An Arrhenius mechanics model for polycrystalline plasticity and creep

Arrhenius kinetics are central to high-temperature creep but have not routinely produced quantitative, parameter-sparse descriptions of low-temperature plasticity, stress–strain response, or Hall–Petch scaling. We introduce Arrhenius analogues of the Taylor hardening and Hall–Petch models that incorporate two essential microstructural descriptors: a local stress concentration factor ϕ and the volume fraction of rate-limiting interaction sites Ξ . When combined with a minimal dislocation-density evolution law, this “Arrhenius mechanics” framework fits Hall–Petch datasets, true stress–strain curves, and the strain-rate and temperature dependence of strength across materials and microstructures. The formulation also reproduces inverse Hall–Petch behavior and strain softening without ad hoc assumptions. Fitted activation parameters are physically plausible, with H * ∼ 0.1 − 5 e V and v * ∼ 0.1 − 10 b 3 . Expressing grain boundary-dislocation interactions and dislocation-segment depinning within a common Arrhenius form yields a compact set of scaling relations in stress, grain size, and dislocation spacing that support (i) cross-experiment parameter transfer (e.g., from nanopillar tests to polycrystalline yield), (ii) extrapolation across strain rates and temperatures, and (iii) construction of deformation-mechanism maps using a small number of measurable quantities . The formulation derives from a convex dissipation potential, ensuring thermodynamic consistency. The results suggest accounting for ϕ and Ξ is sufficient to unify plasticity and creep descriptions within a single Arrhenius framework.