Phase-field modeling of coupled anisotropic plasticity-ductile fracture in rate-dependent solids

In this paper, an anisotropic ductile fracture is studied using a phase-field model. This model is on the basis of the energy principle in which a scalar field is added as a phase-field variable to determine the probability paths of cracks. Therefore, the system of equations, included for the displacement and phase field, is obtained and solved in a nonlinear finite element procedure through a user element subroutine in ABAQUS commercial software. The effect of anisotropy on cracks' paths for an anisotropic fracture is assessed according to the Hill criterion for ductile materials. Moreover, an implicit integration algorithm for an anisotropy model combined with a phase field is shown for the plane strain state. The proposed model can also be used for the combination of various constitutive models along with an anisotropy such as the anisotropic rate-dependent (visco-Hill) and the anisotropic rate-independent (elasto-Hill). Furthermore, the threshold parameter is introduced to examine the plastic deformation influence on cracks initiation and propagation in this study. Finally, the influence of the anisotropy on the responses of different specimens in various fracture processes is interrogated. The accuracy of the suggested model is demonstrated by juxtaposing the achieved and given experimental and numerical results in the way that it can be able to simulate the anisotropy effects on the gradual evolution of cracks from ductile to brittle.