A general stress solution in a plastic region near a traction-free boundary of arbitrary shape under plane-strain conditions

The stress field near voids (or holes, or pores) essentially contributes to the fracture process in metallic and nonmetallic materials. In contrast to strains, it is practically impossible to measure stresses experimentally. Therefore, accurate theoretical methods are required to calculate the stress field near a void of arbitrary shape. The present paper develops such a method for the Mohr–Coulomb yield criterion under plane strain conditions. The boundary value problem is a free surface boundary value problem. The boundary conditions on the void contour result in the Cauchy problem for a hyperbolic system of equations. Therefore, the solution in a plastic region adjacent to the void is independent of other boundary conditions. It is required to evaluate one ordinary integral numerically for calculating the stresses at any point of the plastic region. The general solution applies to determining the stress field near two families of void contours. One family consists of contours with the same aspect ratio, including an ellipse as a particular contour. The other family consists of equal-areal voids, including a circle as a particular contour. This choice of the contour families reveals the void shape’s effect on the stress field. The effect of the internal friction angle of the stress field is also discussed.