Acta mater. 49 (2001) 2309–2320 www.elsevier.com/locate/actamat THREE-DIMENSIONAL PHASE FIELD MODEL OF LOW- SYMMETRY MARTENSITIC TRANSFORMATION IN POLYCRYSTAL: SIMULATION OF z' 2 MARTENSITE IN AuCd ALLOYS Y. M. JIN 1 , A. ARTEMEV 2 and A. G. KHACHATURYAN 1 † 1 Department of Ceramic and Materials Engineering, Rutgers University, 607 Taylor Road, Piscataway, NJ 08854, USA and 2 Department of Mechanical and Aerospace Engineering, Carleton University, 1125 Colonel By Dr., Ottawa, Ontario, K1S 5B6 Canada ( Received 27 October 2000; received in revised form 21 February 2001; accepted 25 February 2001 ) Abstract—A three-dimensional phase field model of the martensitic transformation that produces a low symmetry phase in polycrystals is developed. The transformation-induced strain mostly responsible for the specific features of the martensitic transformation is explicitly taken into account. The high computational efficiency of the model turns out to be almost independent of the complexity of the polycrystal geometry. An example of the cubic→trigonal transformation in AuCd alloys producing z' 2 martensite is considered. The development of the transformation through nucleation, growth and coarsening of orientation variants is simulated for both single crystal and polycrystalline materials. The effect of an external load on the martensitic microstructure in the polycrystalline material is studied. It is shown that the elastic coupling between different transformed grains of the polycrystal drastically affects the microstructure and its response to the applied stress. The obtained self-accommodating morphologies of the multivariant martensitic structure are in agree- ment with those observed in the experiments.  2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Phase transformations (martensite/shear); Theory & modeling (structural behavior); Morphology in polycrystals 1. INTRODUCTION Shape memory alloys and their applications are attracting the increasing interest of researchers. The martensitic transformation (MT) provides a mech- anism for the shape memory effect in these alloys and determines the maximum recoverable strain. A large number of properties in shape memory alloys, such as plasticity, strength, fatigue and stability, are determined by the microscopic and mesoscopic struc- ture patterns produced by the MT. There are many factors that influence the morphology of a martensitic structure and its evolution, for example the transform- ation temperature, applied external field and various defects. Owing to the complexity of the relationships between these parameters and the morphology of the martensitic structure, the experimental studies have serious difficulties in providing a complete under- standing of principles controlling the microstructure † To whom all correspondence should be addressed. Fax: +1-732-445-6780. E-mail address: khach@jove.rutgers.edu (A. G. Khachaturyan) 1359-6454/01/$20.00  2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII:S1359-6454(01)00108-2 formation. In such a situation a theoretical prediction of the outcomes of the material processing becomes crucial. A computational “experiment” based on advances in materials theory and supercomputing would be an effective tool for computer-aided material design. The MT proceeds via diffusionless formation of the martensitic orientation variants (structural domains). The development of these variants produces “islands” of martensitic phase within a parent phase crystal lat- tice with coherent boundaries between the parent phase and martensite and also between domains with different orientation variants of martensite. Since crystal lattices of the parent phase and all martensitic orientation variants differ from each other, fitting them coherently along the interfaces requires atomic displacements that produce the elastic strain. The elastic strain and a coherent conjugation of the crystal lattices of the parent and martensite phases and orien- tation variants are key factors in the understanding of the specifics of the martensitic morphology and kin- etics of the MT. The MT usually produces a complex multivariant configuration with martensitic domains interacting with each other through infinitely long-