Crack-tip field for fast fracture of an elastic-plastic-viscoplastic material coupled with quasi-brittle damage. Part 2. Small damage regime

A parameter perturbation technique is used to obtain asymptotic solutions that apply to a fast moving crack-tip, where small damage condition prevails. The material can be described by an elastic-plastic-viscoplastic constitutive relation including quasi-brittle damage. A dimensionless coefficient, which shows the characteristic damage within this regime, is taken as a perturbation parameter. A set of asymptotic equations is derived in terms of a regular perturbation expansion procedure. Asymptotic solutions are obtained for radial and angular variations of stresses and velocities with first- and second-order accuracy.