13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- 2005 & Li D.M, et al., 1998 & Ramsamooj D.V., 2003), but they are still involved with some human debugs. Therefore, combined Newman-Raju formula, a fatigue crack growth prediction model based on the material’s low cyclic fatigue properties (LCF-FCGM) is proposed to predict the extending process of the surface crack. The proposed LCF-FCGM has been well discussed in author’s previous studies[13-14] (Chen Long et al., 2012). Notice that the influence of the extending direction on the fatigue crack growth properties is ignored. 2. Analysis Theory of Elliptic Surface Crack Growth 2.1. The Proposed LCF-FCGM Theory Based on the HRR field, the stress-strain field near the crack tip was modified to describe the cyclic crack tip stress-strain field[15] (Schwalbe, 1974), ( ) ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛Δ Δ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ = + n n yc r r k r c E r 2 ( ) ( ) 2 2 PZ ( ) P 1/ 1 P ε σ σ ε (1) in which E is Young’s modulus, σyc is cyclic yield stress, k is cyclic hardening coefficient, n is cyclic hardening exponent, r is the distance to the crack tip, and PZc is the cyclic plastic zone size that can be calculated as follows. ( ) 2 2 4 1 1 PZ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Δ + = yc K n c σ πκ (2) Where, ⎪⎩ ⎪ ⎨ ⎧ − − − = strain plane v stress plane 1 2 1 1 κ , v is poison ratio and ΔK is stress intensity factor amplitude. In fact, according to amount of FEA analyses, the curvature of the crack tip is non-zero, and the plastic strain of the crack tip is finite. So, a fatigue blunting factor x1 is introduced into (1), and the cyclic plastic strain amplitude can be further described as follows. ( )n yc r x c E r x + ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + Δ + = 1/ 1 1 1 P 2 PZ ) ( σ ε (3) Informed researches show that material near the crack tip can be considered as a serial of fatigue elements under cyclic loading[15] (Schwalbe, 1974). According to the fatigue theory, the relationship between fatigue life Nf and the cyclic plastic strain amplitude Δεp can be described as follows. ( )c f f N2 2 P ε ε = ′ Δ (4) Where, ε’f and c are plastic hardening coefficient and plastic hardening exponent, respectively. According to the Miner accumulative damage theory, combined (3) and (4), the damage D of the material per one cycle is defined as 1/Nf, where Nf is associated with the plastic strain amplitude. Therefore the distribution of the plastic strain damage along the crack growth direction in the cyclic plastic zone can be described as follows. ( ) ( ) 1 1 1 1 1/ 1 0 PZ PZ 2 r c x r x c E Dr x n c c f yc < ≤ − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ⎟ + ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ′ + = − + − ， ε σ (5) According to the fatigue striations phenomenon of the fatigue fracture image, assuming that each step of the crack advancement size equals to the cyclic plastic zone size (PZc-x1) along the growth
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