Abstract
In this study, a phase field viscoplastic model is proposed to model the influence of the loading rate on the ductile fracture, as one of the main causes of metallic alloys’ failure. To this aim, the effects of the phase field are incorporated in the Peric’s viscoplastic model; the model can efficiently be converted to a standard rate-independent model. The novel aspects of this work include: Describing a coupling between rate-dependent plasticity and phase field formulation by defining an energy function that contains the energy dissipation caused by plastic deformation as well as the fracture process and elastic energy. In addition, the equations required to develop the numerical solution are presented. The governing equations are determined by a minimization principle that results in balance laws for the coupled displacement-phase field problem. Furthermore, an implicit integration algorithm for a viscoplasticity model coupled with a phase field is presented for a three-dimensional stress state. The proposed algorithm can be utilized for different constitutive models of rate-dependent and rate-independent plasticity models coupled with fracture by changing the definition of the plastic multiplier. In addition, to control the influence of the plastic deformation and its work on the crack propagation, a threshold variable is defined in the model. Finally, using the proposed model, the influence of the loading rate on the responses of the different specimens in one-dimensional and multi-dimensional cases is investigated and the accuracy of the results was verified by comparing them with existing experimental and numerical results. The obtained result proves that the model can simulate the impact of the loading rate on the material response, and the gradual change of the fracture phase from ductile to brittle, caused by increasing the loading rate.
Highlights
It is widely accepted that the behavior of many materials, metals, is naturally time-dependent
Duda et al [16] formulated a phase field model of fracture in elastic-plastic solids under small strains assumption. They demonstrated that the phase field approach coupled with rate-independent plasticity is suitable to simulate the plastic deformations role during the surface separation phenomena observed in crack propagation problems
The details of the phase field model for rate-dependent ductile fracture are presented in the previous sections
Summary
It is widely accepted that the behavior of many materials, metals, is naturally time-dependent. Duda et al [16] formulated a phase field model of fracture in elastic-plastic solids under small strains assumption They demonstrated that the phase field approach coupled with rate-independent plasticity is suitable to simulate the plastic deformations role during the surface separation phenomena observed in crack propagation problems. Some modifications to develop phase field models for fracture in rate-independent ductile materials are proposed by Borden et al [21] These modifications include a cubic degradation function, a method for measuring of stress triaxiality as a driving force of initiation and propagation of cracks, and a correction to an error in the configuration update of an elasto-plastic return-mapping algorithm for large deformation models. A phase field model of rate-dependent ductile fracture is developed For this end, a phase field degradation function for the material stiffness and yield stress is introduced in a viscoplastic model. The ability of the proposed model in different loading rates is investigated using the obtained results, quantitatively and qualitatively
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