LAUSR

An autofrettage analysis of an internally pressurized thick-walled spherical shell is performed by using two closed-form solutions for an elastic linear-hardening shell and an elastic power-law hardening shell based on a strain gradient plasticity theory, which contains a microstructure-dependent length-scale parameter and can capture size effects observed at the micron scale. The analysis leads to the analytical determination of the elastic and plastic limiting pressures, the residual stress field, and the stress field induced by an operating pressure for each strain-hardening spherical shell. This is followed by a shakedown analysis of the autofrettaged thick-walled spherical shells, which results in analytical formulas for reverse yielding and elastic reloading shakedown limits. The newly obtained formulas include their classical plasticity-based counterparts as special cases. To quantitatively illustrate the new formulas derived, a parametric study is conducted. The numerical results reveal that the shakedown limit (as the upper bound of the autofrettage pressure) increases with the increase of the strain-hardening level. In addition, it is observed that the shakedown limit based on the strain gradient plasticity solution increases with the decrease of the inner radius when the shell inner radius is sufficiently small, but it approaches that (a constant value independent of the inner radius) based on the classical plasticity solution when the inner radius becomes large. This predicted size (strengthening) effect at the micron scale by the newly obtained formulas agrees with the general trends observed experimentally.