Effect of surface normal variability on local surface strain measurements in StereoDIC

Abstract

Surface shape and surface displacement measurements for non-planar specimens are obtainable using a stereo vision system with digital image correlation (StereoDIC). The surface measurements can be employed with appropriate local surface fitting methods to extract full-field estimates for surface strains on the specimen surface. Since StereoDIC provides a dense set of 3D surface position measurements, Xi, for the entire field of view in the stereo vision system, it has been shown that these measurements will have inherent variability. This variability will propagate into any optimally defined local surface representation, including the surface's local unit vectors, such as the surface normal, n; a surface tangent, t, and the cross product, b = n x t. Once the unit vectors are estimated at surface position, Y, the surface representation at this point can be used with the orthogonal unit vectors n, b and t to obtain a set of local surface strains at Y, with variability in the initial surface shape measurements propagating into variations in the strain estimates.In the enclosed work, the authors develop a set of equations for local strain variability due to inaccuracies in the local unit vectors n, b, and t. Results are reported for the case where the unit vectors are obtained assuming a local planar fit to an N x N set of measurements Xi, and strains are determined along the two estimated in-plane directions b and t. Simulations show that the resulting strains have variability that is a strong function of the estimated normal, n. Specifically, simulations show that the estimated local strains have errors that are a strong function of both the direction of nand variability in the estimated normal, n, relative to the stereo system bisector, even if the surface strains in the original directions are exact. Experimental studies for cylindrical specimens are shown to be in agreement with the trends predicted by the simulations, demonstrating the potential importance of surface normal estimation in experimental studies.