3D Phase Field Modeling of Martensitic Microstructure Evolution in Steels

Abstract

Complex martensitic microstructure evolution in steels generates enormous curiosity among the materials scientists and especially among the Phase Field (PF) modeling enthusiasts. In the present work PF Microelasticity theory proposed by A.G. Khachaturyan coupled with plasticity is applied for modeling the Martensitic Transformation (MT) by using Finite Element Method (FEM). PF simulations in 3D are performed by considering different cases of MT occurring in a clamped system, i.e. simulation domain with fixed boundaries, of (a) pure elastic material with dilatation (b) pure elastic material without dilatation (c) elastic perfectly plastic material with dilatation having (i) isotropic as well as (ii) anisotropic elastic properties. As input data for the simulations the thermodynamic parameters corresponding to Fe - 0.3% C alloy as well as the physical parameters corresponding to steels acquired from experimental results are considered. The results indicate that elastic strain energy, dilatation and plasticity affect MT whereas anisotropy affects the microstructure.

Reverse phase transformation of martensite to austenite in stainless steels: a 3D phase-field study

“…A brief overview of the phase-field model used here to simulate the athermal martensitic transformation as well as the reversion is presented below, detailed derivations can be found in Refs. [34,43].…”

“…where V m is the molar volume and the coefficients A, B, C are expressed in terms of Gibbs energy barrier and the driving force [34]. From a crystallographical point of view, martensite can be formed in 24 different crystallographic variants, which can be grouped into three main groups known as Bain groups [49][50][51].…”

“…where ǫ 3 is a compressive transformation strain, ǫ 1 is a tensile transformation strain and are defined based on the lattice constants of austenite (a F CC ) and martensite (a BCC ) [34]. Thus the martensite (Bain) variants-1, 2 and 3 are governed by ǫ 00 ij (1), ǫ 00 ij (2) and ǫ 00 ij (3) respectively.…”

“…The phase-field method (PFM) [26,27] has been successfully used to study microstructure evolution during martensitic transformations . Elastoplastic phase-field simulations have shown the microstructure evolution during the athermal [29,34,36,39], stress-assisted [41,43] and strain-induced martensite [45] formation in steels. However, phase-field methods have so far not been used to study the microstructure evolution during martensite reversion.…”

Ab initio calculations of the lattice parameter and elastic stiffness coefficients of bcc Fe with solutes

“…Changes in lattice parameters and elastic stiffness coefficients can directly estimate solid-solution 20 strengthening parameters [23,24,3,19] and changes in ductility [25]. Mesoscale phase-field [26] and crystal plasticity models [27] of multi-phase steels are sensitive to the input lattice parameters and elastic stiffness coefficients of the different phases, and DFT data on the solute-dependence of these properties can enhance the predictive capabilities of these models [28]. 25 In the present article, we consider the effects of the substitutional solutes Al, B, Cu, Mn, and Si, and the interstitial solutes C, and N on the lattice pa-rameter and elastic stiffness coefficients of bcc Fe.…”