Proceedings of the International Conference on Martensitic Transformations: Chicago pp 161-165 | Cite as
Nanoscale Phase Field Modeling and Simulations of Martensitic Phase Transformations and Twinning at Finite Strains
Abstract
A thermodynamically consistent phase field approach to martensitic phase transformations for a system with austenite and two martensitic variants has been developed. The model considers two order parameters, describing austenite \( \leftrightarrow \) martensite and variant \( \leftrightarrow \) variant transformations, respectively. The coexistence of three phases at a single material point are consistently penalized. Twinning in the nanoscale sample was studied for two different kinematic models (KMs) for the transformation stretch tensor \( {\mathbf{U}}_{t} \). In KM-I, \( {\mathbf{U}}_{t} \) is taken as a linear combination of the Bain strains, and in KM-II, \( {\mathbf{U}}_{t} \) is an exponential of the logarithm of the Bain stretch tensors. For these two KMs and for an additional model based on simple shear, analytical solutions for elastic stresses within a variant-variant boundary in an infinite twinned sample are presented. The results can be easily generalized for an arbitrary number of variants. They are crucial for further development of phase field approaches to multivariant martensitic transformations coupled to mechanics.
Keywords
Phase field Martensitic transformation Twinning Interfacial stress Finite strainNotes
Acknowledgements
The authors gratefully acknowledge the supports from NSF (CMMI-1536925 and DMR-1434613), ARO (W911NF-12-1-0340), and Iowa State University (Schafer 2050 Challenge Professorship and Vance Coffman Faculty Chair Professorship). Simulations were performed at Extreme Science and Engineering Discovery Environment (XSEDE), allocations TG-MSS140033 and MSS170015.
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