Competitive Hardening Dynamics in Viscoplastic Materials with Evolving Threshold Stress

Abstract

Conventional viscoplasticity frameworks treat the threshold stress as either a material constant or a quantity evolving solely with accumulated plastic strain. Since microstructural evolution — whether precipitation, phase transformation, or solute redistribution — may proceed concurrently with deformation, such a treatment is often inadequate. The present work formulates a constitutive framework, derived from the Clausius–Duhem inequality and Perzyna-type overstress viscoplasticity, in which the threshold stress evolves autonomously with physical time through microstructural kinetics, independently of accumulated strain. Modified Armstrong–Frederick kinematic hardening with static recovery is incorporated, so that back stress develops only during active inelastic flow. The interaction between time-driven threshold evolution and strain-driven back-stress development gives rise to three
behavioural regimes: (I) a purely elastic response, (II) flow arrest, in which inelastic flow initiates but subsequently ceases as the threshold overtakes the effective stress, and (III) continuous flow. A constructive Lyapunov function is employed to prove that flow arrest is asymptotically stable, a result not previously established at the material-point level in the viscoplastic creep literature. It is further shown that back-stress development reduces the time to arrest through a kinematic hardening acceleration effect. A physics-informed neural network employing smooth Macaulay bracket approximation with curriculum learning reproduces all three regimes within a single trained surrogate. The framework is validated against experimental data using the creep-ageing and back-stress test (CABT), which provides independent measurements of inelastic strain and back-stress evolution.