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Interaction of martensitic transformations and vacancy diffusion at the nanoscale under thermal loading: a phase field model and simulations

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Abstract

In this paper, the interaction of martensitic phase transformations (PTs) with vacancy evolution is studied using the phase field approach. The evolution of nanovacancies and martensite is captured by solving the Cahn–Hilliard and Ginzburg–Landau equations, respectively, coupled with elasticity equations. The Helmholtz free energy is considered as the combination of the terms belonging to the evolution of nanovacancies and those of the PT. The phase dependence of mixing energy, the nanovacancy concentration dependence of elastic properties, and the presence of transformation and misfit strain tensors in the constitutive equation are the important features of the interaction model. The finite element approach and the COMSOL code are used to solve the coupled system of equations. The thermally induced phase-vacancy interaction is studied for both the periodic boundary conditions (PBCs) and non-PBCs. A linear relation between the threshold misfit strain for the martensitic growth and temperature is found for both cases. The significant effect of the boundary periodicity on the elastic accommodation is discussed. The PT continuation/suppression is explained based on the thermodynamic equilibrium criterion. The effect of initial nanovacancy radius on the threshold misfit strain and the thermal driving force is investigated which is found temperature dependent and very different for the PBCs and non-PBCs. The threshold misfit strain for any temperature and the threshold thermal driving force for any radius are larger for the non-PBCs than those for the PBCs. They are almost the same for all the radii for the PBCs while they reduce as the radius increases for the non-PBCs. The coupled phase and vacancy evolution from an initially randomly distributed vacancy concentration is also analyzed which pronounces the key role of the vacancy initial conditions on the nanostructure. The proposed model and the obtained results help for a better understanding of the interaction of phase with vacancy and other various defects at the nanoscale.

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Acknowledgements

The support of Isfahan University of Technology and Iran National Science Foundation is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Isfahan University of Technology, 84156-83111, Isfahan, Iran

    Mahdi Javanbakht

  2. Mechanical Engineering Group, Pardis College, Isfahan University of Technology, 84156-83111, Isfahan, Iran

    Mohammad Sadegh Ghaedi

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  1. Mahdi Javanbakht
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Javanbakht, M., Ghaedi, M.S. Interaction of martensitic transformations and vacancy diffusion at the nanoscale under thermal loading: a phase field model and simulations. Acta Mech 232, 4567–4582 (2021). https://doi.org/10.1007/s00707-021-03067-5

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