Coupled heat conduction and deformation in a viscoelastic composite cylinder



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This study analyzes the thermo-mechanical response of a composite cylinder made up of two layers of linear isotropic viscoelastic materials that belong to the class of non-Thermorheologically Simple Material. The effect of time-varying temperature field due to unsteady heat conduction phenomenon is analyzed on the short term and long term material response in terms of stress, strain and displacement fields. The material properties of the two layers of the composite cylinder at any given location and time are assumed to depend on the temperature at that location at that given instant of time. Sequentially coupled analyses of heat conduction and deformation of viscoelastic composite cylinder is carried out to obtain the overall response. The stress and strain field developed in the composite cylinder is evaluated as the discontinuity in hoop stress and radial strain at the interface of the two layers caused due to mismatch in material properties may lead to delamination if it exceeds critical value. Analytical solution for the stress, strain and displacement fields of the viscoelastic composite cylinder is developed from the corresponding solution of linear elasticity problem by using the Correspondence Principle. The analytical solution for determining the temperature dependent stress, strain and displacement fields is further developed by incorporating the temperature dependence on the material properties and modeling the material as non-TSM. To analyze more complex geometry with general loading and boundary conditions, Finite Element(FE) analysis of the composite cylinder is performed and the results of analytical and FE method are found to be in good agreement. Parametric studies are carried out to understand the effect of change in material parameters namely the Prony coefficients in the transient creep compliance, characteristic of creep time in transient creep compliance and the instantaneous elastic compliance, on the overall response of the composite cylinder. The effect of different temperature dependent functions of the material properties, namely linear temperature variation and quadratic polynomial variation on the overall material response is also analyzed. It is observed that the effect of change in elastic properties significantly increases the jump in hoop stress and radial strain. It is also observed that when the materials are highly dependent on temperature the jump in radial strain and hoop stress increases significantly. The radial displacement also increases by a significant amount in both the cases.