Abstract
Metal-forming operations leave residual stresses in formed parts due to nonuniform deformation occurring during the process. An exact method of determining the longitudinal, radial and circumferential (tangential) residual stresses in axisymmetric specimens was proposed by Mesnager1 and further developed by Sachs2. The boring-out technique can be complemented by a similar procedure in which strains are measured on the inner surface of the tube when material is removed from the outer surface.
The work proposed in this paper extends previous analyses of residual stresses to the case where the material exhibits cylindrical elastic anisotropy, i.e., the principal axes of anisotropy correspond to the longitudinal, radial and circum-ferential directions of the tube. In addition, the present analysis considers the case in which a residual-shear stress, developed by twisting the tube about its axis, exists in the tube. When such shearing stresses are present, the principal axes of the residual-stress distribution are not parallel to the principal axes of the tube.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- ε z :
-
longitudinal strain
- εθ :
-
circumferential strain
- σ2 :
-
longitudinal stress
- σθ :
-
circumferential stress
- σ r :
-
radial stress
- a :
-
inside radius of tube
- b :
-
outside radius of tube
- r :
-
instantaneous radius
- E r,E θ,E z :
-
moduli of elasticity in directionsr, θ, andz respectively
- v rθ :
-
Poisson's ratio which characterizes the compression in the θ direction when tension is applied in ther direction
- G θz,G rz,G rθ :
-
shear moduli which characterize the change of angles between directions θ andz, r andz, r and θ
References
Mesnager, M., “Methode de determination des tensions existant dans une cylindre circulaire,”Compt. rend.,169,1391–1393 (1919).
Sachs, G., “Der Nachweis Inner Spannungen in Stangen und Rohren,”Zeitschrift fur Metallkunde,19,352–357 (1929).
Lambert, J.W., “A Method of Deriving Residual Stress Equations,”Proc. SESA,12 (1),91–96 (1954).
Srinivasan, R., Hartley, C.S. andBandy, R., “Residual Stress Determination in Inconel-600 Tubes Using Electrochemical Machining,”Novel Techniques in Metal Deformation Testing, ed. R. Wagoner, TMS-AIME, Warrendale, PA, 163–174 (1983).
Weiss, V., “Residual Stresses in Cylinders,”Proc. SESA,XV (2),53 (1957).
Bandy, R. andZemanian, T., “Effect of Transient Heat Treatment on Throughwall Residual Stresses of Alloy 600 Tubes,”BNL Rep., Brookhaven Nat. Lab. Mat. Res. Group, Dept. of Nuclear Energy, Upton, NY (1983).
Lekhnitskii, S.G., Anisotropic plates, 2 nd Ed., Gordon and Breach Science Publishers, New York (1968).
Alexander, J.M. andBrewer, R.C., Manufacturing Properties of Materials, D. Van Nostrand and Co., New York, 269–270 (1963).
Eisenberg, M.A., Hartley, C.S., Lee, H-C andYen, C.F., “Influence of Texture on the Analysis of Thermoelastic Elastic/Plastic Anisotropy and the Initial Yielding of Zircaloy Tubes,”J. Nucl. Mat.,88,138–151 (1980).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Voyiadjis, G.Z., Kiousis, P.D. & Hartley, C.S. Analysis of residual stresses in cylindrically anisotropic materials. Experimental Mechanics 25, 145–147 (1985). https://doi.org/10.1007/BF02328804
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02328804