An Analytical Framework for the Solution of Autofrettaged Tubes Under Constant Axial Strain Condition

Abstract

Autofrettage is a technique for introducing beneficial residual stresses into cylinders. Both analytical and numerical methods are used for the analysis of the autofrettage process. Analytical methods have been presented only for special cases of autofrettage. In this work, an analytical framework for the solution of autofrettaged tubes with constant axial strain conditions is developed. Material behavior is assumed to be incompressible, and two different quadratic polynomials are used for strain hardening in loading and unloading. Clearly, elastic perfectly plastic and linear hardening materials are the special cases of this general model. This quadratic material model is convenient for the description of the behavior of a class of pressure vessel steels such as A723. The Bauschinger effect is assumed fixed, and the total deformation theory based on the von Mises yield criterion is used. An explicit solution for the constant axial strain conditions and its special cases such as plane strain and closed-end conditions is obtained. For an open-end condition, for which the axial force is zero, the presented analytical method leads to a simple numerical solution. Finally, results of the new method are compared with those obtained from other analytical and numerical methods, and excellent agreement is observed. Since the presented method is a general analytical method, it could be used for validation of numerical solutions or analytical solutions for special loading cases.