Research Papers: Contact Mechanics

Elastic-Plastic Contact Conditions for Frictionally Constrained Bodies Under Cyclic Tangential Loading

[+] Author and Article Information
Satish V. Kailas

e-mail: satvk@mecheng.iisc.ernet.in
Department of Mechanical Engineering,
Indian Institute of Science,
Bangalore 560012, India

1Present address: Nuclear Power Corporation of India Limited, Mumbai 400094, India.

2Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received December 14, 2012; final manuscript received September 12, 2013; published online November 12, 2013. Assoc. Editor: Dae-Eun Kim.

J. Tribol 136(1), 011401 (Nov 12, 2013) (17 pages) Paper No: TRIB-12-1230; doi: 10.1115/1.4025600 History: Received December 14, 2012; Revised September 12, 2013

A Frictionally constrained condition implies dependence of friction force on tangential displacement amplitude. The condition may occur due to chemical, physical, and/or mechanical interaction between the contacting surfaces. The condition, sometimes also referred to as the presliding condition or partial slip condition, is characterized under fretting. Under such conditions, various experimental studies indicate the existence of two distinguishable regions, that is, stick region and slip region. In the present study, frictionally constrained conditions are identified and the evolutions of stick-slip regions are investigated in detail. Investigations have been performed on self-mated stainless steel and chromium carbide coated surfaces mated against stainless steel, under both vacuum and ambient conditions. Contact conditions prevailing at the contact interface were identified based on the mechanical responses and were correlated with the surface damage observed. Surface degradation has been observed in the form of microcracks and material transfer. Detailed numerical analysis has also been performed in order to understand the energy dissipation and the damage mode involved in the surface or subsurface damage. It has been observed that under frictionally constrained conditions, the occurrence of annular slip features are mainly due to the junction growth, resulting from elastic-plastic deformation at the contact interface. Ratcheting has been observed as the governing damage mode under cyclic tangential loading condition.

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Waterhouse, R. B., 1981, Fretting Fatigue, Applied Science Publishers Ltd., London.
Vingsbo, O., and Soderberg, D., 1988, “On Fretting Maps,” Wear, 126, pp. 131–147. [CrossRef]
Zhou, Z. R., and Vincent, L., 1995, “Mixed Fretting Regime,” Wear, 181–183, pp. 531–536.
Mindlin, R. D., 1949, “Compliance of Elastic Bodies in Contact,” J. Appl. Mech., 16, pp. 259–268.
Johnson, K. L., 1955, “Surface Interaction Between Elastically Loaded Bodies Under Tangential Forces,” Proc. R. Soc. London, Ser. A, 230, pp. 531–548. [CrossRef]
Bowden, F. P., Moore, A. J. W., and Tabor, D., 1943, “The Ploughing and Adhesion of Sliding Metals,” J. Appl. Mech., 14, pp. 80–91.
Courtney-Pratt, J. S., and Eisner, E., 1957, “The Effect of a Tangential Force on the Contact of Metallic Bodies,” Proc. R. Soc. London, Ser. A, 238, pp. 529–550. [CrossRef]
McFarlane, J. S., and Tabor, D., 1950, “Relation Between Friction and Adhesion,” Proc. R. Soc. London, Ser. A, 202, pp. 244–253. [CrossRef]
Tabor, D., 1959, “Junction Growth in Metallic Friction: The Role of Combined Stresses and Surface Contamination,” Proc. R. Soc. London, Ser. A, 251, pp. 378–393. [CrossRef]
Bowden, F. P., and Tabor, D., 1950, Friction and Lubrication of Solids, Oxford University, London.
Morrison, J. L., and Shepherd, W. M., 1950, “An Experimental Investigation of Plastic Stress-Strain Relations,” Proc. Inst. Mech. Eng., 163, pp. 1–17. [CrossRef]
Brygman, U., and Soderberg, S., 1986, “Contact Conditions in Fretting,” Wear, 110, pp. 1–17. [CrossRef]
Ödfalk, M., and Vingsbo, O., 1992, “An Elastic-Plastic Model for Fretting Contact,” Wear, 157, pp. 435–444. [CrossRef]
Etsion, I., 2010, “Revisiting the Cattaneo–Mindlin Concept of Interfacial Slip in Tangentially Loaded Complaint Bodies,” ASME J. Tribol., 132(2), p. 020801. [CrossRef]
Johnson, K. L., 2004, Contact Mechanics, Cambridge University, Cambridge.
Kannel, J. W., and Tevaarwerk, J. L., 1984, “Subsurface Stress Evaluation Under Rolling/Sliding Contact,” ASME J. Tribol., 106(1), pp. 96–103. [CrossRef]
Hamilton, G. M., 1983, “Explicit Equations for the Stresses Beneath a Sliding Spherical Contact,” Proc. Inst. Mech. Eng., 197, pp. 53–59. [CrossRef]
Chivers, T. C., and Gordelier, S. G., 1985, “Fretting Fatigue and Contact Conditions: A Rational Explanation of Palliative Behavior,” Proc. Inst. Mech. Eng., 199(4), pp. 325–337.
Hills, D. A., Nowell, D., and Sackfield, A., 1993, Mechanics of Elastic Contacts, Butterworth–Heinemann, London.
Hills, D. A., and Nowell, D., 1994, Mechanics of Fretting Fatigue, Kluwer Academic, Dordrecht.
Proudhon, H., Fouvry, S., and Yantio, G. R., 2008, “Determination and Prediction of the Fretting Crack Initiation: Introduction of the (P,Q,N) Representation and Definition of a Variable Process Volume,” Int. J. Fatigue, 28(7), pp. 707–713.
Talemi, R. H., Wahab, M. A., and De Baets, P., 2011, “Numerical Modeling of Fretting Fatigue,” J. Phys.: Conf. Ser., 305, p. 012061.
Begley, M. R., and Hutchinson, J. W., 1999, “Plasticity in Fretting of Coated Substrates,” Eng. Fract. Mech., 62, pp. 145–164. [CrossRef]
Ambrico, J. M., and Begley, M. R., 2000, “Plasticity in Fretting Contacts,” J. Mech. Phys. Solids, 48, pp. 2391–2417. [CrossRef]
Kogut, L., and Etsion, I., 2003, “A Semi-Analytical Solution for the Sliding Inception of a Spherical Contact,” ASME J. Tribol., 125(3), pp. 499–506. [CrossRef]
Brizmer, V., Kligerman, Y., and Etsion, I., 2007, “Elastic-Plastic Spherical Contact Under Combined Normal and Tangential Loading in Full Stick,” Tribol. Lett., 25(1), pp. 61–70. [CrossRef]
Blau, P. J., ed., 2001, ASM Handbook Volume 18: Friction, Lubrication and Wear Technology, American Society for Metals, Metals Park, OH.
Farwick, D. G., and Johnson, R. N., 1980, “Wear and Corrosion Performance of Metallurgical Coatings in Sodium,” Thin Solid Films, 73, pp. 145–153. [CrossRef]
Garcia, M., and Dominguez, J., 2002, “Fretting Fatigue in a Spherical Contact,” J. Strain Anal., 37(6), pp. 469–478. [CrossRef]
Hamdy, M. M., Overs, M. P., and Waterhouse, R. B., 1981, “A New High Temperature Fretting Wear Test Rig,” J. Phys. E: Sci. Instrum., 14, pp. 889–894. [CrossRef]
Yantio Njankeu Sabeya, G. R., Paris, J.-Y., and Denape, J., 2009, “Utility of a Fretting Device Working Under Free Displacement,” Tribol. Int., 42, pp. 1330–1339. [CrossRef]
Gao, C., Kahlmann-Wilsdrof, D., and Makel, D. D., 1994, “The Dynamic Analysis of Stick Slip Motion,” Wear, 173, pp. 1–12. [CrossRef]
Etsion, I., Kligerman, Y., and Kadin, Y., 2005, “Unloading of an Elastic-Plastic Loaded Spherical Contact,” Int. J. Solids Struct., 42, pp. 3716–3729. [CrossRef]
Filippi, S., Gola, M., and Akay, A., 2004, “Measurement of Tangential Contact Hysteresis During Micro-Slip,” ASME J. Tribol., 126(3), pp. 482–490. [CrossRef]
Zolotarevskiy, V., Kligerman, Y., and Etsion, I., 2011, “The Evolution of Static Friction for Elastic-Plastic Contact in Pre-Sliding,” ASME J. Tribol., 133(3), p. 034502. [CrossRef]
Varenberg, M., Etsion, I., and Halperin, G., 2004, “Slip Index: A New Unified Approach to Fretting,” Tribol. Lett., 17(3), pp. 569–573. [CrossRef]
Johnson, K. L., 1961, “Energy Dissipation at Spherical Surfaces in Contact Transmitting Oscillatory Forces,” J. Mech. Eng. Sci., 3(4), pp. 362–368. [CrossRef]
Ovcharenko, A., Halperin, G., and Etsion, I., 2008, “In Situ and Real-Time Optical Investigation of Junction Growth in Spherical Elastic-Plastic Contact,” Wear, 264, pp. 1043–1050. [CrossRef]
Johnson, K. L., 1995, “Contact Mechanics and Wear of Materials,” Wear, 190, pp. 162–170. [CrossRef]
Srinivasan, V. S., 2000, “Strain Controlled Low Cycle Fatigue and Creep-Fatigue Interaction Behavior of a Type 316L (N) Stainless Steel,” Ph.D. thesis, Indian Institute of Science, Bangalore, India.
Rabinowicz, E., 1965, Friction and Wear of Materials, Wiley, New York.
Waterhouse, R. B., 1972, Fretting Corrosion, Pergamon, New York.
Chander, S., Meikandamurthy, C., Kale, R. D., and Krishmurty, R., 1993, “Experimental Study of Self Welding of Materials in High Temperature Liquid Sodium,” Wear, 162–164, pp. 458–465. [CrossRef]
Bethune, B., and Waterhouse, R. B., 1965, “Adhesion Between Fretting Steel Surface,” Wear, 8, pp. 22–29. [CrossRef]


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Fig. 1

Illustration of fretting conditions

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Fig. 2

Schematic of variation of tangential or frictional force with displacement amplitude under (a) stick regime, (b) partial slip regime, and (c) gross sliding regime (note: Ed is energy dissipation, Kl is slope of the loop, and Ds is interfacial displacement amplitude)

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Fig. 3

Specimens (a) pin of radius 2 mm, (b) pin of radius 15 mm, and (c) flat specimen (note: all dimensions are in mm)

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Fig. 4

Schematic of experimental setup

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Fig. 5

Variation of coefficient of friction with number of cycles under ambient conditions

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Fig. 6

Variation of coefficient of friction with number of cycles under vacuum conditions

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Fig. 7

Comparison of experimental responses with analytical model

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Fig. 8

Running condition fretting loops for SS versus SS under vacuum condition at (a) 1000th cycle and (b) 9000th cycle

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Fig. 9

Running condition fretting loops for HVOF flat coated surfaces mated against SS pin under vacuum condition at (a) 1000th cycle and (b) 9000th cycle

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Fig. 10

X-intercept variation with displacement amplitude

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Fig. 11

Variation of energy dissipated with displacement amplitude

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Fig. 12

Micrographs indicating surface damage observed for self-mated SS under ambient condition at indicated displacement amplitude

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Fig. 13

Micrographs indicating surface damage observed for self-mated SS under vacuum condition at indicated displacement amplitude

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Fig. 14

Micrographs indicating flat surface damage for (a) a self-mated SS at an amplitude of 80 μm under ambient conditions, (b) a self-mated SS at an amplitude of 100 μm under vacuum conditions, and (c) a coated flat surface using the HVOF process mated with SS pin at an amplitude of 100 μm under vacuum condition (R1–region under stick condition and R2–region under slip condition)

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Fig. 15

(a) Variation of stick region (c/a) with displacement amplitude; (b) schematic diagram indicating contact radius and stick radius

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Fig. 16

Micrographs of flat surface indicating (a) shear fracture features in the central region and (b) microcracks in the annular region

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Fig. 17

Micrographs indicating surface damage at displacement amplitude of 100 μm under vacuum conditions of (a) coated flat surface using HVOF coating process and (b) SS pin

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Fig. 18

Magnified micrographs indicating surface damage of SS pin surface in (a) annular region and (b) center region

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Fig. 19

Area mapping of SS pin surface using energy dispersive X-ray spectroscopy for the elements (a) chromium and (b) iron

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Fig. 20

Junction growth variation with displacement amplitude

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Fig. 21

Details of finite element model used for numerical analysis (b1 represents boundary-1, b2 represents boundary-2, b3 represents boundary-3, Q represents oscillatory shear force, and P represents normal load)

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Fig. 22

True stress-strain curve for stainless steel

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Fig. 23

Variation of shear or tangential force with tangential displacement under stick condition

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Fig. 24

Variation in pressure distribution due to tangential loading under normal load (a) P = 70 N, (b) P = 140 N, and (c) P = 210 N

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Fig. 25

Increase in contact area (junction growth) with tangential or shear load

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Fig. 26

Energy dissipated at contact interface under normal load of 210 N and tangential load of (a) 30 N, (b) 60 N, and (c) 80 N

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Fig. 27

Variation of energy dissipated with tangential load under stick condition

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Fig. 28

Equivalent plastic strain at contact edge for normal load (a) 70 N, (b) 140 N, and (c) 210 N

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Fig. 29

Plastic strain at contact edge indicating combined ratcheting and cyclic plasticity under a normal load of 70 N and Q/P = 0.2857

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Fig. 30

Variation of equivalent plastic strain with shear or tangential load

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Fig. 31

Variation of stick radius with displacement amplitude where ao is the initial contact radius under normal load

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Fig. 32

Micrographs indicating surface damage of flat surface at displacement amplitude of 150 μm under (a) ambient conditions and (b) vacuum conditions

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Fig. 33

Contact interface modeled by using a spring element and a viscous damper

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Fig. 34

Variation of force with displacement amplitude




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