A 3-D Model for Evaluating the Residual Stress Field Due to Swage Autofrettage

In order to maximize the performance of modern gun barrels in terms of strength-to-weight ratio and total fatigue life, favorable compressive residual stresses are introduced to the inner portion of the barrel, commonly by the autofrettage process. There are two major autofrettage processes for overstraining the tube: the hydrostatic, and the swage. There are several theoretical solutions for hydrostatic autofrettage, based on Lame´’s solution and the von Mises or Tresca yield criteria. The residual stress field due to hydraulic autofrettage is treated as an axisymetric, two-dimensional problem solved in terms of the radial displacement solely. Once the Bauschinger effect was included in these models they yield very realistic results. Unlike in the case of hydraulic autofrettage, swage autofrettage needs to be modeled by a three-dimensional model. The present analysis suggests a new 3-D axisymmetric model for solving the residual stress field due to swage autofrettage in terms of both the radial and the axial displacements. The axisymetric equilibrium equations are approximated by finite differences and solved then by Gauss-Seidel method. Using the new computer code the stresses, the strains, the displacements and the forces are determined. A full-scale instrumented swage autofrettage test was conducted and the numerical results were validated against the experimental findings. The calculated strains, the permanent bore enlargement, and the mandrel pushing force were found to be in very good agreement with the measured values.