Chapter14 A Spatio-Temporal Approach for iDIC-Residual Stress Measurement Antonio Baldi Abstract Recently, the Integrated-Digital Image Correlation (iDIC) has been proposed as a simple and effective approach for residual stress measurement. iDIC is a variant of the classical Digital Image Correlation where the “standard” displacement functions are replaced by problem-specific ones. By this simple modification, stress components become the unknowns of the problem, thus allowing a single-pass analysis. However, implementation of the Integral Method for estimation of depth-dependent Residual Stress components is difficult. In particular, the Least Squares approach is not possible. This work suggests a two-pass approach: in the former the direct solution of the triangular linear system is solved. In the latter, the previous estimates are used as starting point for a global minimization involving all the acquired images. Keywords Integrated digital image correlation • Residual stress • Integral method • Reverse methods 14.1 Introduction Most technological processes induce (as side effect) self balanced stress fields, known as residual stresses, in mechanical components. Residual stresses are particularly critical because they add to load-induced stress fields, thus potentially inducing failure at load levels significantly lower than expected. The most used residual stress measurement technique is the hole drilling [1], a semi-destructive technique consisting in drilling a small hole in the surface, to successively compute stress components from the strain/displacement field observed on surface. Strains are usually measured using a strain gauge rosette, but various alternative techniques have been proposed. In particular, the Integrated Digital Image Correlation (iDIC) has been recently proposed as an effective approach for residual stress analysis both for isotropic [2] and orthotropic [3] materials. This technique is a direct derivative of Digital Image Correlation [4] and uses the same basic principle: given a pair of images acquired before and after the event of interest (respectively f and g), the intensity of each pixel remains the same irrespectively of the motion of the object under study. From the theoretical viewpoint, this statement can be written as f .x; y/ Dg.x Cu; yCv/ (14.1) whereuandvare the components of the displacement vector u. The expansion in Taylor series truncated to the first or second term of the right side part of Eq. 14.1 gives, after some easy algebraic manipulation, the well knownoptical flowequation @f @xP uC @f @y P v C @f @t D0 (14.2) Looking at Eq. 14.2, it is apparent that its solutions is challenging, because it contains two unknowns, i.e. the problem is illconditioned. The standard approach to the solution of (14.2) is due to Lukas-Kanade [5]: they assumed that the displacement field around a point can be described by simple shape functions—usually constant or bilinear polynomials—thus, reducing the number of unknowns from two times the number of pixels involved in the local area, to the number of controlling parameters of the shape functions. The unknowns are identified by a Least Squares approach minimizing a local functional involving the intensities of the reference and target image: A. Baldi ( ) Department of Mechanical Engineering, Chemical and Materials Engineering, University of Cagliari, Via Marengo 2, 09123, Cagliari, Italy e-mail: antonio.baldi@dimcm.unica.it © The Society for Experimental Mechanics, Inc. 2018 A. Baldi et al. (eds.), Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 8, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-62899-8_14 91
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