Stress field analysis of an infinite plate with a central closed inclined crack under uniaxial compression

Abstract

In view of the shortcomings of existing studies, the mechanical behavior of the closed crack under uniaxial compression is studied. Based on the far-field and the crack surface stress boundary conditions, Kolossoff-Muskhelishvili stress function of an infinite plate with a central closed inclined crack is derived with Muskhelishvili complex theory. Then the calculation methods of the stress components, stress intensity factors and T-stress at the crack tip are proposed. The mainly findings are as follows. First of all, the crack surface stress boundary conditions vary with variation of the far-field stress condition from tension to compression, so it’s false to directly introduce the theory for the crack under tension to that for the closed crack under compression. Next, it is found that there is no KI singular term at the crack tip and meanwhile KII and T-stress are influenced by the effective shear stress on the crack surface. When the effective shear stress is zero, there are two T-stress components (i.e. Tx and Ty, which are parallel and perpendicular to the crack surface respectively). While the effective shear stress is greater than zero, the third T-stress component (namely Txy which is along the xy direction) also exists. Finally, the theoretical predictions with the proposed method are verified with the isochromatic fringe patterns of photoelasticity experiment near the crack tip under uniaxial compression. Meanwhile the distribution of each stress component around the crack is effected obviously by the friction coefficient of the crack surface and the dip angle of crack, but the distribution tendency of these stress components is similar.