Chapter 12 Residual Stress Measurements in Finite-Thickness Materials by Hole-Drilling Gary S. Schajer and Colin Abraham Abstract Hole-drilling measurements of residual stresses are traditionally made on materials that are either very thick or very thin compared with the hole diameter. The calibration constants needed to evaluate the local residual stresses from the measured strain data are well established for these two extreme cases. However, the calibration constants for a material with finite thickness between the extremes cannot be determined by simple interpolations because of the occurrence of local bending effects not present at either extreme. An analytical model is presented of the bending around a drilled hole in a finite thickness material and a practical procedure is proposed to evaluate the corresponding hole-drilling calibration constants. Keywords Residual stress • Hole-drilling • Finite thickness • ASTM E837 • Calibration constants 12.1 Introduction The hole-drilling method [1, 2, 3] is a well-established method for measuring residual stresses in materials. The method, formalized in the ASTM standard test procedure E837-13, is very versatile and can be applied to a wide range of material types and specimens. The measurement procedure involves drilling a small hole in the test specimen and measuring the deformation of the surrounding material caused by the removal of the stressed material within the hole. The stresses originally within the hole can then be evaluated from the surrounding deformations using calibration coefficients determined from prior numerical calibrations. For example, the ASTM procedure involves using specially designed strain gauge rosettes to measure the deformations, for which the document tabulates the numerical values of the needed coefficients. Alternative approaches using optical techniques such as Electronic Speckle Pattern Interferometry (ESPI) [4, 5] and Digital Image Correlation (DIC) [6, 7] require analogous calibrations of the surface deformations. The ASTM document identifies two extreme cases, the first and most common, where the specimen material depth is much greater than the hole diameter, called a “thick” material. The hole depth reaches about half the hole diameter, thus producing a “blind hole”. Under these circumstances, the specimen is effectively “infinitely” deep. The second extreme case occurs in plate specimens where the material depth is much less than hole diameter, called a “thin” material. In this case the hole goes through the entire specimen depth. Both extreme cases allow significant analytical economies to be made. For example, the calibration coefficients required for the residual stress evaluation need only be tabulated for different hole diameters and for the “thick” case, also for different hole depths. In neither case does specimen depth influence the response, so this factor need not be included and the needed tables of calibration constants can be kept compact. The gap between the thickness of “thin” and “thick” specimens defined in ASTM E837-13 is significant. For a typical strain gauge rosette that uses a 2 mm diameter hole, the unavailable range is from 1.03 mm to 5.13 mm [8]. This is a substantial interval and many practical specimens will have thicknesses within it. ASTM E837-13 does not directly address this finite thickness case, apart from suggesting that the residual stress can be approximately estimated by comparisons with the tabulated “thick” and “thin” calibration coefficients. The nature of the required evaluation is not specified. Hole-drilling in a finite-thickness material brings a further important factor into play beyond the need to enlarge the calibration tables required for the “thick” and “thin” material cases. Hole-drilling into a finite-thickness material creates a G.S. Schajer (*) • C. Abraham Department of Mechanical Engineering, University of British Columbia, Vancouver, BC, Canada e-mail: schajer@mech.ubc.ca N. Sottos et al. (eds.), Experimental and Applied Mechanics, Volume 6: Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-06989-0_12, #The Society for Experimental Mechanics, Inc. 2015 89
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