Thermodynamic formulation of a unified multi-mechanism continuum viscoplastic damage model with application to high-Cr steels

Abstract

In this paper, a unified multi-mechanism continuum viscoplastic damage model is proposed to simulate the thermomechanical behavior of high-Cr steels at elevated temperatures. To represent the effects of material degradation under external loads, a total damage tensor is incorporated, which is composed of the low-cycle fatigue damage, the creep damage and the ductile damage. Within the small strain framework, the model is established through a thermodynamically consistent approach. First, some kinematic assumptions are proposed and the concept of effective stress is adopted. Then, based on a state potential with proper constitutive form, the constitutive equations can be derived from the second law of thermodynamics. By further considering the postulate of maximum dissipation, a Lagrangian functional is constructed through a regularization scheme. The stationary points of the Lagrangian functional yield the evolution equations of the dissipative variables. For the isotropic damage case, the damage tensor can be represented by a scalar damage variable and the constitutive evolution equations in the model can be simplified. To be prepared for practical applications, numerical integration algorithms are proposed to solve the constitutive evolution equations, and the material parameters in the model are identified based on the experimental data. To demonstrate the efficiency of the current model, it is applied to simulate the thermomechanical response of high-Cr steels under different loading conditions. The simulation results can fit the experimental data at a quantitative level and the damage mechanisms under the different loading conditions can be revealed. Besides that, the model is further modified to take into account the microcracks closure effect of the ductile damage. The current model would be helpful for the safety design and lifetime evaluation of high-Cr steel components in practical applications.