Finite Deformation of a Panel in Ideal Plasticity and Superplasticity

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 uniforml...

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Bibliographic Details
Published in:Journal of applied mechanics and technical physics 2019-11, Vol.60 (6), p.1141-1148
Main Authors: Glagolev, V. V., Glagolev, L. V., Markin, A. A.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Classical and Continuum Physics
Classical Mechanics
Curvature
Curved panels
Deformation
Equilibrium conditions
Fluid- and Aerodynamics
Mathematical Modeling and Industrial Mathematics
Mechanical Engineering
Physics
Physics and Astronomy
Strain rate
Superplasticity
Threshold stress
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Summary: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.
ISSN:0021-8944
1573-8620
DOI:10.1134/S0021894419060191