Optimization of depth increment distribution in the ring-core method

Abstract

The integral equation method is the most suitable calculation procedure for the determination of non-uniform residual stresses by semi-destructive mechanical methods such as hole and ring-core drilling. However, the high sensitivity to strain measurement errors due to the ill-conditioning of the equation sets has prevented its practical use. Examination of the influence of the strain measurement error on the calculated stresses and its propagation has shown that, for given maximum groove depth and total steps number, the error sensitivity depends on the particular depth increment distribution used. By means of an alternative matrix formulation of the equation sets the depth increment distribution that optimizes the numerical conditioning has been investigated. Numerical simulations carried out by means of the boundary element method as well as an experimental test have corroborated the best performance of the depth increment distribution proposed in comparison with the constant and increasing depth increment distributions commonly used.