Abstract :
A general thermomechanical theory of martensitic phase transformations (PT) in inelastic
materials is presented. The results are derived for small and large strains in the reference and
actual configurations. PT is treated as a thermomechanical process of growth of transformation
strain from the initial to the final value which is accompanied by a change in all materialʹs properties.
The theory is developed first of all for a homogeneously deformed material point (neighborhood)
undergoing the PT which can belong to a new nucleus or a moving interface. It is shown that a
standard thermodynamical approach cannot be directly applied. It can be applied after the averaging
of thermodynamical parameters, related to PT, over a PT duration. PT criterion is derived which
takes into account the plastic dissipation, temperature variation due to the PT and variation of
internal variables. It is shown that the temperature gradient does not contribute to PT criterion.
The twinning criterion is derived as a particular case of the PT criterion. Temperature variation in
the course of PT is determined with the help of the entropy balance equation under the assumption
that the process is adiabatic. After the averaging of the PT criterion over the transforming volume
the nucleation and interface propagation criteria, as well as conditions of nondissappearance of
nucleus are derived. Using the postulate of realizability [Levitas, V.I. (1992a) Post-bifurcation
behavior in finite elastoplasticity. Applications to strain localization and phase transitions, Universitiit
Hannover. Institut filr Baumechanik und Numerische Mechanik, IBNM-Bericht 92/5.
(1995a) The postulate of realizability: formulation and applications to post-bifurcation behavior
and phase transitions in elastoplastic materials. Part I and II. International Journal of Engineering
Science, 33, 921-971.], the extremum principle for the determination of all unknown parameters
(e.g. position, shape and orientation of nuclei, transformation strain and so on) is derived. It is
shown that for the PT in elastic materials the proposed approach gives alternative, but equivalent
to the principle of minimum of Gibbs energy formulation. Some aspects of the formulation of
boundary-value problem (BVP) are analyzed. Some possible ways of formulation of constitutive
relations for inelastic deformations in the course of the PT are discussed. It is obtained that the
dissipative threshold in the PT criterion is proportional to yield stress. The thermomechanical theory
developed is extended to the case with displacement discontinuities across an interface (noncoherence
and fracture). © 1997 Elsevier Science Ltd.
