A non-isothermal thermodynamically consistent phase field model for damage, fracture and fatigue evolutions in elasto-plastic materials

This paper presents a general thermodynamically consistent non-isothermal phase field framework to model effects of damage, fracture and fatigue evolutions in elasto-plastic materials under the hypothesis of small strains. The proposed methodology is obtained from the principle of virtual power, energy balance and second law of thermodynamics in the form of a generalized Clausius-Duhem inequality for entropy. Aspects of the energy degradation functions are thoroughly investigated for an isotropic elasto-plastic material with viscous dissipation and constant specific heat. A new combined degradation function is proposed to degrade both elastic and plastic energy densities as an alternative to the classical degradation functions. Our conceptual framework leads to thermodynamically consistent models that may include contributions not usually considered in the literature, as temperature and inertia effects as well as time-rate dependent processes. The governing nonlinear transient equations obtained are solved adopting a semi-implicit time integration scheme combined with the classical Newton-Raphson iterative procedure. Results for an I-shaped specimen made of 7075-T7351 aluminum alloy under different conditions are presented. The proposed model is able to reproduce qualitative and quantitatively the ductile fracture and the fatigue phenomena. In particular for fatigue, both the S-N experimental data and the Paris crack growth curve over cycles are recovered. In addition, the cycle jump strategy reduces four times the CPU time for fatigue simulations. (C) 2020 Elsevier B.V. All rights reserved.