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

Autofrettage is a technique for introducing beneficial residual stresses into cylinders. Both analytical and numerical methods are used for 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 special cases of this general model. This material model is convenient for description of the behavior of a class of pressure vessel steels such as A723. The Bauschinger effect is assumed fixed and total deformation theory based upon 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 open-end condition for which 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 is believed that it could be used for validation of numerical solutions or analytical solutions for special loading cases.