels and the MMB specimens with H250 core the debond 

propagates directly in the interface. This may be explained by the higher fracture toughness of 

the H250 core compared to H130 and PMI cores. Fibre bridging was observed after more than 4- 

5 mm crack growth in the MMB specimens and panels with H250 core. The similarity between 

the debond propagation paths in the MMB specimens and the panels refutes the role of the 

different propagation paths in the inaccuracy of the determined debond propagation loads. 

60

To examine the effect of initial imperfection magnitude on the behaviour of the panels, panels 

with different initial imperfection magnitudes were analysed. It was shown that the initial 

imperfection magnitude has no significant effect on the energy release rate. Regarding the modemixity 

the effect becomes less important at higher loads. Finally, based on experimental and 

numerical results, the strength reduction factor Rl was plotted against debond diameter. The plot 

is tentative due to the uncertainties regarding the intact strengths as well as the differences 

between test and analysis results. 

61


62

Chapter 4 

Fatigue Crack Growth Simulation in a 

Bimaterial Interface 


Interface fatigue crack growth is one of the most critical damages that layered structures, such as 

monolithic fibre reinforced or sandwich composites, may experience. Design against fatigue 

failure of these types of structures is associated with many challenges due to the complexity of 

the interface fracture problem. To assess the lifetime and behaviour of layered structures exposed 

to cyclic loading, experiments are typically conducted on intact specimens and on specimens 

with a pre-existing (known) crack. This requires special testing facilities and is usually very 

costly and time-consuming. Due to the difficulties and expenses associated with conducting 

fatigue experiments, considerable efforts have been made in recent years to simulate fatigue 

crack growth by applying numerical methods. Maziere and Fedelich (2010) simulated 2D fatigue 

crack propagation using the finite element method and implementation of the strip-yield model. 

Their model assumes that, at each cycle, the crack growth results from the variation of the crack 

tip opening displacement (CTOD). They used cohesive elements with linear-elastic, perfectlyplastic 

behaviour to simulate crack growth. Kiyak et al. (2008) simulated fatigue crack growth 

under low cycle fatigue at a high temperature in a single crystal superalloy. To simulate the crack 

growth, they implemented a node release technique and released the nodes in each cycle 

according to an experimentally measured crack growth rate. The simulation results were 

compared with results from experiments on the single edge notch specimens of the Ni-based 

single crystal superalloy PWA1483 at 950C on the basis of computed crack tip opening 

displacement (CTOD). Shi and Zhang (2009) simulated the interfacial crack growth of fibre 

reinforced composites under tension–tension cyclic loading using the finite element method. In 

their model, the energy release rate is calculated and applied to Paris’ law in order to calculate 

the crack growth rate. Ramanujam et al. (2008) studied the fatigue growth of fibre reinforced 

63

composite laminates under thermal cyclic loading using combined experimental and 

computational investigations. 

In all the above-mentioned studies, the simulation of fatigue crack growth was limited to only a 

few cycles due to the need of a high mesh density at the crack tip and subsequently required high 

computational time. This illustrates the main obstacle confronting any attempt to combine 

fracture mechanics and the finite element method to simulate fatigue crack growth. To overcome 

the problem of simulating many cycles different concepts of cycle jumps have been proposed by 

several researchers. The cycle jump concept was first developed and applied by Billardon et al. 

(1989). They called the approach the jump-in-cycle procedure. The Large Time Increments 

method (LATIN) was proposed two years later by Boisse et al. (1990) and used by Cognard et al. 

(1999) for thermo-mechanical problems. In the large time increments method the equations of 

the initial boundary value problem are divided into two groups: (1) linear equations which are 

global and (2) non-linear equations, which are local. Even though the theory of the LATIN 

method is sound, after the implementation into commercial FEA software it turned out to be 

computationally heavy and not so beneficial. Kiewel et al. (2000) developed a method for 

extrapolation of a group of internal variables over a certain range of cycles. The extrapolation is 

based on spline functions used to evaluate the state variables over jumped cycles for each 

integration point in the finite element model. Fish et al. (2002) developed a new scheme for cycle 

jumps where the time is decomposed into two scales: one micro-chronological (fast) and one 

macro-chronological (slow). The fast micro-chronological time corresponds to the cyclic 

behaviour, and the slow macro-chronological time to the global behaviour of the structure. Van 

Paepegem et al. (2001) proposed a new cycle jump method based on extrapolation of the damage 

parameter exploiting the explicit Euler integration formula. At each integration point of the finite 

element model a local jump length is determined by imposing an input maximum jump allowed 

by the user for the damage variable. The global jump length is then evaluated based on the 

cumulative statistical distribution of local jumps. Cojocaru and Karlsson (2006) employed the 

cycle jump method to simulate the response of thermal barrier coatings (TBC) under cyclic 

thermal loading, where the structure evolves due to changing material properties during high 

temperature. In this case, damage mechanics was not used. They proposed a control function that 

automatically monitors the length of the cycle jump to ensure a realistic solution. Results showed 

their cycle jump scheme is computationally effective and accurate. 

In this chapter, the cycle jump method developed by Cojocaru and Karlsson (2006) is adopted 

with some modifications to take into account the change in the geometry of the finite element 

model due to the fatigue crack propagation. Two finite element routines are developed to 

simulate 2D and 3D accelerated bimaterial fatigue crack growth. In the first routine the crack 

only propagates at one point at the crack tip, but in the second a crack front is modelled and its 

growth at different points in different directions is simulated. 

64

4.2 The Cycle Jump Method 

In structures subjected to cyclic loading, parameters, such as deflection, stress, strain, material 

properties and/or geometry (for example cracks), typically evolve over time. This evolution 

results in both global and local changes of the structural behaviour, where the global changes 

correspond to a general long-term trend, which can be expressed in terms of mathematical 

functions. Based on these mathematical functions, extrapolation schemes can be employed to 

determine the long-term response of the structure. Such an extrapolation scheme can be used in 

numerical simulations to accelerate the analysis and make it computationally effective. The cycle 

jump scheme developed by Cojocaru et al. (2006) will be summarised here for the completeness 

of the presentation. As proposed by Cojocaru et al. in order to accelerate fatigue simulation, a set 

of initial load cycles is simulated, using the finite element method, and the global evolution 

function is established for each state variable monitored. This global evolution function is then 

used to extrapolate the state variables over a number of cycles. The key question here is the 

accuracy of the extrapolated variables. To examine and control the accuracy of the extrapolations 

the number of jump cycles is determined by a criterion with a control parameter. The determined 

extrapolated state is used as an initial state for additional finite element simulations and next 

cycle jumps, see Figure 4.1. 

Figure 4.1: Schematic presentation of the cycle jump method, after Cojocaru et al. (2006). 

Assuming that a finite element analysis has been conducted for at least three computed load 

cycles, see Figure 4.2, for each state variable monitored, y=y(t), where t is time, the discrete 

slope can be defined for every two adjacent cycles as 

65

S 

S 

y( 

t ) y( 

t ) 

( t ) 

2 1 

12 2 

(4.1) 

tcyc 

y( 

t ) y( 

t ) 

( t ) 

3 2 

23 3 

(4.2) 

tcyc 

where tcyc t2 

t1 

t3 

t2 

is the time of each cycle. 

Figure 4.2: Schematic presentation of the cycle jump method, after Cojocaru et al. (2006). 

The parameter qy is introduced as the maximum relative error to control the accuracy of the 

simulation by the following criterion: 

S 

jump 

( t 

3 

t 

y, 

jump ) S 

S ( t ) 

23 

3 

23 

( t3 

) 

q 

y 

where qy is the maximum allowed relative error, t y, 

jump the number of jumped cycles (assuming 

tcyc=1) and S jump is the estimated slope after the jump for the state variable y, using linear 

extrapolation given by 

S ( t ) S ( t ) 

( ) ( ) 

 

(4.4) 

23 3 12 2 

S jump t3 

t y, 

jump S23 

t3 

t y, 

jump 

tcyc 

The introduced criterion ensures that the slope of the increment of the variable y after the cycle 

jump is “close enough” to its slope before the jump. qy is specified by the user for each state 

parameter such as deflection or material properties. From Equations (4.3) and (4.4) the allowed 

jump for each extrapolated parameter is determined by 

66 

S 

S 

23 

12 

y( 

t3) 

y( 

t2) 

( t3) 

 

tcyc 

y( 

t2) 

y( 

t1) 

( t2) 

 

t 

cyc 

(4.3)

S23( 

t3 

) 

t y, 

jump q yt 

cyc 

(4.5) 

S ( t ) S ( t ) 

23 

3 

12 

2 

Since the cycle jump is determined for a set of state variables, the allowed jump t jump is chosen 

as the minimum of the computed allowed jump times for each variable: 

jump 

t t 

t t 

/ 

cyc min y, 

jump cyc 

(4.6) 

To extrapolate the state variables after each jump the Heun integrator is used : 

S23( t3 

) S jump ( t t 

jump t jump 

1 

y 

2 

( t3 

t 

jump ) y( 

t3 

) 

3 ) 

(4.7) 

By substituting Equation (4.4) into Equation (4.7): 

y( 

t 

2 

jump 

3 t 

jump ) y( 

t3 

) S23( 

t3 

) t 

jump S23( t3 

) S12( 

t2 

) 

(4.8) 

2tcyc 

The above extrapolation scheme is most suitable for structures with slowly evolving properties, 

in a quasi-linear manner. In case of more non-linear behaviour, higher order integrators could be 

implemented. However, the extrapolation scheme is able to capture highly non-linear behaviour 

by conducting shorter or no jumps. This, of course, does not save so much computational time, 

but ensures at least an acceptable solution. 

After having introduced the controlled cycle jump procedure, it is now of interest to investigate 

the extrapolation accuracy and the computational efficiency of the cycle jump method 

implemented in a finite element fatigue crack growth routine. Two different finite element 

routines incorporating the cycle jump method have been developed in this chapter. The first 

routine is based on a 2D finite element model suitable for 2D and axisymmetric fatigue crack 

growth, and the second is based on a 3D finite element model which can be used in any 3D 

fatigue crack growth simulation. 

4.3 Face/Core Fatigue Crack Growth in Sandwich Beams 

The cycle jump method described before will now be implemented in a FE-based numerical 

routine for investigating fatigue crack propagation in the face/core interface of a sandwich beam. 

Interface fatigue crack growth in a sandwich beam consisting of 2.8 mm thick plain-woven Eglass/epoxy 

face sheets over a 50 mm thick Divinycell H130 PVC foam core is simulated by a 

commercial finite element code, ANSYS version 11. Face sheet and core material properties are 

67 

( t 

)

listed in Table 4.1. The length and width of the beam are 215 mm and 65 mm respectively. The 

beam contains an initial 10 mm long face/core crack. 8-node isoparametric elements (PLANE82) 

are used in the finite element model. The finite element model of the beam is shown in Figure 

4.3. The strain energy release rate and mode-mixity are calculated from the finite element 

analysis at the end of each cycle. Utilising the relationships between crack growth rate and strain 

energy release rate for a range of mode-mixities as inputs to the FE routine, the crack increment 

for each cycle is determined and the finite element model with a new crack length is updated. A 

remeshing algorithm is employed to simulate the crack growth. Due to the current lack of 

suitable experimental fatigue crack growth rate data, the crack growth rate vs. strain energy 

release rate is for simplicity assumed to be constant for mode-mixity phase angles larger and 

smaller than -10 and chosen arbitrarily as 

da 

dN 

da 

dN 

0 . 001G 

for k>-10 (4.9) 

0 . 0008G 

for k

Figure 4.3: Finite element model of the sandwich beam. The smallest element size is 3.33 m. 

Figure 4.4: Route diagram of the developed fatigue crack growth scheme. 

69 

x 

y

The strain energy release rate, G, and the mode-mixity phase angle, , are determined from 

relative nodal pair displacements along the crack flanks obtained from the finite element analysis 

by application of the CSDE method outlined in the Introduction of this thesis. h, which is the 

characteristic length of the crack problem, is chosen as the face sheet thickness. The strain 

energy release rate and the mode-mixity phase angle are used as the two state variables for the 

extrapolation and cycle jump in the cycle jump method. These two parameters are selected since 

they are the only required parameters for determination of the crack growth length. 

Figures 4.5 (a) and (b) show the strain energy release rate and phase angle diagrams as a function 

of the crack length obtained from the numerical simulations of the analysed debonded sandwich 

beam at the maximum loading amplitude. The energy release rate increases with increasing crack 

length up to 60 mm and then decreases. This can be attributed to the increasing membrane forces 

as the crack length increases. Due to small membrane forces in the first cycles with increasing 

crack length, the deflection at the crack tip increases, resulting in higher strain energy release 

rate. However, as the crack length grows, the membrane forces increase and a larger part of the 

total strain energy in the specimen goes into stretching of the debonded face sheet rather than 

creating new crack surfaces, which results in a decreasing energy release rate at the crack tip. 

Figure 5 (b) shows that the phase angle increases with increasing crack length, indicating that the 

crack tip loading is less mode I dominated at larger crack lengths. The negative phase angle 

shows the tendency of the crack to kink towards the face sheet. 

(a) (b) 

Figure 4.5: (a) Strain energy release rate vs. crack length (b) phase angle vs. crack length 

diagrams for the debonded sandwich beam at maximum loading amplitude. 

The fatigue crack growth simulation was conducted on the sandwich beam for 500 cycles. To 

study the effect of the control parameter on the accuracy and speed of the simulation, simulations 

with different control parameters, qy, were conducted. A reference simulation of all individual 

cycles was performed to verify the accuracy of the simulations by application of the cycle jump 

method. Figures 4.6 (a) and (b) show the deflection of the loading point (Y deflection) as a 

function of cycles for two different control parameters, qG=q=0.05 and qG=q=0.2. 

70

(a) (b) 

Figure 4.6: Deflection of the face sheet at the point of loading (Y deflection) vs. number of 

cycles for (a) control parameter qG=q= 0.05 and (b) qG=q= 0.2. 

More cycles are needed in the simulation with smaller control parameters qG=q=0.05 as 

expected, but the calculated deflections agree well with the reference analysis. When the control 

parameters are increased to qG=q=0.2 fewer simulation cycles are needed, but as it is seen from 

Figure 4.6 (b), the deflection of the debonded face sheet in the simulation using the cycle jump 

method is lower than in the reference simulation, which shows the inaccuracy of the simulation. 

Figure 4.7 presents G vs. number of cycles. Even though G has a highly non-linear behaviour, 

the cycle jump method is able to capture this behaviour by conducting small or no jumps. In the 

simulation with the control parameters qG=q=0.05 there is fair agreement between the reference 

analysis and the cycle jump simulation, see Figure 4.7 (a). However, the results from the 

simulation with the control parameters qG=q=0.2 show some inaccuracies, see Figure 4.7 (b). 

(a) 

(b) 

Figure 4.7:G at the crack tip vs. cycles for (a) control parameters qG=q= 0.05 and (b) 

qG=q= 0.2. 

Crack length vs. cycle diagrams for the two control parameters qG=q=0.05 and qG=q=0.2 are 

shown in Figure 4.8. In the initial cycles (up to 200 cycles) the crack growth rate is large due to a 

71

high growth rate of G (see Figure 4.7), but approaching the end of 500 cycles with decreasing 

G, crack increment becomes smaller. The simulation with qG=q=0.05 follows the reference 

simulation with good agreement, but the simulation with qG=q=0.2 shows again less accuracy. 

(a) 

(b) 

Figure 4.8: Crack length vs. number of cycles for control parameters (a) qG=q = 0.05 and (b) 

qG=q = 0.2. 

Figure 4.9 presents the phase angle vs. number of cycles. The same conclusion may be drawn 

upon the accuracy of the simulation using the cycle jump method and the two control parameters 

qG=q=0.05 and qG=q=0.2. 

(a) 

(b) 

Figure 4.9: (a) Mode- mixity phase angle vs. number of cycles for the reference analysis and 

the analyses with qG=q=0.05 and qG=q=0.2 as control parameters. 

To measure the computational efficiency of the cycle jump method for analyses with different 

control parameters, the ratio R is introduced: 

N jump 

R (4.11) 

N 

ref 

where Njump is the number of jumped cycles and Nref is the total number of cycles in the reference 

72

analysis. A larger N shows increased computational efficiency. To measure the accuracy of the 

simulations the relative error is defined as 

yref 

y jump 

Er 

100 

(4.12) 

y 

ref 

where yref and yjump are the measured parameters from the reference and cycle jump analysis, 

respectively. The overall average error of the cycle jump method is determined as 

 

Er 

N 

Er (4.13) 

N 

where N is the number of simulated cycles and Er is the average error of each cycle. Number of 

jumped cycles, computational efficiency, average relative error for G, crack length and phase 

angle for simulations with different control parameters are listed in Table 4.2. The computational 

efficiency of the simulation increases by increasing control parameters, but the accuracy of the 

simulation decreases. It is seen that for qG=q=0.05, with reasonably good accuracy, using the 

cycle jump method, only 175 cycles are required for the simulation of 500 cycles, resulting in a 

65% reduction in computational time. 

Table 4.2: Number of jumped cycles, computational efficiency, average relative error for G, 

crack length and phase angle. 

Control 

parameter 

qG=q 

Number of 

simulated 

cycles 


jumps 

occurred 

R 

73 

Average 

relative error of 

G (%) 

Average 

relative error 

of crack 

length (%) 

Average 

relative 

error of 

phase 

angle (%) 

0.025 234 37 0.53 1.30 0.77 0.87 

0.05 175 25 0.65 1.39 1.06 1.22 

0.1 115 16 0.77 5.79 4.83 4.82 

0.2 70 12 0.86 5.96 7.46 5.55

4.4 Face/Core Fatigue Crack Growth in Sandwich Panels 

In this section the 2D fatigue crack growth finite element routine is further developed to account 

for 3D fatigue crack growth. Here, instead of having a crack tip and one point of crack 

propagation, a crack front propagates in different points in different directions. As schematically 

described in Figure 4.10, an iterative procedure is devised to couple the debond propagation 

routine and the cycle jump method, including a control criterion to ensure accuracy and 

computational efficiency of the simulation as described earlier in this chapter. 

Figure 4.10: Route diagram of the 3D fatigue debond growth and cycle jump routines. 

Initially, a set of station points defining the debond shape is chosen and the finite element model 

of the debonded panel is generated. The debond front is defined by passing a spline through the 

station points. To evaluate the direction of debond propagation, the normal and tangential 

directions of the debond front at each station point are determined and an orthogonal mesh at the 

debond front is imposed. The debond only propagates at the station points used to define the 

debond front. The finite element model is solved for the first three cycles. The strain energy 

74

elease rate and mode-mixity phase angle at each station point along the debond front are 

evaluated, and by means of experimentally determined relationships between crack growth rate 

and strain energy release rate for a range of mode-mixity phase angles as inputs to the FE 

routine, the crack growth at each station point in the debond front is determined. After evaluating 

the debond growth at each station point, a new debond front is defined by passing a spline 

through the new location of the station points. By means of a control function introduced earlier 

(Equation (4.5)) ensuring the accuracy and efficiency of the simulation, the number of cycle 

jumps is evaluated and state variables and the new position of the station points defining the 

debond front are estimated after the cycle jump. With the new debond shape defined after the 

cycle jump, the debonded panel is reconstructed and new normal and tangential directions of the 

debond front are determined, and the procedure is repeated for the next iteration. 

The efficiency of the devised methodology is examined by the simulation of sandwich panels 

with an elliptical face/core debond at the centre of the panels, exposed to cyclic loading. To 

study the effect of debond geometry, panels with different elliptical debond shapes are analysed. 

The sandwich panels are fully constrained at all four edges and the centre of the debond is loaded 

by a cyclic load. Due to geometry and loading symmetry, only a quarter panel is modelled and 

symmetry boundary conditions are applied to the symmetry planes, see Figure 4.11. A schematic 

presentation of the boundary conditions imposed on the finite element model is given in Figure 

4. 11. Finite element models with different element densities were generated and analysed to 

ensure the sufficiency of the mesh refinement. The mesh refinement convergence analysis 

showed that a minimum element edge length of 0.02 mm at the crack tip is needed for an 

accurate simulation. 

75

Debond 

310 mm 

Symmetry B. C. 

a 

Figure 4.11: Quarter finite element model of the debonded panels with an elliptical debond. 

The smallest element size is 10 m. 

In the majority of recent studies (see e.g. Gaudenzi et al., 2001, Riccio et al., 2001, and Shen et 

al., 2001), due to difficulties associated with tracing the orientation of the new debond front after 

the crack growth, it was assumed that the normal and tangential directions of the debond front do 

not change during the crack growth. This assumption is correct for the initiation of the debond 

growth in the first cycles, but for the subsequent debond growth the normal and perpendicular 

directions of the debond front are not similar to the initial debond. To avoid adopting this 

assumption, a remeshing algorithm imposing an orthogonal mesh with edges parallel and 

perpendicular to the actual debond front is implemented as illustrated in Figure 4.12. 

76 

Clamp B. C. 

x 

310 mm 

x 

y 

z 

y

Figure 4.12: Orthogonal mesh at the debond front. 

The mode I+II strain energy release rate, GI+II, and the associated mode-mixity phase angle, I+II, 

are determined from relative nodal pair displacements, obtained from the finite element analysis 

using the CSDE method, as outlined in the introduction. The mode I+II energy release rate and 

the related phase angle are given by 

2 14 H11 

2 

G 

 

I II 

GI 

GII 

y x 

8H11x 

H 22 

2 

 

 

 

 

77 

(4.14) 

 

1 

tan H 22 x x 1 

I II 

 

ln 

tan 2 (4.15) 

 

11 

 

H y h 

where y and x are the opening and sliding relative displacement of the crack flanks (see Figure 

4.13), H11, H22 and the oscillatory index are bimaterial constants determined from the elastic 

stiffnesses of the face and core, see the introduction chapter. h is the characteristic length of the 

crack problem. h has no direct physical meaning. Thus, it is here arbitrarily chosen as the face 

sheet thickness. 

To investigate the effect of mode III loading at the debond front, the mode III strain energy 

release rate, GIII, is evaluated. The mode III energy release rate is given by (Suo, 1990): 

G 

III 

2 

z 

 

8x( B1 

B2 

) 

(4.16) 

where z is the out-of-plane (crack plane) relative displacement of the crack flanks as shown in 

Figure 4.13, and x is the distance of the nodal pairs from the crack tip as shown in Figure 4.13. 

Subscript 1 and 2 refer to two materials in a bimaterial interface, and B is the inverse of an 

equivalent shear modulus given by (Suo, 1990):

B 

2 1/ 

2 

( S44 

S55 

S45) 

(4.17) 

where S44, S55 and S45 are compliance elements given by 

1 

S 44 

G 

23 

1 

S55 (4.18) 

G 

13 

S45 is zero for on-axis directions but appears for off-axis directions if G13G23. The total strain 

energy release rate is given by 

G G G 

(4.19) 

I 

II 

Mode II 

III 

x deflection at the crack tip 

Figure 4.13: Definition of x, y and z at the crack tip. 

The decomposition of the strain energy release rate to two components of GI+II and GIII is 

considered more useful for practical applications due to a present lack of experimental 

characterisation aimed at measuring the effect of GIII in terms of crack growth rate. In all recent 

studies the main focus has been on measuring the crack growth rate under pure mode I, II or 

mixed-mode loading at the crack tip. Due to difficulties associated with the mode III loading of 

the crack tip, this component has always been neglected. Thus, in the numerical routine 

presented, only the GI+II component of the energy release rate is used in the crack growth 

algorithm. This may introduce inaccuracy in the debond growth simulation if the mode III 

energy release rate contribution is large. These possible inaccuracies will be discussed later in 

this chapter. 

Debonded sandwich panels consisting of 2 mm thick plain-woven E-glass/polyester face sheets 

over 50 mm thick Divinycell H45 PVC foam are considered the simulation. Face sheet and core 

material properties are similar to those of the sandwich beam specimen analysed earlier, as listed 

78 

Mode I 

y deflection at the crack tip 

Mode III 

z deflection at the crack tip

in Table (4.1). The debonded panels are square with a side length of 310 mm. An elliptical 

face/core debond with a short radius (b) of 45 mm and a large radius (a) of 76.5 is created at the 

centre of the panel. 8-node isoparametric brick elements (SOLID45) are used in the finite 

element model. Due to the current lack of suitable experimental fatigue crack growth rate data, 

the crack growth rate vs. strain energy release rate is simply assumed to be constant for modemixity 

phase angles larger and smaller than -10 degrees and chosen arbitrarily as 

da 

dN 

da 

dN 

2 

0. 000005GI 

II 

for >-10 (4.20) 

2 

0. 000002GI 

II 

for -10 (4.21) 

where GI+II is the difference between maximum and minimum strain energy release rate in each 

cycle and da/dN is the crack growth rate. The simulation is conducted in load control with a 

maximum amplitude of 0.35 kN and loading ratio of R=Fmin/Fmax=0.1. 

To investigate the distribution of mode I, II and III components of strain energy release rate and 

mode-mixity phase angle along the debond front, radar diagrams from the analysis of the 

debonded panels exposed to maximum amplitude of the fatigue load are shown in the following 

figures. Debonded panels with a short radius of 45 mm and a ratio of large radius/short radius 

(a/b) of 1.7, 1.4 and 1.1 are analysed. In the diagrams 0 and 90 degrees correspond to the points 

on the debond front on the short and large radiuses of the ellipse. Figures 4.14 (a) and 4.14 (b) 

illustrate the distribution of mode I+II energy release rate (GI+II) and the related phase angle in 

the first cycle along the debond front. Maximum GI+II and mode-mixity phase angle occur at the 

short ellipse radius because of smaller crack length and decrease towards the larger radius. This 

can be attributed to the development of membrane forces in the face sheet at larger radiuses. As 

the radius of the ellipse increases the membrane forces become larger, and a subsequently larger 

part of the strain energy in the specimen should be used to stretch the debonded face sheet rather 

than create new crack surfaces, decreasing the energy release rate at the crack tip. As the ratio 

a/b decreases to one (circle) distribution of both GI+II and mode-mixity, the phase angle becomes 

more even as expected. The mode-mixity phase angle for all a/b ratios is between -5 and -10 

degrees along the debond front, which indicates a mode I dominated loading at the crack tip. 

The mode III strain energy release rate along the debond front is shown in Figure 4.15. In the 

symmetry plane (0 and 90 degrees) - due to the symmetry effect and the boundary conditions - 

the out-of-plane deformation (crack plane) at the crack flanks is zero and consequently the mode 

III strain energy release rate is zero. The maximum GIII on the panels with an a/b ratio of 1.7 is 

almost 9% of the maximum GI+II , implying the importance of mode III loading at the crack tip in 

the elliptical debond case with a large a/b ratio. The mode III strain energy release rate is very 

small for the a/b ratio of 1.1 and is not shown in the diagrams. For debonds with a small a/b ratio 

the debond is close to a circle and the mode III effects are insignificant. Figure 4.15 reveals that 

the maximum mode III crack tip loading occurs close to the longer radius of the ellipse (around 

79

75), which illustrates possible inaccuracies in the measurement of the debond growth at these 

points due to the negligence of GIII in the debond growth FE routine. 

120 

135 

105 

G(J/m 2 ) 

(a) 

165 

180 

195 

150 

600 

450 

300 

150 

0 

90 

75 60 

45 

30 

15 

0 

345 

210 

330 

225 

315 

240 

255 

270 

300 

285 

a/b=1.7 a/b=1.4 a/b=1.1 

Figure 4.14: Distribution of (a) GI+II and (b) related phase angle in the debond front. 

165 

180 

195 

150 

120 

135 

105 

60 

40 

20 

0 

90 

To evaluate the accuracy of the implemented cycle jump method, the fatigue debond propagation 

simulation was conducted for 500 cycles. To study the effect of the control parameter on the 

accuracy and computational efficiency of the simulation, simulations with different control 

parameters, qy, were conducted. A reference simulation, simulating all individual cycles was 

performed to verify the accuracy of the simulations based on the cycle jump method. The debond 

growth at different points along the debond front vs. cycles is shown in Figure 4.16 (a) from the 

reference simulation. Because of a larger strain energy release rate, the debond front in the 0degree 

position (short radius of the ellipse) grows more than at the other points. The crack 

80 

() 

165 

180 

195 

75 60 

150 

120 

135 

105 

-5 

-6 

-7 

-8 

-9 

-10 

90 

75 

60 

45 

30 

15 

0 

345 

210 

330 

225 

315 

240 

255 

270 

285 

300 

a/b=1.7 a/b=1.4 a/b=1.1 

45 

30 

210 

330 

225 

315 

240 

255 

270 

300 

285 

a/b=1.7 a/b=1.4 

Figure 4.15: Distribution of mode III strain energy release rate in the debond front. 

(b) 

15 

0 

345

growth descreases as the 90-degree position (large radius of the ellipse) is approached. Figure 

4.16 (b) illustrates the variation of the mode III strain energy release rate as the debond 

propagates. The mode III effects decrease significantly as the debond propagates and turns into a 

circle from its initial elliptical shape. 

80 

Debond front locations at: 

(a) 

60 

(b) 9 27 45 

Crack length (mm) 

70 

60 

50 

40 

0 18 36 

54 72 90 

0 100 200 300 400 500 

0 100 200 300 400 500 

Cycle 

Cycle 

Figure 4.16: (a) Debond growth and (b) mode III strain energy release rate vs. cycles at 

different points along the debond front from the reference simulation. 

Figures 4.17 (a) and 4.18 (b) show GI+II and phase angle vs. cycles from the reference 

simulation. The largest change in both diagrams occurs in the debond front location close to 0 

degree due to the large crack growth in this location. It is seen that GI+II decreases from 0 until 

approximately 54 and increases as the 90 degree position is approached. The mode-mixity 

variation along the debond front decreases as the debond shape changes from an ellipse to a 

circle. 

G I+II (J/m 2 ) 

500 

400 

300 

200 

100 

0 



0 18 36 

54 72 90 

(a) 

0 100 200 300 400 500 

Cycle 

Figure 4.17: (a) GI+II and (b) phase angle vs. cycles at different points along the debond front 

from the reference simulation. 

81 

G III (J/m 2 ) 

Phase angle (degree) 

50 

40 

30 

20 

10 

0 

-4 

-5 

-6 

-7 

-8 

-9 

63 81 

Cycle 

0 100 200 300 400 500 

(b) 


0 18 36 

54 72 90

Figure 4.18 (a) presents the deflection at the loading point (Z deflection) as a function of cycles 

for the reference and the cycle jump simulation with the control parameters qG=q=2.5. It is seen 

that the evaluated deflections from the cycle jump method agree well with the reference 

simulation. By use of the control parameters qG=q=2.5, the cycle jump method simulation 

requires 171 cycles to simulate 500 cycles, resulting in a 66% reduction in the computational 

time with excellent accuracy. The debond growth in three crack front locations along the debond 

is shown in Figure 4.18 (b) based on the reference and the cycle jump simulations with the 

control parameters qG=q=2.5. It appears that in all locations the cycle jump simulations 

estimates the debond growth with excellent accuracy. The same conclusion can be drawn for the 

mode I+II strain energy release rate and phase angle as shown in Figure 4.19. 

Figure 4.18: (a) Deflection at the loading point (Z deflection) and (b) debond growth vs. cycles 

for the reference and cycle jump simulations with control parameters qG=q=2.5. 

G I+II (J/m 2 ) 

(a) 

500 

400 

300 

200 

100 

0 

0 Reference 54 Reference 

72 Reference 0CJ qG=q=2.5 

52CJ qG=q=2.5 72CJ qG=q=2.5 

(a) 

0 100 200 300 400 500 

Cycle 

Figure 4.19: (a) GI+II and (b) phase angle vs. cycles for the reference and cycle jump 

simulations with control parameters qG=q=2.5. 


82 

75 

65 

55 

45 

Phase angle (degree) 

-4 

-5 

-6 

-7 

-8 

-9 



54CJ qG=q=2.5 72CJ qG=q=2.5 

0 100 200 300 400 500 

Cycle 

Cycle 

0 100 200 300 400 500 

(b) 

(b) 



54CJ qG=q=2.5 72CJ qG=q=2.5

As described before in Equations (4.11)-(4.13) the number of jumped cycles, the computational 

efficiency, the average relative error, for the debond growth for simulations with different 

control parameters are listed in Table 4.3. It is seen that by increasing the control parameter, the 

number of simulated cycles decreases significantly, but the accuracy of the simulation decreases 

as well. Nevertheless, the average error in the evaluation of the debond length is less than 0.1% 

for all control parameters. It should be noted that for qG=q=4 with a good accuracy and by use 

of the cycle jump method, only 145 cycles are required for the simulation of 500 cycles, which 

results in a 71% reduction in the computational time. 

Table 4.3: Number of jumped cycles, computational efficiency and average relative error for 

the debond length. 

Control parameter 

qG=q 


simulated cycles 

Number of jumps 

occurred 

83 

R 

Average relative error 

of crack length (%) 

1 303 16 0.39 0.03 

2.5 171 17 0.66 0.05 

4 145 15 0.71 0.08 

Fatigue debond growth is simulated for 2500 cycles using the control parameter qG=q=4 and 

the a/b ratio of 1.7, 1.4, 1.1 and 1. Figures 4.20 and 4.21 show the debond radius in different 

crack front locations along the debond. During the initial cycles, the debond growth is small in 

the proximity of the large radius of the ellipse, but as the debond propagates the radius at 

different points along the debond front converges, which leads to a change in the debond shape 

from ellipse to circle. 

Debond radius (mm) 

100 

90 

80 

70 

60 

50 

a/b=1.7 a/b=1.4 

90 

0 27 

45 72 

90 

40 

40 

0 500 1000 1500 2000 2500 

0 500 1000 1500 2000 2500 

Cycle 

Cycle 

(a) 

(b) 

Figure 4.20: Debond radius vs. cycle for sandwich panels with elliptical debond with an a/b 

ratio of (a) a/b=1.7 and (b) a/b=1.4. 


100 

80 

70 

60 

50 

0 27 

45 72 

90


100 

90 

80 

70 

60 

a/b=1.1 a/b=1 

90 

0 27 

50 

45 

90 

72 

50 

40 

40 

0 500 1000 1500 2000 2500 

0 500 1000 1500 2000 2500 

Cycle 

Cycle 

(a) 

(b) 

Figure 4.21: Debond radius vs. cycle for sandwich panels with elliptical debond with an a/b 

ratio of (a) a/b=1.1 and (b) a/b=1. 

For debonded panels with a/b=1.1, the radius in locations along the debond front converges fast. 

For the circular debond, due to similar energy release rate and phase angle in different locations 

along the debond front, the debond shape does not change as the debond grows, and remains 

circular. The number of simulation cycles and the computational efficiency of the simulations are 

shown in Table 4.4. By exploiting the cycle jump method, an approximate 80% reduction in 

computational time is achieved. Furthermore, it appears that despite using the same control 

parameter, the number of simulated cycles is different for panels with different debond a/b ratio 

because of different behaviour of the state variables (energy release rate and phase angle) for 

each case. 

Table 4.4: Number of jumped cycles and computational efficiency for the simulation of 

debonded panels with the control parameter qG=q=4 for 2500 cycles. 

a/b Number of simulated cycles R=Njumped/Ntotal 

1.7 588 0.77 

1.4 376 0.85 

1.1 288 0.89 

1 415 0.83 

84 


100 

80 

70 

60


A cycle jump method for accelerated simulation of fatigue crack growth in a bimaterial interface 

was presented in this chapter. The proposed method is based on finite element analysis for a set 

of cycles to establish a trend line, extrapolating the trend line which spans many cycles, and use 

the extrapolated state as an initial state for additional finite element simulations. Two finite 

element routines for accelerated fatigue crack growth simulation were developed. The first 

routine is suitable for 2D crack growth and the second is applicable to any 3D fatigue crack 

growth simulation with an arbitrary crack front shape. To assess the computational efficiency 

and accuracy of the developed finite element routines, they were used to simulate face/core 

interface fatigue crack growth in a sandwich beam (2D) and a sandwich panel (3D). The results 

were compared with a reference analysis simulating all individual cycles. 

By application of the cycle jump method, fatigue crack growth in the interface of a sandwich 

beam was simulated for 500 cycles as a numerical example. The computational efficiency and 

accuracy of the cycle jump method was discussed and verified based on the three parameters: 

crack length, difference between maximum and minimum energy release rate in a cycle (G) and 

mode-mixity phase angle against the reference analysis. The effect of the control parameters 

governing the implementation of the cycle jump method on the computational efficiency and 

accuracy was studied. The results suggest that the computational efficiency of the simulations 

increases considerably with increasing the control parameters. However, the accuracy of the 

simulations decreases for crack length, G and mode-mixity phase angle determination. For the 

control parameters qG=q=0.05 the cycle jump method requires 175 cycles to simulate 500 

cycles, resulting in a 65% reduction in computational time with reasonably good accuracy 

(around 1% error). 

The second routine (3D) was used to simulate fatigue debond propagation in sandwich panels 

with an elliptical face/core debond at the centre of the panels. To make the simulation suitable 

for practical applications and due to lack of experimental methods for characterization of the 

effect of the mode III energy release rate, GIII, on the crack growth rate, only mode I and II 

components of the strain energy release rate were used in the crack growth routine. However, to 

analyse the effect of mode III loading at the crack tip, the mode III strain energy release rate was 

determined along the debond front. It was shown that the mode III crack tip loading is 

considerable close to the longer radius of the ellipse for an elliptical debond with large a/b radius 

ratios, which implies the importance of the development of new experimental methods for 

characterisation of the effect of mode III loading at the crack tip on the crack growth rate in such 

debond geometries. 

To examine the accuracy and computational efficiency of the developed 3D cycle jump method, 

a reference simulation, simulating all individual cycles and simulations based on the cycle jump 

method with different control parameters were conducted. It was shown that with good accuracy 

85

using the cycle jump method, more than a 70% reduction in the computational time can be 

achieved. Finally, debonded panels with different elliptical shape debonds were simulated for 

2500 cycles by application of the cycle jump method, which illustrated similar beneficial 

reductions in the computational time. This study illustrates that the cycle jump method is a 

reliable method for accelerating fatigue crack growth simulations with good accuracy, but to 

develop an authentic life prediction method fatigue experiments should be conducted to validate 

and modify the developed scheme. 

86


87

Chapter 5 

Face/Core Interface Fatigue Crack 

Propagation in Sandwich Structures 


Fatigue behaviour of sandwich structures has been of great interest to researchers recently. 

Sandwich specimens with and without initial damages have been fatigue tested and analysed by 

various authors. Fatigue analysis of undamaged sandwich beams has typically been carried out 

by beam bending tests to investigate the fatigue response of foam cores subjected to shear 

loading. Shenoi et al. (1995) conducted flexural fatigue tests on sandwich composites with glass 

aramid/epoxy face sheets and cross link foam. They used a ten-point configuration with simply 

supported ends approximating a uniformly distributed load over the span of the beam. Burman et 

al. (1997) analysed the fatigue response of H100 PVC and Rohacell WF51 foams by four-point 

bending tests on undamaged sandwich beams. Kanny and Mahfuz (2002, 2005) studied the 

fatigue behaviour of sandwich beams exposed to flexural loading with different loading 

frequencies. They found that by increasing the loading frequency, the crack growth rates in the 

tested sandwich beams decrease. Kulkarni et al. (2003) studied fatigue crack growth in foam 

cored sandwich composites exposed to flexural cyclic loading in a modified three-point bending 

test rig. It was observed that the first visible damage was face/core debonding in the centre of the 

sandwich beams. Zenkert et al. (2011) studied the failure mode shift from core shear failure to 

face sheet tensile failure, as a function of load amplitude in GFRP/foam cored sandwich beams. 

Bezazi and co-authors (2007 and 2009) investigated experimentally and analytically the fatigue 

behaviour of sandwich composites in a three-point bending test rig. Mahi et al. (2004) studied 

the flexural behaviour of sandwich composites exposed to cyclic loading in a three-point bending 

test rig. He proposed a damage accumulation model for the sandwich specimens and used the 

model to analyse the fatigue life of sandwich composites. Quispitupa and Shafigh (2006) 

conducted fatigue tests on sandwich beams via three-point bending. They observed both global 

mode I and mode II cracking in the face/core interface of the specimens. In the case of debond 

88

damaged sandwich composites subjected to cyclic loading, a limited number studies can be 

found in the literature. Fatigue experiments have been carried out by Shipsha et al. (1999, 2000, 

2003) on debond damaged sandwich beams to determine stress-life S-N diagrams, crack growth 

rates and indentify fatigue crack growth mechanisms. They evaluated face/core interface crack 

growth rates under global mode I and II loading by use of the Double Cantilever Beam (DCB) 

and Cracked Sandwich Beams (CSB), respectively. Additionally, he studied the fatigue 

behaviour of foam cored sandwich beams in the presence and absence of initial damage under 

shear loading in a specially designed four-point bending test rig. Burman et al. (1997, 2000) also 

conducted four-point bending tests on debond damaged sandwich beams. They tested sandwich 

beams in a modified four-point bending test rig with different loading amplitudes. At higher load 

amplitudes the failure mode was core shear failure, but at smaller load amplitudes the failure 

mode was governed by tensile failure of the face sheet. Bozhevolnaya and co-authors (2009) 

conducted three-point bending fatigue tests on sandwich beams with peel stoppers. They 

reported that even though the peel stoppers have no significant effect on the fatigue life of the 

sandwich beams, they may prevent cracks from propagating in the face/core interface. Berkowits 

and Johnson (2005) carried out fatigue tests on double cantilever beams (DCB) of honeycomb 

core and carbon/epoxy face sheets. They used the compliance of the DCB specimen to determine 

the crack length and the crack growth rates. Liu and Holmes (2007) investigated fatigue crack 

propagation in thin-foil Ni-base and honeycomb core sandwich structures. Edge-notched 

honeycomb core sandwich panels were tested under tension-tension and tension-compression 

fatigue loading. 

All the above-mentioned studies are either purely experimental, or the proposed numerical or 

analytical methods for modelling the fatigue behaviour of sandwich structures are limited to a 

specific loading condition or geometry (e.g. beams). Thus, a more general approach is desirable. 

In Chapter 4 a general scheme for an accelerated simulation of fatigue crack growth in bimaterial 

interfaces was proposed. The main idea behind the proposed method is that once a specific 

interface has been characterised under cyclic loading, the extracted crack growth rates vs. energy 

release rates for different explicit mode-mixity phase angles can be utilised to simulate fatigue 

crack growth, and thus fatigue lifetime, of any structural component with an arbitrary loading 

condition as long as a similar face/core interface exists. 

In this chapter the proposed numerical scheme is applied to analysis of face/core interface fatigue 

crack growth in foam cored sandwich components. Moreover, the proposed numerical scheme 

will be validated against fatigue tests conducted on debonded sandwich beams and panels. In the 

first part of this chapter face/core fatigue crack growth in sandwich X-joints is studied 

experimentally. Furthermore, the face/core interface of the X-joints is characterised under cyclic 

loading. The obtained fatigue crack growth rates data is subsequently used as input for the 2D 

fatigue crack growth finite element routine developed in the previous chapter. In the second part 

89

of this chapter, sandwich panels with a circular face/core debond exposed to cyclic loading are 

tested and simulated by use of the developed 3D fatigue crack growth finite element routine. 

5.2 Face/Core Fatigue Crack Growth in Sandwich X- 

Joints 

Sandwich X-joints are widely applied to sandwich structures in order to connect panels which 

are attached perpendicularly to the face sheets of each other. An example of an application can 

be found in naval ships constructed of fibre composite sandwich materials, here among other 

locations an X-joint exists where the end bulkhead of the superstructure is attached to the deck, 

with an internal bulkhead placed in the same vertical plane below the deck. This joint will be 

subjected to alternating tensile and compressive loading in the vertical direction for respectively 

hogging and sagging bending deformation of the hull girder. When the core material is polymer 

structural foam, such joints are often strengthened by the insertion of a higher-density core 

material or core inserts of a stiffer material in the deck panel in the immediate region of the joint, 

see Hayman et al. (2007). The load transferred through X-joints can be tension or compression. 

Compressive load may lead to core indentation or crushing, whereas tensile loads may cause 

face/core debonding. Berggreen et al. (2007) proposed the Sandwich Tear Test (STT) specimen 

representing a debonded sandwich X-joint under tensile load, see Figure 5.1. 

In this section interface fatigue crack growth in sandwich X-joints is studied experimentally 

using a series of STT specimens. The STT specimens include variants with three different core 

densities and are tested under static and fatigue loading. Furthermore, the experimental results 

will be used to validate the numerical fatigue crack growth scheme presented in Chapter 4. 

Finally, a detailed analysis of the fatigue crack growth in sandwich X-joints will be presented 

and efficiency, accuracy and limitations of the proposed numerical scheme will be discussed. 

(a) 

Face/core debond 

Figure 5.1: Simplified geometry and boundary conditions for (a) sandwich X-joints and (b) 

Sandwich Tear Test (STT) specimen. 

90 

(b)

5.2.1 Experimental Study of the STT Specimens 

Static and fatigue tests were conducted on STT specimens to study the residual lifetime of 

debond damaged sandwich X-joints. Fifteen foam cored STT specimens with glass/polyester 

face sheets were manufactured for static and fatigue tests. The polyester resin is Polylite 413- 

575, which is specially designed for vacuum injection due to its low viscosity. The sandwich 

faces consist of four DBLT quadraxial mats from Devold Amt, each of a thickness of 0.75 mm 

and a dry area weight of 850 g/m2 and the fibre directions relative to the longitudinal direction of 

the specimen [90,45,0,-45], where the -45 degree ply is placed closest to the core. The core 

materials applied include Divinycell PVC foams of the types H45, H100 and H250 with nominal 

densities of 45, 100 and 250 kg/m 3 , respectively. The core thickness is 50 mm. The properties of the 

core and face materials are given in Table 5.1. Face sheet material properties are obtained from the 

tests conducted on samples from the face sheet. 

Table 5.1: Face and core material properties. 

Material E (MPa) G (MPa) 

Face sheet 19400 7400 0.31 

Core: H45 50 15 0.33 

Core: H100 130 35 0.33 

Core: H250 300 104 0.33 

A selection of manufactured STT specimens is shown in Figure 5.2. All specimens were reinforced 

by wooden inserts at the ends to avoid crushing of the core when mounting them in the STT test 

rig. The debond defect was introduced during the manufacturing process by inserting a sheet of 

0.025 mm thick Airtech release film on the core and sealing the edges with resin before vacuum 

injection. The panels were resin injected molded and cured with vacuum consolidation. The STT 

specimens were cut from the manufactured panels. The release film was placed along 480 mm of 

the specimen length so that the crack only propagates in one side, see Figure 5.2. The reason for 

not just testing simply a half part of the specimen where the crack propagates is that as the crack 

propagates the membrane forces in the face sheet becomes larger, generating harmful side forces 

on the testing machine actuator. The side loads can therefore be decreased by carrying the loads 

by the tension in the part of the face sheet which is not glued to the core. 

91

H250 Specimen 

H100 Specimen 

H45 Specimen 

z 

y 

x 

50 

480 

Wood Wood insert 

insert Release Teflon film film 

Foam 

Foam 

core 

core 

Figure 5.2: Manufactured STT specimens and a drawing of STT specimens including 

dimensions (mm). 

At the centre of the specimens steel plates were glued to the top and bottom face sheets with 

epoxy. Using the steel plates the top and bottom faces were fixed to the actuator of the testing 

machine and the test rig respectively by four bolts. The test rig consists of welded steel profiles 

of a wall thickness of 6 mm, see Figure 5.3. The wood reinforced ends of the specimens were 

clamped to the test rig by square section steel profiles using four bolts. Furthermore, a 4 Mpix 

Digital Image Correlation (DIC) measurement system (ARAMIS 4M) as shown in Figure 5.4 

was used to monitor 2D surface strains to locate the crack tip continuously during the 

experiments. The crack tip can be located by the strain concentration at the loaded crack tip, 

which is visible in the DIC strain contours. Finally, a servo-hydraulic Instron actuator with a 

maximum capacity of 100kN was used to load the STT specimens. However, a smaller 25 kN 

load cell was mounted on the actuator to increase the accuracy of the load measurements, see 

Figure 5.5. 

92 

1000 

860 

(Width 65mm)

(a) 

(b) 

Figure 5.3: Drawing of the STT test rig including a detailed drawing of connections. 

Test rig 

Figure 5.4: Layout of the experimental setup. 

93 

30 o

Figure 5.5: Test setup. 

Initially, to investigate the static behaviour and maximum load carrying capacity of the STT 

specimens, static tests were carried out on two specimens for each core density. Ramped 

displacement controlled loading with a piston displacement rate of 1 mm/min was applied to all 

tests. A sample rate of one image per second was used for the DIC measurements. Figure 5.6 

shows typical load vs. axial actuator displacement for the STT specimens, for additional results 

see Appendix C. The load initially increases linearly until face/core debond crack initiation 

occurs. After the first crack propagation the load drops, but as the crack propagates further the 

maximum load remains approximately constant. The maximum load in fatigue tests is chosen as 

a portion of the average of this mainly constant load. It is also seen that by increasing the core 

density, the crack initiation and propagation loads increase, which can be attributed to the larger 

fracture toughness of heavier cores. 

Force (kN) 

Measurement area 

1.2 

0.8 

0.4 

0 

H45 Specimen 

0 2 4 6 8 10 


Figure 5.6: Typical axial displacement of the actuator vs. force for specimens with H45, H100 

and H250 core densities. 

94 

Actuator piston 

Load cell 

H250 Specimen 

H100 Specimen 

H45

Crack growth paths for the STT specimens with H45, H100 and H250 cores from the static tests 

are shown in the following figures. For the specimens with H45 core, the crack kinks into the 

core up to 4-5 mm below the interface and then approaches the face/core interface as the crack 

propagates further. However, since the fracture toughness of the H45 core is low compared to 

that of the face/core interface, the crack never kinks into the interface and continues to propagate 

in the core just below the resin-rich region of the core, see Figure 5.7. For the specimens with 

H100 core, the crack initially kinks into the core and continues to propagate 2-3 mm below the 

interface. After 45-55 mm of crack growth it eventually kinks into the face/core interface and 

subsequently into the face sheet, which leads to large-scale fibre bridging, see Figures 5.8 and 

5.9. For the specimens with H250 core, the crack starts to propagate in the face/core interface. 

Subsequently, it kinks into the face sheet after 25-35 mm propagation and continues to propagate 

in the face sheet, resulting in large-scale fibre bridging, see Figure 5.10. The static crack 

initiation and propagation loads are listed in Table 5.2. It is seen that the mainly constant crack 

propagation load is much lower that the crack initiation load, which can be attributed to the 

initial resistance of the crack due to the accumulation of resin at the crack tip during the 

manufacturing process at the predefined face/core crack. 

H45 Specimen 

Figure 5.7: Static crack growth path for an STT specimen with H45 core at the beginning and 

end of the test. 

95

H100 Specimen 

Fibre bridging 

Figure 5.8: Static crack growth path for an STT specimen with H100 core at the beginning 

and end of the test. 

Figure 5.9: Fibre bridging in an STT specimen with H100 core. 

96

H250 Specimen 

Fibre bridging 

Figure 5.10: Static crack growth path for an STT specimen with H250 core at the beginning 

and end of the test. 

Table 5.2: Static crack initiation and propagation load. 

STT Specimen Static crack initiation load (kN) Static crack propagation load (kN) 

H250 core 1.08±0.07 0.63±0.06 

H100 core 1.05±0.06 0.56±0.09 

H45 core 0.45±0.09 0.31±0.04 

Using the static tests results and a few trial specimens, reasonable load levels for the fatigue tests 

were designated to have a stable crack propagation. 80% of the static propagation load of the 

STT specimens was used as the maximum fatigue load with a loading ratio of R=Fmin/Fmax=0.1 

and frequency of 2 Hz. Load controlled fatigue tests were conducted on the STT specimens and 

two specimens of each core type were tested. To break the initial resin accumulation at the predefined 

crack tip, pre-cracking was performed on the specimens. A cyclic load, at approximately 

50-60% of the static crack propagation load, was applied to the specimens to break the blunt 

crack tip, which resulted in approximately 5-10 mm crack propagation. When all the specimens 

were pre-cracked, the crack tip was located underneath the face/core interface in the core. The 

following crack growth paths were observed in the fatigue experiments: 

1. For the specimens with the H45 core, unstable crack growth occurs initially and the crack 

propagates up to a length of 150 mm in a few cycles, see Figure 5.11. After the unstable 

97

propagation, the crack continues to propagate in the core underneath the resin rich-cells 

approaching the interface, which indicates the existence of negative mode-mixity at the 

crack tip. At negative mode-mixity the crack tends to kink towards the interface but since 

the interface is tougher than the H45 core, the crack is forced to remain in the core unable 

to penetrate through the resin-rich cells, see Figure 5.11. 

2. For the specimens with the H100 core, the crack propagates initially in the core up to a 

length of approximately 120 mm, but eventually kinks into the interface and continues to 

propagate directly in the interface, see Figure 5.12. It is seen that the static and the fatigue 

crack growth paths for H100 STT specimens are different. No fibre bridging is observed 

during the fatigue tests even though a similar mode-mixity exists at the crack tip for a 

given crack length for both static and fatigue experiments. The difference in the crack 

growth paths can be addressed to the smaller maximum fatigue load level compared to 

the critical static propagation load, which fails to provide enough energy at the crack tip 

to penetrate the first layer of the face sheet. 

3. For the specimens with the H250 core, the crack propagates initially in the core up to a 

length of 5-8 mm and then kinks into the interface. The interface crack eventually kinks 

into the face sheet, which results in large-scale fibre bridging, see Figure 5.13 and 14. As 

the crack continues to propagate in the face sheet, fibre bridging becomes more and more 

extensive, resisting the crack growth, and eventually results in crack growth seizure, see 

Figure 5.15. 

H45 Specimen 

Crack underneath the resin-rich 

Figure 5.11: Crack growth path in the specimens with H45 core. 

98

H100 Specimen 


H250 Specimen 

Interface crack 

Fiber bridging 


99

Figure 5.14: Kinking of the crack into the face sheet in an STT specimen with H250 core. 

Figure 5.15: Fiber bridging in the rear side of an STT specimen with H250 core. 

A 4 Mpix Digital Image Correlation (DIC) measurement system (ARAMIS 4M) was utilized to 

monitor 2D surface major strains and locate the crack tip position by the strain concentration at 

the crack tip in the measured 2D strain contours. To ensure the accuracy of the measurement a 

tape ruler was glued to the bottom side of the specimens to locate the crack tip as well and 

measure the crack length by a calliper with an accuracy of ±0.05 mm. Figure 5.16 shows a 

majore strain contour from an STT specimen with H45 core used to locate the crack tip position 

by the DIC system. 

Fatigue crack growth length vs. load cycle diagrams for the STT specimens from both the visual 

measurements and the measurements using the DIC system are presented in Figure 5.17. The 

crack length measurements by the DIC system agree well with the physical crack measurements, 

as shown in Figure 5.17. Crack growth length vs. load cycle results from the two repetitions of 

each type of STT specimens are shown in Figure 5.18. It is seen that for all core densities the 

crack initially grows fast, but the crack growth rate decreases as the crack propagates further. 

This can be attributed to increasing membrane forces and subsequent decreasing energy release 

rates for the H100 and H45 specimens and fully developed fibre bridging resisting the crack 

growth for the H250 specimens. For both STT specimens with H45 core, unstable crack 

propagation was observed during the initial load cycles where the crack propagated unstably 

100

around 150 mm. After the unstable crack propagation, the crack continued to propagate in a 

stable manner. A small deviation between the two test repetitions is observed for the H45 and 

H100 specimens. However, Figure 5.18 (c) illustrates a large deviation between the two test 

repetitions for the STT specimens with H250 core, which can be attributed to the different scales 

of fibre bridging in H250 specimens. 

Crack length [mm] 

Figure 5.16: Surface major strain contour of the STT specimens from the DIC system. 

250 

200 

150 

100 

50 

0 

Strain concentration 

at the crack tip 

200 

(a) (b) 

0 20000 40000 60000 80000 

Cycles, N 

Visual 

DIC 

101 


160 

120 

80 

40 

0 

Visual 

DIC 

0 20000 40000 60000 80000 100000 

Cycles, N



150 

120 

90 

60 

30 

0 

0 20000 40000 60000 80000 100000 

Cycles, N 

Figure 5.17: Fatigue crack growth from the visual measurements and measurements using 

DIC vs. cycles for the STT specimens with (a) H45 (b) H100 and (c) H250 core. 

250 

200 

150 

100 

50 

0 

(c) 


200 

150 

100 

Figure 5.18: Fatigue crack growth vs. cycles for the STT specimens with (a) H45 (b) H100 

and (c) H250 core. 

5.2.2 Fatigue Characterisation of the Face/Core Interface 

Mixed Mode Bending (MMB) tests were conducted on pre-cracked MMB sandwich specimens, 

as introduced in Chapter 3, to characterise the fatigue behaviour of the face/core interface of the 

STT specimens, as shown in Figure 5.19. The MMB test rig allows a range of mode-mixities to 

be achieved at the crack tip for different lever arm distances, denoted as c in Figure 5.19. A 

servo-hydraulic MTS 858 testing machine with a maximum capacity of 100kN was used to load 

the MMB specimens. However, a smaller 25 kN load cell was mounted on the actuator to 

increase the accuracy of the load measurements. 

102 

Visual 

50 

STT H45-1 

STT H45-2 

50 

0 

STT H100-1 

STT H100-2 

0 

STT H250-1 

STT H250-2 

0 50000 100000 0 50000 100000 0 50000 100000 

Cycles, N 

Cycles, N 

Cycles, N 

(a) (b) (c) 

DIC 


150 

100

Since the observed large-scale fibre bridging in the STT specimens with H250 core violates the 

initial assumptions of linear elastic fracture mechanics in the developed numerical fatigue crack 

growth scheme, the H250 specimens were discarded and characterisation of the interface was 

only performed for the specimens with H100 and H45 core. MMB sandwich specimens of each 

core type were manufactured with 20 mm core and 2 mm face sheet thickness. An initial 20 mm 

long start crack was defined in the face/core interface of the MMB specimens by inserting a 

Teflon film, 30 m thick, during the manufacturing process. Similar face sheets, core materials 

and manufacturing processes as for the STT specimens were used in the manufacturing of the 

MMB specimens. The specimens were 35 mm wide with a span length (2L) of 160 mm. 

Figure 5.19: Mixed mode bending rig with the MMB sandwich specimen. 

To determine the mode-mixity at which the face/core interface fatigue behaviour should be 

characterised by MMB tests, the mode-mixity phase angle at the crack tip of the STT specimens 

was evaluated by the finite element method at a load corresponding to the maximum fatigue load 

in the STT fatigue tests (to be presented in the next section). In all the STT specimens the modemixity 

phase angle for different crack lengths is between -5 to -20 , which implies mode I 

dominant loading at the crack tip. The MMB lever arm distances (c) resulting in similar modemixities 

as those of the STT specimens were determined from the finite element model of the 

MMB specimen shown in Figure 5.20. The FE model was developed using PLANE42 elements 

in the commercial finite element code ANSYS. The phase angle and the energy release rate are 

determined from relative nodal pair displacements along the crack flanks obtained from the finite 

element analysis using the CSDE method as outlined in Chapter 1. The characteristic length h is 

arbitrarily chosen as the face sheet thickness. Figure 5.21 shows the variation of the mode-mixity 

phase angle vs. the lever arm distance (c) in the MMB specimens. At small level arm distances 

the mode-mixity phase angle increases significantly and mode II dominant loading is present at 

the crack tip. Increasing the c distance, the phase angle converges to around -20 for the present 

specimen geometry. It appears that with the current design of the test rig and the MMB specimen 

it is not possible to reach mode-mixity phase angles more than -20. Therefore, only a -20 

103

mode-mixity phase angle was chosen in the finite element model of the MMB specimen to 

determine the appropriate lever arm distance (c). It is assumed that because of the mode I 

dominant loading for phase angles more than -20, the characterisation of the face/core interface 

for only -20 phase angle and using the resulting crack growth rates for the simulation of STT 

specimens with slightly lower phase angle magnitudes (-20

Displacement controlled static tests with 1 mm/min loading rate were conducted on two MMB 

specimens of each core type to determine the static crack propagation load. Typical load vs. 

displacement curves from the static tests are presented in Figure 5.22. The point where the crack 

starts to propagate is marked with an open circle (“”). The critical failure load is marked 

according to the ASTM D6671/D 6671M-06 recommendation and complemented by visual 

inspection. 

Load (N) 

80 

60 

40 

20 

0 

0 

0 1 2 3 

0 2 4 6 



(a) 

(b) 

Figure 5.22: Typical load vs. displacement curves (“” onset of crack growth) for the MMB 

sandwich specimens with (a) H45 core and (b) H100 core. 

Fatigue tests in displacement control with sinusoidal wave form were conducted on three 

specimens of each core type at a frequency of 2 Hz and with a loading ratio R=0.1. Displacement 

controlled testing was chosen for better servo-hydraulic control of the loading and to avoid any 

unstable crack growth in the MMB specimens. To have a stable crack growth, 80% of the static 

crack propagation load was chosen as the maximum fatigue load after testing a few trial 

specimens. The crack length was determined every 50 cycles using the compliance of the MMB 

specimen as 

 

 

 

 

 

 

 

 

 

105 

( 5.1) 

Where c is the lever arm distance, L the half-span length, is the load partitioning parameter. C1, 

C2 and C3 are compliances of the sub-beams according to Quispitupa et al. (2009) as introduced 

in Chapter 3. For further details see Chapter 3. Moreover, visual crack length measurement was 

performed by a calliper with an accuracy of ±0.05 mm. The maximum fatigue load (Pmax) and 

the corresponding displacement (max) were used to determine the compliance of the MMB 

specimens and subsequently the crack length. The MMB compliance in Equation (5.1) is a 

function of the crack length. Knowing the maximum load (Pmax) and displacement (max) from 

the testing machine, the compliance CMMB=/P can be calculated and subsequently the crack 

length can be determined, see Chapter 3. Furthermore, since the MMB test rig has several hinge 

connections and load introduction points, the deflections of the test rig during the fatigue tests 

Load (N) 

160 

120 

80 

40

should be taken into account for a realistic determination of the compliance of the MMB 

specimens. To consider the effect of test rig deformations, the compliance of the test rig was 

determined by use of a thick stiff steel beam of a thickness of 10 mm, width of 25 mm and length 

of 250 mm. To determine the compliance of the test rig, denoted as Crig in Equation (5.2), the 

compliance of the steel specimen, Csteel, was subtracted from the measured total compliance, 

Cmeasured. 

C C C 

( 5.2) 

rig 

measured 

steel 

The compliance of the steel specimen is calculated as 

C 

steel 

cL 2 

2L 

( 5.3) 

3 

E b t 

st 

s 

where bs is the width of the steel specimen, c is the lever arm distance, t is the thickness of the 

steel specimen, L is the span distance and Est is Young’s modulus of the steel specimen. Finally, 

the compliance of the MMB specimens is determined as 

C C C 

( 5.4) 

MMB 

Exp 

rig 

The MMB rig with the steel specimen was loaded in displacement control with 1 mm/min 

loading rate up to 100N for the different lever arm distances (c). The results of the compliance 

calibration are presented in Figure 5.23. It appears that the compliance of the test rig increases in 

a nearly linear fashion with increasing c values. 

Compliance of the test rig (m/N) 

0.8 

0.6 

0.4 

0.2 

0 20 40 

c (mm) 

60 80 

5.23: Compliance of the MMB test rig as a function of lever arm distances, c. 

To have an initial crack location for the MMB specimens similar to the initial crack location in 

the STT specimens, and to penetrate the resin blob at the crack tip, pre-cracking was conducted 

on the MMB specimens. A pre-cracking method proposed by Quispitupa et al. (2011) was used. 

The pre-cracking was conducted on a variant of a double cantilever beam configuration as shown 

in Figure 5.24. The specimen is clamped between two steel 20 mm thick blocks. A steel block is 

106

clamped approximately 5–10 mm from the crack tip to limit the crack extension and ensure a 

straight crack front during pre-cracking. The upper debonded face sheet was loaded using a 

sinusoidal cyclic loading with a load ratio of R=0.1 and frequency of 2 Hz. A maximum of 50- 

60% of the static crack initiation load was applied during the pre-cracking as the maximum 

fatigue load to the specimens to avoid large crack increments. During the pre-cracking the crack 

always kinked either to the face sheet or to the core. This can be attributed to the tougher 

face/core interface compared to the core and face sheet. As to the face sheets it is believed that 

the main reason for this is the polyester resin used as the matrix, making the face sheets less 

tough than the interface and prone to matrix cracking. To prevent the crack from kinking into the 

face sheet and resulting fibre bridging, a downward force is applied to the lower debonded part 

of the MMB specimens (core+ lower face sheet) by using a screw type configuration as shown in 

Figure 5.24. This small force provokes the crack to kink into the core from the interface by 

creating shear forces at the crack tip as shown in Figure 5.25. The crack location and growth was 

observed continuously using a calliper with an accuracy of ±0.05 mm during the cyclic loading. 

The pre-cracking was stopped after 5-10 mm of crack growth. During pre-cracking the 

predefined face/core debond kinked into the core in most of the specimens. However, in few 

specimens with H100 core the debond kinked into the face sheet and the specimens were 

discarded, see Figure 5.26. 

a 

Fatigue load 

Downward load 

a 

Figure 5.24: Pre-cracking test setup. 

107

Figure 5.25: Kinking of the crack into the core during pre-cracking for an MMB specimen 

with H100 core. 

Crack kinking into the face 

Figure 5.26: Kinking of the crack into the face sheet during pre-cracking for an MMB 

specimen with H100 core. 

After pre-cracking, fatigue tests were performed on the MMB specimens. Fatigue crack growth 

paths for the MMB specimens are shown in Figure 5.27. The crack propagates in both specimens 

just underneath the face/core interface and below the resin-rich cells. 10-12 mm stable crack 

growth was measured for all MMB specimens where the crack growth eventually seized. 

108

Figure 5.27: Fatigue crack growth path for H45 and H100 MMB specimens. 

The fatigue crack growth rates data are plotted against the energy release rate (G) obtained 

from the finite element analysis in Figure 5.28. As it was mentioned earlier, due to large-scale 

fibre bridging in the H250/GFRP interface, linear elastic fracture mechanics is not valid and no 

measurements were conducted for this interface. In the Paris regime, which corresponds to stable 

crack growth and exhibits a linear relation between the crack growth rates and the energy release 

rates, the crack growth rates can be written as a modification of the traditional Paris Law: 

 

 

Crack path underneath the face/core 

interface for typical H45 MMB specimens 

Crack path underneath the face/core 

interface for typical H100 MMB specimens 

109 

( 5.5) 

where m is the slope of the curve and G is the difference between maximum and minimum 

energy release rates at the crack tip in each cycle. The energy release rate is determined from the 

finite element analysis of the MMB specimens. Figure 5.28 illustrates the influence of core 

density on the crack growth rates. As seen in Figure 5.28 the scatter of the results for the 

H45/GFRP is larger than that for H100/GFRP, which can be attributed to a larger cell size and 

increased brittleness of the H45 core. Furthermore, the magnitude of m is larger in the 

H45/GFRP than in the H100/GFRP interface, which indicates a faster crack growth rate due to 

the lower density and brittleness of the H45 core.

log (da/dN) (mm/cycle) 

10 log G (J/m 1000 

0.01 

2 ) 

0.001 

0.0001 

H45 

=-20 

m=7.45 

C=1.08 10 -18 

Figure 5.28: Crack growth rates for the H45/GFRP and H100/GFRP interfaces. Each marker 

type presents an experiment. 

5.2.3 Finite Element Modelling of the STT Specimen 

A 2D finite element model of the STT specimen is developed in the commercial finite element 

code ANSYS. 4-node iso-parametric elements (PLANE42) are used in the finite element model. 

To simplify the model the bottom face sheet and the core in the half of the STT specimen where 

the face sheet is not glued to the core is not modelled. The finite element model consists of top 

face sheet and half of the core and bottom face sheet. Symmetry boundary conditions are 

imposed in the symmetry plane on the core and bottom face sheet. The finite element model of 

the STT specimen is shown in Figure 5.29. 

Figure 5.29: Finite element model of the STT specimen. The smallest element size is 3.33 m. 

110 

Crack tip 

H100 

=-20 

m=6.15 

C=1. 5 10 -18 

x 

y

An accelerated simulation of fatigue crack growth (the cycle jump method) developed in the 

previous chapter is performed on the STT specimens. The energy release rate and mode-mixity 

phase angle are chosen as state variables in the cycle jump method. Figures 5.30 (a) and (b) show 

the strain energy release rate and phase angle diagrams as a function of crack length obtained 

from the finite element analysis of the STT specimens at maximum fatigue load in each cycle. 

G (J/m 2 ) 

450 

350 

250 

150 

STT H100 

STT H45 

-20 

50 

20 40 60 80 100 120 


-25 

(a) 

(b) 

Figure 5.30: Energy release rate and phase angle as a function of crack length for the STT 

specimens. 

The energy release rate increases with increasing crack length up to 60 mm and then decreases 

due to the increasing membrane forces as the crack propagates. In smaller crack lengths with 

increasing crack length, because of small membrane forces, the deformations at the crack tip 

increase, which leads to higher energy release rate. However, as the crack propagates, resulting 

in at increasing membrane forces, a larger part of the strain energy is used to stretch the 

debonded face sheet rather than create new crack surfaces, decreasing energy release rate at the 

crack tip. Figure 5.30 (b) shows that the mode-mixity phase angle magnitude increases with 

increasing crack length, which indicates the existence of higher mode II loading at the crack tip 

at larger crack lengths. The negative phase angle illustrates the tendency of the crack to kink 

towards the face sheet. The fatigue crack propagation simulation was conducted on the STT 

specimens for 100000 cycles. In order to study the effect of the control parameters on the 

accuracy and speed of the simulation, simulations with different control parameters, qy, were 

carried out. Figures 5.31 (a) and (b) show the crack length as a function of cycles for four 

different control parameters qG=q=0.05, 0.1, 1.5 and 0.2. A significant dependency on the 

control parameters is seen in the simulations of the H45 specimens. Large deviations are 

observed between the simulations using 0.15 and 0.25 as control parameters. However, the 

simulation results converge at smaller control parameters. During the initial cycles the 

simulations using qG=q=0.15 and 0.25 control parameters show small differences but as an 

unstable crack growth zone is approached the deviations increase. This takes place due to the 

111 

Phase angle () 


20 40 60 80 100 120 

-5 

-10 

-15 

STT H100 

STT H45

erroneous extrapolations in the transition from stable to unstable crack growth zone and the 

extreme non-linearity of this transition. With smaller control parameters smaller jumps occur and 

the cycle jump scheme is able to extrapolate accurately the stable-unstable crack transition zone. 

H100 specimens due to slightly different crack growth rate relations and stable crack growth, as 

also observed in the fatigue experiments, show much less dependency on the control parameters. 

Additionally, with the chosen initial crack length, the H100 specimens have already passed the 

highly non-linear region of transition from very slow crack growth rates to much larger growth 

rates. 

200 

200 q=qG=0.05 

q=qG=0.15 

q=qG=0.25 


150 

100 

50 

0 

q=qG=0.01 

q=qG=0.05 

q=qG=0.15 

q=qG=0.25 

0 20000 40000 60000 80000 100000 

Cycles 

Cycles 

(a) 

(b) 

Figure 5.31: The effect of the control parameters on the simulation of (a) H45 and (b) H100 

STT specimens. 

In order to model the initial highly non-linear crack growth zone for the H100 STT specimens, 

simulations were conducted on the specimens with H100 core and 5 mm smaller initial crack 

length (20 mm crack length) for a range of different control parameters, see Figure 5.32. 

Deviations similar to those of the STT specimens with H45 core are seen this time for the 

qG=q=0.05, 0.15 and 0.25 control parameters, illustrating one of the main limitations of the 

developed cycle jump scheme. In the case of highly non-linear behaviour of the structure, the 

control parameters should be chosen carefully to be able to simulate the non-linear zone 

accurately. This limitation makes the sensitivity and convergence analysis an essential part of 

incorporating the cycle jump method in the simulation of general fatigue crack growth in 

structural analysis. Simulation results using qG=q=0.05 control parameters are presented 

together with experimental results in Figure 5.33. The simulations of the specimens with H100 

core show fair accuracy compared to the experimental results. However, large deviations are 

seen between the simulations and experimental results for the specimens with H45 core. The 

deviations start at the beginning of the unstable crack growth and remains constant throughout 

the stable crack growth zone. The reason for this deviation can be found in the interface fatigue 

characterisation. Since the interface fatigue characterisation was only made for the stable linear 

part of the crack growth rate diagram (the Paris regime), the resulting da/dN vs. G relation is 

112 


150 

100 

50 

0 

1 mm 

0 20000 40000 60000 80000 100000

not valid for unstable crack growth and produces incorrect results. Utilising stable da/dN vs. G 

relations for unstable fatigue crack growth will result in smaller crack growth estimations, which 

is seen in Figure 5.33 (a). 


Figure 5.32: The effect of the control parameters on H100 specimens with an initial crack 

length of 20 mm. 

250 

200 

150 

100 

50 

0 


200 

150 

100 

50 

0 

Cycles 

(a) 

0 20000 40000 60000 80000 100000 

Test #1 

Test #2 

Simulation 

0 25000 50000 75000 100000 

Cycles 

113 

q=qG=0.05 

q=qG=0.15 

q=qG=0.25 

0 25000 50000 

Cycles 

(b) 

75000 100000 

Figure 5.33: Crack length vs. cycles for the STT specimens with (a) H45 and (b) H100 core 

from experiments and simulations. 

The number of simulated cycles and the computational efficiency are listed in Table 5.3. Results 

show that up to 98% of the simulation time can be saved by use of the cycle jump method with 

reasonable accuracy, which proves a significant computational efficiency. It is seen that 


200 

150 

100 

50 

0 

Test #1 

Test #2 

Simulation

compared to the 65% efficiency obtained for the simulation of fatigue crack growth in sandwich 

beams in Chapter 4, the computational efficiency is here more than 33% higher. This is due to a 

somewhat unrealistic and arbitrary choice of da/dN vs. G relations in the simulations in Chapter 

4, where the da/dN vs. G relations were chosen so that the crack reaches the end of the 

specimens in hundreds of cycles to make the reference simulation of all individual cycles 

possible. The use of realistic da/dN vs. G relations here makes the crack growth significantly 

smaller in every cycle and provides room for more cycle jumps in the simulation. 

Table 5.3: Computational efficiency of the simulations with different control parameters. 


qG=q 

Number of simulated cycles 

H45 specimen Saved cycles (%) H100 specimen Saved cycles (%) 

0.05 1104 98.896 1096 98.904 

0.10 548 99.452 557 99.443 

0.15 411 99.589 381 99.619 

0.20 312 99.688 323 99.677 

0.25 243 99.757 188 99.812 

5.3 Fatigue Crack Growth in the Face/Core Interface of 

Sandwich Panels 

In this section the 3D fatigue crack growth scheme developed in Chapter 4 is used to simulate 

fatigue crack growth in debonded sandwich panels with a circular debond at the centre. The 

simulation results will be compared with fatigue experiments at the end of this section. 

5.3.1 Fatigue Experiments on Debonded Panels 

Five sandwich panels with a circular face/core debond at the centre were manufactured for 

fatigue experiments. The panel face sheets consist of three layers of Devold AMT DBLT 850 

quadraxial glass fibre mats of a total thickness of 2 mm, each with a dry density of 850g/m 2 . The 

core materials are H45 Divinycell PVC foam with nominal densities of 45 kg/m 3 . The core thickness 

is 50 mm. The properties of the core materials, taken from the manufacturers’ data sheets (DIAB), 

and the face materials are given in Table 5.4. Figure 5.34 presents a drawing of the panels, including 

the dimensions, and an image showing one of the manufactured panels. 

114

Figure 5.34: Drawing of debonded sandwich panels with an image of a manufactured panel. 

Table 5.4: Face and core material properties. 

Material E (MPa) G (MPa) 

Face sheet 19400 7400 0.31 

Core: H45 50 15 0.33 

All specimens were reinforced with wooden inserts at the edges to avoid crushing of the core. 

The debond was introduced before the resin infusion by inserting a piece of 0.025 mm thick 

Airtech release film on the core in the centre of the panels and sealing the edges with resin. The 

test rig consists of welded steel square profiles with a wall thickness of 3 mm. A 4 Mpix Digital 

Image Correlation (DIC) measurement system (ARAMIS 4M) was placed above the panels to 

monitor 2D surface strains and displacements in order to estimate the crack growth continuously 

during the experiments. The test rig was inserted in an MTS 810 servo-hydraulic testing machine 

with a maximum capacity of 100kN and an integrated T-slot table upon which the test rig was 

positioned and fixed. However, a smaller 25 kN load cell was used in the experiments to increase 

the accuracy of the load measurements, see Figure 5.35. To load the centre of the debond using 

the actuator of the testing machine a hole of a diameter of 6 mm was drilled at the centre through 

the entire thickness of the panels, and the centre of the debond was bolted to a long steel rod 

connected to the actuator piston, see Figure 5.37 and 5.38. The panels were fixed to the test rig 

by twelve steel clamps and four 6 mm thick steel plates as shown in Figure 5.37. To avoid 

harmful side forces on the testing machine actuator, which may be generated by an uneven 

debond growth during the fatigue loading, the setup in Figure 5.36 was used. The setup includes 

a lubricated bronze cylinder in which the actuator piston of the testing machine can move freely. 

The cylinder is connected to the four columns of the testing machine by adjustable steel arms. In 

115 

Wood inserts 

Debond

the case of uneven debond growth, the generated side forces will be taken by the cylinder and 

transferred to the steel columns instead of the actuator. This will produce friction forces, which 

will make the load measurements inaccurate if the load cell is connected to the top of the 

actuator piston. To avoid this inaccuracy, a 25 kN load cell was connected to the bottom of the 

actuator piston as shown in Figure 5.35. 

Figure 5.35: Test setup. 

Figure 5.36: Actuator protection setup. 

116 

Force 

DIC cameras 

25 kN 

Load cell

Steel plates and clamps 

Figure 5.37: Centre of the debond connected to the actuator using a bolt. 

Figure 5.38: Schematic presentation of the connection between the debonded face sheet and 

actuator. 

To determine the maximum static carrying capacity of the panels, static tests were performed on 

two panels. Ramp displacement controlled loading with a piston displacement rate of 1 mm/min 

was applied in both tests. Figure 5.39 shows the axial piston displacement vs. load curves from 

the static tests. It is seen that the load increases in a linear manner until the crack propagation. As 

the crack propagates, the load drops due to the displacement controlled loading. 

117 

Centre of the debond

Load (kN) 

2 

1.5 

1 

0.5 

0 

Panel 1 

Panel 2 

Crack propagation point 

0 1 2 3 


Figure 5.39: Axial piston displacement vs. load diagram from the static tests. 

To obtain stable crack growth 80% of the static crack propagation load was applied in the fatigue 

tests as maximum cyclic load with a loading ratio of R=0.1 and a frequency of 2 Hz. Load 

controlled fatigue tests were performed on the debonded panels and a DIC system was used to 

monitor the debond shape and the crack growth. Four images every second were captured from 

the surface of the panel every six hundred cycles by the DIC cameras. The debond front position 

was located using the out-of-plane displacement contour from the surface of the panels. Locating 

the debond front from the out-of-plane displacement of the debond is not as accurate as the 

method used in the previous section for the measurement of the crack growth in STT specimens, 

which was based on monitoring the crack tip and the strain concentration at the crack tip. 

However, since it was not possible to gain access to the crack tip due to closed debonding, the 

best possible option was to use the out-of-plane displacement contours and iso-surfaces to 

monitor the debond growth, as shown in Figure 5.40. Pre-cracking was performed to penetrate 

the resin accumulation at the predefined crack tip by loading the specimens up to 50-60% of the 

static crack propagation load by cyclic loading. Pre-cracking was stopped after approximately 5- 

7.5 mm crack growth. Following the pre-cracking the specimens were loaded up to 100000 

cycles until the debond reached the edges of the panels. Fatigue crack growth vs. cycle diagrams 

for the debonded specimens are presented in Figure 5.41. It is seen that initially the crack growth 

rate is large, but decreases as the crack propagates due to development of membrane forces 

resulting in a decreasing energy release rate at the crack tip. 

To investigate the crack growth paths after the panel tests, all tested panels were cut. Figure 5.43 

illustrates the crack growth path in the sandwich panels at zero and ninety degrees, as shown in 

Figure 5.42, along the debond front. During the pre-cracking and initial loading cycles the crack 

118

kinks into the core because of very low fracture toughness of the H45 core compared to the 

interface. It is observed that the crack continues to propagate in the core below the resin-rich 

cells after kinking. 

121 mm 

149 mm 

16000 cycles 70000 cycles 

Figure 5.40: Out-of-plane deflection of the debond from DIC measurements. 

Diameter (mm) 

160 

150 

140 

130 

120 

110 

100 

0 20000 40000 60000 80000 100000 

Figure 5.41: Fatigue crack growth vs. cycles. 

119 

Cycle 

Test #1 

Test #2 

Test #3

Figure 5.42: Zero and ninety degrees positions along the debond front. 

Initial crack 

0 debond section 

Initial crack 

90 debond section 

Crack growth path 

Crack growth path 

Figure 5.43: Fatigue crack growth paths in the tested sandwich panels. 

5.3.2 Finite Element Modelling of the Debonded Panels 

A 3D finite element model of the debonded panels is developed in the commercial finite element 

code ANSYS. 8-node iso-parametric elements (PLANE45) are exploited for finite element 

modelling. Because of geometrical and loading symmetry only a quarter of the panel is 

120 

90 

0

generated. Symmetry boundary conditions are imposed in the symmetry planes. The edges of the 

panels are clamped by imposing a zero displacement boundary condition. The finite element 

model of the debonded panel is shown in Figure 5.44. The accelerated fatigue crack growth 

simulation scheme (cycle jump method) developed in the previous chapter is used to simulate 

fatigue crack propagation in the sandwich panels. The energy release rate and mode-mixity phase 

angle are chosen as state variables in the cycle jump scheme. Figure 5.45 illustrates the 

distribution of the energy release rate and the related mode-mixity phase angle during the first 

cycle along the debond front using the maximum fatigue load amplitude. As expected the energy 

release rate and mode-mixity phase angle are evenly distributed along the debond front because 

of the circular shape of the debond and the large distance to the panel boundaries. Figure 5.46 

shows the energy release rate and mode-mixity phase angle vs. debond diameter using the 

maximum fatigue load amplitude. 

Debond 

Figure 5.44: Quarter finite element model of the debonded panels with a circular debond. The 

smallest element size is 10m. 

121 

Clamp B. C. 

Symmetry B. C. 

310 mm 

x 

y

G(J/m 2 ) 

180 

150 

210 

120 

150 

100 

50 

0 

90 

60 

30 

0 

330 

240 

300 

240 

300 

270 

270 

Figure 5.45: The energy release rate and mode-mixity phase angle at the debond front during 

the first load cycle using the maximum fatigue load amplitude. 

Energy release rate (J/m 2 ) 

120 

100 

80 

60 

100 120 140 160 

Debond diameter (mm) 

Figure 5.46: Energy release rate and phase angle as a function of debond diameter from the 

analysis of the debonded panels subjected to the maximum fatigue load amplitude. 

The energy release rate decreases with increasing debond diameter in a linear manner. This can 

be attributed to the increasing membrane forces as the debond propagates. The membrane forces 

increase with the debond propagation and a smaller part of the strain energy in the sandwich 

panel is available to create new surfaces and increase the debond, which results in a decreasing 

energy release rate at the crack tip. The mode-mixity phase angle magnitude initially increases 

with increasing debond diameter and decreases after 130 mm debond diameter. However, the 

variation of mode-mixity phase angle is very small, less than one degree, showing the 

122 

() 

Phase angle () 

180 

150 

210 

-5.4 

-5.5 

-5.6 

120 

0 

-2 

-4 

-6 

-8 

-10 

90 

60 

Debond diameter (mm) 

30 

0 

330 

100 120 140 160 

-5.3

insensitivity of the mode-mixity to the debond diameter. The low mode-mixity phase angle 

illustrates the mode I dominant loading at the crack tip. 

The fatigue crack propagation simulation was carried out on the sandwich panels for 100000 

cycles. Because of similar material and interface properties the crack growth rates vs. the energy 

release rate relations determined in the previous section were used for the simulations. To choose 

the appropriate and most effective control parameter values in the cycle jump routine, 

simulations with different control parameters were carried out. Figure 5.47 shows the debond 

diameter vs. cycles for five different control parameters qG=q=0.4, 0.45, 0.5, 0.75 and 1. It is 

seen that the results of the simulations with the control parameters qG=q= 1 and 0.75 are very 

different due to large and inaccurate jumps, but decreasing the control parameter to 0.5 and 0.4 

leads to converging results and the deviation becomes smaller. Based on the results presented in 

Figure 5.47 the control parameter qG=q=0.4 was chosen for the simulation of debond growth in 

the tested sandwich panels. 

Diameter (mm) 

150 

140 

130 

120 

110 

q=qG=0.75 q=qG=1 

100 

q=qG=0.5 

q=qG=0.4 

q=qG=0.45 

0 20000 40000 60000 80000 100000 

Cycle 

Figure 5.47: The effect of the control parameter on the simulation of the debonded panels. 

Simulation results for the debond diameter vs. cycles using the control parameters qG=q=0.4 are 

shown together with the experimental results in Figure 5.48. The accuracy of the simulation is 

less compared to that of the STT specimen simulations presented in the previous sections in this 

chapter. Nevertheless, the deviation in the final debond diameter after 100000 cycles between the 

simulation and the experiments is less than 5 mm. The maximum deviation of approximately 7 

mm occurs around 70000 cycles. This inaccuracy can be attributed to the uncertainties in the 

debond diameter measurement using the DIC system during the experiments, as well as the 

observed scatter in the input crack growth rates data. 

123

110 

q=qG=0.4 Test #1 

100 

Test #2 Test #3 

0 20000 40000 60000 80000 100000 

Cycle 

Figure 5.48: Debond diameter vs. cycles for the simulation with the control parameters 

qG=q=0.4. 

The number of simulated cycles and the computational efficiency of the simulations with 

different control parameters are listed in Table 5.5. By application of the cycle jump method up 

to 94% of the simulation time has been saved with fair accuracy. Increasing the control 

parameters leads to increasing computational efficiency up to 96%, but the accuracy of the 

simulations is considerably lower. 

Table 5.5: Computational efficiency of solutions with different control parameters. 


qG=q 

Diameter (mm) 

160 

150 

140 

130 

120 

Simulation of debonded sandwich panels 

Number of simulated cycles Saved simulation cycles (%) 

0.4 7121 92.879 

0.45 6087 93.913 

0. 5 5896 94.104 

0.75 5051 94.949 

1 3778 96.222 


In this chapter the accelerated fatigue crack growth simulation scheme developed in Chapter 4 

was used to study interface fatigue crack growth in sandwich composites. Moreover, the 

accuracy and efficiency of the developed scheme were validated against fatigue experiments 

conducted on debond damaged sandwich beams and panels. 

124

Sandwich Tear Test (STT) specimens with face/core debonding exposed to cyclic loading have 

been tested to study the fatigue behaviour of the interface cracked sandwich X-joints. Fatigue 

tests were performed on the STT specimens with H45, H100 and H250 PVC cores and 

glass/polyester face sheets. The following fatigue crack growth paths were observed during the 

experiments: 

For the specimens with H45 core, unstable crack growth took place initially. After the 

unstable propagation the crack propagated in the core underneath the resin-rich cell layer 

moving towards the interface. However, the crack never kinked into the interface due to 

low fracture toughness of the H45 core compared to the interface. 

For the specimens with H100 core, the crack propagated initially in the core and then 

kinked into the interface and continued to propagate in the interface. 

For the specimens with H250 core, the crack initially propagated in the core and kinked 

into the interface. The interface crack eventually kinked into the face sheet, resulting in 

large-scale fibre bridging. 

By application of the finite element method mode-mixity phase angles at the crack tip of the STT 

specimens were evaluated at different crack lengths using the maximum fatigue load amplitude. 

To characterise the fatigue response of the interface of the STT specimens, fatigue tests were 

performed on Mixed Mode Bending (MMB) specimens at similar mode-mixity phase angles. 

The da/dN vs. G relations measured by the MMB fatigue tests were used to simulate fatigue 

crack growth in the STT specimens by the finite element method. To accelerate the simulation, 

the cycle jump method was exploited. Control parameters were introduced to control the 

accuracy of the cycle jumps. Simulations with different control parameters and a convergence 

analysis were carried out to choose the most accurate and efficient control parameters. 

Simulations of the specimens with H100 core showed fair accuracy compared to the fatigue 

experiments. However, the simulation of H45 specimens was found to be less accurate due to 

unstable crack growth observed in the fatigue experiments of the H45 STT specimens. This 

inaccuracy can be attributed to the interface fatigue characterisation. Since the interface fatigue 

characterisation was only performed for the stable linear part of the crack growth rate diagram 

(the Paris regime), the resulting da/dN vs. G relation is not valid for unstable crack growth and 

produces incorrect results. 

The numerical scheme developed in Chapter 4 to simulate 3D fatigue crack growth in bimaterial 

interfaces was used to simulate fatigue crack growth in sandwich panels with a circular debond. 

Fatigue experiments were conducted on debonded sandwich panels to validate the numerical 

scheme. Sandwich panels with a circular face/core debond at the panel centre were exposed to 

cyclic loading. Fatigue tests were performed on the debonded panels with H45 PVC core and 

glass/polyester face sheets. It was observed that the debond initially kinked into the core and 

continued to propagate underneath the resin-rich cell layer of the core. Using the finite element 

method, the energy release rate and mode-mixity phase angle at the crack tip of the debonded 

125

panels were determined for different debond diameters for the maximum applied fatigue load. It 

was shown that the mode-mixity phase angle is not sensitive to the debond diameter and is 

around -5. Since no strong dependency between the mode-mixity and crack growth rate is 

expected at low manitudes of mode-mixity phase angles and the loading is predominantly mode 

I, the crack growth rate relations for the mode-mixity phase angle -20, measured using the 

MMB specimen, were used for the simulation of the debonded panels. To accelerate the 

simulation the cycle jump method outlined in Chapter 4 was exploited. A convergence analysis 

was carried out for different control parameter values to choose appropriate control parameters. 

Simulations of the debonded sandwich panels showed fair accuracy compared to the fatigue 

experiments with a maximum deviation of 7 mm in debond diameter estimations. The observed 

deviation can be attributed to the crude crack length measurement technique using the DIC 

technique, which was based on out-of-plane deflections of the debond and scatter of the input 

crack growth rate data. 

The presented 2D and 3D fatigue crack growth schemes and the cycle jump method proved to be 

reliable tools for simulation of stable fatigue crack growth, but in highly non-linear cases the 

presented method should be used carefully. To mitigate inaccuracies and uncertainties 

concerning simulation of highly non-linear problems, a convergence sensitivity analysis must be 

carried out due to strong dependency of the accuracy of the cycle jump method on the control 

parameters. However, for complete validation of the developed numerical scheme, simulations 

should be compared with fatigue tests on more complicated loading scenarios and debond 

geometries. 

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127

Chapter 6 

Conclusion and Future Work 

6.1 Face/Core Debond Propagation in Sandwich 

Structures under Static Loading 

In the first chapters of this thesis a methodology for the estimation of face/core debond 

propagation load in sandwich structures under static loading was developed and validated against 

experiments. The developed finite element scheme involves three overall steps: 

1) Generating a global model of cracked structures, and estimating the global response of 

the structures with a coarse mesh around the crack tip. 

2) Generating a sub model of the crack tip (front) with a very fine mesh, interpolating the 

boundary conditions in the cutting boundaries of the submodel and solving the detailed 

finite element model of the debond front for the interpolated boundary conditions. 

3) Extracting the energy release rate and mode-mixity at the crack tip from the submodel 

using the Crack Surface Displacement Extrapolation (CSDE) method (Berggreen et al, 

2005). 

By application of the developed scheme, debond initiation loads were predicted in debonded 

sandwich columns and panels. 

Initially, the compressive failure of foam cored sandwich columns containing a face/core debond 

was investigated using the developed scheme. Compression tests were performed on sandwich 

columns to validate the finite element model. Sandwich columns with glass/epoxy face sheets 

and H45, H100 and H200 PVC foam cores with different debond lengths were tested under static 

compressive loading. It was observed that most of the debonded columns failed by unstable 

debond propagation at the face/core interface towards the column ends. However, face sheet 

compression failure was observed in all columns with H200 core and smallest debond length, 

128

due to the proximity of the debond propagation load and the compression failure load of the face 

sheets. Bifurcation type buckling of the debonded face sheet was not observed and the debond 

opening occurred gradually, which can be attributed to large initial imperfections. Slight kinking 

of the debond into the core was observed in the columns with a low-density H45 and H100 core. 

Modified Tilted Sandwich Debond (TSD) specimens were tested under different tilt angles to 

measure the fracture toughness of the interface at the calculated mode-mixity phase angles for 

the column specimens associated with the debond propagation. 

The measured interface fracture toughness was used to determine crack propagation loads from 

the finite element model of the columns. Instability and crack propagation loads of the columns 

were predicted on the basis of a geometrically non-linear finite element analysis and linear 

elastic fracture mechanics. Fair agreement was achieved for the comparison of the measured outof-plane 

deflection, instability, and debond propagation loads from the experiments and the finite 

element analysis. For most of the investigated column specimens, it was shown that the 

instability and debond propagation loads are very reasonable estimates of the ultimate failure 

load, unless the other failure mechanisms occur prior to buckling instability. 

To examine the accuracy of the developed scheme in case of sandwich panels, debond 

propagation in sandwich panels with a circular debond at the centre was modelled. To validate 

the finite element model of the debonded panels, intact and debonded sandwich panels with 

glass/polyester face sheets and H130, H250 and PMI foam cores were tested under static inplane 

compressive loading. The following damage mechanisms were observed during the 

experiments: 

1) All debonded panels failed by the propagation of the debond to the edges of the panels. 

2) All intact panels with H130 and H250 core failed by the compressive failure of a face 

sheet very close to the wooden inserts, which can be attributed to additional peeling 

stresses arising due to the junction between the wooden insert and the core and to a slight 

unintentional mismatch between the core and the thicknesses of the insert. 

3) Intact panels with PMI core failed by a combination of shear crimping and global 

buckling. 

This time instead of using the TSD specimen, characterisation tests were performed on Mixed 

Mode Bending (MMB) specimens to measure the fracture toughness of the face/core interface 

for a span of mode-mixity phase angles. As expected it was shown that the fracture toughness is 

increasing with increasing magnitude of the mode-mixity phase angle. The obtained fracture 

toughness data was used to determine the crack propagation load in the debonded sandwich 

panels. Instability and crack propagation loads of the panels were estimated on the basis of 

geometrically non-linear finite element analysis and linear elastic fracture mechanics. It was 

shown that the FEA predictions in few cases are much higher than the experimental ones (a 

maximum deviation of 46%), which can be attributed to the large scatter in the measured fracture 

129

toughness using MMB fracture toughness results and differing crack tip details between the 

panels and the MMB specimens due to mechanical releasing of the debonded area in the panels. 

However, in most cases an acceptable deviation (a minimum deviation of 9%) was obtained. It 

was observed that in the panels and the MMB specimens with H130 and PMI cores the debond 

initially kinks into the core and propagates beneath the face/core interface, but in the panels and 

the MMB specimens with H250 core the debond propagates directly in the interface. Finally, 

based on experimental and numerical results, the strength reduction factor Rl was plotted against 

the debond diameter. The plot is tentative because of the uncertainties regarding the intact 

strengths as well as the differences between test and analysis results. 

6.2 Fatigue Crack Growth in Bimaterial Interfaces 

After developing a methodology for analysis of interface crack propagation in sandwich 

structures exposed to quasi-static loading, it was applied to simulation of fatigue crack growth in 

bimaterial interfaces. However, in order to achieve acceptable computational efficiency, the 

problem of very high computational time due to simulation of many cycles and the need for a 

heavy element mesh density at the crack tip (front) must first be solved. 

To overcome the above-mentioned problem a cycle jump method for accelerating the simulation 

of fatigue crack growth in a bimaterial interface was developed. The proposed method is based 

on finite element analysis for a set of cycles to establish a trend line, extrapolating the trend line 

spanning many cycles, and use the extrapolated state as an initial state for additional finite 

element simulations. Two finite element routines were developed in order to simulate fatigue 

crack growth in bimaterial interfaces. The first routine is suitable for 2D crack growth and the 

second is applicable to any 3D fatigue crack growth simulation with an arbitrary crack front 

shape. To examine the computational efficiency and accuracy of the developed numerical 

schemes, they were applied to simulation of face/core interface fatigue crack growth in sandwich 

beams (2D) and sandwich panels (3D). The results of the simulations were compared with 

reference analyses simulating all individual cycles. 

Using the cycle jump method, fatigue crack growth in the interface of a sandwich beam was 

simulated for 500 cycles and verified against a reference analysis. The computational efficiency 

and accuracy of the cycle jump method were discussed on the basis of three parameters: crack 

length, difference between maximum and minimum energy release rate in a cycle (G), and 

mode-mixity phase angle. The effect of the control parameters governing the computational 

efficiency and accuracy of the developed cycle jump method was studied. The results suggest 

that the computational efficiency of the simulations increases considerably by increasing the 

control parameters. However, the accuracy of the simulations decreases. It was shown that with 

an appropriate choice of control parameters more than 65% savings in computational time can be 

achieved with reasonably good accuracy. 

130

Fatigue debond propagation in sandwich panels with an elliptical face/core debond at the centre 

of the panels was simulated by means of the second finite element routine (3D). The distribution 

of the mode III energy release rate, GIII, along the crack front was studied for different elliptical 

debonds. However, only mode I and II components of the strain energy release rate were used in 

the crack growth routine due to the present lack of experimental methods for characterisation of 

the effect of GIII on fatigue crack growth. Results show that the mode III crack tip loading is 

significant close to the longer radius of the ellipse for an elliptical debond with large a/b radius 

ratios. 

A reference simulation, simulating all individual cycles, and simulations exploiting the cycle 

jump method with different control parameters were performed to examine the accuracy and 

computational efficiency of the developed 3D cycle jump method. Use of the cycle jump method 

shows good accuracy and leads to a reduction in computational time of more than 70%. 

6.3 Face/Core Interface Fatigue Crack Growth in 

Sandwich Structures 

After the initial analysis of the developed accelerated fatigue crack growth simulation scheme, it 

was validated in the last chapter of this thesis against experimental testing and used to study 

interface fatigue crack growth in sandwich composites. 

The first finite element routine (2D) was utilised to study face/core fatigue crack growth in 

cracked sandwich X-joints. Sandwich Tear Test (STT) specimens with a face/core debond 

representing a cracked sandwich X-joint, were tested under cyclic loading. Fatigue tests were 

conducted on STT specimens with H45, H100 and H250 PVC cores and glass/polyester face 

sheets. Digital Image Correlation (DIC) technique was used to locate the crack tip and monitor 

the crack growth. Different fatigue crack growth paths were observed during the fatigue 

experiments: 

For the specimens with H45 core the crack grew unstably in the beginning up to a length 

of 150 mm in a few cycles. The crack initially propagated unstably in the core underneath 

the resin-rich cells. After the unstable crack growth, stable crack growth was observed in 

all specimens. During the stable crack growth the growing crack approached the 

interface, but never kinked into the interface. This can be attributed to the very low 

fracture toughness of H45 core compared to the interface. 

For the specimens with H100 core, the crack initially propagated in the core in a stable 

manner and then kinked into the interface. The kinked crack continued to propagate in 

the interface until the end of the experiments where the crack growth eventually stopped 

due to decreasing energy release rate at the crack tip. 

131

For the specimens with H250 core the crack first propagated in the core due to the initial 

crack location after pre-cracking. The crack consequently kinked into the interface due to 

the presence of negative mode-mixity phase angle and large fracture toughness of the 

H250 core. The interface crack eventually kinked into the face sheet, which resulted in 

large-scale fibre bridging. 

A 2D finite element model of the STT specimen was developed to determine the mode-mixity 

phase angle and the energy release rate at the crack tip of the STT specimens. To characterise the 

interface fatigue behaviour of the STT specimens, fatigue tests were conducted on Mixed Mode 

Bending (MMB) specimens at a mode-mixity phase angle similar to that of the STT specimens. 

The resulting da/dN vs. G relations generated by the MMB fatigue tests were utilised in the 

developed crack growth finite element routine to simulate fatigue crack growth in the STT 

specimens. To choose appropriate control parameters, simulations with different control 

parameters were performed. A convergence analysis was conducted and an appropriate control 

parameter was chosen. Simulations of the H45 STT specimens showed a very high dependency 

on the control parameters. During the initial cycles, simulations using different control 

parameters showed small differences, but as the unstable crack growth zone was approached the 

deviation became larger. This dependency is attributed to the extrapolations in the transition 

from stable to unstable crack growth zone and the extreme non-linearity of this transition, which 

implies the importance of appropriate choice of control parameters in the case of highly nonlinear 

problems. With smaller control parameters the crack growth diagrams converged to one 

diagram since the cycle jump scheme was able to extrapolate accurately the stable-unstable crack 

transition zone by performing small or no jumps. H100 specimens, due to less non-linearity and 

stable crack growth, showed much less dependency to the control parameters. The developed 

finite element models were validated against the conducted fatigue tests. Simulations of the 

specimens with H100 core showed fair accuracy compared to the fatigue experiments. However, 

the simulation of the H45 specimens was much less accurate due to unstable crack growth 

observed in the fatigue experiments of the H45 STT specimens. Since the interface fatigue 

characterisation using the MMB specimens was only conducted for the stable linear part of the 

crack growth rates diagram (Paris’ regime), the resulting da/dN vs. G relation was not valid for 

unstable crack growth observed during the experiment of the H45 STT specimens and produced 

incorrect results. 

To validate the 3D fatigue crack growth numerical scheme, it was used to simulate fatigue crack 

growth in sandwich panels with a circular debond. Fatigue tests were carried out on a limited 

number of debonded sandwich panel specimens with a circular face/core debond at the centre 

with H45 PVC core and glass/polyester face sheets. It was observed that the crack initially kinks 

into the core and continues to propagate below the resin-rich core cells at the core. Because of a 

similar mode-mixity at the crack tip and similar face/core materials, da/dN vs. G relations from 

the MMB tests obtained previously were employed as input to the crack growth routine. A 

convergence analysis was conducted for different control parameter values to choose appropriate 

132

control parameters. Simulations of the debonded sandwich panels showed fair accuracy 

compared to the fatigue experiments with a maximum deviation of 7 mm in determination of the 

debond diameter. This deviation can be attributed to the crude crack length measurement 

technique using the DIC technique, which was based on out-of-plane deflections of the debond 

and scatter of the input crack growth rates data. 

The presented 2D and 3D accelerated fatigue crack growth schemes proved to be reliable tools 

for the simulation of stable fatigue crack growth. However, for highly non-linear problems the 

presented method should be used more carefully. To reduce the uncertainties concerning the 

simulation of highly non-linear problems, a convergence sensitivity analysis must be carried out 

due to a strong dependency of the accuracy of the cycle jump method on the control parameters. 

6.4 Future Works 

This thesis was an effort to develop different methodologies for studying with the residual 

strength and fatigue lifetime of debonded sandwich composites. The study was carried out at two 

main levels: 

1) A material level by characterisation of face/core interface behaviour of foam cored 

sandwich composites under static or cyclic loading. 

2) A structural level by finite element modelling and testing of debonded sandwich 

columns, panels, and X-joints. 

At the material level different types of PVC foam/GFRP interfaces were characterised under 

static or cyclic loading at different mode-mixities. The fracture toughness of different 

foam/GFRP interfaces was determined by use of TSD and MMB specimens for a full range of 

negative mode-mixity phase angles. However, the fatigue characterisation of the face/core 

interface was only conducted for one negative mode-mixity phase angle. A full fatigue 

characterisation of a face/core interface for a large range of mode-mixities is necessary for a 

general use of the proposed fatigue crack growth simulation scheme. Furthermore, in this thesis 

only linear elastic fracture mechanics was employed for determination of fracture parameters, 

which is not valid where the fracture process zone is large compared to the dimensions of the 

specimen, e.g. when fibre bridging occurs, which was often observed in the testing of interfaces 

with heavier foams. Cohesive zone modelling utilising cohesive laws along with a kinking 

criterion can be incorporated in the developed fatigue crack growth scheme to simulate kinking 

and fatigue crack growth in the presence of fibre bridging. 

In Chapter 4 a very short analysis of the distribution of the mode III energy release along the 

debond front in debonded sandwich panels was presented. Results showed that in some cases the 

mode III effects are significant and need to be taken into account. However, there have not been 

many studies addressing the mode III loading problem at the crack tip in a bimaterial interface. 

133

Development of testing methods for measuring the effect of mode III loading at the crack tip on 

fracture toughness and fatigue crack growth rates, is necessary for the development of accurate 

damage assessment tools for analysis of the residual strength and lifetime of debonded sandwich 

composites. 

In the last chapters of the thesis, fatigue experiments were conducted on sandwich panels with a 

circular debond to validate the developed 3D numerical scheme. However, to fully examine the 

effectiveness of the developed numerical scheme and its limitations, more experiments on more 

complex geometries like curved structures and loading conditions, such as e.g. lateral pressure 

and in-plane compression, should be conducted. Additionally, since direct access to the crack in 

debonded panels is not possible, methods of measurement such as FBG sensors or ultra-sonics 

should be used instead of DIC technique to obtain better measurement of the debond growth. 

Different finite element based models have been put forward in this thesis based on fracture 

mechanics tools. However, all these models are limited to very simple, small geometries due to 

the need for high-density mesh at the crack tip (front) and practical/geometrical limitations 

regarding the generation of 3D finite element models in complex large geometries. In summary, 

in the case of damage assessment of large structures the global response of the structure should 

be accounted for in these models making the resulting finite element model extremely 

computationally heavy. An important step in further development of the devised damage 

assessment schemes is to develop new methodologies for the analysis of delamination/debonding 

in composite structures, taking into account the global response of the structures. The 

submodelling concept, as used in Chapters 2 and 3 of this thesis, can be used in a new way which 

allows for coupling between the global response of the structure and the local effects of the 

damage. As schematically described in Figure 6.1, an iterative procedure may be devised which 

couples the global complete model of structures and a detailed model of the damaged region as 

developed in this thesis. The global stiffness properties and behaviour of a structure, e.g. a wind 

turbine blade, can be determined using finite element modelling of the blade by shell elements as 

the first step. By reducing the stiffness of the elements in the damaged zone the effect of initial 

damage on the global behaviour of the structure can be estimated. The displacement boundary 

conditions of the 3D submodel, detailing the damaged zone of the structure, are subsequently 

updated on the basis of the results from the global shell finite element model by shell to solid 

submodelling technique, which is available in most of the commercial finite element software 

like ANSYS. The detailed analysis of the damaged zone can be conducted by means of state-ofthe-art 

fracture mechanics tools developed in this thesis. In the case of cyclic loading by 

determining the debond growth at the end of each cycle (cycle jump), the geometry of the 

debond can be updated in the global shell model accordingly. Finally, the global shell FE model 

of the blade can be reconstructed once again and the procedure is repeated for the next iteration, 

e.g. loading cycle. Thus, it is possible to overcome the scale limitations and couple the local 

scale effects of the debond damage with the global scale response of the blade. 

134

As an alternative approach to modelling of the global structure using shell elements, which may 

be computationally expensive, beam cross sectional analysis, see e.g. Blasques et al. (2011), may 

be applied to analysis of the global response of the structure and extraction of interpolated 

boundary conditions in the cutting boundaries of the detailed submodel. Moreover, the cross 

section stiffness properties of the beam are then recomputed based on a 2D finite element 

representation of the cross section where the shape of the debonded area has been updated. 

Figure 6.1: Schematic presentation of the suggested multi-scale approach to the analysis of 

debond damaged sandwich structures. 

135


136

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144

Appendix A 

Additional Results from the Column Compression Tests 

In this appendix additional results from the compression tests performed on debonded columns 

studied in Chapter 2 are presented. 

A.1 Debonded Columns with H45 Core 

In this section the axial displacement vs. load and load vs. out-of-plane displacement curves of 

the columns with H45 core are presented. The out-of-plane deflection refers to the centre of the 

debond. 

Load (kN) 

16 

12 

8 

4 

0 

12 

8 

(a) (b) (c) 

Column 1 

Column 2 

Column 3 

0 0.5 1 1.5 2 

Axial Displacement (mm) 

Load (kN) 

8 

4 

0 

0 0.5 1 1.5 2 


Figure A.1: Axial displacement vs. load for the H45 columns with a debond length of (a) 25.4 

mm, (b) 38.1 mm and (c) 50.8 mm. 

145 

Column 1 

Column 2 

Column 3 

Load (kN) 

6 

4 

2 

0 

Column 1 

Column 2 

0 0.2 0.4 0.6 

Axial Displacement (mm)


1 

0.8 

0.6 

0.4 

0.2 

0 

3 

3 

(a) (b) (c) 

Column 1 

Column 2 

Column 3 

0 4 8 12 16 

Load (kN) 


Figure A.2: Load vs. out-of-plane displacement for the H45 columns with a debond length of 

(a) 25.4 mm, (b) 38.1 mm and (c) 50.8 mm. 


2 

1 

0 

Column 1 

Column 2 

Column 3 

0 3 6 9 12 

Load (kN) 



debond. 

Load (kN) 

16 

12 

8 

4 

0 

12 

10 

(a) (b) (c) 

Column 1 

Column 2 

Column 3 

0 0.3 0.6 0.9 1.2 


Load (kN) 

9 

6 

3 

0 

Figure A.3: Axial displacement vs. load for the H100 columns with a debond length of (a) 

25.4 mm, (b) 38.1 mm and (c) 50.8 mm. 

146 

Column 1 

Column 2 

Column 3 

0 0.3 0.6 0.9 1.2 



Load (kN) 

2.4 

1.8 

1.2 

0.6 

8 

6 

4 

2 

0 

0 

Column 1 

Column 2 

0 2 4 

Load (kN) 

6 

Column 1 

Column 2 

0 0.3 0.6 0.9 1.2 



3 

2 

1 

0 

3 

3 

(a) (b) (c) 

Column1 

Column2 

0 4 8 

Load (kN) 

12 16 



(a) 25.4 mm, (b) 38.1 mm and (c) 50.8 mm. 


2 

1 

0 

Column1 

Column2 

Column3 

0 3 6 9 12 

Load (kN) 



debond. 

Load (kN) 

10 

8 

6 

4 

2 

0 

16 

10 

(a) (b) (c) 

Column 1 

Column 2 

Column 3 

0 0.2 0.4 0.6 0.8 1 


Load (kN) 

12 

8 

4 

0 

Figure A.5: Axial displacement vs. load for the H200 columns with a debond length of (a) 25.4 


147 

Column 1 

Column 2 

Column 3 

0 0.4 0.8 1.2 1.6 



Load (kN) 

2 

1 

0 

8 

6 

4 

2 

0 

Column1 

Column2 

Column3 

0 3 6 9 

Load (kN) 

Column 1 

Column 2 

Column 3 

0 0.2 0.4 0.6 0.8 1 



3 

2 

1 

0 

2 

(a) (b) 

Column1 

Column2 

Column3 

0 5 10 

Load (kN) 

15 


(a) 38.1 mm and (b) 50.8 mm. 

A.4 Initial Imperfections in Debonded Columns 

In this section DIC images of initial out-of-plane imperfections in columns with H45, H100 and 

H200 core are shown. 

Figure A.7: Initial imperfections in columns with H45 core and a debond length of (a) 25.4 


148 


1.5 

1 

0.5 

(a) (b) 

0 

Column1 

Column2 

Column3 

0 3 6 

Load (KN) 

9 

(c)

(a) (b) (c) 



(a) (b) (c) 



149

A.5 Out-of-plane deflection of Debonded Columns 

In this section DIC images of out-of-plane deflection of columns with H45, H100 and H200 core 

are shown before and right after debond propagation or face sheet compression failure. 

(a) 

Figure A.10: Out-of-plane deflection from DIC measurements of a column with H45 core and 

a debond length of 25.4 mm, (a) prior to propagation and (b) after propagation. 

(a) 



150 

(b) 

(b)

(a) 



(a) 

Figure A.13: Out-of-plane deflection from DIC measurements of a column with H100 core 

and a debond length of 25.4 mm, (a) prior to propagation and (b) after propagation. 

151 

(b) 

(b)

(a) 



(a) 



152 

(b) 

(b)

(a) 


and a debond length of 25.4 mm, (a) prior to face sheet compression failure and (b) after face 

sheet compression failure. 



153 

(b) 

(a) (b)

(a) (b) 



154

Appendix B 

Additional Results from the Panel Compression Tests 

In this appendix additional results from the compression tests performed on debonded sandwich 

panels studied in Chapter 3 are presented. 

B.1 Load vs. In-plane Displacement Curves 

In this section load vs. in-plane displacement curves for the tested panels are presented. 

Load (kN) 

150 

100 

50 

0 

200 

200 

(a) (b) (c) 

Panel 1 

Panel 2 

Panel 3 

0 1 2 3 4 5 


Load (kN) 

150 

100 

50 

0 

Panel 1 

Panel 2 

Panel 3 

0 1 2 3 4 5 


Figure B.1: Displacement vs. load for panels with PMI core and a debond diameter of (a) 100 

mm, (b) 200 mm and (c) 300 mm. 

155 

Load (kN) 

150 

100 

50 

0 

Panel 1 

Panel 2 

Panel 3 

0 1 2 3 4 5 

Displacement (mm)

Load (kN) 

250 

200 

150 

100 

50 

250 

300 

(a) (b) (c) 

Panel 1 

Panel 2 

Load (kN) 

200 

150 

100 

50 

Panel 1 

Panel 2 

0 

0 

0 

0 2 4 6 0 2 4 6 0 2 4 6 8 




Figure B.2: Displacement vs. load for panels with H130 core and a debond diameter of (a) 100 


250 

(a) 

250 

(b) 

250 

(c) 

Load (kN) 

200 

150 

100 

50 

Panel 1 

Panel 2 

Load (kN) 

200 

150 

100 

50 

Panel 1 

Panel 2 

0 

0 

0 

0 2 4 6 8 0 2 4 6 0 2 4 6 




Figure B.3: Displacement vs. load for panels with H250 core and a debond diameter of (a) 100 


350 

(a) 

400 

(b) 

400 

(c) 

Load (kN) 

300 

250 

200 

150 

100 

50 

Panel 1 

Panel 2 

Panel 3 

Load (kN) 

300 

200 

100 

Panel 1 

Panel 2 

Panel 3 

0 

0 

0 

0 2 4 6 0 2 4 6 8 10 0 2 4 6 8 10 




Figure B.4: Displacement vs. load for the intact panels with (a) PMI, (b) H130 and (c) H250 

core. 

156 

Load (kN) 

Load (kN) 

Load (kN) 

250 

200 

150 

100 

50 

200 

150 

100 

50 

300 

200 

100 

Panel 1 

Panel 2 

Panel 1 

Panel 2 

Panel 1 

Panel 2 

Panel 3

B.2 Out-of-plane Deflection vs. Load Curves 

In this section out-of-plane displacement vs. load curves of the tested panels are presented. The 

out-of-plane deflection refers to the centre of the debond. 



8 

6 

4 

2 

0 

6 

6 

(a) (b) (c) 

Panel 1 

Panel 2 

Panel 3 

0 30 60 90 120 

Load (kN) 


4 

2 

0 

Panel 1 

Panel 2 

Panel 3 

0 20 40 

Load (kN) 

60 80 

Figure B.5: Load vs. out-of-plane displacement for the panels with PMI core and a debond 

diameter of (a) 100 mm, (b) 200 mm and (c) 300 mm. 

8 

6 

4 

2 

0 

8 

8 

(a) (b) (c) 

Panel 1 

Panel 2 

0 50 100 150 200 

Load (kN) 


6 

4 

2 

0 

Panel 1 

Panel 2 

0 30 60 90 120 

Load (kN) 

Figure B.6: Load vs. out-of-plane displacement for the panels with H130 core and a debond 


157 



4 

2 

0 

6 

4 

2 

0 

Panel 1 

Panel 2 

Panel 3 

0 20 40 60 

Load (kN) 

Panel 1 

Panel 2 

0 25 50 75 100 

Load (kN)


4 

3 

2 

1 

0 

8 

9 

(a) (b) (c) 

Panel 1 

Panel 2 

0 50 100 150 200 

Load (kN) 


6 

4 

2 

0 

Panel 1 

Panel 2 

0 50 100 150 

Load (kN) 

Figure B.7: Load vs. out-of-plane displacement for the panels with H250 core and a debond 


B.3 Out-of-plane Deflection of the Debonded Panels 

In this section DIC images of out-of-plane deflection of panels with PMI, H130 and H250 core 

are shown before and right after debond propagation. 

(a) 

Figure B.8: Out-of-plane deflection from DIC measurements of a panel with PMI core and a 

debond diameter of 100 mm, (a) prior to propagation and (b) after propagation. 

158 

(b) 


6 

3 

0 

Panel 1 

0 50 100 150 

Load (kN)

(a) (b) 



(a) 



159 

(b)

(a) (b) 

Figure B.11: Out-of-plane deflection from DIC measurements of a panel with H130 core and 

a debond diameter of 100 mm, (a) prior to propagation and (b) after propagation. 

(a) (b) 



160

(a) (b) 



(a) (b) 



161

(a) (b) 



(a) (b) 



162

Appendix C 

Additional Results from the Tests on the STT Specimens 

In this appendix additional results from the static and fatigue tests performed on STT specimens 

studied in Chapter 5 are presented. 

C.1 Axial Displacement vs. Force Curves from the Static 

Tests 

In this section axial displacement vs. force curves for the STT specimens with H45, H100 and 

H250 are presented. 

Force (kN) 

0.6 

0.4 

0.2 

0 

(a) 1.2 (b) 1.2 (c) 

Specimen 1 

Specimen 2 

0 0.5 1 1.5 


Force (kN) 

0.8 

0.4 

0 

0 1 2 3 


Figure C.1: Axial displacement vs. force for STT specimens with (a) H45, (b) H100 and (c) 

H250 core. 

163 

Specimen 1 

Specimen 2 

Force (kN) 

0.8 

0.4 

0 

Specimen 1 

Specimen 2 

0 1 2 3 

Axial displacement (mm)

DTU Mechanical Engineering 

Section of Coastal, Maritime and Structural Engineering 


Nils Koppels Allé, Bld. 403 

DK- 2800 Kgs. Lyngby 

Denmark 

Phone (+45) 45 25 13 60 

Fax (+45) 45 88 43 25 

www.mek.dtu.dk 

ISBN: 978-87-90416-42-3 

DCAMM 

Danish Center for Applied Mathematics and Mechanics 

Nils Koppels Allé, Bld. 404 

DK-2800 Kgs. Lyngby 

Denmark 

Phone (+45) 4525 4250 

Fax (+45) 4593 1475 

www.dcamm.dk 

ISSN: 0903-1685

Residual Strength and Fatigue Lifetime of ... - Solid Mechanics

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