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Nonequilibrium statistical thermodynamics of thermally activated dislocation ensembles: part 1: subsystem reactions under constrained local equilibrium

  • The Physics of Metal Plasticity: in honor of Professor Hussein Zbib
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Abstract

This three-part paper lends new insight into the interpretation of internal state variable (ISV) theory and fundamentals of the behavior of thermally activated dislocation ensembles. We formally define important physical concepts undergirding ISV theory such as configurational subsystems (e.g., individual grains or phases), constrained local equilibrium, and thermally activated dislocation reactions in the context of crystal plasticity and then implement these concepts within a nonequilibrium statistical thermodynamics framework. The primal importance of the Gibbs free energy barrier to dislocation reactions within each subsystem is emphasized since the enthalpy barriers are affected by local constraint and resulting long-range and short-range athermal internal stresses acting within subsystems. Kinetic and kinematic aspects of individual dislocation reactions are defined. The role of athermal internal stresses in stabilizing the positions of dislocations between barriers is acknowledged by the formal identification of the anelastic deformation, along with its role in contributing to thermal dissipation. Thermal and configurational intrinsic entropy change that contribute to the change of Gibbs free energy as a driving force for reactions are formally introduced in the same way as in first principles methods and are based on probability of pending dislocation reactions at each step. We distinguish equilibrium thermodynamics up to the saddle point of reactions, for which change of both configurational and thermal entropy applies, from post-saddle point extended glide of dislocations, which couples with the thermal bath via dispersive phonon dynamics. We write subsystem and ensemble relations for intrinsic entropy production. The concept of “degree-of-correlation” of the enthalpy barriers of thermally activated dislocation processes is introduced at both the subsystem level and across the overall ensemble of subsystems, based on the ratio of the weighted average enthalpy barrier to the maximum (rate-limiting) enthalpy barrier. It is argued that nonequilibrium trajectories progressively move toward correlated behavior of the ensemble by virtue of internal stress redistribution among interacting subsystems that are favorable and unfavorable to reactions. The degree-of-correlation is a many-body concept involving populations of dislocations within and among various configurational subsystems.

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Acknowledgements

This work is the culmination of an extended effort to bring together thoughts and ideas developed over the past 30 years in a graduate course developed and taught by the author at Georgia Tech on nonequilibrium kinetics and ISV theory of metals and alloys. This effort is conducted in tribute to the legacy of collaborations and contributions made by Hussein Zbib in modeling and understanding multiscale aspects of dislocation plasticity using methods and tools ranging from DDD to crystal plasticity to generalized continua descriptions. His monumental and insightful contributions to various advanced aspects of modeling dislocations in both continuum and discrete theories are surely of lasting value, along with the memory and example of his gentle and genuine spirit as a friend and colleague. Support of the Carter N. Paden, Jr. Distinguished Chair in Metals Processing is gratefully acknowledged.

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    David L. McDowell

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McDowell, D.L. Nonequilibrium statistical thermodynamics of thermally activated dislocation ensembles: part 1: subsystem reactions under constrained local equilibrium. J Mater Sci 59, 5093–5125 (2024). https://doi.org/10.1007/s10853-023-09165-0

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