An Analytical Solution of Residual Stresses for Shrink-Fit Two-Layer Cylinders After Autofrettage Based on Actual Material Behavior

Abstract

To enhance the pressure capacity and the life of a pressure vessel, different processes such as shrink-fit and autofrettage are usually employed. For autofrettaged and shrink-fit multilayer cylinders, numerical solutions for determining the residual stress distribution have been reported. However, few studies about the analytical method are available. In this study, an analytical solution was presented for shrink-fit two-layer cylinders after autofrettage based on the actual tensile-compressive stress–strain curve of material. The new analytical method accurately predicted a residual stress distribution, and it could be used to design two-layer compound cylinders. In this method, unloading and shrink-fitting were considered as a simultaneous operation for an inner cylinder, allowing for a simple and accurate analysis. Some significant factors were taken into account, including the nonlinear behavior of an original autofrettaged inner layer in the shrink-fitting process and a material’s different unloading behavior at different maximum tensile affects back-yielding. The results of the proposed method were in excellent agreement with the results from the simulation performed by ansys. The results indicated that an increased shrink-fit pressure expanded the back-yielding zone of the inner cylinders, and did not affect the back-yielding zone of the outer cylinders. The optimum percentages overstrain depend on the working pressure when the shrink-fit pressure, cylinder size, and material are defined, and inner and outer cylinders have different optimum percentages overstrain.