Crack-tip field for fast fracture of an elastic-plastic-viscoplastic material incorporated with quasi-brittle damage. Part 1. Large damage regime

An asymptotic analysis of the near-tip field is presented in terms of the coordinate perturbation technique for fast crack propagation in an elastic-plastic-viscoplastic material with damage. A damage variable is incorporated in the constitutive relation based upon the strain-equivalence principle of damage mechanics. The damage evolution law used is a quasi-brittle type, in which both equivalent and hydrostatic stresses are involved. A non-singular stress field is obtained, as the damage has such a substantial influence on the material behaviour that the high stresses are relaxed at the crack tip. An analytical expression is obtained which explicitly shows the variation of stresses approaching the crack tip, and numerical computations of the angular distributions of stresses and strains are also presented.