A unified thermomechanically-consistent framework for fatigue failure entropy

Abstract

This paper aims to develop a cyclic thermo-elastoplastic constitutive model to assess entropy generated due to uniaxial fatigue loading. The study is based on a finite element discretization for repetitive loading/unloading cycles to determine the internal dissipation and associated entropy generation. The primary objective of the study is to explore the internal friction effect as a non-destructive dissipative mechanism through the application of two distinct approaches: creep-like entropy for phenomenological yield stress relaxation and an extrapolated scheme from the thermoelastic constitution. The first facilitates a seamless transition for yield stress values, allowing them to pass smoothly from macro-plasticity to microplasticity, while incorporating a unified scheme of deformation-induced internal friction effects into constitutive equations as the material's internal state evolves. A simple self-consistent homogenization scheme is applied to establish a link between the plasticity scale submitted to cyclic loading. The latter was introduced for the first time via a rate-dependent creep-plasticity entropy to account for the non-damaging part of dissipation in both macro- and micro-plastic-dominated fatigue. This establishes a link between the mechanical degradation rate and the progression of the fatigue cycle. An additive decomposition of total entropy can individualize the inelastic entropy rate as an additional thermal part, representing a phenomenological creep-like relaxation, indicative of internal friction. Furthermore, the progression of the thermo-plastic friction effects is evaluated using the dual thermo-elastoplastic tangent modulus to provide the possibility of activating natural cooling, particularly when the mechanical loads are halted. The results of the finite element simulations show that the calculated Fracture Fatigue Entropy (FFE) values fall within a narrow range, confirming its constancy and usefulness as a material property.