Towards a theory of superplasticity

TL;DR

This paper develops a theoretical framework for superplasticity, emphasizing wave plastic deformation and defect interactions, and derives constitutive equations explaining superplastic flow and related phenomena.

Contribution

It introduces a unified theory of superplasticity based on non-linear wave deformation and macro/micro defect interactions, providing new constitutive equations and insights.

Findings

Superplastic flow velocity includes wave macroprocess, fluctuation, and intragranular slip components.

Transformation is essential for superplastic flow, unlike creep.

Strain rate dependence on grain size, stress, and temperature explained.

Abstract

This work deals with an investigation of general principles of superplasticity (SP) in deformed materials. It is shown that a non-linear, wave plastic deformation is the basic process for all plastic deformation phenomena, it makes an individual contribution into these phenomena, allows describing them from the same standpoints, and offers a way to follow the relationship between the physics of defects and the mechanics of plasticity. It is to be noted that macro and meso defects - discontinuities in the vector fields of macro and meso elastic displacements, are no less fundamental than are the microdefects - dislocations and disclinations, it is the latter which form the process of localized macrodeformation. General mechanisms of this process are analyzed in this study. Constitutive equation of superplastic state is obtained, which relates the strain rate, its rotational modes, local irreversible stresses, temperature, and density of heat and mass transfer. Special cases and their derived relations are analyzed. It is shown that SP is determined by plastic equilibrium concurrent with the composition and structure fluctuations. An expression is obtained for the superplastic flow velocity, containing three terms: velocity of wave plastic macroprocess, increased by fluctuations, velocity prescribed by the gradient of external sources (diffusion, etc.), and velocity of the delayed intragranular slip. It should be noted that transformation is a characteristic and necessary feature of SP flow. In the absence of transformations, deformation occurs via creep. Fragmentation of the deforming region and grain-boundary sliding (GBS) are discussed and so are their mechanisms and characteristic features. Formulas are derived for the strain rate under conditions of GBS and the reasons for its non-monotonic dependence on grain size, applied stresses and temperature are analyzed.