Martensitic transformation and stress-strain relations of shape-memory alloys

Z. K. Lu, G. J. Weng

Research output: Contribution to journalArticlepeer-review

110 Scopus citations


A micromechanical theory is developed to predict the stress-strain relations of shape-memory alloys (SMAs) at various temperatures above the martensitic-start temperature Ms. The theory is based upon the irreversible thermodynamic principle associated with the stress-induced martensitic transformation where the reduction in Gibbs' free energy is evaluated by considering the morphology of the product phase. The volume concentration, inclusion shape, and the normal and shear components of the transformation strain have all been incorporated. The influence of applied stress through the mechanical potential energy and the influence of temperature through the chemical free energy have also been established. Departing from the traditional constant-entropy assumption, a linear entropy-temperature relation is introduced to calculate the chemical free energy. The resulting chemical energy is non-linear, and is found to have strong influence on several basic properties of SMAs, including a non-linear stress-dependence for Ms and the austenitic-start temperature As. Despite the complexity of the microgeometry, the outcome is a set of explicit constitutive equations which provide a direct link between the applied stress and the evolution of the product phase, and between the stress and overall strain of the transforming system. Finally, the theory is applied to study the stress-strain relations of a Ti-49.8 at% Ni single crystal during the forward austenite-to-martensite transformation and the reversed martensite-to-austenite transformation. Apart from several noble qualitative features of the theory, the quantitative predictions are found to be in accord with experimental observations over a wide range of temperature.

Original languageEnglish (US)
Pages (from-to)1905-1921
Number of pages17
JournalJournal of the Mechanics and Physics of Solids
Issue number11-12
StatePublished - 1997

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


  • A. phase transformation
  • A. thermomechanical processes
  • B. constitutive behavior
  • C. energy method


Dive into the research topics of 'Martensitic transformation and stress-strain relations of shape-memory alloys'. Together they form a unique fingerprint.

Cite this