An Expanded Martensite Variant Selection Theory Accounting for Transformation Rotations and Applied Stress Fields: Predi
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https://doi.org/10.1007/s11837-020-04327-w Ó 2020 The Minerals, Metals & Materials Society
PRACTICAL RESEARCH IN PROCESSING SCIENCE
An Expanded Martensite Variant Selection Theory Accounting for Transformation Rotations and Applied Stress Fields: Predictions of Variant Clusters in Titanium ZACH D. BRUNSON,1 ADAM L. PILCHAK,2 SATISH RAO,2,3 ERIC J. PAYTON,2 and AARON P. STEBNER4,5 1.—Mechanical Engineering, Colorado School of Mines, 1500 Illinois St., Golden, CO 80401, USA. 2.—Air Force Research Laboratory, Materials and Manufacturing Directorate, 2230 Tenth St., Wright-Patterson AFB, OH 45433, USA. 3.—UES, Inc., 4401 Dayton-Xenia Rd., Beavercreek, OH 45432, USA. 4.—Departments of Mechanical Engineering, Materials Science & Engineering Georgia Institute of Technology, 771 Ferst Dr NW, Atlanta, GA 30332, USA. 5.—e-mail: [email protected]
An expanded strain energy-based criterion for predicting preferred martensite variants and multivariant clusters is developed and verified. Building upon previous inclusion-based formulations that considered only the strain energy of lattice stretches, here the authors also incorporate the strain energy of lattice rotations that result from martensitic transformations. Using this more complete single-variant strain energy formulation as a foundation, a micromechanical construct is developed to calculate energy reductions from transforming to clusters of multiple martensite variants from a single austenite crystal. Using elastic constants calculated at the b-transus temperature for pure titanium via molecular dynamics simulations, this new energy criterion is verified to exactly predict the same eight preferred self-accommodation variant cluster triplets identified in previous experiments. Finally, a modification to the strain energy formulation is made to consider externally applied fields. Using this modification, effects of applied loads during transformation are considered in calculating predictions of stress-accommodating multivariant triplets.
INTRODUCTION The invariant plane-strain-based phenomenological theory of martensite crystallography (PTMC).1,2 is central to nearly all micromechanical martensite research. This theoretical construct is capable of predicting a myriad of martensite microstructure features in diverse material systems including steels, titanium alloys, shape memory alloys, and even bacteria (e.g., Refs. 3–14), given only the austenite and martensite crystal structures, the appropriate plane of lattice invariant deformation, and the lattice invariant shear mechanism. One of the primary limitations to the PTMC is that these predictions do not consider interactions, geometric effects of transformed regions, and internally developed or externally imposed fields, which may bias the variant(s) of
(Received June 30, 2020; accepted August 6, 2020)
martensite formed, thereby impacting material properties, as was definitively shown for stress-induced transformations in shape memory alloys by Paranjape et al. and Bucsek et al.15–17 Examples of considering t
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