It was recalled that a static crack-front increasingly deviated from a straight line when the number of dislocations, generated by the crack front, increased and/or the temperature increased. The influence of dislocation generation upon the shape of a static crack-front, and upon the conditions for crack motion, was investigated here. An elastic-plastic crack model was considered in which, due to dislocation generation during mode-I loading, the initially straight crack-front deviated into a sinusoidal form in a plane which was perpendicular to the average crack plane and to the direction of fracture propagation. No crack opening displacement was permitted. The dislocations which were generated formed a plastic zone that was separated from the crack by a dislocation-free zone. Both the crack and the plastic zone were described in terms of continuous distributions of dislocations that were sinusoidal and straight edges, respectively. Expressions were evaluated for the dislocation distributions, relative displacement of the crack faces, the number of dislocations in the plastic region and the crack-opening force per unit length of crack front. Similarities to isolated cracks (planar or wavy) were emphasized. It was shown that the stress at the front of the sinusoidal crack was unbounded in the mean fracture plane, but bounded outside. Thus, only crack-front sites which were located on the average crack plane were potential sites for the initiation of crack motion. The crack-opening force per unit length of crack front differed, from that of a planar crack, by a geometrical factor that depended upon a new parameter. This was the crack-front inclination angle, θ. This was an acute angle which was measured, in the plane perpendicular to the crack propagation direction, between the crack front and the average fracture plane. As θ increased with the number of dislocations generated, the crack-opening force decreased and became zero at a critical value which was related to the Poisson ratio. This was a new condition for crack arrest. Upon applying the theory to a steel, it was found that the condition could be satisfied during localized plastic yielding at the crack tips.

Significance of the Deviations of the Crack Front into the Plane Perpendicular to the Crack Propagation Direction – I. Crack-Front Dislocation Generation. P.N.B.Anongba, V.Vitek: International Journal of Fracture, 2003, 124[1-2], 1-15