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

An energy criterion is developed to calculate the stress-strain behavi or 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 surfac e energy of the parent and product phases, and the mechanical potentia l energy of the nonlinear system. The inclusions thus formed are assum ed to be thin spheroidal platelets, randomly oriented in the matrix, e ach possessing a normal and shear component of transformation strain. A micromechanical theory is established to determine the nonlinear pot ential energy and the change in Gibbs free energy of the two-phase sys tem al a given stage of transformation It is found that the stress-str ain 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 i nclusions, 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, charac teristically different from that of an ordinary ductile phase. The the ory 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. No r 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 expe rimental data for the stress-strain behavior of a TRIP steer and the c orresponding evolution of the martensite content further shows a reaso nable agreement.