Theory of finite strain superplasticity

TL;DR

This paper develops a theoretical framework for understanding finite strain superplasticity in polycrystals, emphasizing grain boundary sliding and shape accommodation, and explains how grain geometry influences deformation and fracture.

Contribution

It introduces a novel theory that accounts for grain shape and boundary constraints, providing quantitative explanations for superplastic behavior and fracture mechanisms.

Findings

Plastic deformation involves grain volume variations, which are elastic.

The theory explains the role of grain boundary sliding in superplasticity.

Fracture is a necessary consequence of the deformation process.

Abstract

The plastic flow of a polycrystal is analyzed assuming grains as fine that the rate limiting process is grain boundary sliding, and grains readily accommodate their shapes by slip to preserve spatial continuity. It is shown that thinking of a polycrystal with randomly oriented grains as an homogeneous and isotropic continuum when dealing with it as a dynamical medium, even in a scale much larger than the grain size, leads to gross errors. The polyhedral nature of grains influences the plastic flow in a radical manner, as the relative velocity of adjacent grains is constrained to the common boundary plane, and only the in--plane shear stress contributes to their relative motion. This constriction determines that the divergency of the velocity field of the material medium does not vanish, and plastic deformation necessarily involves grain volume variations, which can only be elastic. As this has a limit, fracture follows as a necessary step of plastic flow. A theoretical approach to plastic flow is developed, and emphasis is done in superplastic deformation, from zero to fracture strain. The theory allows to quantitatively explain the observed features of superplastic materials and responds to many open questions in the field.