Constitutive modeling and finite element methods for TRIP steels

A constitutive model that describes the mechanical behavior of steels exhibiting “TRansformation Induced Plasticity” (TRIP) during martensitic transformation is presented. Multiphase TRIP steels are considered as composite materials with a ferritic matrix containing bainite and retained austenite, which gradually transforms into martensite. The effective properties and overall behavior of TRIP steels are determined by using homogenization techniques for nonlinear composites. A methodology for the numerical integration of the resulting elastoplastic constitutive equations in the context of the finite element method is developed and the constitutive model is implemented in a general-purpose finite element program. The model is calibrated by using experimental data of uniaxial tension tests in TRIP steels. The problem of necking of a bar in uniaxial tension is studied in detail. The constitutive model is used also for the calculation of “forming limit diagrams” for sheets made of TRIP steels; it is found that the TRIP phenomenon increases the strain at which local necking results from a gradual localization of the strains at an initial thickness imperfection in the sheet.