On a unique constitutive equation for steady state isotropic optimal structural superplastic deformation in all classes of materials

Abstract

Structural Superplasticity in materials has been reported in so many different classes of materials that there is a case to state that this phenomenon is (near)-ubiquitous. Yet, many authors have proposed different rate controlling processes for different superplastic materials. Such an approach goes against Newton’s (Principia, Part 3) axiom that “to the same natural effects we must, so far as possible, assign the same causes”. In contrast, a viewpoint also exists that steady state, isotropic, optimal structural superplastic deformation in different classes of materials can be attributed to a grain-boundary-sliding-rate-controlled process that develops to a mesoscopic scale (defined to be of the order of a grain diameter or more). If this were the case, it should be possible to generate in properly normalized spaces material-independent “universal” curves (2D) and surfaces (3D) for the relationships among the different experimental variables/parameters like stress, strain rate, strain rate sensitivity index, temperature, real activation energy for the rate controlling process and viscosity. In this paper, by a careful analysis of experimental data concerning 175 states of superplastic materials of different classes it is demonstrated that such universal curves and surfaces indeed exist. The existence of such universal curves and surfaces that describe the phenomenology of steady state, isotropic, optimal structural superplastic deformation in different classes of materials in terms of unique equations reinforces the view experimentally arrived at that a unique physical mechanism of deformation is responsible for the near-ubiquitous phenomenon of steady state, isotropic, optimal structural superplasticity.