Micromechanical modelling of stress-assisted martensitic transformation

Abstract

A computational micromechanics study of stress-assisted martensitic transformation using finite elements is carried out within a thermomechanical framework including the aspect of plastic deformation. The phase transformation is treated by a stress-free transformation tensor corresponding to a certain habit plane variant involving a shape change resulting from shear and dilatational deformations which are eigenstrains within the emerging martensitic phase. General plane strain and axisymmetric analyses are carried out introducing different micromechanical models with appropriate boundary conditions required for the microfield approach. The introduced models are compared with a micromechanical model developed by Tvergaard in the viewpoint of thermodynamic aspects concerning the formation of martensite. The representative volume elements are specified with respect to the Schmid factor for the transformation shear corresponding to an average crystallographic orientation of a grain. We examine elastic-plastic deformations and distribution of transformation-induced microstress fields in both the parent and the emerging product phase due to accommodation of the transformation shape change. Analytical results for the linear elastic case based upon the Eshelby approach will be compared with numerical results. The plastic behavior of austenitic and martensitic microconstituents is described in the context of J2-flow theory with isotropic hardening. The thermomechanical framework is based on an explicit form of a potential suggesting the form of Gibbs free energy, from which transformation conditions on the mesodomain-, interface- and nucleation-site level are derived. The arrangement of martensitic microregions transforming in a stress field is studied considering the thermomechanical coupling of orientation and accommodation effects.

Crystallographically based model for transformation-induced plasticity in multiphase carbon steels

“…(23) Observe that the volume fraction of austenite ξ A is not used as an independent state variable since it is related to ξ via (3) 3 . Combining (18), (21), and (23) with (17) leads to the following expression for the dissipation:…”

“…In the past decades, various constitutive models have been proposed to elucidate the complex interactive mechanisms that occur in steels assisted by transformation-induced plasticity; see e.g., [4,10,11,16,21,22,26]. In most cases, the models are developed within a small-strain, isotropic elastoplasticity framework.…”

Analysis of banded microstructures in multiphase steels assisted by transformation-induced plasticity

“…It further increases the ductility of the steel, due to plastic deformations induced in the ferritic and bainitic phases by a volumetric expansion of the transforming austenitic phase. These two microstructural mechanisms essentially characterize the TRIP-effect, and therefore have been taken into account in various macroscopic and microscopic continuum models developed during the last four decades [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Computer Simulation of Martensitic Transformation Under Stress

“…Several investigators have contributed a lot in this area using different methods such as molecular dynamics [3], self consistent schemes [4] and finite elements (FEM) [5-91. Whereas molecular dynamics simulations are carried out on the atomic level, the simulations by means of FEM have been done on mainly two levels: the mesolevel, where the behaviour of a set of grains representative for the whole sample is described [6,7], and the microlevel, where the grain behaviour is modeled [5,8,9].…”

“…[6] and Simonsson [7] focussed on the description by FE of the behaviour of a set of grains considering 24 possible orientations in the grain (either in 2D [6] or in 3D [7]) and elastoplastic behaviour of the phases. The transformation strain is a shear in the habit plane and a volumic variation normal to the habit plane.…”