Significance of the deviations of the crack front into the plane perpendicular to the crack propagation direction - I. Crack-front dislocation generation

Abstract

A static crack front deviates more and more from straight line in a solid as I. the number of dislocations generated from the crack front increases and/or II. the temperature increases. The significance of these deviations into the plane perpendicular to the crack propagation direction is the subject of the present study, which we divide into two parts. In this paper (Part I), the influence of dislocation generation on the shape of a static crack front and on the conditions for crack motion are investigated. We have considered an elastic-plastic crack model in which, due to dislocation generation during mode I loading, the initially straight crack front deviates in the sinusoidal form in a plane perpendicular to both the average crack plane and the direction of fracture propagation. No crack opening displacement is allowed. The dislocations generated form a plastic zone separated from the crack by a dislocation free zone. Both the crack and the plastic zone are described in terms of continuous distributions of dislocations that are sinusoidal and straight edges, respectively. Expressions for the dislocation distributions, the relative displacement of the faces of the crack, the number of dislocations in the plastic region, and the crack opening force G per unit length of the crack front are evaluated. The similarities with isolated cracks (planar and wavy) are emphasized. It is shown that the stress at the front of the sinusoidal crack is unbounded in the mean fracture plane but bounded outside. Consequently, only the crack front sites located on the average crack plane are possible sites for the initiation of crack motion. G differs from that of the planar crack by a geometrical factor that depends on a new parameter, the crack front inclination angle θ. This is an acute angle, measured in the plane perpendicular to the crack propagation direction, between the crack front and the average fracture plane. As θ increases with the number of dislocations generated, G decreases and is ultimately zero for a critical value θ_c=tan ⁻¹(1/sqrtν) where ν is the Poisson ratio. This is a new condition for crack arrest in solids. Applying the theory to a steel, it is found that this condition could be achieved under localized plastic yielding at crack tips.