DYNAMIC SIMULATION OF DISLOCATION MICROSTRUCTURES IN MODE III CRACKING

We have developed a new, self-consistent simulation method for modeling crack growth with dislocation generation and motion in constant-loading-rate, Mode-III fracture. The dislocations emitted from the crack initially self-organize and propagate in very sharply defined lines. These lines undergo bifurcations, forming multiple new branches and shortening the initial line. The growth and bifurcation of these lines occurs repeatedly. Away from the crack, a highly structured plastic zone is formed that is approximately elliptical in shape with a dislocation free zone along its mid-plane. The rate of generation of new dislocations is limited by the rate at which previously generated dislocations move away from the crack tip. This rate is controlled by the crack loading rate K̇_III and the dislocation mobility. The size of the plastic zone scales as (K²_III/K̇_III)^2/3. The crack tip stress intensity factor K_tip is very much smaller than the applied stress intensity factor. K_tip increases sub-linearly with the load and exhibits both jumps and serrations corresponding to instabilities in the dislocation microstructure. K_tip increases, however, with increasing loading rate at fixed load and a transition is seen between brittle and ductile behavior with decreasing loading rate. Crack propagation occurs when dislocations cannot be generated at the crack tip at a rate sufficient to counterbalance the increasing loading. This generation rate increases with increasing dislocation mobility. Since dislocation motion is thermally activated, this demonstrates that the brittle-to-ductile transition is ultimately controlled by dislocation migration.