Thermo-elasto-plastic modeling of thermal autofrettage in thick-walled cylinders using distortion-energy-based yielding

Thermal autofrettage is one of the newly developed alternative strengthening techniques for cylinders operating under high pressure and temperature conditions. The process induces a compressive residual stress field within the cylinder wall by imposing and subsequently removing a radial temperature difference. While the existing analytical models have predominantly adopted maximum shear stress theory, the influence of distortion-energy-based yielding together with nonlinear strain hardening on thermally induced plastic behavior has received limited attention. This work develops a generalized plane strain-based analytical model for analyzing thermo-elasto-plastic behavior under a radial temperature gradient in a long thick-walled cylinder incorporating the distortion-energy-based yielding condition (von Mises) coupled with nonlinear strain hardening described by the Ludwik relation. The solutions for elastic-plastic interface evolution, thermal stresses, strains and displacements during the loading phase are obtained by solving the resulting coupled nonlinear boundary value problem using a shooting-Newton approach. The resulting residual stresses upon removal of the imposed temperature gradient are obtained from the elastic unloading response superimposed on the elastic-plastic loading solution. The computed residual stress fields are compared with available experimental measurements obtained through Sachs boring technique, demonstrating improved agreement relative to Tresca-based solutions. The developed mathematical framework is exemplified for two representative cylinders made of SS304 and Al6061-O. For the SS304 cylinder, thermal autofrettage with a temperature difference of 100°C generates compressive hoop residual stresses approaching 170 MPa near the bore. The average deviations between the predicted and experimentally measured radial, hoop and axial residual stresses are within 1.1, 6.2, and 8.1 MPa, respectively. The results further demonstrate that yield surface selection influences the depth of plastic deformation, residual stress magnitude, and predicted pressure-carrying capacity.