A Discrete Algorithm of Integrated Photoelasticity for Axisymmetric Problems

Abstract

By measuring stresses in cylinders with no stress gradient in axial direction, the cross-section of the cylinder may be considered as consisting of concentric rings in each of which the stresses are constant. Axial stress distribution in the cylinder is determined stepwise starting with the outermost ring (the so-called onion-peeling method). This paper generalizes the onion-peeling method for the case of axisymmetric stress distributions when stress gradient in the axial direction is present. Measurement of the integrated isoclinic and optical retardation is carried out in two parallel sections which are perpendicular to the specimen axis, Δz apart from each other. The distributions of the axial stress and shear stress are determined directly from the measurement data, using linear approximation of integrated photoelasticity. Other stress components are determined using the equilibrium equation and the compatibility equation (if stresses are due to external loads) or using the generalized sum rule (if residual stresses in glass are measured). The method is less sensitive to measurement errors than the Abel inversion. In comparison with the polynomial approximation of the stress distributions, the onion-peeling method gives more adequate results if stress distribution is not smooth. The paper is illustrated with several applications.