116 R. Moutou Pitti et al. Fig. 16.1 (a) Fatigue crack growth tests data, (b) standard Al7075-T6 tensile test specimen 16.2 Experimental Results Five fatigue crack growth tests are performed on standard Al7075-T6 tensile test specimen to determine the material properties needed to define the fatigue crack growth model. The aluminum alloy test specimen measures 13.78 inches (350 mm) tall by 1.97 inches (50 mm) wide and 0.093 inches (1.6 mm) thick. An initial notch 0.01 inches (0.254 mm) long was made at the edge of the hole 0.187 inches (4.76 mm) diameter. A detailed drawing is shown in Fig. 16.1b. Fatigue crack growth tests were run on axial-load fatiguetesting machine which allows to applying an oscillatory load with a minimum load Pmin D500 N and a maximum load Pmax D5000 N, which correspond to a tensile-tensile test with a load ratio RD0.1. As the crack propagates through the specimen, the crack length is recorded every ND500 loading cycles. As can be seen in Fig. 16.1a the scatter between the date of the five conducted tests is not significant. Consequently, the analysis will be performed on the mean data. 16.3 M-Integral Formulation and Finite Element Implementation Independent path integral techniques, such as M-integral [3], seem to be a good tool to compute the fracture parameters such as energy release rate and stress intensity factors. Let us consider a cracked medium subjected to mechanical loads, and ! a continuous derivable vector field defined around the crack tip as depicted in Fig. 16.2. The M-integral reads: MDZ 1 2 v ij;k ui u ij vi;k k;j ds CZ 1 2 Fi vi;j j dx1 (16.1) The first term is the generalized definition of the M-integral which represents the effect of mechanical loads applied far away from the crack tip, where v ij and u ij are stress components associated to the auxiliary displacement fieldv and the real displacement fieldu, respectively. The second term represents the effect of mechanical loadFi applied on the crack edges . The real stress intensity factors Ku I and Ku II, associated to the opening and in plan shear fracture modes respectively, can be easily derived by performing two distinct computations for particular values of the auxiliary stress intensity factors Kv I and Kv II, such as:
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