Higher-Order Asymptotic Solution Of Growing Cracks In Elastic Perfectly Plastic Media

The higher-order asymptotic solutions of a quasi-static, steadily propagating Mode I plane strain crack in an elastic perfectly plastic material are studied.For the incompressible materials, with the velocities ahead of the crack tip supposed to be singular, a higher-order asymptotic solution with fully continuous stress and velocity fields around the crack tip is obtained and the corresponding stable crack growth criterion is constructed. The detailed comparisons between the higher—order near tip solution and the well—known modified Prandtl field are also given in this paper.For the compressible materials, in order to satisfy the higher-order compatibility equation of the rate of deformation in the centered fan sector, which is a quite difficult problem unresolved in the previous studies, a particular term must be added to the expansions of the stress components in the regular logarithmic power series adopted by many researchers before. A higher-order near tip field with tangential velocity jump ahead of the crack tip is derived first, of which the dominant terms are the solution widely accepted. Unfortunately, there is a loophole in this asymptotic solution due to the discontinuity of the tangential velocity, which suggests us to study the solutions without any discontinuities of all the components of the stress and velocity fields. Finally, with the introduction of a fast varying zone ahead of the crack tip, a solution with fully continuous stress and velocity fields is obtained.