Computational Methods for Debonding in Composites

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6 Study of Delamination with in Composites 133 Table 6.2 Insert material mechanical properties Insert material properties Tensile modulus 1,000 GPa Shear modulus 10 −9 GPa Poisson modulus 0.0 Volume content 100% The damage model used requires knowing the relation between the compression strength and the tension strength of the material in order to obtain the correct damage evolution. As these parameters are unknown, what is done in the present document is to consider that both strengths the same and to define the fracture energy of the material as the mode II fracture energy obtained from the experimental results. The value of this energy, for the 3M101 beam, is: GII = 1.02kJ/m 2 . The definition of the insert material properties has been done taking into account its structural performance. The main effect of this material in the beam is allowing the sliding of the section found above the insert along the section found below it. To do so, a material with a shear modulus nearly zero has been defined (it has not been defined as strictly zero to avoid numerical instabilities during the simulation). On the other hand, the longitudinal and transversal elastic modulus have been defined with a high value to avoid the penetration of the section above the insert into the section below it. This material has been defined as an elastic material. Its main mechanical properties are described in Table 6.2. 6.3.3 Comparison Between the Numerical and the Experimental Results The numerical and the experimental results are compared with the force–displacement graph obtained for both cases. The displacement represented corresponds to the vertical deflection of the point where the load is applied. This graph is shown in Fig. 6.5, in which the results for the 2D and 3D numerical simulations and the experimental test are represented. Figure 6.5 shows that the two dimensional simulation provides exactly the same results as the three dimensional one, thus, for these kind of problems, 2D simulations are preferable, as the computer cost is much lower. However, the most important result shown in Fig. 6.5 is the agreement between the numerical and the experimental results. The beam initial elastic stiffness obtained in the numerical simulation is nearly the same that is obtained from the experimental test. And this agreement between results is even better when comparing the beam maximum load capacity or failure point. The only result that differs in the numerical simulation is the final beam stiffness, when the crack has reached its maximum length. In this case, the
134 X. Martínez et al. Fig. 6.5 Force–displacement graph obtained for the different models Load applied [N] 2500 2000 1500 1000 500 0 0 Experimental’ Numerical 2D & 3D’ -0.2 -0.4 -0.6 -0.8 -1 -1.2 Load point displacement [mm] Fig. 6.6 Damage in matrix material when the maximum deflection has been reached numerical beam is a 6% stiffer than the experimental one (the stiffness obtained in each case is, respectively, 1,146 N/mm and 1,076 N/mm). The other result to be compared is the final crack length. The experimental values obtained for this final crack length for the sample being compared (3M101) is of 50.34 mm, and the mean value of the crack length for all the GRIN006 serie is around 49.0 mm; this is, a bit less than half the beam. In the numerical simulation, the crack points correspond to those in which the damage parameter, in matrix material, is equal to one. These points have a matrix stiffness equal to zero. This implies that the composite serial stiffness is also zero, due to the iso–stress condition imposed by the Serial/Parallel mixing theory. Those points with matrix completely damaged cannot develop any shear strength. Hence, the final crack length can by obtained by finding the point, closer to the beam mid–span, with a value of the damage parameter, in matrix material, equal to one. Figure 6.6 shows the damage parameter in matrix in the load step in which the beam reaches its maximum deflection. In this figure can be seen that the crack length obtained with the numerical simulation also nearly reaches the mid–span section. The exact value of the damage parameter is shown, for the points represented in Fig. 6.7a, in Fig. 6.7b. In this figure can be seen that point 13 (corresponding to mid– span) reaches a damage value of 0.6, while the value of point 12 is approximately 0.98. Considering this last value close enough to one and thus, the section completely broken, the numerical crack length obtained is of 48 mm. The point found at 49 mm of the support has a damage value in matrix material of 0.89, which is also close enough to one to consider that the numerical results are exactly the same as the experimental ones. In this last figure is also represented the force–displacement graph (with the force value divided by 2,500 N, to fit into the figure). It can be seen that the main crack -1.4
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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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184 N. Zobeiry et al. In compressio
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186 N. Zobeiry et al. c = 38.7 mm h
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188 N. Zobeiry et al. displacement
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190 N. Zobeiry et al. No Notched St
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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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246 E. Lund and L.S. Johansen 12.2.
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258 E. Lund and L.S. Johansen 12.6
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266 M. Kästner et al. 13.1.1.2 Per
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274 M. Kästner et al. x2 x 3 x1 Br
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14 Development of DST for the Model
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306 H. Miled et al. Eqs. 15.28 and
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