Temperature-induced phase transformation in a shape memory alloy: Phase diagram based kinetics approach

A. Bekker, L Catherine Brinson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

117 Scopus citations


In this article we develop a general framework to model the one dimensional thermomechanical behavior of shape memory alloys (SMAs) based on phase diagram kinetics and a phenomenological constitutive law with martensite fraction as an internal variable. As part of this framework, we construct a consistent mathematical description for martensite fraction evolution to be used in conjunction with an experimentally defined phase diagram; the kinetics formalism is illustrated with examples of isostress and isothermal cycling. As an application, we consider the thermo-induced martensite transformation of a ID prestressed SMA polycrystalline body which proceeds by migration of the austenite-martensite two-phase zone from the cooled boundary, converting the SMA body from an austenite (A) to a detwinned martensite (M) state. The mathematical model for the two-phase zone migration is based on the nonstationary equation of energy balance and the quasistationary approximation for the linear momentum equation and utilizes a quasistatic kinetic law, a macroscale constitutive law and an incompressibility constraint. To close the formulated system of equations, the internal energy of an A/M mixture in the two-phase zone is heuristically derived. The mixed initial-boundary value problem is then solved numerically and compared to analytical results for a simplified model. The results stress the significance of the stress dependency in the kinetic law and the transformation heat to the progress of transformation.

Original languageEnglish (US)
Pages (from-to)949-988
Number of pages40
JournalJournal of the Mechanics and Physics of Solids
Issue number6
StatePublished - Jan 1 1997


  • A. phase transformation
  • A. thermomechanical processes
  • B. constitutive behavior
  • C. finite differences
  • Principles
  • Shape memory alloy

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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