Efficient estimate of residual stress variance using complex variable finite element methods

摘要

The incorporation of residual stress states into structural components is often used to improve fatigue performance. However there is frequently significant uncertainty regarding the magnitude of the induced residual stresses due to variation in material properties, loading, geometry, the thermo/mechanical processes, and measurement uncertainty. This variation should be quantified to have confidence that desired residual stress state has been induced and that the probability of failure over the operating life of the structural component has been reduced. This research demonstrates an approximate but efficient method whereby the variance in the residual stress state is estimated using a first order Taylor series approximation. The key component of the method consists of evaluating the sensitivities of the residual stresses with respect to random variables by performing a few complex-variable finite element analyses. The method was verified by approximating the residual stress variance of a sphere subjected to an autofrettage process and having random input parameters. The analysis was performed for two material models, elastic-perfectly plastic and bilinear isotropic hardening. The variance approximations provided by the proposed method were compared against Monte Carlo sampling estimates. For the elastic-perfectly plastic case, the Monte Carlo sampling was conducted on the analytical solution of the residual stress field. This numerical example required the derivation of analytical expressions of the residual stresses and their sensitivities to the random variables for the cases of full or partial yielding during loading and reverse yielding during unloading. For the bilinear isotropic hardening material model, the Monte Carlo sampling was conducted on a finite element model of the sphere. The proposed method provided good accuracy and required less than 2% of the computational time required for the Monte Carlo sampling approach. In addition, this new approach provides sensitivity information regarding the contribution of each random variable to the overall variance of the residual stress state.