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Nanoscale Phase Field Modeling and Simulations of Martensitic Phase Transformations and Twinning at Finite Strains

  • Anup Basak
  • Valery I. Levitas
Conference paper
Part of the The Minerals, Metals & Materials Series book series (MMMS)

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 strain 

Notes

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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Copyright information

© The Minerals, Metals & Materials Society 2018

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringIowa State UniversityAmesUSA
  2. 2.Departments of Aerospace Engineering, Mechanical Engineering, and Material Science and EngineeringIowa State UniversityAmesUSA
  3. 3.Ames Laboratory, Division of Materials Science and EngineeringAmesUSA

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