Phase field fracture in elasto-plastic solids: Variational formulation for multi-surface plasticity and effects of plastic yield surfaces and hardening
- Publication Type:
- Journal Article
- International Journal of Mechanical Sciences, 2019, 156 pp. 382 - 396
- Issue Date:
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© 2019 Elsevier Ltd The phase field modelling has been extended from brittle fracture to ductile fracture by incorporating plasticity. However, the effects of plastic yield functions and hardening on the fracture behaviour have not been examined systematically to date. The phase field fracture coupled with multi-surface plasticity is formulated in the variational framework for the unified yield criterion, which is able to facilitate the study on different yield surfaces. First, the homogeneous solutions of fracture in elasto-plastic solids are derived analytically for 1D and 2D cases. The results show that a greater hardening modulus would lead to an ascending branch of the stress versus strain curve; and the yield function may significantly affect the stress state and phase field damage. Second, the finite element (FE) technique is implemented for modelling the phase field fracture in elasto-plastic solids, in which the stress update and consistent tangent modular matrix are derived for the unified yield criterion. Finally, three numerical examples are presented to explore the effects of the yield function and material hardening. It is found that the yield function and material hardening could significantly affect the crack propagation and the final fracture pattern. In particular, the Tresca yield function tends to create a straight crack path orthogonal to the first principal stress, while the other yield functions show no sizeable difference in their crack paths.
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