Alagappan Ponnalagu

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.

We extend the methodology introduced for the initiation of damage within the context of a class of elastic solids to a class of viscoelastic solids (Alagappan et al. 2016 Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci. 472, 20160231. (doi:10.1098/rspa.2016.0231)). In a departure from studies on damage that consider the body to be homogeneous, with initiation of damage being decided by parameters that are based on a quantity such as the strain, that requires information concerning a special reference configuration, or the use of ad hoc parameters that have no physically meaningful origins, in this study we use a physically relevant parameter that is completely determined in the current deformed state of the body to predict the initiation of damage. Damage is initiated due to the inhomogeneity of the body wherein certain regions in the body are unable to withstand the stresses, strains, etc. The specific inhomogeneity that is considered is the variation of the density in the body. We consider damage within the context of the deformation of two representative viscoelastic solids, a generalization of a model proposed by Gent (1996 Rubber Chemistry and Technology 69, 59-61. (doi:10.5254/1.3538357)) for polymeric solids and a generalization of the Kelvin-Voigt model. We find that the criterion leads to results that are in keeping with the experiments of Gent & Lindley (1959 Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci. 249, 195-205. (doi:10.1098/rspa.1959.0016)).