Martensitic Phase Transformations in Inelastic Materials:
        Thermomechanical Theory, Some Analytical and
   Numerical Solutions And Interpretations of Experiments

                             by

                     Valery I. Levitas

        AEB 340, 3:20pm Wednesday, October 30, 1996

                          Abstract


A general thermomechanical theory of martensitic phase
transitions (PT) in inelastic materials is presented. 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 material's
properties.

Nucleation and interface propagation criteria are derived
which take into account the plastic dissipation, temperature
variation due to the PT and variation of internal variables.
Using the postulate of realizability (Levitas, 1992a,
1995a), 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.

The thermomechanical theory developed is extended to the
case with displacement discontinuities across an interface
(noncoherence and fracture).

Three boundary--value problems are solved analytically: PT
in a thin layer in a rigid--plastic half--space under the
action of applied pressure and shear stresses; PT under
compression and shear of materials in Bridgman anvils; the
appearance of the spherical nucleus in an infinite
elastoplastic sphere under applied pressure (without and
with fracture on a interface) with application to
temperature--induced PT in steel and pressure--induced PT
graphite--diamond.

The following problems are solved numerically: phase
transition in a spherical particle embedded in cylindrical
matrix (for coherent and noncoherent interface as well as
interface with fracture); propagation of coherent and
noncoherent interface in cylindrical sample; nucleation at
shear-band intersection. A number of experimental results
are explained, and some of the interpretations are
completely unexpected.  Some methods to control of PT by
means of the purposeful control of stress--strain fields are
suggested.


Requests for preprints and reprints to: cherk@math.utah.edu
This source can be found at http://www.math.utah.edu/research/

Valery Levitas
University of Hannover,
Institute for Structural and Computational Mechanics,
Appelstrasse 9A, 30167 Hannover, Germany