, Volume 51, Issue 5, pp 287-299

A thermomechanical description of materials with internal variables in the process of phase transitions

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Summary

A continuum mechanical description is presented for thermoplastic materials in the process of solid-solid phase transition. The material is assumed to be characterized by three different internal state variables: two internal variables which specify the crystallographic structural change during the plastic deformation, and a set of scalar internal variables which describes the extent of phase transition. Applying Edelen's decomposition theorem, the plastic quantities are determined from the dissipation potential, while the elastic quantities are specified by the internal energy. The explicit form of the flow rule and the evolutional equations for the internal variables are derived. The constitutive equations for the stress and the entropy are obtained in rate-type. It is shown that the continuous cooling transformation (C-C-T) diagram and the isothermal time-temperature-transformation (T-T-T) diagram could be derived from the theory developed here. The infinitesimal case is discussed in detail.

Übersicht

Eine kontinuumsmechanische Darstellung für thermoplastische Stoffe während eines Phasenübergangs wird gegeben. Das Material wird mit Hilfe von verschiedenen Zustandsvariablen charakterisiert: zwei Variablen, die kristallographische Änderungen während der plastischen Deformation angeben und ein Satz von Variablen, welche den Umfang des Phasenübergangs beschreiben. Stoffgleichungen werden hergeleitet. Außerdem wird gezeigt, daß C-C-T- und T-T-T-Diagramme aus der entwickelten Theorie hergeleitet werden könnten.