13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- geometry under different loading and boundary conditions. FRANC3D adaptively remeshes an existing finite element model with the inserted initial crack to generate a cracked model. Furthermore, FRANC3D is also used to calculate stress intensity factor (SIF) for an entire crack front. y z x (a) Figure 2. (a) Finite element model, (b) Crack initiation sites 2.2. Crack driving force calculation In the present paper, mode I and mode II SIFs, KI and KII in one cycle under non-proportional tension combined with torsion loading are computed for the sake of obtaining the equivalent SIF, Keq. Erdogan and Sih proposed that the equivalent stress intensity factor according to the maximum tangential stress criterion can be described by: * * * * 1 3 3 3 3cos cos sin sin 4 2 2 4 2 2 eq K K K θ θ θ θ Ι ΙΙ ⎛ ⎞ ⎛ ⎞ = + − + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ (1) *θis a function of KI and KII, representing the direction where the tangential stress σθθ in the vicinity of the crack tip is maximum. And also the shear stress τrθ vanishs along this direction on the basis of MTS criterion. 2 * 1 1 2arctan 8 4 4 K K K K Ι Ι ΙΙ ΙΙ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ θ = ± ⎜ ⎟ + ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ (2) The stress intensity factors for mode I and mode II are calculated by FRANC3D software for tension F=1 and torsion MT =1. The combined tension and torsion mixed mode stress intensity factors KI and KII are obtained from the superposition according to equation (3): ( ) ( ) ( ) I I, I, t t t F M T K K F K M = ⋅ + ⋅ ( ) ( ) ( ) II II, II, t t t F M T K K F K M = ⋅ + ⋅ (3) The combined SIFs computed from equation (3) are inserted to equation (2) to find the angle *θ, which is put into equation (1). The equivalent stress intensity factor Keq is calculated for a full loading cycle. Among all the equivalent stress intensity factors, the peak value Keq,max is taken as the crack driving force, which means the loads at this instant tmax, F(tmax) and MT(tmax) are used for
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