Three-Dimensional Computational-Cell Modeling of the Micromechanics of the Martensitic Transformation in Transformation-Induced-Plasticity–Assisted Multiphase Steels TIM VAN ROMPAEY, FREDERIC LANI, PASCAL J. JACQUES, BART BLANPAIN, PATRICK WOLLANTS, and THOMAS PARDOEN A three-dimensional finite-element microstructural cell model involving an inclusion of retained austen- ite embedded within a ferrite grain, which is surrounded by a homogeneous matrix representing the behav- ior of a transformation-induced-plasticity (TRIP)–assisted multiphase steel, was developed in order to address the micromechanics of the martensitic transformation in small isolated austenite grains. The trans- formation of a single martensite plate is simulated after various amounts of prior plastic deformation under different in-plane loading conditions. The values of the mechanical driving force and of the elas- tic and plastic accommodation energies associated with the transformation are calculated as a function of the externally applied loading conditions. The mechanical driving force and the total accommodation energy are of the same order of magnitude. The mechanical driving force depends upon the stress state and is the highest for plane-strain conditions. The total accommodation energy is almost independent of the stress state. It is affected by the amount of plastic straining prior to transformation and is very much dependent on the level of the shear component of the transformation strain. The results of this study pro- vide guidelines for the development of realistic stress-state-dependent transformation evolution laws for TRIP-assisted multiphase steels. I. INTRODUCTION TRANSFORMATION-INDUCED-PLASTICITY (TRIP)–assisted multiphase steels show remarkable mechan- ical properties of formability and crashworthiness, resulting from the occurrence of concurrent modes of plastic defor- mation: essentially, dislocation strengthening and mechani- cally induced martensitic transformation. There is an urgent need, especially coming from the automotive industry, to develop constitutive models that properly account for the couplings between phase transformation, loading conditions, and evolution of the material properties, while remaining suf- ficiently simple to allow tractable implementation and use with finite-element codes. Such models are essential for both the optimization of forming operations and the control of the properties after forming and bake-hardening. Since the martensitic transformation is associated with con- siderable shape and volume changes, the local-stress state varies drastically during the transformation both inside the newly formed martensitic inclusion and in the surrounding austenite and ferrite phases. These changes of morphology and strain energy strongly affect the transformation evolution. The prod- uct of the transformation strain by the local-stress inside the retained austenite corresponds to a mechanical driving force, whereas the accommodation of the transformation strain in the surrounding material opposes the transformation. Mechanical considerations must, thus, be included in the thermodynamic description of the martensitic transformation. The goal of this work is to provide a better understanding and quantify more precisely these mechanical contributions to the transformation kinetics in the case of multiphase TRIP steels. The starting point of this study is the local thermodynamic condition for the growth of a martensitic region, proposed by Fischer and Reisner. [1] This transformation criterion is an energy balance, which compares driving and dragging forces (or energies). The transformation is initiated when the sum of the chemical and the mechanical driving forces exceeds the transformation barrier. The transformation barrier or drag- ging force results from the energy consumed by interfacial friction and elastic and plastic accommodation. The interfa- cial friction is the energy barrier associated with the atomic movement required to form the new crystal lattice. This bar- rier can be evaluated experimentally or from ab-initio com- putations. The elastic and plastic accommodation energies result from the transformation strain and are stored or dissi- pated in the material surrounding the martensite. Even though analytic solutions exist for specific simplified situations, i.e., a two-phase structure with ellipsoidal inclusions in an infi- nite elastic matrix (as proposed by Eshelby [2] or Mori and Tanaka [3] ), the evaluation of the accommodation-energy terms for realistic geometry and realistic flow properties requires advanced numerical simulations. METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 37A, JANUARY 2006—99 TIM VAN ROMPAEY, formerly Doctoral Researcher, with the Department of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium, is Project Leader, Umicore Research, B-2250 Olen, Belgium. FREDERIC LANI, Doctoral Researcher, formerly with the Department of Materials Science and Processes, Université Catholique de Louvain, IMAP, B-1348 Louvain-la-Neuve, Belgium, is Group Leader, Centre of Excellence in Aeronautical Research, CENAERO, Gosselies, Belgium. BART BLANPAIN, Professor, and PATRICK WOLLANTS, Professor and Head of Department, are with the Department of Metallurgy and Materials Engineering, Katholieke Uni- versiteit Leuven, PASCAL J. JACQUES, Qualified Researcher of FNRS, and THOMAS PARDOEN, Professor, are with the Department of Materials Science and Processes, Université Catholique de Louvain, IMAP, Place Sainte Barbe 2, B-1348 Louvain-la-Neuve, Belgium. Contact e-mail: pardoen@imap.ucl.ac.be Manuscript submitted February 24, 2005.