On process-zone-size fracture criteria for brittle solids

Abstract

We propose a new method for the formulation of two-criteria conditions of failure based on the fracture criterion introduced by Novozhilov. We consider a model problem of fracture mechanics of uniaxial tension of a plane containing a crack. It is shown that the proposed method can be applied to the analysis of the problems of short cracks in ceramics. Ando et al. [1] introduced a new criterion of brittle failure of media containing short cracks based on the investigation of a special process zone near the crack tip. The fracture diagrams obtained by using the process-zone-size fracture criterion and the corresponding experimental data for ceramic specimens were also presented in [ 1]. On the other hand, these diagrams can be regarded as a basis of the so-called two-criteria approaches in failure analysis proposed in [2-4]. In the present work, we consider a simpler alternative method for the analytic formulation of twocriteria conditions based on the fracture criterion proposed by Novozhilov [5] and a more explicit expression for elastic stresses near the crack. Let us now consider a model problem of fracture mechanics of uniaxial tension of an elastic plane containing a crack of length 2L (y = 0, -L < x < L). The appropriate asymptotic expression for the maximum tensile stresses in the line of crack propagation has the form