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Finite strain continuum theory for phase transformations in ferromagnetic elastic–plastic solids

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Abstract

A continuum mechanical theory is formulated to address deformation of ferrous alloys under combined high-pressure, high-rate loading in the presence of potentially large magnetic fields. The material may undergo forward and reverse solid–solid phase transformations, e.g., martensitic transformations. The general theory encompasses numerous other physical phenomena that may arise depending on material composition and thermo-magneto-mechanical loading regime: finite thermoelasticity, plastic deformation, damage, and magnetoelastic coupling. A homogenization procedure motivates constitutive relations for the mixed-phase region. Phase transformations are driven by total Gibbs free energy differences between co-existing phases, including contributions from magnetic fields. The theory is fully consistent with local governing equations of nonlinear electromagnetic continua, including conservation laws of momentum and energy, Maxwell’s equations in the Galilean approximation, and the entropy production inequality. Kinetic relations for rates of plastic deformation, damage, and phase fractions all incur non-negative dissipation. Calculations demonstrate capabilities of the theory for ferrous polycrystals in loading regimes pertinent to static and shock compression, with and without superposed magnetic fields. The increase in pressure required for the \(\alpha \rightarrow \epsilon \) transformation in pure iron is quantified for very large external magnetic fields.

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  1. Impact Physics, DEVCOM ARL, Aberdeen, MD, 21005, USA

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Clayton, J.D., Lloyd, J.T. Finite strain continuum theory for phase transformations in ferromagnetic elastic–plastic solids. Continuum Mech. Thermodyn. 34, 1579–1620 (2022). https://doi.org/10.1007/s00161-022-01150-3

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