Computational Methods for Debonding in Composites

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7 Interaction Between Intraply and Interply Failure in Laminates 157 • Lamina softening properties: H = −0.8,V = 0.1/s, loading rate: 0.5 mm/s (1%/s). • Interface properties: K = 50 · 103 N/mm3 , tmax n = 10 MPa, tmax r = 6MPa,GIc = 0.35 N/mm, GIIc = 0.70 N/mm, η = 1. The values for the elastic properties of a unidirectional lamina and the interface properties are those given by Yang and Cox for a carbon/epoxy laminate [30]. However, the interface strength parameters are reduced, as proposed by Turon et al. [26] to allow for the use of a relatively coarse mesh (this reduction leads to an increase in the length of the cohesive zone). The lamina strength properties are those provided by Daniel and Ishai [6] for a unidirectional carbon/epoxy lamina. A similar analysis has been executed by Wisnom and Chang [29] and by Yang and Cox [30]. The former used stacked plane stress elements connected with springs, the latter used volume elements. In both references, not only the interply failure, but also the intraply failure was modeled with interface elements. In experiments it has been observed that a splitting crack grows from the notch tip in the 0-layers. This crack has been modeled in [29] and [30] by inserting interface elements where the crack is expected. The orthotropic plasticity model used here is more general, since the crack path need not be specified beforehand. Moreover, it allows for the modeling of ultimate failure of the laminate. The evolution of plasticity in the ply with fibers in loading direction is shown in Fig. 7.11. It can be observed that the split grows as long as the load increases. In the continuum approach, the splitting mechanism is necessarily represented by a band with localized deformation. This band is parallel to the fiber direction, which is in correspondence with the experimental observations. Then tensile failure initiates at the notch tip and propagates throughout the cross section. Eventually, the band with tensile failure deviates from the plane of symmetry, after which the assumption of a symmetric response is no longer realistic. Viscoplastic regularization preserves the mesh objectivity of the results. The final size of the delamination area due to the growth of the splitting crack is shown in Fig. 7.12. This figure displays the state at peak load level. After this, the triangular delamination area that accommodates the splitting crack in the 0-layer does not grow any further. In the post peak part of the simulation, some delamination in the vicinity of the tensile failure has been observed. Figure 7.13 shows part of the deformed mesh, shaded where softening in the plies occurs. The two areas of plastic strain, corresponding with the different failure mechanisms, can be distinguished. The sliding between the two plies is also visible. Fig. 7.11 Evolution of softening variable h in 0-ply. The arrow indicates the notch tip
158 F.P. van der Meer and L.J. Sluys Fig. 7.12 Interface damage near the notch tip at peak load level. The arrow indicates the notch tip. Part of the mesh is shown, the arrow is scaled accordingly (cf. Fig. 7.11) Fig. 7.13 Load displacement diagram and zoom of final deformed mesh (displacements in load direction only). The arrow indicates the notch tip. Part of the mesh is shown, the arrow is scaled accordingly (cf. Fig. 7.11) 7.5 Discussion A model for mesoscale analysis of failure in composite laminates has been presented. An existing model for delamination has been combined with a new softening plasticity model for lamina failure. The combined model is robust, due to a carefully designed stress evaluation algorithm and the use of a consistent tangent operator. The simulation of failure processes in laminates that involve both interply and intraply processes and their interaction is possible with this model. In the analysis of a notched laminate a sequence of interacting failure events is simulated: the growth of a splitting crack in one of the plies, which is accommodated by delamination between this ply and its neighbor, and subsequently the tensile failure in all plies, which constitutes final failure of the laminate. In developing the softening model, several non-trivial choices had to be made. Firstly for the failure criterion. An interactive criterion has been chosen for reasons of computational efficiency and robustness, in spite of the appealing physical motivation of failure mode based criteria. Secondly for the degradation law. The simplest possible formulation with which complete local failure can be simulated has been chosen, with the motivation to keep the computation robust and to limit the number of input parameters. Some drawbacks of the softening model in its current form are that the direction of plastic strain is often unrealistic resulting in spurious transverse strains, and that viscoplastic regularization is a method that is not clearly linked to physical phenomena. Furthermore, it would be ideal if fracture energy values measured in different uniaxial tests would be direct input parameters for the material model, which is currently not the case.
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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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100 C. Schuecker and H.E. Petterman
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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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252 E. Lund and L.S. Johansen Table
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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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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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306 H. Miled et al. Eqs. 15.28 and
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