Computational Methods for Debonding in Composites

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Chapter 8 A Numerical Material Model for Predicting the High Velocity Impact Behaviour of Polymer Composites Lucio Raimondo, Lorenzo Iannucci, Paul Robinson, and Silvestre T. Pinho Abstract This paper describes key features of an advanced, physically-based, numerical material model for predicting the static and dynamic, failure and damage, response of polymer matrix composites with fibrous UD plies. The model has been implemented into the explicit Finite Element code LS-DYNA3D for solid brick elements with one integration point. A comprehensive test programme was conducted for characterising the high velocity impact response of a class of NCF/Epoxy composites. The impact tests were conducted for varying impact conditions and parameters such as: impact angle, coupon thickness, laminate lay-up and projectile material. Data from these tests was reduced in the form of ballistic curves, mass of target debris generated upon complete penetration, and (C-Scan) impact damage areas. This data was used for validation of the proposed model. General conclusions from this work indicate that physically-based modelling approaches can improve considerably the predictive capabilities of current FE codes for structural analysis applications. 8.1 Introduction There are four main different strategies that have been employed for predicting composite impact damage within the low and medium velocity regime [6]: 1. A failure criteria approach (which can be based on the equivalent stress or strain) 2. A fracture mechanics approach (based on energy release rates) 3. A plasticity or yield surface approach 4. A damage mechanics approach L. Raimondo, L. Iannucci, P. Robinson, and S.T. Pinho Imperial College London, Department of Aeronautics, South Kensington Campus, London SW7 2AZ, United Kingdom, e-mail: {lucio.raimondo, lo.iannucci, p.robinson, silvestre.pinho}@imperial.ac.uk 161
162 L. Raimondo et al. Published works can be found in the open literature on composites for high velocity impact modelling. The approaches used for high velocity impact modelling typically fall in one or more of the categories listed above. The good results obtained from application of the model in [16] indicate that “hybrid approaches” can be particularly effective. An attractive failure and damage modelling strategy was proposed in [9, 10] based on the simultaneous application of the strategies (1), (2) and (4) that were listed above: phenomenological failure criteria were applied to predict damage initiation, a DM (Damage Mechanics) approach based on fracture mechanics was applied for predicting damage evolution. Such hybrid techniques proved to be accurate in predicting the low-velocity impact response of polymer composites [3]. In this work, a damage model is proposed for high velocity impact modelling based on the combined application of different modelling strategies, i.e. the application of plasticity, failure, damage mechanics and fracture mechanics. This work is an enhanced version of a model previously implemented in LS-DYNA3D [9,10]. 8.2 A Phenomenological Model for Predicting Material Non-linear Effects in UD Plies Under Compressive/Shear Loading Conditions 8.2.1 Premise In UD polymer plies, compressive failure is ultimately driven by shear mechanisms. This is evident from visual examination of failed composite specimens: the fracture plane orientation for the case of transverse compressive failure is inclined to the loading directions and principal material symmetry axes. The non-linear behaviour of composites under loading conditions that promote matrix deformation indicates that failure is, for these loading cases, a progressive and continuous process. The term “progressive failure”, or “damage”, can be used in a macro-mechanical framework to define the physical processes that result in degradation of composites mechanical properties, such as plasticity, matrix micro-cracking or a combination of both. In the present work, “progressive failure” is assumed to be driven by shear mechanisms. 8.2.2 Outline of the Modelling Approach In [11], Puck and Schurmann discuss an adaptation of the Mohr-Coulomb failure criterion for predicting composite failure in the transverse matrix compressive/shear: � fmc = τT ST − µT σn �2 � + τL SL − µLσn � 2 (8.1)
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Mechanical Response of Composites
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Pedro P. Camanho • C.G. Dávila S
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Preface The methodology for designi
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Acknowledgements The Editors of thi
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x Contents 3 Practical Challenges i
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xii Contents 8.2.4 Modelling Effect
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xiv Contents 13.1.2 EffectiveProper
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xvi List of Contributors Clara Schu
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Chapter 1 Computational Methods for
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1 Computational Methods for Debondi
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28 R. Rolfes et al. functions by me
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30 R. Rolfes et al. Microscale fibe
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32 R. Rolfes et al. symmetric, whic
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34 R. Rolfes et al. Fig. 2.5 Discre
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36 R. Rolfes et al. Unit cell (a) S
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38 R. Rolfes et al. stress state. T
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40 R. Rolfes et al. biaxial compres
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42 R. Rolfes et al. Damage Evolutio
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44 R. Rolfes et al. Fig. 2.14 Radia
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46 R. Rolfes et al. Table 2.2 Elast
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48 R. Rolfes et al. A dev is the de
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50 R. Rolfes et al. uniaxial compre
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52 R. Rolfes et al. Stress in MPa -
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54 R. Rolfes et al. 2.4.2 Results o
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56 R. Rolfes et al. 12. Hughes TJR
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58 B.N. Cox et al. inform models; a
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60 B.N. Cox et al. 3.2 The Structur
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62 B.N. Cox et al. be successfully
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64 B.N. Cox et al. high fluxes of c
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66 B.N. Cox et al. provides poor in
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68 B.N. Cox et al. For example, a c
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70 B.N. Cox et al. failures in comp
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72 B.N. Cox et al. mixed-mode crack
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74 B.N. Cox et al. 24. Elices M, Gu
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Chapter 4 Analytical and Numerical
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4 Analytical and Numerical Investig
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10 Elastoplastic Modeling of Multi-
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224 J.A. Oliveira et al. 11.1 Intro
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226 J.A. Oliveira et al. written as
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228 J.A. Oliveira et al. asymptotic
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230 J.A. Oliveira et al. χ jk i (0
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232 J.A. Oliveira et al. (a) (b) Fi
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234 J.A. Oliveira et al. Fig. 11.7
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236 J.A. Oliveira et al. Fig. 11.10
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238 J.A. Oliveira et al. (a) (b) (c
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240 J.A. Oliveira et al. (a) (b) (c
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242 J.A. Oliveira et al. 20. Suquet
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246 E. Lund and L.S. Johansen 12.2.
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256 E. Lund and L.S. Johansen λ1 =
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258 E. Lund and L.S. Johansen 12.6
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260 E. Lund and L.S. Johansen 34. T
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262 M. Kästner et al. Micro-level
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264 M. Kästner et al. elastic stra
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266 M. Kästner et al. 13.1.1.2 Per
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268 M. Kästner et al. 13.1.2 Effec
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272 M. Kästner et al. In order to
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274 M. Kästner et al. x2 x 3 x1 Br
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276 M. Kästner et al. Fig. 13.12 I
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278 M. Kästner et al. Table 13.4 C
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14 Development of DST for the Model
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296 H. Miled et al. Fig. 15.2 Diffe
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298 H. Miled et al. Each member of
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300 H. Miled et al. temperature is
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306 H. Miled et al. Eqs. 15.28 and
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