13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- direction. The plastic strain amplitude is much bigger than the elastic strain amplitude in the cyclic plastic zone, so the damage of elastic strain can be ignored. Then, a unit average damage parameter over the cyclic plastic zone along the crack extending direction is defined as 1 PZ 0 1 PZ ( )d 1 c x D r x r D c x − + = ∫ − . According to the Miner accumulative damage theory, when 1 = D the crack will grow forward one step. Therefore, the life and the rate of each step can be calculated as follows. ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ + = − ⎟ = ⎠ ⎞ ⎜ ⎝ ⎛ + − = = ∫ ∫ − − 1 1 PZ 0 1 1 PZ 0 1 1 ( )d PZ d d ( )d PZ 1 c x i fi i c x fi D r x r N ci x N a D r x r c x Di N (6) From (6), it is found that the fatigue crack growth equals to the sum of the nodes’ damages in the cyclic plastic zone. Combined (5) and (6), a new FCG prediction model based on the mean plastic strain in the cyclic plastic zone can be given as (7). ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⋅ − + + + ⋅ ⋅ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ′ ⎟ = ⎠ ⎞ ⎜ ⎝ ⎛ + + ) 1 1/( 1 1/ PZ 1 1 PZ 2 d d c cn c yc f i ci x c cn c cn ci E N a σ ε (7) As known to all, in the initiation stage of the FCG curve, where the stress intensity factor amplitude ΔK=ΔKth, no crack growth occurs approximately. So, the fatigue blunting factor x1 can be calculated through (8). ( ) 2 th 2 1 4 1 1 PZ th ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Δ + = = yc K n c x σ πκ (8) From (8), the fatigue blunting factor equals the cyclic plastic zone size corresponding to ΔKth. Then a zero range of cyclic plastic strain damage is obtained from (8) and (5) nearby the crack initiation, which means there is no damage accumulated under this condition. Then the LCF-FCGM can be further developed as (9), ( ) 1/ 2 2 2/( ) th 2 d PZ d 1 2 1 i f i c c cn f i yc yc i ci x a N N E K K c c cn K ε πκ σ σ + + − ⎛ ⎞ ⎜ ⎟ = ⎝ ⎠ ⎛ ⎞ ⎡ ⎤ ′ ⎛ ⎞ ⎛ ⎞ Δ Δ ⎜ ⎟ ⎢ ⎥ = • • • − ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ + + ⎢ Δ ⎥ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ ⎝ ⎠ i=1,2,3…… (9) where i is the serial number. 2.2. Simulation of Surface Crack Growth Theory As for the surface crack front, the crack growth behavior can not be described as one point, which must be considered as a whole curve, two controller points are defined: the crack deepest point B and the crack surface point A, shown in Fig. 1. Follow the assumption on surface crack by Newman and Raju, during the extending process, the crack front shape always can be described with ellipse function. Therefore, the prediction of the surface crack front shape can be achieved by applying the LCF-FCGM at the two controller points A and B. The maximum average plastic strain damage { A B , D D }max decides the main controller point, and the corresponding minimum growth life {NfA ,
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