A Criterion For Quasibrittle Crack Growth

INTRODUCTION In this paper we derive an expression to predict the onset of growth of a crack in a quasibrittle material. We employ an energy criterion, which was first proposed by Griffith (1920), and is essentially equivalent to the first two laws of thermodynamics. The criterion is applied to the elastic-plastic crack of Olesiak and Wnuk (1968), which is a three-dimensional generalization of the Dugdale (1960) crack. Our expression for the onset of growth differs in several respects from a criterion based on a crack in a brittle material (i.e., using linear elastic fracture mechanics) . Furthermore, the new features are in qualitative agreement with the experimental data. Among these new features are 1) the dependence of the apparent surface energy, or critical strain energy release rate on crack size (the shape of the R-curve); 2) the effect of in-plane stresses (i.e., the stresses that do not lead to any traction on the crack faces) on crack growth; and 3) a brittle-ductile transition. The energy criterion, as a necessary condition for crack growth, rests on a firm theoretical basis. However, its role as a sufficient condition is less secure. Several alternate criteria have been proposed as necessary and sufficient conditions for the onset of crack growth. We will contrast several of these, including critical strain (Olesiak and Wnuk, 1968; Goodier and Field, 1963) and crack opening displacement ("COD", Burdekin and Stone, 1966) with the energy criterion. We will show that these alternate approaches are inconsistent with the energy criterion, in the sense of being necessary conditions, and so should be rejected as criteria for growth--at least for the elastic-plastic crack.