Abstract
Fretting is essentially a surface phenomenon, but bulk stresses and material properties contribute to subsequent failure. This feature of fretting demands a thorough understanding of near surface stresses under the joint action of normal, shear and thermal loading. Axisymmetric fretting is of great concern in piping and coupling design. In this paper, we develop design tools for Near Surface Analysis (NSA) for understanding axisymmetric fretting. Axisymmetric Fretting Analysis (AFA) becomes formidable owing to localised tractions that call for Fourier transform techniques. We develop two different NSA strategies based on two-dimensional plane strain models: 2D strip model (2DS) and half-plane Flamant model (2DF). We compare the results of 2DS and 2DF with the exact results for AFA obtained using Love’s stress function in conjunction with Fourier transform. There is a good correspondence between stress components obtained from 2D-models.
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References
Bentall R H, Johnson K L 1967 Slip in the rolling contact of two dissimilar elastic rollers. Int. J. Mech. Sci. 9: 389–404
Boniface V, Simha K R Y 1991 Aplastic zone model of mixed mode fracture. Int. J. Fract. 48: R9–R12
Conway H D, Farnham K A 1967 Contact stresses between cylindrical shafts and sleeves. Int. J. Eng. Sci. 5: 541–544
Dini D, Nowell D 2004 Flat and rounded fretting contact problems incorporating elastic layers. Int. J. Mech. Sci. 46: 1635–1657
Dobromirsky J, Smith I O 1986 A stress analysis of a shaft with a press-fitted hub subjected to cyclic axial loading. Int. J. Mech. Sci. 28(1): 41–52
Farris T N, Murthy H, Matlik J F 2003 Fretting fatigue, In R O Rithcie and Y Murakami, (eds.), Comprehensive structural integrity Elsevier, Pergamon Press 4: 281–326
Fellows L, Nowell D, Hills D A 1995 Contact stresses in a moderately thin strip (with particular reference to fretting experiments) Wear 185: 235–238
Hills DA, Nowell D Sackfield A 1993 Mechanics of elastic contacts (Oxford: Butterworth-Heinmann)
Johnson K L 1985 Contact mechanics. (Cambridge, UK: Cambridge University Press)
Lee D S 1995 Axisymmetric constriction of a circular cylinder under uniform axial compression. Q. J. Appl. Math. 48: 89–110
Lee H, Mall S 2004 Effect of dissimilar mating materials and contact force on fretting fatigue behaviour of Ti-6Al-4V. Tribol. Int. 37: 35–44
Mugadu A, Hills D A, Limmer L 2003 A theoretical and experimental procedure for predicting the fretting fatigue strength of complete contacts. Fretting fatigue: Advances in the basic understanding and applications ASTM-STP 1425: 145–155
Nowell D, Hills D A 1988 Contact problems incorporating elastic layers. Int. J. Solids and Struct. 24(1): 105–115
Ramesh M, Satish V Kailas, Simha K R Y 2007 Fretting stresses in axisymmetric components. National Conference of Research Scholars in Mechanical Engineering, Indian Institute of Technology Kanpur, India
Rankin AW, Schenectady N Y 1944 Shrink-fit stresses and deformations. J. Appl. Mech. A?77-A?85
Singh S 1994 On the shrink-fit problem of a thin cylinder. Int. J. Pressure Vessels and Piping 60: 167–175
Sneddon I N 1951 Fourier Transforms. McGraw-Hill Book Company, Inc.
Spillers W R 1964 A shrink-fit problem. J. Math. Phys. 43: 65
Steven G P 1975 The shrink-fit problem with both components being elastic. Int. J. Eng. Sci. 13: 663–673
Szolwinski M P, Farris T N 1996 Mechanics of fretting fatigue crack formation. Wear 198: 93–107
Timoshenko S P, Goodier J N 1970 Theory of Elasticity. Engineering Mechanics Series. (New York: McGraw-Hill International Editions)
Tranter C J, Craggs J W 1945 The stress distribution in a long circular cylinder when a discontinuous pressure is applied to the curved surface. Philos. Mag. 36: 241–250
Williams D K 1996 Circular cylinders with bands of pressure: axisymmetric closed form solutions utilizing Bessel’s functions and Fourier series. Pressure Vessels and Piping Design, Analysis and Severe Accidents 331: 77–87
Williams D K, Ranson W F 2003 Pipe-anchor discontinuity analysis utilizing power series solutions, Bessel’s functions and Fourier series. Nucl. Eng. Des. 220: 1–10
Yau W W F, Cakmak A S 1966 The indentation problem of an infinite, hollow, elastic cylinder for an axisymmetric punch of finite length and arbitrary profile. Int. J. Eng. Sci. 4: 463–481
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Ramesh, M., Kailas, S.V. & Simha, K.R.Y. Near surface stress analysis strategies for axisymmetric fretting. Sadhana 33, 273–297 (2008). https://doi.org/10.1007/s12046-008-0020-7
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DOI: https://doi.org/10.1007/s12046-008-0020-7