The impact of neglecting the smooth crack closure condition when determining the critical load

Abstract

The finite stress condition is a correctness requirement that has to be met, when the problem of crack mechanics is solved using the cohesive zone model. This condition is equivalent to the one of smooth closure of crack faces, which models a crack with a fracture zone near its front. The condition is satisfied by the accurate estimation of the length of the cohesive zone, which is a part of the modelling cut along the continuation of a crack with a cohesive stress applied to its faces; the intensity of the stress is connected with the corresponding crack opening displacements by the non-uniform traction—separation law. The cohesive length can be found analytically only for a small number of problems of fracture mechanics, for example, for the problem of a crack in an infinite plane with uniformly distributed load applied at a considerable distance from the crack. When using numerical methods, the cohesive length is found approximately by an iterative procedure. In this paper, we analyze how the precision of determination of the cohesive length influences the critical load at which fracture begins. For this purpose, an edge crack in a finite-size plate is considered. The finite element method was used to obtain the solution, which was analyzed in terms of the effect of inaccurate determination of the cohesive length on the critical load value. A comparison of the numerical solution with the semi-analytical one of a similar problem for a semiinfinite plane is illustrated. It is established that the use of a smaller cohesive length value compared with one which satisfies the smooth crack closure leads to an overestimation of the critical load value, when the fracture criterion stays the same. A simple iterative method of finding the cohesive length that satisfies the condition of smooth crack closure is illustrated.