We give the closed-form solutions for the two-dimensional adhesive contact of a flat-ended wedge with an elastic half-space, including contact pressure distribution and load-contact width relationship. The approach is derived from contact mechanics in plane-strain elasticity and fracture mechanics concepts. The contact pressure has stress singularities both at the edges of contact due to molecular attractive forces and at the wedge corners, and is compared with those without adhesion. Under zero load, we find the contact strip has a finite width which is greater than that of the wedge end, and the central region of contact is under compression, similar to that of a flat punch problem, while the regions near the contact edges are under tension. Unlike the usual experiments with smooth and low modulus materials, we conduct molecular dynamics (MD) experiments via embedded-atom method (EAM), brownian dynamics algorithm and dynamical theory of crystal lattices. The results, including the “pull-off” force for contacting surfaces to peel apart, conform reasonably well with those derived from a continuum model.

Issue Section:
Research Papers
Topics:
Adhesives, Computers, Wedges, Pressure, Stress, Adhesion, Algorithms, Atoms, Compression, Contact mechanics, Corners (Structural elements), Crystal lattices, Dynamics (Mechanics), Elastic half space, Elasticity, Fracture mechanics, Molecular dynamics, Plane strain, Stress singularity, Strips, Tension
1.
Alber
I.
,
Bassani
J. L.
,
Khantha
M.
, et al.,
1992
, “
Grain Boundaries as Heterogeneous Systems: Atomic and Continuum Elastic Properties
,”
Phil. Trans: R. Soc., London, Series A
, Vol.
339
, pp.
555
–
586
.
2.
Barquins
M.
,
1988
, “
Adherence and Rolling Kinetics of a Rigid Cylinder in Contact with a Natural Rubber Surface
,”
J. Adhesion
, Vol.
26
, pp.
1
–
12
.
3.
Berendsen, H. J. C., and van Gunsteren, W. F., 1986, “Practical Algorithms for Dynamical Simulations,” Proc. Int. School of Physics 〈Enrico Fermi〉, North-Holland, Amsterdam, pp. 43–65.
4.
Born, M., and Huang, K., 1954, Dynamical Theory of Crystal Lattices, Clarendon Press, Oxford.
5.
Chaudhury
M. K.
,
Weaver
T.
,
Hui
C. Y.
, and
Kramer
E. J.
,
1996
, “
Adhesive Contact of Cylindrical Lens and a Flat Sheet
,”
J. Appl. Phys.
, Vol.
80
, No.
1
, pp.
30
–
37
.
6.
Daw
M. S.
, and
Baskes
M. I.
,
1984
, “
Embedded-Atom Method: Derivation and Application to Impurities, Surfaces, and Other Defects in Metals
,”
Phys. Rev. B
, Vol.
29
, No.
12
, pp.
6443
–
6453
.
7.
Derjaguin
B. V.
,
Mullet
V. M.
, and
Toporov
Y. P.
,
1975
, “
Effect of Contact Deformations on the Adhesion of Particles
,”
J. Colloid Interface Sci.
, Vol.
53
, pp.
314
–
326
.
8.
Ejike
U. B. C. O.
,
1981
, “
The Stress on an Elastic Half-Space Due to Sectionally Smooth-Ended Punch
,”
J. Elasticity
, Vol.
11
, No.
4
, pp.
395
–
402
.
9.
Hoagland
R. G.
,
Daw
M. S.
, and
Hirth
J. P.
,
1991
, “
Some Aspects of Forces and Fields in Atomic Models of Crack Tips
,”
J. Mater Res.
, Vol.
6
, No.
12
, pp.
2565
–
2577
.
10.
Homola
A. M.
,
Israelachvili
J. N.
,
Mcguiggan
P. M.
, and
Gee
M.
,
1990
, “
Fundamental Experimental Studies in Tribology: the Transition from ‘Interfa-cial’ Friction of Undamaged Molecularly Smooth Surfaces to ‘Normal’ Friction with Wear
,”
Wear
, Vol.
136
, pp.
65
–
83
.
11.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press.
12.
Johnson
K. L.
,
1997
, “
Adhesion and Friction Between a Smooth Elastic Spherical Asperity and a Plane Surface
,”
Proc. R. Soc., London, Series A
, Vol.
453
, pp.
163
–
179
.
13.
Johnson
K. L.
,
Kendall
K.
, and
Roberts
A. D.
,
1971
, “
Surface Energy and the Contact of Elastic Solids
,”
Proc. R. Soc., London, Series A
, Vol.
324
, pp.
301
–
313
.
14.
Johnson, K. L., 1998, private communication.
15.
Johnson
R. A.
,
1988
, “
Analytic Nearest-Neighbor Model for FCC Metals
,”
Phys. Rev. B
, Vol.
37
, No.
8
, pp.
3924
–
3931
.
16.
Kaneko
R.
,
Umemura
S.
,
Hirano
M.
, et al.,
1996
, “
Recent Progress in Microtribology
,”
Wear
, Vol.
200
, pp.
296
–
304
.
17.
Kendall
K.
,
1971
, “
The Adhesion and Surface Energy of Elastic Solids
,”
J. Phys. D: Appl. Phys.
, Vol.
4
, pp.
1186
–
1195
.
18.
Komvopoulos
K.
,
1996
, “
Surface Engineering and Microtribology for Microelectromechanical Systems
,”
Wear
, Vol.
200
, pp.
305
–
327
.
19.
Lantz
M. A.
,
O’Shea
S. J.
,
Welland
M. E.
, and
Johnson
K. L.
,
1997
, “
Atomic-Force-Microscope Study of Contact Area and Friction on NbSe2
,”
Phys. Rev. B
, Vol.
55
, No.
16
, pp.
10776
–
10785
.
20.
Maugis
D.
,
1992
, “
Adhesion of Spheres: The JKR-DMT Transition Using a Dugdale Model
,”
J. Colloid Interface Sci.
, Vol.
150
, No.
1
, pp.
243
–
269
.
21.
Maugis
D.
, and
Barquins
M.
,
1978
, “
Fracture Mechanics and the Adherence of Viscoelastic Bodies
,”
J. Phys. D: Appl. Phys.
, Vol.
11
, pp.
1989
–
2023
.
22.
Maugis
D.
, and
Barquins
M.
,
1983
, “
Adhesive Contact of Sectionally Smooth-Ended Punches on Elastic Half-Spaces: Theory and Experiment
,”
J. Phys. D: Appl. Phys.
, Vol.
16
, pp.
1843
–
1874
.
23.
Sneddon
Ian N.
,
1965
, “
The Relation Between Load and Penetration in the Axisymmetric Boussinesq Problem for a Punch of Arbitrary Profile
,”
Int. J. Eng. Sci.
, Vol.
3
, pp.
47
–
57
.
24.
Tabor
D.
,
1977
, “
Surface Forces and Surface Interactions
,”
J, Colloid Interface Sci.
, Vol.
58
, No.
1
, pp.
2
–
13
.
This content is only available via PDF.
Copyright © 1999
 by The American Society of Mechanical Engineers
You do not currently have access to this content.