Asymptotic fields ahead of mixed mode frictional cohesive cracks

Abstract

AbstractThis paper discusses the asymptotic fields ahead of mixed mode frictional cohesive cracks in quasi‐brittle materials. These fields have been derived after reformatting the cohesive‐law in a special but universal polynomial containing fractional or integer powers. This special form ensures that the radial and angular variations of the asymptotic fields are separable as in the Williams expansions for a traction‐free crack. The coefficients of the expansions however depend nonlinearly on the softening law and the boundary conditions. As expected, the asymptotic field of a frictional cohesive crack reduces to that of a frictionless cohesive crack with normal cohesive separation when the friction coefficient becomes zero. It is also shown that the asymptotic field of a frictionless cohesive crack can be used to a non‐cohesive crack opened by crack face loading, after including the singular terms corresponding to the eigenvalue 1/2. Furthermore, the coefficients are given explicitly for two special softening laws that are commonly used in practice. The leading terms of the true displacement asymptotic field are also derived explicitly. These are especially useful as the enrichment functions at the tip of a mixed mode cohesive crack for accurate simulation of crack growth in quasi‐brittle materials using the extended finite element (XFEM).