A mechanistic model for boundary sliding controlled optimal superplastic flow. I. Theory

Optimal structurally superplastic flow in metals and alloys is characterized by the dominance of grain/interphase boundary sliding (GBS). Further, it can be argued that the significant grain rotation seen during optimal superplastic flow is indicative of the presence of unbalanced shear stresses at the boundaries and this can be taken as evidence for boundary sliding contributing independently to the external strain. Based on this premise, a model has been developed by Padmanabhan and Schlipf which involves a detailed analysis of the boundary sliding process by treating this phenomenon as one involving isoconfigurational flow kinetics which is then treated by the transition state theory. In this paper, a brief description of the mechanistic model for GBS controlled optimal superplastic flow is presented and the details of the sliding process are spelled out. This model takes care of the basic problem of relating the deformation in a small unit or groups of small units to that of the material deforming in the bulk. It has been shown that for a complete description of optimal isostructural superplastic flow, knowledge of four constants and a true activation enrgy is necessary. In view of the transcendental nature of the equations involved, the long range threshold stress associated with sliding was set as zero and this reduced the number of constants required to be determined to three. A procedure for the evaluation of the three constants and the true activation energy for the rate controlling deformation process has been outlined