Simulation of temperature history-dependent phenomena of glass-forming materials based on thermodynamics with internal state variables

Abstract

In ref. [1], a profound ansatz for modelling the various phenomena associated with the glass-transition was presented. It extends classical theories, such as the concept of fictive temperature or order parameters, for example, in two ways. Firstly, temperature excitations as well as mechanical loadings are accounted for in a single consistent approach. Secondly, it is not formulated in the θ– p– V space, but rather in the θ – T ̲ ̲ – E ̲ ̲ space, taking the tensor character of stress T ̲ ̲ and strain E ̲ ̲ into account. Hence, it is a three-dimensional theory where the basic thermodynamic potential, the Gibbs free energy, depends on the stress tensor, the temperature and a set of internal variables. In the current article, expressions for the enthalpy, the entropy, the thermal expansion and the specific heat are derived. The specific heat and the thermal expansion behaviour are looked at for various temperature excitations. It is shown, that the results are in accord with experimental observations in literature.