Crack growth in an elastic-plastic material and effects on near tip constraint

The J-Q field of O'Dowd and Shih [1,2] provides a characterisation of the plastic fields near the tip of a stationary crack, for the full range of crack tip constraints. In this paper, the fields ahead of a growing crack under varying constraint are examined. Initially, a numerical analysis of the small scale yielding problem, with K and T applied remotely, is carried out. The near tip constraint increases with crack growth and when distances are normalized appropriately, the transient near tip fields approach the high constraint steady-state fields of Varias and Shin [3] even for large negative values of applied T stress. Crack growth in finite sized specimens is also examined with different resistance curve behaviour prescribed. Consistent with what was observed in the small scale yielding analysis, the near tip constraint increases with crack growth, though falling somewhat below the steady state field. The numerical results have implications for the mode of failure in plastically deforming materials - the rise in constraint with crack growth, suggests the possibility of failure occuring by cleavage after some amount of stable tearing.