Micromechanics of stress-induced martensitic phase transformations

Date

2007-12

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Publisher

Texas Tech University

Abstract

Martensitic phase transformation is a solid-solid transformation which represents the main deformation mechanism of shape memory alloys. The formed microstructure determines the mechanical and generally physical properties of the material and distribution of the local stresses and strains, which play an important role in a lot of advanced engineering processes including the thermomechanical treatment of steel. Knowledge of the influence of applied load and local stress fields, on microstructure evolution during phase transformation is very important for the understanding, simulation and improvement of the engineering processes, as well as for the development of new technologies and materials. Therefore, it is necessary to develop a continuum approach to martensite crystallography to take into account internal stresses, interface friction, and nonequilibrium evolution of all crystallographic parameters under multiaxial loading.

In this study, the universal (i.e. independent of the constitutive equations) thermodynamic driving force for coherent interface reorientation during first-order martensitic phase transformations in solids is derived for small and finite strains. Dissipation function for coupled interface (or multiple parallel interfaces) reorientation and propagation is derived for combined athermal and drag interface friction. The relation between the rates of single and multiple interface reorientation and propagation and the corresponding driving forces are derived using extremum principles of irreversible thermodynamics. They are used to derive complete system of equations for evolution of martensitic microstructure (consisting of austenite and a fine mixture of two martensitic variants) in a representative volume under complex thermomechanical loading. General relationships for a representative volume with moving interfaces under piece-wise homogeneous boundary conditions are derived. It was found that the driving force for interface reorientation appears when macroscopically homogeneous stress or strain are prescribed. The developed theory is applied to the numerical modeling of the evolution of martensitic microstructure under three-dimensional thermomechanical loading during cubic-tetragonal and tetragonal-orthorhombic phase transformations. A solution method for the phase transformation in inelastic materials is also proposed.

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