Relaxation of stresses in crazes at crack tips and rate of craze extension

Abstract

The Barenblatt theory of cohesive stresses at crack tips is used to investigate the effect of the relaxation of craze stresses at crack tips on the rate of craze extension. The craze stresses are equated to the cohesive stresses of the Barenblatt theory. The cancellation by the cohesive/craze stress of the singularity that would exist at the crack tip in their absence is assumed to hold for an extending craze. With this assumption, relaxation of the craze stresses produces craze extension, an effect which has been called ‘relaxation controlled growth’ by Williams and Marshall. A general equation relating the rate of change of craze length to the rate of change of stress intensity factor ( K 1) and the rate of change of the craze stress is derived. It is argued from this equation that uniform crack growth with a constant craze length can occur only at constant K 1. Using plausibility arguments for the behaviour of the craze stress with time and position in the craze, and assuming a generalized Dugdale model, differential equations for the rate of craze extension with no crack growth are derived for the constant load and constant K 1 cases. These equations relate the rate of change of craze length to the craze stress at the tip of the crack. Assuming a specific form for the time dependence of this stress, the equation for the constant K 1 case is solved to yield an expression for the craze length as a function of time.