Autofrettage and reautofrettage of a spherical pressure vessel

There is a numerical procedure for modeling autofrettage of thick-walled cylinders that incorporates the Bauschinger effect as a function of prior plastic strain and Von Mises' yield criterion. In this paper the numerical procedure is extended to solve the analogous problem of a spherical, thick walled steel vessel. An equivalent new analytical solution for the case of a spherical vessel is also formulated. The analytical and numerical solutions are shown to be in close agreement. It is demonstrated numerically that a reautofrettage procedure, previously proposed for cylindrical vessels, may be extremely beneficial for spherical vessels. Additional commentary is provided on the limitations of certain analytic solutions.