Constitutive modelling of mechanically induced martensitic transformations

Abstract

Purpose: The purpose of this work is to apply a recently proposed constitutive model for mechanically induced martensitic transformations to the prediction of transformation loci. Additionally, this study aims to elucidate if a stress-assisted criterion can account for transformations in the so-called strain-induced regime.Design/methodology/approach: The model is derived by generalising the stress-based criterion of Patel and Cohen (1953), relying on lattice information obtained using the Phenomenological Theory of Martensite Crystallography. Transformation multipliers (cf. plastic multipliers) are introduced, from which the martensite volume fraction evolution ensues. The associated transformation functions provide a variant selection mechanism. Austenite plasticity follows a classical single crystal formulation, to account for transformations in the strain-induced regime. The resulting model is incorporated into a fully-implicit RVE-based computational homogenisation finite element code.Findings: Results show good agreement with experimental data for a meta-stable austenitic stainless steel. In particular, the transformation locus is well reproduced, even in a material with considerable slip plasticity at the martensite onset, corroborating the hypothesis that an energybased criterion can account for transformations in both stress-assisted and strain-induced regimes.Originality/value: A recently developed constitutive model for mechanically induced martensitic transformations is further assessed and validated. Its formulation is fundamentally based on a physical metallurgical mechanism and derived in a thermodynamically consistent way, inheriting a consistent mechanical dissipation. This model draws on a reduced number of phenomenological elements and is a step towards the fully predictive modelling of materials that exhibit such phenomena.

Consistent modeling of the coupling between crystallographic slip and martensitic phase transformation for mechanically induced loadings

“…The lattice parameters are those of an ASTM A-564 alloy (also known as Sandvik Nanoflex) -a A = 3.59690 Å and a M = 2.87351 Å ‡ ‡ . 53 This metastable austenitic stainless steel is extensively documented in References 38,76,77. In addition, the critical mechanical energy is set to ΔG mech = 30 MPa.…”

“…Moreover, martensitic transformation is allowed — FCC‐to‐BCC, where the elasticity properties of the martensitic phase are considered equal to those of the austenitic phase †† . The lattice parameters are those of an ASTM A‐564 alloy (also known as Sandvik Nanoflex) — and ‡‡ 53 . This metastable austenitic stainless steel is extensively documented in References 38,76,77.…”

“…plastic multipliers) and the associated transformation functions provide the active transformation systems selection, under isothermal conditions and within the temperature range defined by the martensite start temperature () and by the temperature at which austenite and martensite chemical free energies are identical (). An initial version of the model proposed here can be found in de Bortoli et al 53 The unified constitutive model is implemented in LINKS, an in‐house finite element program entirely written in FORTRAN that stands for Large Strain Implicit Nonlinear Analysis of Solids Linking Scales . It allows the resolution of single scale (macro and micro analysis) and coupled problems ().…”

Evolution of face-centered-cubic polycrystalline plastic anisotropy under biaxial loading by crystal plasticity finite element method

“…In recent years, with the development of computer technology, the finite element methods have been gradually used to deal with complex issues (Karimzadeh et al, 2014;Wang et al, 2018;Xu et al, 2019;Zhou et al, 2019), especially the multi-scale problems (Karimzadeh et al, 2014;Wang et al, 2018) and intricacy structure materials (Xu et al, 2019;Zhou et al, 2019). Crystal Plasticity Finite Element Method (CPFEM) has been proposed and used to simulate the responses of material's microstructures (de Bortoli et al, 2018;Prueger et al, 2018) and various mechanical behaviors because of the evolution of the deformation texture (Sheikh et al, 2016;Zhang et al, 2014). The microscopic factors of the plastic deformation, e.g.…”