Fracture Initiation Due to Asymmetric Impact Loading of an Edge Cracked Plate

The two-dimensional elastodynamic problem of a semi-infinite plate containing an edge crack is considered. Initially, the plate is stress-free and at rest. To simulate the asymmetric impact of a projectile on the cracked edge of the plate, a normal velocity is suddenly imposed on the boundary of the plate on one side of the edge crack. The boundary of the plate and the crack faces are otherwise traction-free. Due to the nature of the loading, a combination of transient mode I and mode II deformation fields is induced near the crack tip. The corresponding stress intensity factor histories are determined exactly by linear superposition of several more readily obtainable stress wave propagation solutions, including a fundamental solution arising from a particular problem in the dynamic theory of elastic dislocations. The stress intensity factor histories are determined for the time interval from initial loading until the first wave scattered at the crack tip is reflected at the plate edge and returns to the crack tip. In experiments on fracture initiation in a high-strength steel based on essentially this specimen and loading configuration, Kalthoff and Winkler (1987) reported a fracture grew from the original crack either as a tensile crack inclined to the original crack plane or as a straight-ahead shear fracture, depending on the intensity of the applied velocity. The observations are considered in light of the solution reported here.