Mechanistic origin of size effects in crystal plasticity: strain gradients and other theories explained

Abstract

Mechanical properties–strength, fracture toughness, fatigue resistance–arise from the inherently multiscale nature of deformation and failure. Forces at the macroscopic level drive atomic-scale processes, which are regulated by mesoscale attributes such as grain size and dislocation structures. Thus, the engineering of novel materials requires a thorough understanding of complex interactions across multiple length scales. However, mechanistic explanations for size effects remain elusive in the literature. Instead, most modeling efforts have relied on phenomenological formulations, which offer limited predictive accuracy beyond their calibration domains. This paper systematically explores mechanistic contributions to size effects to predict single- and poly-crystal mechanical responses. We identify three size-dependent mechanisms that can be incorporated into plastic deformation models to capture size effects in single- and poly-crystals for metals and alloys under tension, compression, and bending. The size-dependent algorithms do not introduce new phenomenological parameters but rely on material-invariant formulations that can be employed across single-phase FCC materials without recalibration. Notably, this understanding enables the tuning of microstructures for specific mechanical properties before manufacturing. The analysis further explains the relative contribution of size effects on isotropic and kinematic hardening as well as their significance for different crystallographic orientations. We further provide a physical interpretation for the origin of strain gradient theories and mechanistic size effects in the absence of geometry-induced strain gradients. We conclude by highlighting the coupling of mechanisms and their relative contributions at different strain levels.