LOCALIZATION OF PLASTIC-DEFORMATION IN SHEAR DUE TO MICROCRACKS

A constitutive relation for simple shear of an elastic-plastic material containing a periodic array of cracks is developed. The relation is based on finite element analysis and slip-line field solutions for interacting cracks in simple shear. Typical shear stress-strain curves display a peak in the nominal shear stress due to competition between strain hardening of the matrix and material softening due to rotation and stretching of cracks with deformation. The effect of nonuniform crack distributions on localization behavior is studied by determining the critical conditions for which the shear strain in a band of cracks becomes unbounded relative to that in the surrounding, uncracked material. The results show that the strain to localization depends strongly on the ratio of crack length to crack spacing, crack orientation, crack-face friction and matrix hardening. The results are helpful to understanding shear localization under confining pressures, where voids adopt a crack-like morphology. © 1990.