Issue 35

S. El Kabir et alii, Frattura ed Integrità Strutturale, 35 (2016) 64-73; DOI: 10.3221/IGF-ESIS.35.08 69 The initial crack length is fixed to 49 * mm a , with the coefficient a = 1; ¾; ½ ; ¼ . The factor b is used to modify the thickness and takes the following values b = 1; ¾; ½ . For different MMCG specimens, the simulation presents a crack growth process to a final crack length of 70 iterations. In the literature, the initial Arcan fixture is proposed by [1]. In this work, new shapes and dimensions of the experimental loading device are proposed, see e.g. Fig. 5. The system allows considering, during the test, the specimens for the factor a= ½ and a = 1 , and different thicknesses for MMCG specimen. Figure 5 : MMCG specimen and loading device adapted for 1 a  and 1 2 a  . Numerical results In this section, the results of parametrical study are exposed. In order to observe the stability of MMCG specimen, the energy release rate is computed for different sizes and thicknesses of the MMCG specimen. Finite element computation is realized with the software Cast3m, produced by French Energy Atomic Commission CEA [12]. For some significant cases, we plot the evolution of the energy release rate as function of the crack growth. The decrease of the energy release rate for specimen of new sizes translates the stability of the crack growth. The computation is realized assuming a plane stress state. Radial meshes and θ field are shown in Fig. 6. In Fig 6 (a), the size of radial mesh and the field θ are the same, and the mesh is constructed with 10 elements around the crack tip. Greater is the number of elements, more accurate is M θ value. For more stability, M θ field has to be included inside the radiating mesh as seen in Fig 6 (b). Mesh density and M θ field are two parameters which allow less disruption and more numerical stability. Figure 6 : M θ field around the crack tip and outside radial meshes (a) , or inside radial meshes (b) . Fig. 7 presents the contributions of the opening mode and the shear mode to the energy release rate for the mixed mode ratio of 45° for different size coefficients a and the same thickness. In Fig. 7 (a), results for three different sizes versus crack length are presented and we show that the value of G increases when the size increases. Simultaneously, Fig. 7 (b) and (c) (a) (b)