Analysis of size effects associated to the transformation strain in TRIP steels with strain gradient plasticity

The size dependent strengthening resulting from the transformation strain in Transformation Induced Plasticity (TRIP) steels is investigated using a two-dimensional embedded cell model of a simplified microstructure composed of small cylindrical metastable austenitic inclusions within a ferritic matrix. Earlier studies have shown that within the framework of classical plasticity or of the single length parameter Fleck–Hutchinson strain gradient plasticity theory, the transformation strain has no significant impact on the overall strengthening. The strengthening is essentially coming from the composite effect with a marked inclusion size effect resulting from the appearance during deformation of new boundaries constraining the plastic flow. The three parameters version of the Fleck–Hutchinson strain gradient plasticity theory is used here in order to better capture the effect of the plastic strain gradients resulting from the transformation strain. The three parameters theory incorporates separately the rotational and extensional gradients in the formulation, which leads to a significant influence of the shear component of the transformation strain, not captured by the single-parameter theory. When the size of the austenitic inclusions decreases, the overall strengthening increases due to a combined size dependent effect of the transformation strain and of the evolving composite structure. A parametric study is proposed and discussed in the light of experimental evidences giving indications on the optimization of the microstructure of TRIP-assisted multi-phase steels.