A Mathematical Model for Internal Friction and Local Fatigue Damage Based on Populations of Yielding Microelements

Abstract

A mathematical model for internal friction and fatigue damage based on populations of yielding microelements is described. Using two parameters, the model accounts for amplitude dependence of material damping. For low excitation levels the Zener theory of thermoelasticity is reproduced. The significance of this new damping model is that fatigue damage due to local accumulations of microplastic deformation is quantified. The entropy production is defined by expressing the second law of thermodynamics for irreversible processes as an equality, and quantifying local accumulations of microplastic strain energy as the source of irreversibility. A critical entropy threshold is defined in terms of the local microplastic strain energy density of local failure. The hypothesis is offered that local fatigue damage leading to crack nucleation occurs by exceeding the critical entropy threshold.