The Dynamic Stress Intensity Factor Due to Arbitrary Screw Dislocation Motion

The dynamic stress intensity factor for a stationary semi-infinite crack due to the motion of a screw dislocation is obtained analytically. The dislocation position, orientation, and speed are largely arbitrary. However, a dislocation traveling toward the crack surface is assumed to arrest upon arrival. It is found that discontinuities in speed and a nonsmooth path may cause discontinuities in the intensity factor and that dislocation arrest at any point causes the intensity factor to instantaneously assume a static value. Morever, explicit dependence on speed and orientation vanish when the dislocation moves directly toward or away from the crack edge. The results are applied to antiplane shear wave diffraction at the crack edge. For an incident step-stress plane wave, a stationary dislocation near the crack tip can either accelerate or delay attainment of a critical level of stress intensity, depending on the relative orientation of the crack, the dislocation, and the plane wave. However, if the incident wave also triggers dislocation motion, then the delaying effect is diminished and the acceleration is accentuated.