A Phase Field Model for Rate-Dependent Ductile Fracture

Abstract

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.

A simple and unified implementation of phase field and gradient damage models

“…(50) is the part of total energy dissipated by the plastic mechanisms, represented by the following rate form [42,46]:…”

“…Within the context of coupled models, which take into account that degra-et al [35], the phase field elastoplastic models by Duda et al [36] and Ambati et al [37], the crystal plasticity phase field coupled model of Padilla et al [38], the phase field based anisotropic damage model of Mozaffari et al [39] and the variational based, large deformation plasticity-phase field model by Miehe et al [40,41] and rate-dependent plasticity phase field model of Badnava et al [42] mostly concentrated on approximating the postpeak material behavior via a phase field methodology. Also in [43], de Borst et al studied several similar and different aspects of gradient enhanced damage-based approaches and the phase field framework and a discussion has made over the solution of the broadening of the damaged zone in the wake of the crack tip with these methods.…”

A Modified Phase-Field Damage Model for Metal Plasticity at Finite Strains: Numerical Development and Experimental Validation

“…In this section, an overview of the well-known stress integration algorithm for von Mises large strain plasticity is presented with the two new steps 11 and 12 which are necessary for solving the PFDM governing equation given in Equation (26). The value of elastic strain energy ψ E 0 is calculated at the integration point level as well as the coupling variable p. In the following equation, the complete algorithm is given to provide the implementation.…”

“…They used the S355 type of steel for validation purposes. Badnava et al [26] proposed a phase-field and ratedependent plasticity coupling by energy function. The influence of plastic strain energy on crack propagation was defined by a threshold variable.…”

Improving the Reliability of Mechanical Components That Have Failed in the Field Due to Repetitive Stress

“…In particular, intergranular fractures of austenitic stainless steels have been identified and discussed in a similar way to the failure of the helix dispenser [31]. A phase field visco-plastic model has also been proposed to describe the influence of the loading rate on the ductile fracture [32]. Cracks in the helix dispenser require the manufacturer to redesign the product to keep it functioning for its expected lifetime.…”