13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- NfB }min is chose as the crack growth life. What’s over, the corresponding extending steps of the two controller points A and B have the following relationship. ( ) ( ) B A A 1 B 1 A B 2 2 2/( ) 2 2/( ) A th th A B B d PZ d PZ 1 1 f f c cn c cn c c x N a c x N K K K K K K + + + + − = • − ⎡ ⎤ ⎡ ⎤ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ Δ Δ Δ = • − − ⎢ ⎥ ⎢ ⎥ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ Δ Δ Δ ⎢ ⎥ ⎢ ⎥ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ ⎣ ⎦ (10) Fig. 1. scheme of flat surface crack under tension loading The famous Newman-Raju formula[1] (Newman and Raju, 1981) is applied to obtain the stress intensity amplitude along the surface crack front, as Eq..11, ( ) ( ) [ ] ( )ϕ κ π σ σ / , / , / , / K H aE FacatcW s b t = + (11) where E(κ) can be approximated by ( ) ( ) [ ] ( ) [ ] ⎪⎩ ⎪ ⎨ ⎧ > + ≤ + = , / 1 / 1 1.464 , / 1 / 1 1.464 1.65 2 1.65 2 a c c a a c a c E κ (12) and the load combination factor H can be calculated through ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )1.5 0.75 2 1 2 2 1 2 1 3 2 1 / 0.47 / 0.55 1.05 / 1.22 0.12 / / 1 / * / / 0.11 1 0.34 / 0.6 / , 0.2 sin a c a c G a c G H G a t G a t a c a t a t H a c a t p H H H H p + = − =− − + = + − = − = + + = + + ϕ (13) The geometry modifying factor Fs is obtained by FEA as ( ) ( ) [ ] W sF M M a t M a t gf fϕ 4 3 2 2 1 / / + = + (14) in which ( ) ( ) [ ] ⎩ ⎨ ⎧ > + ≤ − = / , / 1 / 1 0.04 , / 1 / 1.13 0.09 1 c a a c c a a c a c M (15) ( ) [ ] ( ) ⎩ ⎨ ⎧ > ≤ + − + = , / 1 0.2 / , / 1 / 0.54 0.89 / 0.2 4 2 a c c a a c a c M (16)
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