AN ENERGY CRITERION FOR THE STRESS-INDUCED MARTENSITIC-TRANSFORMATION IN A DUCTILE SYSTEM

An energy criterion is developed to calculate the stress-strain behavior of a ductile system involving martensitic transformation under the application of stress. The martensitic inclusions are taken to develop from the ductile austenitic matrix due to the reduction in the Gibbs free energy, which consists of the chemical free energy and the surface energy of the parent and product phases, and the mechanical potential energy of the nonlinear system. The inclusions thus formed are assumed to be thin spheroidal platelets, randomly oriented in the matrix, each possessing a normal and shear component of transformation strain. A micromechanical theory is established to determine the nonlinear potential energy and the change in Gibbs free energy of the two-phase system al a given stage of transformation It is found that the stress-strain behavior of the metastable system is the outcome of two competing effects, one from the ductility due to the plastic deformation of the ductile matrix and the phase transformation strain of the martensite inclusions, and the other from the stiffness due to the purely elastic response of the transformed martensites. While the ductility prevails in the early stage of deformation the stiffening effect later becomes more dominant with increasing amount of transformation. The resulting stress-strain curve then exhibits the familiar sigmoidal shape, characteristically different from that of an ordinary ductile phase. The theory does not assume any a priori law for the evolving Volume fraction of the martensite; it is calculated incrementally based on the change of Gibbs free energy between the current and the transformed state. Nor does the theory assume any a priori flow rule for the transformation strains, which are calculated strictly from the lattice parameters of the parent and transformed phase. Comparison with some available experimental data for the stress-strain behavior of a TRIP steer and the corresponding evolution of the martensite content further shows a reasonable agreement.