A Two-Parameter Description of the Behaviour of a Process Zone at a Crack Tip: Part I — General Theory

Abstract

In quantifying the behaviour of a sharp crack, considerable use has been made of the cohesive process zone description of the non-linear micro-mechanistic processes that are operative in the immediate vicinity of a crack tip. With this description, the non-linearity is modelled so that it is confined to an infinitesimally thin strip, and the analysis is considerably simplified if the description is coupled with the assumption that the stress is uniform within the process zone. When the process zone size is very small compared with the crack size and other dimensions associated with a configuration (the so-called small-scale yielding situation), the crack tip stress intensity factor defines the various parameters associated with the crack: crack tip opening displacement vT, process zone size s, crack opening area A and the effective opening area AD of the process zone. The stress intensity factor relates to the first term in the expansion of the expression for the relative displacement of the faces of an elastic crack, or the expression for the stress ahead of an elastic crack. This paper shows how the various crack parameters vT, s, A and AD are also related to the second term in the expansion of the relative displacement expression, when we relax the assumption that the process zone is very small, i.e. when we proceed beyond the small-scale yielding situation.