Finite Deformation of a Panel in Ideal Plasticity and Superplasticity

Abstract

Finite deformation of a panel under the influence of pressure is considered. The statement of the problem in displacements with equilibrium conditions represented via true stresses in Lagrangian coordinates is proposed. It is proven that the initial equations are satisfied when the panel is uniformly curved during deformation. The use of the previously proposed defining relation makes it possible to determine a differential relationship of the laws of pressure and curvature with time at an arbitrary strain rate. Ideally plastic and superplastic deformations are considered. The dependences of pressure on the curvature and strain time are obtained at which superplasticity occurs. It is revealed that, in this case, the range of stable changes in the curvature does not depend on the strain rate, and the threshold stress does not affect the time it takes to reach a given curvature of the panel.