Issue34

M. Kikuchi et alii, Frattura ed Integrità Strutturale, 34 (2015) 318-325; DOI: 10.3221/IGF-ESIS.34.34 322 nearly symmetrical loading condition is subjected. In case (b), loading condition is not symmetric, and supporting load in PMMA is near to initial crack. In case (c), supporting load becomes much nearer to the initial crack. The distance between initial crack and phase boundary is 10mm in Case1 and Case 3, and 16mm in Case 2. In all cases, stress field at initial crack tip becomes under mixed mode loading condition, and crack grows by changing the growing direction. Table 2 shows material constants of two materials. In this case, Young’s modulus of PMMA is much smaller than that of aluminum alloy. Experimental results are shown in Fig. 7 (a)-(c) with those of numerical simulation where experimental results are shown by yellow lines, and numerical results are expressed by red line. In case 1, crack grows toward inside of PMMA and goes far from phase boundary. Numerical simulation well predicts the crack growth path, and agrees very well with experimental one. In case 2, crack grows nearly straight forward in numerical simulation and experiment. In this case agreement of numerical prediction and experiment is well. In case 3, difference between experiment and numerical simulation becomes clear. By the experiment, crack grows into the phase boundary and grows along the phase boundary. But numerical simulation predicts that crack grows once nearer to the phase boundary, but after some amount of crack growth, it goes far from the phase boundary. This difference is due to the numerical model in which phase boundary is not modelled correctly. Numerical model assumes that two materials are bonded tightly and there is no phase boundary thickness. But in the real structure, phase boundary has some small thickness and has its’ own strength. Then phase boundary is modelled in S-FEM simulation. Fig. 8 shows mesh pattern around phase boundary. The thickness of the phase boundary is assumed to be 0.5mm, and three layered finite element mesh is used. Material constants of the phase boundary are also shown in Tab. 2. It is assumed that phase boundary has very small stiffness comparing with other materials. It is because two materials are bonded using some bond, and it is reasonable to assume that it has very low stiffness. Numerical result is shown in Fig. 9 (a). By assuming phase boundary layer, crack grows into the phase boundary and grows along it. It is similar to experimental result, but path does not agree completely. This may be due to the phase boundary model. In this simulation, the thickness of phase boundary is assumed to be 0.5mm, which may be much larger than the real structure. Also, material constants in the phase boundary are assumed to be very small value, without any verification. By studying in detail on the effects of phase boundary thickness and material constants, better phase boundary model may be proposed in future. Fig. 9 (b) shows detailed crack path in the phase boundary. It grows in the phase boundary layer in zig-zag manner. As the crack grows in the phase boundary, and does not grow along the border line between different materials, it is easy to evaluate stress intensity factors by the conventional VCCM method [11]. In many composite materials, for example, CFRP, crack growth along phase boundary is observed. The strength of phase boundary is key parameter for the discussion on the strength of composite material. Experimental studies have been done by many authors [12-14], but it has been very difficult to discuss this problem based on numerical simulation. Through these simulations, it is shown that crack growth process along phase boundary becomes possible, if the phase boundary is properly modelled. (a) Case 1 (b) Case 2 (c) Case 3 Figure 6 : Initial carack location and loading conditions of bi-material of PMMA and A6061. PMMA A6061 Phase boundary E [GPa] 3.24 69 0.15  0.35 0.3 0.35 Table 2 : Material constants. 156mm 94mm 150m 150m 150m 30m 150mm 50mm PMMA A6061