Fatigue in a class of viscoelastic solids

Abstract

We study fatigue (weakness induced by cyclic loading) in a viscoelastic body described by a generalization of the Kelvin-Voigt constitutive relation, employing a novel damage initiation criterion developed by Alagappan et al. [13-15]. The main premise is that damage is a consequence of the inhomogeneity of the material which leads to some locations in the body being naturally weaker, say for instance due to the density being lower and the material moduli depending on the density and decreasing with density, leading ultimately to failure at that location. This approach has been used successfully for polymers, elastomers and concrete subject to monotonic loading. In this study, we consider the initiation of damage due to cyclic loading, which is referred to as fatigue. Since the body under consideration is viscoelastic, it dissipates energy in each cycle which leads to an increase in temperature. We shall not take the effect of the temperature of the material moduli, instead we assume that the material moduli depend on the density and the rate of dissipation. In the case of our specific study the shear modulus of the material depends on the density and dissipation (in the case of the constitutive relation considered the shear rate), and the structure of the shear modulus is such that it decreases with decrease in density and decreases with increase in dissipation (tantamount to the assumption that it decreases with increasing shear rate for the constitutive relation under consideration) leading to damage of the material. We find that after sufficient number of cycles, the body under consideration undergoes significant loss in load carrying capacity due to fatigue.