In the current study, a semi-analytical model for contact between a homogeneous, isotropic, linear elastic half-space with a geometrically anisotropic (wavelengths are different in the two principal directions) bisinusoidal surface on the boundary and a rigid base is developed. Two asymptotic loads to area relations for early and almost complete contact are derived. The Hertz elliptic contact theory is applied to approximate the load to area relation in the early contact. The noncontact regions occur in the almost complete contact are treated as mode-I cracks. Since those cracks are in compression, an approximate relation between the load and noncontact area can be obtained by setting the corresponding stress intensity factor (SIF) to zero. These two asymptotic solutions are validated by two different numerical models, namely, the fast Fourier transform (FFT) model and the finite element (FE) model. A piecewise equation is fit to the numerical solutions to bridge these two asymptotic solutions.
Issue Section:
Contact Mechanics
References
1.
Westergaard
, H. M.
, 1939
, “Bearing Pressure and Cracks
,” ASME J. Appl. Mech.
, 6
, pp. 49
–53
.2.
Dundurs
, J.
, Tsai
, K. C.
, and Keer
, L. M.
, 1973
, “Contact Between Elastic Bodies With Wavy Surfaces
,” J. Elast.
, 3
(2
), pp. 109
–115
.10.1007/BF000458173.
Manners
, W.
, 1998
, “Partial Contact Between Elastic Surfaces With Periodic Profiles
,” Proc. R. Soc. London, Ser. A
, 454
(1980), pp. 3203
–3221
.10.1098/rspa.1998.02984.
Johnson
, K. L.
, 1995
, “The Adhesion of Two Elastic Bodies With Slightly Wavy Surfaces
,” Int. J. Solids Struct.
, 32
(3–4
), pp. 423
–430
.10.1016/0020-7683(94)00111-95.
Adams
, G. G.
, 2004
, “Adhesion at the Wavy Contact Interface Between Two Elastic Bodies
,” ASME J. Appl. Mech.
, 71
(6
), pp. 851
–856
.10.1115/1.17947026.
Maugis
, D.
, 1992
, “Adhesion of Spheres: The JKR-DMT Transition Using a Dugdale Model
,” J. Colloid Interface Sci.
, 150
(1
), pp. 243
–269
.10.1016/0021-9797(92)90285-T7.
Carbone
, G.
, and Mangialardi
, L.
, 2004
, “Adhesion and Friction of an Elastic Half-Space in Contact With a Slightly Wavy Rigid Surface
,” J. Mech. Phys. Solids
, 52
(6
), pp. 1267
–1287
.10.1016/j.jmps.2003.12.0018.
Block
, J. M.
, and Keer
, L. M.
, 2008
, “Periodic Contact Problems in Plane Elasticity
,” J. Mech. Mater. Struct.
, 3
(7
), pp. 1207
–1237
.10.2140/jomms.2008.3.12079.
Johnson
, K. L.
, Greenwood
, J. A.
, and Higginson
, J. G.
, 1985
, “The Contact of Elastic Regular Wavy Surfaces
,” Int. J. Mech. Sci.
, 27
(6
), pp. 383
–396
.10.1016/0020-7403(85)90029-310.
Jackson
, R. L.
, and Streator
, J. L.
, 2006
, “A Multi-Scale Model for Contact Between Rough Surfaces
,” Wear
, 261
(11–12
), pp. 1337
–1347
.10.1016/j.wear.2006.03.01511.
Krithivasan
, V.
, and Jackson
, R. L.
, 2007
, “An Analysis of Three-Dimensional Elasto-Plastic Sinusoidal Contact
,” Tribol. Lett.
, 27
(1
), pp. 31
–43
.10.1007/s11249-007-9200-612.
Jackson
, R. L.
, Krithivasan
, V.
, and Wilson
, W. E.
, 2008
, “The Pressure to Cause Complete Contact Between Elastic Plastic Sinusoidal Surfaces
,” Proc. Inst. Mech. Eng., Part J
, 222
(7
), pp. 857
–863
.10.1243/13506501JET42913.
Rostami
, A.
, and Jackson
, R. L.
, 2013
, “Predictions of the Average Surface Separation and Stiffness Between Contacting Elastic and Elastic-Plastic Sinusoidal Surfaces
,” Proc. Inst. Mech. Eng., Part J
, 227
(12
), pp. 1376
–1385
.10.1177/135065011349518814.
Rostami
, A.
, Goedecke
, A.
, Mock
, R.
, and Jackson
, R. L.
, 2014
, “Three-Dimensional Modeling of Elasto-Plastic Sinusoidal Contact Under Time Dependent Deformation Due to Stress Relaxation
,” Tribol. Int.
, 73
, pp. 25
–35
.10.1016/j.triboint.2013.12.02015.
Yastrebov
, V. A.
, Anciaux
, G.
, and Molinari
, J.-F.
, 2014
, “The Contact of Elastic Regular Wavy Surfaces Revisited
,” Tribol. Lett.
, 56
(1
), pp. 171
–183
.10.1007/s11249-014-0395-z16.
Johnson
, K. L.
, 1985
, Contact Mechanics
, Cambridge University Press
, Cambridge
, pp. 95
–96
.10.1017/CBO978113917173117.
Bueckner
, H. F.
, 1958
, “The Propagation of Cracks and the Energy of Elastic Deformation
,” ASME J. Appl. Mech.
, 80
, pp. 1225
–1230
.18.
Barenblatt
, G. I.
, 1962
, “The Mathematical Theory of Equilibrium Cracks in Brittle Fracture
,” Adv. Appl. Mech.
, 7
, pp. 55
–129
.10.1016/S0065-2156(08)70121-219.
Manners
, W.
, and Greenwood
, J. A.
, 2006
, “Some Observations on Persson’s Diffusion Theory of Elastic Contact
,” Wear
, 261
(5–6), pp. 600
–610
.10.1016/j.wear.2006.01.00720.
Xu
, Y.
, Jackson
, R. L.
, and Marghitu
, D. B.
, 2014
, “Statistical Model of Nearly Complete Elastic Rough Surface Contact
,” Int. J. Solids Struct.
, 51
(5
), pp. 1075
–1088
.10.1016/j.ijsolstr.2013.12.00521.
Greenwood
, J. A.
, 2014
, “On the Almost-Complete Contact of Elastic Rough Surfaces: The Removal of Tensile Patches
,” Int. J. Solids Struct.
(in press).22.
Stanley
, H. M.
, and Kato
, T.
, 1997
, “An FFT-Based Method for Rough Surface Contact
,” ASME J. Tribol
, 119
(3
), pp. 481
–485
.10.1115/1.283352323.
Kalker
, J. J.
, and van Randen
, Y.
, 1972
, “A Minimum Principle for Frictionless Elastic Contact With Application to Non-Hertzian Half-Space Contact Problems
,” J. Eng. Math.
, 6
(2
), pp. 193
–206
.10.1007/BF01535102Copyright © 2015 by ASME
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