# Constitutive modelling of mechanically induced martensitic transformations: Prediction of transformation surfaces

## TL;DR

This paper applies a physically-based constitutive model to predict transformation surfaces in martensitic transformations, demonstrating good agreement with experimental data and unifying stress-assisted and strain-induced regimes.

## Contribution

It introduces a thermodynamically consistent, physically-based model for mechanically induced martensitic transformations that effectively predicts transformation loci and accounts for different transformation regimes.

## Key findings

- Accurately predicts transformation loci in stainless steel
- Validates the energy-based criterion for both regimes
- Demonstrates model's agreement with experimental data

## 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 energy-based 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.