Computational Methods for Debonding in Composites

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188 N. Zobeiry et al. displacement (POD) are shown. Localization of the strains into a zone with a height of approximately 20.8 mm can be easily identified from this graph as the distance between the two intersection points. These intersection points differentiate the zone in which the strains are increasing (damage localization) from the zones in which the strains are decreasing (unloading in undamaged material). This allows for an estimate of the height of damage without the need for time consuming sectioning. The height of damage serves as a key parameter for determining the size of the zone used for non-local regularization in the numerical simulations (see Sect. 9.5.2). 9.4 Model Validation 9.4.1 Simulation of OCT Test The OCT test that was used for characterizing some of the model parameters was also used to validate the performance of CODAM in predicting the behaviour of a composite structure undergoing damage and fracture under tensile loading. Finite element simulations of the OCT test were carried out using both the LS-DYNA and ABAQUS implementations of CODAM. Figure 9.7 compares the predictions of the applied force versus crack mouth opening displacement (CMOD) with the corresponding test results for a class of carbon fibre reinforced plastic (CFRP) laminates with a [45/ − 45/02/90/02/ − 45/45]6 layup [18]. In this model, the sublaminate elastic properties used are: Ex = 75.0 GPa,Ey = 32.0 GPa,νxy = 0.161 and Gxy = 17.1 GPa. Also, the peak stress as measured from a 4 pt bend test is 460 MPa and the fracture energy release rate G f = 80 kJ/m 2 based on the findings of Load (kN) 18 16 14 12 10 8 6 4 2 Simplified CODAM in ABAQUS Implicit CODAM in LS-DYNA Explicit Experimental E results 0 0 0.5 1 1.5 2 2.5 3 3.5 4 CMOD (mm) Fig. 9.7 Longitudinal strain profiles at two different levels of pin opening displacement (POD) along a vertical line through the damage zone in an OCT test specimen using the image analysis software, DaVis [12]
9 Progressive Damage Modeling of Composite Materials 189 the OCT experiment. According to this figure, the numerical predictions agree well with the experimental results. Simulation results in the form of predicted damage patterns will be presented in Sect. 9.5.2 within the context of non-local models. 9.4.2 Simulation of Open Hole Plates Under Compression Soutis and Spearing [29] presented an investigation into the compressive strength of CFRP laminates. They performed quasi-static compressive tests on panels with different specimen and notch sizes. In their study they used specimen sizes of 50 × 50 mm and notch diameters ranged from 2.5 to 25 mm resulting in holediameter/width ratios of 0.05 to 0.5. The material used in this experiment was a quasi-isotropic [(±45/0/90)3]s CFRP laminate with an approximately 3 mm thickness and elastic properties Ex = Ey = 63 GPa, νxy = 0.315 and Gxy = 24 GPa. To use CODAM in modeling these experiments, first we need to derive the damage parameters in compression. The damage initiation strain is the strain at which matrix cracking; fibre rotation and delamination start to propagate. In the experiments by Soutis and Spearing [29] on notched specimens, this strain was measured to be around 80% of the strain at the peak stress point. The average strain at peak stress was reported to be almost 1.0%. Therefore, the damage initiation strain can be estimated to be −0.008 (negative sign implies compression). This value is taken to be the damage initiation strain for both the fibre and the matrix due to the fact that matrix cracking and fibre rotation initiate at the same strain level in the kinking process. The compressive fracture toughness for a variety of lay-ups for T800 carbon fibres embedded in Ciba-Geigy BSL 924C epoxy resin was measured by Soutis et al. [28] to be 40 MPa m 1/2 . Here we use the same value of fracture toughness for these panels. This yields a fracture energy of 25.4 kJ/m 2 . Sivashanker [24] has performed an experimental study on the compressive response of the same lay-up and material as in [29], except that he used T300 carbon fibres in his study. We can reasonably ignore this difference in the fibre type as the damage mechanism in these panels is driven mainly by the matrix properties. In Sivashanker’s work, the plateau stress was reported to be in the range of 100–133 MPa. Here we use a plateau stress of 100 MPa. Figure 9.8 shows a comparison between the experimental results and the predicted compressive strengths of notched laminates using the new implementation of CODAM in LS-DYNA. It can be seen that using the above parameters the predictions lie well within the experimental bounds. Sensitivities of the strength predictions to variations in some of the key constitutive parameters in the compression regime, such as the plateau stress and fracture energy have been carried out and reported in [32].
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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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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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248 E. Lund and L.S. Johansen The D
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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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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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308 H. Miled et al. 15.4.2 Effectiv
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