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Nonequilibrium statistical thermodynamics of thermally activated dislocation ensembles: part 3—Taylor–Quinney coefficient, size effects and generalized normality

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

The nonequilibrium statistical thermodynamics framework for thermally activated dislocation ensembles introduced in Parts 1 and 2 is applied to interpret and explain the fraction of plastic work done by the external applied stress that is dissipated as heat, the so-called Taylor–Quinney coefficient, for both pure metals and complex alloys. Important roles played by internal stresses and anelastic deformation are discussed for certain alloys, leading to their very low fraction of plastic work converted to heat. Conditions for the formation and development of new configurational subsystems are outlined and discussed, including the key role played by transitional or accommodational subsystems associated with interface regions between adjacent configurational subsystems with mismatch of reaction enthalpy. Size effects are attributed to decreased likelihood of access to energetically favorable accommodational configurations of dislocations in these transitional subsystems as a function of increased surface area-to-volume ratio, rather than the more common attribution to geometrically necessary dislocations or pileups. Generalized normality is discussed in terms of the requirement that post reaction glide should have the same thermodynamic driving force as that driving the dislocation through the saddle point of the reaction pathway. Noteworthy exceptions are considered based on physical mechanisms. It is argued that although the maximal intrinsic entropy production (MEP) rate heuristic cannot be rigorously proven, the Jaynesian approach of maximum information entropy change for each increment of nonequilibrium evolution is physically consistent with that of maximal intrinsic entropy production for a statistically representative set of dislocation barriers and subsystems. This consistency emerges from the increasing number density of reactions as the degree of correlation of enthalpy barriers increases among subsystems (with associated constrained local equilibrium states), which manifests corresponding increase of the configurational entropy change of pending reactions; the latter serves as a proxy for thermal dissipation associated with post reaction saddle point dynamic reconfiguration and extended glide of dislocations. Implications are discussed for both the bottom-up construction of ensemble intrinsic entropy production and the top-down construction which imposes MEP with constraints. Applicability of the Meyer–Neldel Rule for enthalpy–entropy compensation for dislocation reactions is considered at the ensemble level; it is argued to apply only under scenarios with strongly stress-assisted thermally activated reactions and for high degree of correlation of enthalpy barriers among subsystems. Certain contrasts are drawn between the present statistical thermodynamics framework and contemporary theories that emphasize the role of configurational entropy of dislocations. We close with discussion of utility of atomistics and discrete dislocation modeling methods in addressing some key outstanding issues to advance understanding, along with potentially fruitful roles for data science and machine learning.

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Acknowledgement

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. 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 3—Taylor–Quinney coefficient, size effects and generalized normality. J Mater Sci 59, 5161–5200 (2024). https://doi.org/10.1007/s10853-023-09143-6

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