Crack Propagation in Mixed-Mode Ductile Fracture with Continuum Damage Mechanics

Abstract
This paper presents a crack propagation model based on an anisotropic theory of continuum damage mechanics proposed earlier by the authors capable of characterizing sub-critical crack growth in mixed-mode ductile fracture. The embedded β angles of mixed-mode specimens include 75, 60, 45 and 30 degrees. The crack growth criteria chosen are essentially those developed for crack initiation and are postulated as: 1. A crack propagates in the direction of maximum effective damage equivalent stress αd. 2. The threshold condition of crack initiation is satisfied when the overall damage w in an element ahead of the crack tip at the prospective crack growth direction reaches its critical value, wc. The crack growth behaviours of the mixed-mode specimens are analysed using a finite element formulation of the non-proportional loading based on the anisotropic model, and the predicted and measured results are found to be satisfactory. The proposed model is also adapted to predict the critical loads of unstable crack propagation and the results are compared favourably with those determined experimentally. Hence the application of the above two fracture criteria can be made to address the entire history of crack development from initiation to rapid growth.

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