Modes I and II cracks in a linear hardening solid in general yielding
In the preceding paper (Weertman (1993), Mech. Mater. 15, 65-74) solutions were found for modes I, II and III stationary cracks in a linear work hardening solid (of true shear modulus G and of effective elastic-plastic shear modulus G) in general yielding. A satisfactory solution was found for the mode III crack. However, the mode I and mode II crack solutions, constructed in the same way as the mode III crack solution, failed because they require reverse slip. The present paper presents a satisfactory complete solution for this problem for the mode I crack and for the mode II crack. The solution does not require reverse slip. The key change in the solution is how the total rotation field is partitioned into an elastic component and a plastic component. In contrast to the earlier mode I and mode II solutions, the existence of a non-redundant dislocation density field is required in the solutions. For the mode I crack (but not for the mode II crack) no dislocations enter the solid from the crack faces or from a crack tip (and blunt the tip). This observation is the important result of this paper. This result supports the conjecture that no dislocation injection from the crack plane or crack tip occurs for the mode I crack in an elastic-perfectly plastic solid in small scale yielding (Weertman (1992), Physica Status Solidi (b) 172, 27-40).
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