A phase field framework for dynamic adiabatic shear banding. (February 2020) - Xu, Yun; Ming, Pingbing; Chen, Jun
Highlights: We propose a general phase field formulation for dynamic adiabatic shear banding (ASBing). ASB surface energy is derived from shear banding energy density and the Griffith's regularized function. The phase field formulation reduces to a standard strain-gradient plasticity model by energy minimization. The phase-field and plasticity coupled constitutive model is developed. Numerical simulations demonstrate the capability of this predictive ASB phase field formulation. Abstract: We present a general variational formulation of phase field framework for dynamic adiabatic shear banding (ASBing). The ASB surface energy is derived from the Griffith's regularized ASB surface function, and the concept of shear banding energy density that characterized by the energy jump contour integral. We reveal that the ASB phase field formulation reduces to a standard strain-gradient plasticity model by energy minimization and ASB canonical analysis, which indicates that strain-gradient regularization for problems involving strain softening has been incorporated reasonably. The phase-field and plasticity coupled constitutive relations are developed within an atomistic potentials consistent hyperelastic-plasticity framework. The degraded volumetric strain energy governs the elastic responses, while the degraded deviatoric strain energy, as well as the ASB surface energy, accounts for the combined effects of shear localization, plasticity and fracture, which directly relates energy dissipation to the evolution of dynamic ASBs. Numerical simulations demonstrate the ability of this predictive ASB phase field framework in capturing discontinuous surfaces, and the removal of pathological mesh-dependence.