Effects of superimposed eigenstrains on the overall thermoelastic moduli of composites

Abstract

This study investigates the effects that an initial local eigenstrain field, when superimposed on the thermal eigenstrain field, has on the overall thermal expansion coefficients and heat capacities of thermoelastic composites. The study can also be seen as an investigation into how a local residual stress field affects these overall moduli, as initial eigenstrains are generally a source of residual stresses. The approach taken is thermodynamic. Expressions that include the superimposed eigenstrain field are developed for the overall moduli within the framework of small strain thermoelasticity with temperature dependent materials. These expressions, which are written in terms of the concentration tensors and residual fields (stress and strain fields given rise to by the eigenstrains under zero overall stress and strain, respectively), contain correction terms that are absent in the expressions developed within linear thermoelasticity. Taking into account the temperature dependence of the constituent moduli is shown to be essential to capture the effects of the superimposed eigenstrain field. A Ti-6Al-4V/ZrO2 composite is investigated for which the correction terms are found to be negligible for the heat capacities but significant for the thermal expansion coefficients. This suggests that, for applications with large temperature changes, using the linear-thermoelasticity-based expressions can affect the accuracy of the estimates of the overall moduli, and therefore the accuracy of thermostructural analyses of composite structures. The proposed expressions can be of use to estimate the overall thermoelastic moduli in contexts in which the strains remain small, temperature changes are large, and superimposed eigenstrains may be present.

Coupled heat equation in thermoelasticity with temperature dependent moduli

“…The Helmholtz potential per unit reference volume, expressed in terms of its natural variables, is given by [44] f…”

“…This amounts to assuming that the elasticity tensor and, as to be expected from a thermoelasticity model, the thermal strain tensor are temperature dependent. This assumption fixes the form of the thermodynamic potentials as functions of temperature and either stress or strain [44], and therefore that of the remaining thermoelastic moduli, i.e., the heat capacities, the coefficient of thermal expansion (CTE) tensor, and the stress-temperature tensor.…”