A systematic study is performed on the plane contact and adhesion of two elastic solids with an interface groove. The nonadhesion and Johnson–Kendall–Roberts (JKR) adhesion solutions for a typical groove shape are obtained in closed form by solving singular integral equations and using energy release rate approaches. It is found that the JKR adhesion solution depends solely on a dimensionless parameter α and the groove is predicted to be unstably flattened with no applied load when α0.535. Furthermore, the corresponding Maugis–Dugdale adhesion model has been revisited with three possible equilibrium states. By introducing the classical Tabor parameter μ, a complete transition between the nonadhesion and the JKR adhesion contact models is captured, which can be recovered as two limiting cases of the Maugis–Dugdale model. Depending on two nondimensional parameters α and μ, where α2 represents the ratio of the surface energy in the groove to the elastic strain energy when the grooved surface is flattened, different transition processes among three equilibrium states are characterized by one or more jumps between partial and full contact. Larger values of α and μ tend to induce more energy loss due to adhesion hysteresis. Combination values of α and μ are also suggested to design self-healing interface grooves due to adhesion.

References

References
1.
Etsion
,
I.
,
2005
, “
State of the Art in Laser Surface Texturing
,”
ASME J. Tribol.
,
127
(
1
), pp.
248
253
.
2.
Nakano
,
M.
,
Korenaga
,
A.
,
Korenaga
,
A.
,
Miyake
,
R.
,
Murakami
,
T.
,
Ando
,
Y.
,
Usami
,
H.
, and
Sasaki
,
S.
,
2007
, “
Applying Micro-Texture to Cast Iron Surfaces to Reduce the Friction Coefficient Under Lubricated Conditions
,”
Tribol. Lett.
,
28
(
2
), pp.
131
137
.
3.
Yong
,
X.
, and
Zhang
,
L. T.
,
2009
, “
Nanoscale Wetting on Grooved-Patterned Surfaces
,”
Langmuir
,
25
(
9
), pp.
5045
5053
.
4.
Sharp
,
K. G.
,
Blackman
,
G. S.
,
Glassmaker
,
N. J.
,
Jagota
,
A.
, and
Hui
,
C. Y.
,
2004
, “
Effect of Stamp Deformation on the Quality of Microcontact Printing: Theory and Experiment
,”
Langmuir
,
20
(15), pp.
6430
6438
.
5.
Hsia
,
K. J.
,
Huang
,
Y.
,
Menard
,
E.
,
Park
,
J. U.
,
Zhou
,
W.
,
Rogers
,
J.
, and
Fulton
,
J. M.
,
2005
, “
Collapse of Stamps for Soft Lithography Due to Interfacial Adhesion
,”
Appl. Phys. Lett.
,
86
(
15
), p.
154106
.
6.
Li
,
T.
, and
Zhang
,
Z.
,
2010
, “
Substrate-Regulated Morphology of Grapheme
,”
J. Phys. D: Appl. Phys.
,
43
(
7
), p.
075303
.
7.
Gao
,
W.
, and
Huang
,
Y.
,
2011
, “
Effect of Surface Roughness on Adhesion of Graphene Membranes
,”
J. Phys. D: Appl. Phys.
,
44
(
45
), p.
452001
.
8.
Hu
,
D.
, and
Adams
,
G. G.
,
2016
, “
Adhesion of a Micro-/Nano- Beam/Plate to a Sinusoidal/Grooved Surface
,”
Int. J. Solids Struct.
,
99
, pp.
40
47
.
9.
Gao
,
H.
, and
Yao
,
H.
,
2004
, “
Shape Insensitive Optimal Adhesion of Nanoscale Fibrillar Structures
,”
Proc. Natl. Acad. Sci. U.S.A.
,
101
(
21
), pp.
7851
7856
.
10.
Waters
,
J. F.
,
Gao
,
H.
, and
Guduru
,
P. R.
,
2011
, “
On Adhesion Enhancement Due to Concave Surface Geometries
,”
J. Adhes.
,
87
(
3
), pp.
194
213
.
11.
Jin
,
F.
,
Guo
,
X.
, and
Zhang
,
W.
,
2013
, “
A Unified Treatment of Axisymmetric Adhesive Contact on a Power-Law Graded Elastic Half-Space
,”
ASME J. Appl. Mech.
,
80
(
6
), p.
061024
.
12.
Johnson
,
K. L.
,
Kendall
,
K.
, and
Roberts
,
A. D.
,
1971
, “
Surface Energy and the Contact of Elastic Solids
,”
Proc. R. Soc. London A
,
324
(
1558
), pp.
301
313
.
13.
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
(
2
), pp.
314
326
.
14.
Tabor
,
D.
,
1977
, “
Surface Forces and Surface Interactions
,”
J. Colloid Interface Sci.
,
58
(
1
), pp.
2
13
.
15.
Maugis
,
D.
,
1992
, “
Adhesion of Spheres: The JKR-DMT Transition Using a Dugdale Model
,”
J. Colloid Interface Sci.
,
150
(
1
), pp.
243
269
.
16.
Baney
,
J. M.
, and
Hui
,
C. Y.
,
1997
, “
A Cohesive Zone Model for the Adhesion of Cylinders
,”
J. Adhes. Sci. Technol.
,
11
(
3
), pp.
393
406
.
17.
Johnson
,
K. L.
, and
Greenwood
,
J. A.
,
2008
, “
A Maugis Analysis of Adhesive Line Contact
,”
J. Phys. D: Appl. Phys.
,
41
(
15
), p.
155315
.
18.
Jin
,
F.
,
Zhang
,
W.
,
Guo
,
X.
, and
Zhang
,
S.
,
2014
, “
Adhesion Between Elastic Cylinders Based on the Double-Hertz Model
,”
Int. J. Solids Struct.
,
51
(
14
), pp.
2706
2712
.
19.
Kesari
,
H.
, and
Lew
,
A.
,
2011
, “
Effective Macroscopic Adhesive Contact Behavior Induced by Small Surface Roughness
,”
J. Mech. Phys. Solids
,
59
(
12
), pp.
2488
2510
.
20.
Jin
,
C.
,
Khare
,
K.
,
Vajpayee
,
S.
,
Yang
,
S.
,
Jagota
,
A.
, and
Hui
,
C. Y.
,
2011
, “
Adhesive Contact Between a Rippled Elastic Surface and a Rigid Spherical Indenter: From Partial to Full Contact
,”
Soft Matter
,
7
(
22
), pp.
10728
10736
.
21.
Wu
,
J. J.
,
2012
, “
Numerical Simulation of the Adhesive Contact Between a Slightly Wavy Surface and a Half-Space
,”
J. Adhes. Sci. Technol.
,
26
(
1–3
), pp.
331
351
.
22.
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
.
23.
Waters
,
J. F.
,
Lee
,
S.
, and
Guduru
,
P. R.
,
2009
, “
Mechanics of Axisymmetric Wavy Surface Adhesion: JKR-DMT Transition Solution
,”
Int. J. Solids Struct.
,
46
(
5
), pp.
1033
1042
.
24.
Jin
,
F.
,
Guo
,
X.
, and
Wan
,
Q.
,
2016
, “
Revisiting the Maugis-Dugdale Adhesion Model of Elastic Periodic Wavy Surfaces
,”
ASME J. Appl. Mech.
,
83
(
10
), p.
101007
.
25.
McMeeking
,
R. M.
,
Ma
,
L.
, and
Arzt
,
E.
,
2010
, “
Bi-Stable Adhesion of a Surface With a Dimple
,”
Adv. Eng. Mater.
,
12
(
5
), pp.
389
397
.
26.
Papangelo
,
A.
, and
Ciavarella
,
M.
,
2017
, “
A Maugis-Dugdale Cohesive Solution for Adhesion of a Surface With a Dimple
,”
J. R. Soc. Interface
,
14
(
127
), p.
20160996
.
27.
Martynyak
,
R.
,
2001
, “
The Contact of a Half-Space and an Uneven Base in the Presence of an Intercontact Gap Filled by an Ideal Gas
,”
J. Math. Sci.
,
107
(1), pp.
3680
3685
.
28.
Chumak
,
K.
,
Chizhik
,
S.
, and
Martynyak
,
R.
,
2014
, “
Adhesion of Two Elastic Conforming Solids With a Single Interface Gap
,”
J. Adhes. Sci. Technol.
,
28
(
16
), pp.
1568
1578
.
29.
Chumak
,
K.
,
2016
, “
Adhesive Contact Between Solids With Periodically Grooved Surfaces
,”
Int. J. Solids Struct
,
78–79
, pp.
70
76
.
30.
Malanchuk
,
N.
, and
Martynyak
,
R.
,
2012
, “
Contact Interaction of Two Solids With Surface Groove Under Proportional Loading
,”
Int. J. Solids Struct.
,
49
(
23–24
), pp.
3422
3431
.
31.
Johnson
,
K. L.
,
1985
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, UK
.
32.
Johnson
,
K. L.
,
1995
, “
The Adhesion of Two Elastic Bodies With Slightly Wavy Surfaces
,”
Int. J. Solids Struct.
,
32
(
3–4
), pp.
423
430
.
33.
Jin
,
F.
,
Wan
,
Q.
, and
Guo
,
X.
,
2016
, “
A Double-Westergaard Model for Adhesive Contact of a Wavy Surface
,”
Int. J. Solids Struct.
,
102–103
, pp.
66
76
.
34.
Hills
,
D. A.
,
Nowell
,
D.
, and
Sackfield
,
A.
,
1993
,
Mechanics of Elastic Contacts
,
Butterworth–Heinemann
,
Oxford, UK
.
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