Generally, it is assumed that under any applied force there will always be some gap between the surfaces in a contact of rough elastic surfaces, resulting in a discontinuous (i.e., multiply connected) contact. The presence of gaps along the line contact relates to the ability to form an adequate mechanical seal across an interface. This paper will demonstrate that for a twice continuously differentiable rough surface with sufficiently small asperity amplitude and/or sufficiently large applied load and/or sufficiently low material elastic modulus, singly connected contacts exist. The solution of a contact problem for a rough elastic half-plane and a perfectly smooth rigid indenter with sharp edges is considered. First, a problem with artificially created surface irregularity is considered and it is shown that, for such a surface, the contact region is always multiply connected. An exact solution of the problem for an indenter with sharp edges resulting in a singly connected contact region is considered and it is conveniently expressed in the form of a series in Chebyshev polynomials. A sufficient (not necessary) condition for a contact of an indenter with sharp edges and a rough elastic surface to be singly connected is derived. The singly connected contact condition depends on the surface microtopography, material effective elastic modulus, and applied load. It is determined that, in most cases, a normal contact of a twice continuously differentiable rough surface with sufficiently small asperity amplitude, sufficiently low material elastic modulus, and/or sufficiently large applied load is singly connected.

References

References
1.
Greenwood
,
J. A.
, and
Williamson
,
J. B. P.
,
1966
, “
Contact of Nominally Flat Surface
,”
Proc. R. Soc. London, Ser. A
,
295
, pp.
300
312
.10.1098/rspa.1966.0242
2.
Ciavarella
,
M.
,
Delfine
,
V.
, and
Demelio
,
V. G.
,
2006
, “
A “Re-Vitalized“ Greenwood and Williamson Model of Elastic Contact Between Fractal Surfaces
,”
J. Mech. Phys. Solids
,
54
(
12
), pp.
2569
2591
.10.1016/j.jmps.2006.05.006
3.
Johnson
,
K. L.
,
Kendall
,
K.
, and
Roberts
,
A. D.
,
1971
, “
Surface Energy and the Contact of Elastic Solids
,”
Proc. R. Soc. London, Ser. A
,
324
, pp.
301
313
.10.1098/rspa.1971.0141
4.
Derjaguin
,
B. V.
,
Muller
,
V. M.
, and
Toporov
,
Y. P.
,
1975
, “Effect of Contact Deformations on the Adhesion of Particles,”
J. Colloid Interface Sci.
,
53
, pp.
314
326
.10.1016/0021-9797(75)90018-1
5.
Kalker
,
J. J.
,
1990
,
Three-Dimensional Elastic Bodies in Rolling Contact, Solid Mechanics and Its Applications
, Vol.
2
,
Kluwer
,
Dordrecht, The Netherlands
.
6.
Kudish
,
I. I.
, and
Covitch
,
M. J.
,
2010
,
Modeling and Analytical Methods in Tribology
,
Chapman & Hall/CRC
,
Boca Raton, FL
.
7.
Kudish
,
I. I.
,
2011
, “
Contact Fatigue of Elastic Surfaces With Small Roughness
,”
ASME J. of Tribol.
,
133
, July, p.
031405
.10.1115/1.4004346
8.
Kudish
,
I. I.
,
1987
, “
Contact Problem of the Theory of Elasticity for Prestressed Bodies With Cracks
,”
J. Appl. Mech. Tech. Phys.
,
28
, pp.
144
152
.10.1007/BF00918737
9.
Ciavarella
,
M.
,
Demelio
,
G.
,
Barber
,
J. R.
, and
Jang
,
Y. H.
,
2000
, “
Linear Elastic Contact of the Weierstrass Profile
,”
Proc. Roy. Soc. London, Ser. A
,
456
, pp.
387
405
.10.1098/rspa.2000.0522
10.
Snidle
,
R. W.
, and
Evans
,
H. P.
,
1994
, “
A Simple Method of Elastic Contact Simulation
,”
Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
,
208
, pp.
291
293
.10.1243/PIME_PROC_1994_208_384_02
11.
Lebeck
,
A. O.
,
1991
,
Principles and Design of Mechanical Face Seals
,
John Wiley & Sons
,
New York
.
12.
Galin
,
L. A.
,
1980
,
Contact Problems in Elasticity and Visco-Elasticity
,
Nauka
,
Moscow
.
13.
M.
Abramowitz
and
I.A.
Stegun
, eds.,
1964
,
Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables
,
National Bureau of Standards
, Vol.
55
,
Washington, DC.
14.
Szegö
,
G.
1959
,
Orthogonal Polynomials
, Vol.
XXIII
,
American Mathematical Society
,
Colloquim, New York
.
15.
Wong
,
R.
,
2001
,
Asymptotic Approximations of Integrals
,
Academic
,
New York
.
You do not currently have access to this content.