Finite Element Simulation of Martensitic Transformation in Single-Crystal TRIP Steel Based on Crystal Plasticity Theory with Cellular Automata Approach

Due to the strain-induced martensitic transformation (SIMT), the strength, ductility and toughness of TRIP steel are enhanced. The deformation behavior of TRIP steel is mainly yielded on this SIMT behavior and the deformation behaviors of the austenitic and martensitic phases. TRIP steel possesses such favorable mechanical properties due to the appropriate combination of these behaviors. However, the SIMT and deformation behavior of each phase strongly depend on the temperature and strain rate imposed, the excellent mechanical properties are realized under quite restricted circumstances. Here, the constitutive equation for single crystal TRIP steel including transformation strain on the each variant system is formulated based on continuum crystal plasticity theory. Then, the deformation behavior with patterning process of martensitic phase is simulated under plane strain condition by introducing formulated constitutive equation to FEM with cellular automata approach. Introduction Recently, there are a lot of research works based on a continuum crystal plasticity theory (CCTP) [1] which can describe the plastic deformation in crystal lattice by a slip on a certain slip system, and its importance is begun to recognize. For the TRIP steel with strain-induced martensitic transformation (SIMT), martensite is transformed obeying the certain relationships of the crystallographic orientation between the austenitic parent phase ( phase) and the martensitic product phase ( phases) in the length scale of crystal as can be seen in the past micrographic observations [2]. Therefore, to evaluate the SIMT and deformation behavior of single-crystal TRIP steel, the CCTP becomes quite important and martensitic transformation (MT) theory in length scale of crystal [2] must be included. After the frontier research work by Tokuda et al. [3] who proposed the constitutive equation based on the concept of CCTP for shape memory alloy (SMA), there are the experimental research [4] and computational analyses by FEM [5] on the transformation texture due to the interaction between MT and texture in the parent phase. It can be easily guess that the complex transformation texture forms by the combination of crystallographic orientation in martensite formed, and the rotation of orientation in the parent phase and martensite during the plastic deformation. Its prediction and the discussions are quite indispensable in length scale of crystal. On the other hand, Cherkaoui et al. [6] derived the macroscopic constitutive equation for the single-crystal TRIP steel by the formulations of free energy and dissipative function including the transformation strain on the multi-variant systems. Ganghoffer and Simonsson [7] simulated that the MT process in a rectangular austenitic material under plane stress tension by infinitesimal elastoplastic FEM with periodic boundary condition. In FE analyses for SMA [5], the constitutive equations are derived by the analogy of CCTP; however, the plastic deformation by slip is not Key Engineering Materials Online: 2004-10-15 ISSN: 1662-9795, Vols. 274-276, pp 679-684 doi:10.4028/www.scientific. net/KEM.274-276.679 © 2004 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications Ltd, www.scientific. net. (Semanticscholar.org-13/03/20,17:14:11) included. On the above-mentioned research works about TRIP steel [6],[7], the concepts of CCTP including the plastic deformation is introduced. However, there are the assumption of infinitesimal deformation, the lack of the decomposition of deformation gradient and the other important formulations. Here, to investigate the coupling effect between a slip deformation on a slip plane and a transformation strain on a habit plane about the SIMT and deformation behavior of TRIP steel, the constitutive equation with transformation strain for a single-crystal TRIP steel is derived based on an conventional CCTP [1]. Then, simulation method for the SIMT and deformation behavior of single-crystal TRIP steel is proposed by the combination of FEM along with derived constitutive model and cellular automata approach with the transformation criterion as local rule proposed by Kitajima et al. [5]. Finally, the SIMT and deformation behavior of single-crystal TRIP steel under plane strain condition is simulated for the case of symmetrical periodic boundary condition. Basic formulations Constitutive equation for single-crystal TRIP steel. Let consider a single-crystal undergoing an elasto-plastic deformation. Including the deformation due to MT on a variant system into the concept of the conventional CCTP [1] as shown in Fig. 1, the total deformation gradient can be split into the deformation gradient due to stretching and rotation of crystal lattice , slip deformation on a slip plane and MT on a habit plane as follows [8]: . In Fig. 1, is unit vector in direction to slip deformation, is normal vector on the slip plane, is shear strain on the slip plane and index means the th slip system. On the other hand, is unit vector in direction to deformation due to MT, is normal vector on a habit plane and is transformation strain. Transformation strain means shear and volumetric strains due to differences of crystal structure between and phases [2]. Index , denotes the th variant system composed of the combination in plane and direction which MT occurs. = 12 if crystal orientation between and obeys Nishiyama’s relationship and = 24 if crystal orientation between and obeys Kurdjmov-Sachs’ relationship [2]. , , and can be expressed after deformation as follows: (1) Fig 1 Decomposition of the deformation gradient 680 Advances in Engineering Plasticity and Its Applications