A constitutive hardening model of coupled plastic deformation and martensitic transformation in steels

• The constitutive model has been proposed for the coupled monotonic and cyclic plastic deformation and phase transformation.
• The yield and transformation conditions are assumed to depend on back stresses evolving during plastic deformation and transformation processes.
• The hardening effect induced by martensite growth was accounted for by introducing the coupled back stress nonlinear component.

The article presents a constitutive model aimed at simulation of martensitic transformation induced by stress and plastic strain coupled with the hardening process in austenitic steels. The yield and transformation conditions are assumed to depend on back stresses evolving during plastic deformation and transformation processes. Their interaction affects essentially the hardening rate of a material. The thermodynamic background is reviewed and applied with both free energy and dissipation functions used in derivation of the rules of flow, hardening and transformation kinetics. The constitutive model parameters are specified and next the simulation of strain hardening for monotonic and cyclic loading is presented for the cases of uniaxial tension-compression and for combined tension-torsion deformation programs. The effect of strain ratcheting is analyzed for the cases of uniaxial and combined loading. It is shown that the transformation process is shown to essentially reduce the ratcheting strain.