Steady state crack growth in elastic-viscoplastic materials

A recent theory of Hart for the steady state propagation of a mode III crack in a ductile material is extended to modes I and II. When a crack is moving at non-zero velocity v, it is shown that for a broad class of materials the stress state at the crack tip is characterized by a r^1/2 singularity and by a local stress intensity factor K. The local K is the sum of the apparent stress intensity factor K_A and a plastic contribution K_P. The value of K_A is calculated from the remote loading and the crack geometry under the assumption of linear elastic response alone. The quantity K_P characterizes stress relief of non-elastic flow. Numerical calculations are made to determine K as a function of K_A and v for elastic-viscoplastic materials. A dependence of v on K_A is obtained by imposing a kinetic law for v as a function of K. The plots of v vs. K_A show that below some critical values of K_A, steady state conditions cannot be sustained. Corresponding to the threshold value of K_A there is a definite value for the velocity.