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Equilibrium Multi-precipitate Configurations

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Abstract

In this paper, we formulate a phase-field model for the computation of equilibrium configurations of multiple phases that arise out of a solid-state precipitate reaction, in the presence of coherency stresses. Here, we utilize the phase-field framework to minimize the sum of the elastic and the interfacial energies for a given volume of the precipitates using an extension of the volume-preserved Allen–Cahn algorithm (Garcke et al. in Math Models Methods Appl Sci 18(08):1347–1381, 2008; Bhadak et al. in Metall Mater Trans A 49A(11):5705–5726, 2018). Using this technique, we investigate the precipitate organization for three solid-state reactions. The first is the classical two-phase precipitate reaction that leads to the formation of core–shell microstructures, where we clarify the influence of elasticity on the formation of such clusters. Following this, we investigate two symmetry-breaking transitions (cubic to tetragonal) and (hexagonal to orthorhombic), that lead to the formation of multi-variant clusters where we study the organization of the precipitates as a function of the elastic properties of the precipitate and the matrix.

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Acknowledgments

We thank Prof. T.A. Abinandanan (IISc) and Prof. S. Bhattacharya (IITH) for many valuable inputs and stimulating discussions on the subject. We express our appreciation to Boeing-India for the support under the Project PC36032.

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  1. Department of Materials Engineering, Indian Institute of Science, Bangalore, 560012, India

    Bhalchandra Bhadak, Ravi Kumar Singh & Abhik Choudhury

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  1. Bhalchandra Bhadak
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  3. Abhik Choudhury
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Correspondence to Bhalchandra Bhadak.

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Manuscript submitted January 1, 2020.

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Bhadak, B., Singh, R.K. & Choudhury, A. Equilibrium Multi-precipitate Configurations. Metall Mater Trans A 51, 5414–5431 (2020). https://doi.org/10.1007/s11661-020-05903-0

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