In-plane stress analysis using tensor field photoelasticity

Few experimental methods exist for evaluating all in-plane stress components in solid materials; because of the tensor nature of these quantities. Full field measurement of all three stress components is desirable, since plastic deformation or failure can result from any combination of the three. A new photoelastic stress measurement method is presented for evaluating all three in-plane stress components within a two-dimensional photoelastic material. The measurement method is based on the observation that the complex transmission factors that describe the optical phase changes due to stress-induced birefringence have a second order tensor character, similar to that of other tensor quantities such as stress and strain. The same transformation equations and Mohr’s circle construction can be applied to the rotation of optical axis. A Michelson type interferometer and phase shifting are used to quantify the phases of the complex transmission factors. Mohr’s circle calculation is applied to obtain the principal transmission factors and principal axis orientation. The principal stresses are then obtained from the principal transmission factors through the stresss optical relationship. The effectiveness of this technique is demonstrated by comparing the experimental and analytical results for a hollow circular ring under diametric compression.Applied Science, Faculty ofMechanical Engineering, Department ofGraduat