Computational Methods for Debonding in Composites

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Chapter 7 Interaction Between Intraply and Interply Failure in Laminates F.P. van der Meer and L.J. Sluys Abstract A mesoscale model for finite element analysis of failure in laminates is presented. The model consists of separate parts for failure inside a ply (intraply) and failure between plies (interply). Both parts offer a description from onset of failure to complete local failure, thus allowing for progressive failure analysis. Intraply failure is simulated with a softening plasticity model based on a Tsai-Wu criterion with viscoplastic regularization. Details are presented on the implementation of the softening law for orthotropic materials in finite element computation. Interply failure is modeled using interface elements with a damage law for mixed mode delamination. The performance of the model is illustrated by means of an analysis of a laminate with a sharp internal notch – a case in which different modes of ply failure successively take place and interact with failure between the plies. 7.1 Introduction Failure of laminated composites is generally analyzed on the mesolevel, i.e. the laminate is modeled as a stack of homogeneous plies, each with its own orthotropic properties that depend on the fiber direction (see e.g. [6,10] and references therein). With this approach, two distinct failure mechanisms may occur in the laminate: failure inside a ply (intraply) and failure between the plies (interply). The first of these can be connected to different underlying micromechanical failure modes, such as fiber fracture, fiber buckling, matrix cracking and fiber/matrix debonding. The second is referred to as delamination. Ultimate failure of a laminate is often preceded by both failure mechanisms. Therefore, simulation of failure in laminated composites requires a model which includes both intraply and interply failure as well as interaction. In this paper, such a model is presented. For both failure mechanisms, F.P. van der Meer and L.J. Sluys Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands, e-mail: f.p.vandermeer@tudelft.nl 141
142 F.P. van der Meer and L.J. Sluys constitutive models are incorporated that give a complete description of the local process from initial elastic behavior to complete loss of integrity. For intraply failure, numerous theories exist that provide criteria to evaluate the stresses inside a ply, either based on the different failure modes [7, 9, 17] or defined as polynomial interaction between stress components [11, 24]. However, not much is known on what happens inside a ply after such a criterion has been violated, even though this information is necessary to predict redistribution of stresses and ultimate failure of the laminate. We have used an interactive criterion and extended it with a new softening plasticity model for the simulation of progressive failure. For interply failure, models for the nonlinear material behavior are available in literature. The interface can be modeled with interface (or decohesion) elements [4,12,14,21,25,30], thin volume elements [27], or embedded discontinuities incorporated through the partition of unity method [18]. Here, we have used interface elements with a constitutive law developed by Turon et al. [25] to capture the onset and growth of delamination cracks. The outline of this paper is as follows. First, the softening orthotropic material model for intraply failure is presented. Next, the delamination model is described. And finally, the performance of the framework combining the two models is exemplified. 7.2 Softening Orthotropic Plasticity The single expression failure criteria for orthotropic materials by Hoffman [11] and Tsai and Wu [24] may be written in tensor notation (cf. [19]): f (σ)= 1 σ · Pσ + σ · p − 1 (7.1) 2 where σ is the stress in Voigt notation, and the components of matrix P and vector p are computed from the uniaxial strength parameters. Every stress state for which f ≤0 is considered admissible. For the generalized Von Mises version of the Tsai Wu criterion, P and p are defined as ⎡ 2 1 − √ F1tF1cF2tF2c − ⎤ 1 0 0 0 ⎢ ⎢− ⎢ ⎢− P = ⎢ ⎣ √ F1tF1c F1tF1cF2tF2c √ 1 2 − F1tF1cF2tF2c F2tF2c 1 F2tF2c √ 1 − F1tF1cF2tF2c 1 2 F2tF2c F2tF2c 1 0 0 0 F2 4 0 0 0 0 1 F2 6 0 0 0 0 0 1 F2 6 ⎥ 0 0 0 ⎥ 0 0 0 ⎥ 0 0 ⎥ 0 ⎥ ⎦ (7.2)
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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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192 N. Zobeiry et al. where g f is
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194 N. Zobeiry et al. References 1.
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Chapter 10 Elastoplastic Modeling o
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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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244 E. Lund and L.S. Johansen In th
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246 E. Lund and L.S. Johansen 12.2.
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248 E. Lund and L.S. Johansen The D
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250 E. Lund and L.S. Johansen Subje
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252 E. Lund and L.S. Johansen Table
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254 E. Lund and L.S. Johansen Layer
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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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270 M. Kästner et al. including pr
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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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Chapter 14 Development of Domain Su
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14 Development of DST for the Model
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294 H. Miled et al. for this type o
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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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302 H. Miled et al. Fig. 15.7 Compa
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304 H. Miled et al. Table 15.3 Prop
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306 H. Miled et al. Eqs. 15.28 and
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308 H. Miled et al. 15.4.2 Effectiv
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310 H. Miled et al. Fig. 15.13 Comp
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