13th International Conference on Fracture June 16–21, 2013, Beijing, China 2 α=1 represents a part-circular crack [9-10, 14-16]. Carpinteri [9] discussed the crack aspect ratio influence on the stress-intensity factor of elliptical-arc crack front. The maximum stress intensity factor is attained in correspondence to the deepest point on the crack front in the case of a/b=0, while it is attained near the external surface in the case of a/b=1. Shin and Cai [15] evaluated stress intensity factors along an elliptical surface crack front in a rod using experimental backtracking technique and finite analysis. Figure 1. Sketch of surface crack geometry. For the present specimens, the known solutions cannot directly be applied due to arbitrary crack front. The virtual crack closure technique (VCCT) is widely applied in computing energy release rates based on finite element analysis. The VCCT method provides the energy release rate GI based on the work to be done by the nodal force Fy,i(a) against the relative nodal point displacement Δuy,i(a+Δa) in order to close the crack by Δa [17]. The nodal force Fy,i(a) can be obtained from the first step analysis where the crack is closed. The nodal point displacement can be obtained from the second step analysis where the crack has been extended to its full length a+ Δa, as illustrated in Fig. 2. ) ( ( ) 2 1 , , E F a u a a y i y i y Δ+ ⋅Δ = Δ (1) t a E G y D I ⋅Δ Δ −= Δ 2 (2) Figure 2. Illustration of VCCT. Equation (2) is derived under assumption that the crack front is straight. For an arbitrary shaped crack front the mode definition constantly changes along the counter. A local crack tip coordinate system is
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