13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 E11*103 Σ11/σc (matrix) (c) (d) Figure 2: Concrete plate containing unbreakable particles enveloped by ITZ (a), crack patterns at peak of the loading (b), at the end of the loading and global response (d) of the concrete plate 4.3: Fracture in laminate composites Let’s consider a plane strain composite laminate cell of dimension 20×18.2 mm² formed by 3 phases: matrix, fibres and interfaces. The thicknesses of these layers are: 0.625mm for matrix, 0.625mm for fibres and 0.025mm for interphases. The entire cell was divided into pixels by a 400×728 Fourier grid. Each layer of the composite is assumed to be linearly elastic and isotropic. The material parameters of each component are listed in Table 1: Table 1: Material constants of the components E (MPa) ν σc (MPa) KIc (MPa√mm) R (mm) Matrix (epoxy) 5100 0.35 100 50 or 200 0.105 or 1.486 Fibre (carbon) 210000 0.27 1400 700 0.105 Interphase 10451 0.3483 40 or 60 20 or 30 0.2906 The external loads can be applied by imposing average stresses Σ11 > 0, Σ22 = Σ12 =0 or average strains E11 > 0, E22 = E12 =0. The FFT simulations were carried out step by step with small crack growth (about 0.1mm) at each step until the full failure of the cell. We present hereafter a FFT simulation with a reference configuration, i.e., the basic cell subjected to a uniaxial tension by imposing average stresses Σ11 > 0 and Σ22 = Σ12 = 0 as remote loads. Figure 3a illustrates the global response, i.e., the E11−Σ11 curve of the cell during the loading. Figures 3b, shows the fracture patterns of the cell at the end of the failure process. With the aid of these figures, we can describe the fracture process of the composite as follows: 1. Under uniaxial tension, the global response of the composite laminate presents a saw-tooth snap-back feature. Each tooth represents the crack growth though a fibre layer;
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