Computational Methods for Debonding in Composites

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184 N. Zobeiry et al. In compression, on the other hand, this softening occurs due to matrix cracking or yielding and fibre instability. In addition, the instability and rotation of the fibres combined with fibre breakage and splitting contribute to the overall softening behaviour under compression. In fact, in compression, matrix cracking leads to the instability of fibres which is not the case in tension. The overall reduction in the laminate tangential stiffness, which leads to the softening behaviour, has been modeled using fuses and springs. Fuses fail sequentially upon application of a remote displacement to the laminate sub-model. This results in the overall stiffness reduction of the laminate sub-model and an ensuing softening behaviour similar to the composite response under tension. The rubble sub-model represents the behaviour of the damaged material in compression. Upon reaching the damage initiation strain under compressive loads, the matrix starts to crack or yield resulting in the formation of multiple cracked surfaces or rubble. With further damage growth under compression, the friction between the newly cracked surfaces results in an increase in the load carrying capacity of the material. This damaged material can continue to carry compressive loads. The behaviour of the rubble sub-model can be represented with an analogue model consisting of gap and spring elements to model the compressive load carrying response with an increasing stiffness. The gap element is inactive (open) before damage initiation. After damage initiates, new surfaces form resulting in an increased stiffness of the damaged material. This is modeled by sequential closure of the varying sized gaps in compression. By virtue of the gaps remaining open, the rubble sub-model cannot carry any load in tension. The slider simulates the damage band (kink band) propagation. The yield strain is assumed to coincide with the saturation strain of the rubble sub-model. At the instant of final gap closure, the slider activates, indicating progressive specimen end shortening (damage zone broadening) under a constant applied load. This results in the damage propagation into the undamaged interior material and an increasing damage height for compressive failure. Together, the Laminate and Rubble sub-models represent the overall response of the composite in the force-displacement space during progressive damage growth in tension or compression. Figure 9.3 shows a schematic example of the response of a RVE under controlled displacement loading based on the analogue model. First displacement is applied in the tensile mode until fibre and matrix damage occurs in the RVE. Subsequently the RVE is unloaded and then reloaded in the compressive regime. In this case, the initial reduced modulus (dashed line) compared to the undamaged modulus (solid curve) is due to the previous damage incurred in tension. After reaching a saturation state of matrix damage in the RVE, upon further application of displacement, the damage broadens into the undamaged material resulting in the band broadening phenomena and the corresponding plateau stress. The band broadening then continues up to the point of complete failure (fibre damage saturation). The analogue model described above has been used to extend the compression modeling capabilities of a continuum damage mechanics model (CODAM) previously developed by Williams et al. [31] for gross damage development in polymeric
9 Progressive Damage Modeling of Composite Materials 185 Ultimate failure (Compression) Ki Kink BandBroadening Matrix El Elastic Matrix Ultimatefailure (Tension) and fibre region and fiber damage damage Fig. 9.3 An example of the constitutive response obtained from the proposed analogue model matrix composites. CODAM is a phenomenological model that smears the material response (stress-strain behaviour) over a finite RVE of the laminate made up of a repeating unit or sub-laminate through the thickness and a characteristic size, hc,in the plane of the laminate. The construction of the model at this scale ensures that: (1) by considering a sub-laminate the lamina interactions in terms of damage initiation and evolution are implicitly taken into account, and (2) the characteristic planar length provides a measure of the inherent toughness (or brittleness) of the material (the smaller the hc the more brittle the material). The latter is also related to the size of the fully developed fracture process zone (i.e. the height of the damage zone ahead of a crack in a test configuration that leads to a stable crack growth). In formulating CODAM two sets of curves are defined: one relating the damage variables to an effective strain, and the other relating modulus reduction to the damage variables. This results in a strain-softening type stress-strain curve for the characteristic RVE. Damage variables are defined for each of the principal orthotropic directions as well as in shear loading, and the damage growth and modulus reduction curves are unique in each case and sensitive to differences in tension and compression. The CODAM approach has been designed to be computationally oriented, conceptually simple and easy to characterize. The model has been implemented as a user material model in the commercial finite element code, LS-DYNA, and combined with a modified crack band scheme to address mesh sensitivity. Its ability to predict the response of composites under a variety of loading scenarios has been demonstrated elsewhere [16, 17, 31–33]. A simplified version of CODAM has also been successfully implemented in the commercial implicit finite element code, ABAQUS. 9.3 Model Calibration For its characterization, the CODAM constitutive model requires some basic input parameters such as the amount of fracture energies under compression and tension, the plateau stress and peak stresses in addition to the standard elastic constants. To obtain some of these parameters, results from experiments such as the over-height s e
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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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Chapter 6 Study of Delamination in
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6 Study of Delamination with in Com
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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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312 H. Miled et al. 9. Carreau P, D
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Computational Methods for Debonding in Composites

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