Constitutive relations for viscoelastic materials under thermorelaxation transition

Abstract

A mathematical model of the mechanical behavior of viscoelastic bodies in a complex stress state under thermorelaxation transition is considered. The constructed constitutive equations allow one to describe the relations between the stress and strain tensors over a wide temperature interval including temperatures of relaxation transition. It is assumed that the characteristic relaxation times of the isotropic homogeneous polymer in a highly elastic state are much shorter than the characteristic times of external forces, which makes it possible to describe its behavior using the elastic model. In the glassy state, the behavior of the polymer is described in the framework of linear viscoelasticity. It is also assumed that the process of glass transition is accompanied by the formation of new intermolecular bonds, each being unstressed at the time of its appearance. It has been shown that the obtained constitutive relations of the hereditary type do not violate the second law of thermodynamics. A finite element procedure based on the stepwise integration has been developed and applied for solving quasi-stationary boundary value problems in mechanics of vitrifying polymers. The numerical technique is generalized to the case of taking into account the viscoelastic properties of the material in the glassy state. The validity of the physical and numerical models has been verified in the experiments, in which the residual stresses in the cylindrical EDT-10 epoxy resin specimens subject to non-uniform cooling are determined by the split ring method and polarization-optical method. It has been shown that the results of calculations agree well with the experimental data.