Abstract
Digital image correlation techniques are commonly used to measure specimen displacements by finding correspondences between an image of the specimen in an undeformed or reference configuration and a second image under load. To establish correspondences between the two images, numerical techniques are used to locate an initially square image subset in a reference image within an image taken under load. During this process, shape functions of varying order can be applied to the initially square subset. Zero order shape functions permit the subset to translate rigidly, while first-order shape functions represent an affine transform of the subset that permits a combination of translation, rotation, shear and normal strains.
In this article, the systematic errors that arise from the use of undermatched shape function, i.e., shape functions of lower order than the actual displacement field, are analyzed. It is shown that, under certain conditions, the shape functions used can be approximated by a Savitzky-Golay low-pass filter applied to the displacement functions, permitting a convenient error analysis. Furthermore, this analysis is not limited to the displacements, but naturally extends to the higher-order terms included in the shape functions. This permits a direct analysis of the systematic strain errors associated with an undermatched shape function. Detailed numerical studies are presented for the case of a second-order displacement field and first- and second-order shape functions. Finally, the relation of this work to previously published studies is discussed.
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References
Photomechanics, chapter on Advances in 2D and 3D Computer Vision for Shape and Deformation Measurements, P.K. Rastogi, ed., Topics in Applied Physics, Springer-Verlag,77 323–372 (2000).
Zink, A.A.G., Davidson, R.W., andHanna, R.B., “Strain Measurement in Wood Using a Digital Image Correlation Technique,”Wood Fiber Science,27,346 (1995).
Vendroux, G. andKnauss, W.G., “Submicron Deformation Field Measurements: Part II, Improved Digital Image Correlation,” EXPERIMENTAL MECHANICS,38,86 (1998).
Sutton, M.A., Boone, M.L., Ma, F., andHelm, J.D., “A Combined Modeling-experimental Study of the Crack Opening Displacement Criterion for Characterization of Stable Crack Growth Under Mixed Mode I/II Loading in Thin Sheet Materials,”Engineering Fracture Mechanics,66,171–185 (2000).
Reynolds, A.P., andDuvall, F., “Digital Image Correlation for Determination of Weld and Base Metal Constitutive Behavior,”The Welding Journal Research Supplement,78 (10),355–360 (1999).
Sutton, M.A., Bruck, H.A., andMcNeill, S.R., “Determination of Deformations Using Digital Correlation with the Newton-Raphson Method for Partial Differential Corrections,” EXPERIMENTAL MECHANICS,29,261 (1989).
Lu, H. andCary, P.D., “Deformation Measurements by Digital Image Correlation: Implementation of a Second-order Displacement Gradient,” EXPERIMENTAL MECHANICS,40 (4)393–400 (2000).
Davis, P. “Levenberg-Marquardt Methods and Nonlinear Optimization,” SIAM News,26 (6) (1993).
Schreier, H.W., Braasch, J.R., andSutton, M.A., “Systematic Errors in Digital Image Correlation caused by Gray-value Interpolation,”Opt. Eng.,39 (11),2915–2921 (2000).
Savitzky, A., Golay, M.J.E., Smoothing and Differentiation of Data by Simplified Least-squares Procedures, Analytical Chemistry,36,1627–1639 (1964).
Jähne, B., “Practical Handbook on Image Processing for Scientific Applications,”CRC Press, Boca Raton (1997).
Wattrisse, B., Chysochoos, A., Muracciole, J.-M., andNémoz-Gaillard, M., “Analysis of Strain Localization During Tensile Tests by Digital Image Correlation,” EXPERIMENTAL MECHANICS,41 (1),29 (2001).
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Schreier, H.W., Sutton, M.A. Systematic errors in digital image correlation due to undermatched subset shape functions. Experimental Mechanics 42, 303–310 (2002). https://doi.org/10.1007/BF02410987
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DOI: https://doi.org/10.1007/BF02410987