13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- ( ) ( ) [ ] ( ) ( ) ⎩ ⎨ ⎧ > − ≤ + − + − = , / 1 0.11 / , / 1 / / 141 0.5 1/ 0.65 4 24 3 a c c a a c a c a c M (17) ( ) [ ]( ) ( )( ) [ ]( ) ⎩ ⎨ ⎧ > + + + ≤ + + + = , / 1 / 1 sin 1 0.1 0.35 / , / 1 / 1 sin 1 0.1 0.35 2 2 2 2 a c c a a t a c a t g ϕ ϕ (18) The function fφ, an angular function from the embedded elliptical-crack solution[16] (Green and John, 1965), is ( ) [ ] 2 0.25 2 2 cos / sin ϕ ϕ ϕ + = f a c (19) The function fW, a finite-width correction from reference[17] (Newman, 1976), is ( ) ( ) [ ]0.5 / sec / 2 c W a t fW π = (20) so, the corresponding stress intensity amplitude can described as △K=(1-R)K. The specific prediction approach is given in Fig. 2. 3 Results and Discussion 3.1 Comparable Analysis of The Proposed Model The crack growth behavior of the Al 7075-T6 alloy elliptic surface crack in tension plate was tested[18] (Putra and Schijve, 1992), and the shape change of the crack front had been obtained, shown in Fig. 4. A literature [19] (Noroozi, 2005 ) had studied the fatigue properties of Al 7075-T6 alloy, and the specific fatigue data are shown in Table. 1, and the feasibility of LCF-FCGM is tested as shown in Fig. 3. It is found that the prediction result by LCG-FACGM is consistent with the reference result [19](Noroozi et al., 2005). Based on the proposed prediction theory, the shape change of the elliptic crack front with different initiate crack shape is predicted by following the prediction process, which has been compared with the reference paper in Fig. 4. The geometry scale and the material properties are the same as the reference paper, in which the initiate crack depth a0 is fixed as 0.2 mm. Seen from Fig. 4, the prediction results for different initiate crack shape are consistent with the test results, especially for the initiate shape parameter α0 equals 0.8,0.4 and 0.2. Table. 1. Geometry size and low cycle fatigue properties Material E /GPa σyc /MPa n εf' c R △Kth /MPa.m1/2 71 469 0.0865 0.19 -0.52 0.1 1.45 H /mm α0 W /mm t /mm Al 7075-T6 65 2.5,1,0.8 ,0.6,0.4,0.2 20 10
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