Study on the maximum tangential strain criterion for the initiation of the wing-crack under uniaxial compression

The global stress field function of an infinite plate with a closed inclined crack under uniaxial compression is presented, then the stress field at the crack tip is obtained, namely the formulae of K-I, K-II and T-stress are obtained. A new maximum tangential strain (MTSN) criterion is proposed to predict the initiation of the crack under compression by considering singular and non-singular terms based on the classical MTSN criterion. The influence factors on K-II are analyzed and the effects of T-stress on the tangential strain at the crack tip under different critical plastic zones (r(c)), dip angel of crack (beta), friction coefficients of crack surface (f) and Poisson's ratio (nu) are studied. The comparison of the wing-crack initiation angle measured from the experimental results and predicted by the proposed criterion and other researchers' models are made. The following findings are obtained. First of all, the proposed global stress field function satisfies the far-field and crack surface stress boundary conditions. The singular term of K-II and non-singular term of T-stress vary with the effective shear stress along the crack surface. When the effective shear stress is zero, there is still singularity at the crack tip, which is completely opposite to the classical theory, and there are two components of T-stress (i.e. T-x and T-y, which is parallel and perpendicular to the crack surface respectively). While there is a third component of T-stress (i.e. T-xy which along the xy direction) when the effective shear stress is greater than zero. Next, the comparison of the wing-crack initiation angle measured from the experimental results and predicted by the proposed criterion and other researchers' models are made. The results of the proposed method are consistent with the experiments very well, especially when the effective shear stress decreases to zero with the increase of friction coefficient (f). Finally, the tangential strain field at the crack tip are effected significantly by the critical plastic zones (r(c)), dip angel of crack (beta), friction coefficients of crack surface (f) and Poisson's ratio (nu).