Abstract
An experimental method is described which can measure the direction and magnitude of residual and applied stress in metals. The method uses optical interference to measure the permanent surface deformation around a shallow spherical indentation in a polished area on the metal specimen. The deviation from circularly symmetrical surface deformations is measured at known values of applied stress in calibration specimens. This deviation from symmetry can then be used to determine the direction and magnitude of tensile residual stress in specimens of the same material. Determination of compressive residual stress is more limited.
A model of the indentation process is offered which qualitatively describes experimental results in 4340 steel for both tensile and compressive stress. The model assumes that the deformation around an indentation os controlled by stresses analogous to those around a hole in an elastic plate. Various conditions are discussed which affect the indentation process and its use to measure stress, including (a) the rigidity of support of the indentor and specimen, (b) the size and depth of the indentation, (c) the uniaxial stress-strain behavior of the specimen material.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- C :
-
concentration factor for stresses around an indentation
- d :
-
indentation contact diameter
- D :
-
indentor-ball diameter
- n :
-
optical-interference fringe number
- n ‖ :
-
fringe number along the radial line perpento the load direction
- n ⊥ :
-
fringe number along the radial line perpendicular to the load direction
- p :
-
indentation depth
- x :
-
radial distance from the edge of the indentation
- α:
-
ball contact angle with original surface
- \(\sigma _b\) :
-
applied or residual stress in the body under consideration
References
Sines, G. and Carlson, R., “Hardness Measurements for Determination of Residual Stress,” ASTM Bulletin 35–37 (Feb. 1952).
Blain, P. A., “Influence of Residual Stress on Hardness,”Metal Progress,71,99–100 (Jan.1957).
Oppel, G. U., “Biaxial Elasto-plastic Analysis of Load and Residual Stress,”Experimental Mechanics,4 (5),135–140 (1964).
Beeuwkes, A., “Plastic Flow and Fracturing of Metals,” Watertown Arsenal Lab. Tech. Report #53-893/154-11, ed. by G. Sachs (Apr. 1954).
Sturm, R. G., “The Total Stress Gage,” Tech. Note 001, Sturm-Stress, Inc. (Nov. 1970); also presented at 1968 SESA Spring Meeting held in Albany, N. Y. (May 7–10).
Kendall, D. P., “The Effect of Material Removal on the Strength of Autofrettaged Cylinders,” Watervliet Arsenal Tech. Report WVT-7003 (Jan. 1970).
Milligan, R. V., Koo, W. H. andDavidson, T. E., “The Bauschinger Effect in a High Strength Steel,”Trans. ASME, J. of Basic Eng.,88,480–488 (June1966).
Tolansky, S., “Multiple-Beam Interferometry in Analytical Metallography,”Metallography,2,1–18 (1969).
Underwood, J. H. andKendall, D. P., “Measurement of Microscopic Plastic-strain Distributions in the Region of a Crack Tip,”Experimental Mechanics,9 (7),296–304 (1969).
Underwood, J. H., Swedlow, J. L. andKendall, D. P., “Experimental and Analytical Strains in an Edge-Cracked Sheet,”Engn. Fracture Mech.,2,183–196, (1971).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Underwood, J.H. Residual-stress measurement using surface displacements around an indentation. Experimental Mechanics 13, 373–380 (1973). https://doi.org/10.1007/BF02324039
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02324039