Unified Elastic Plastic Constitutive Equation and Application to Hydraulic Autofrettage Problems.
Final rept. 15 Jan-14 Dec 77,
ILLINOIS INST OF TECH CHICAGO
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Work is reported on the development of a set of unified rate type constitutive equations for elastic and plastic behavior, and of the formulation of generalized plane strain problems of hydraulic autofrettage in terms of these equations, as well as some initial computations in terms of the formulation. The unified equations apply to both loading and unloading. Elasticity is related to uniqueness of solutions of differential equations and occurs when a Lipshitz condition is in force. Plastic yield response occurs during loading when the Lipshitz condition fails. Failure of the Lipshitz condition corresponds to the von Mises yield condition. During yield, the equations automatically become those of Prandtl-Reuss. During unloading, the stable solution dictates a reentry to an elastic regime. Linear elastic-perfectly plastic behavior can be approximated arbitrarily closely. Extension to strain hardening can be included. The problem of generalized plane strain in hydraulic autofrettage is reduced to a system of ordinary differential equations with initial conditions. A computer program is written for the open end condition in the incompressible case with an instruction which insures a slight perturbation during yield.
- Numerical Mathematics