In this paper, a solution to the quasi-static adhesive contact problem between a rigid cylinder and a transversely isotropic substrate is extended to the most general case by taking adhesion hysteresis into account. An analytical solution to the contact stress is obtained by solving the integral equations established on the basis of the Green's function for the two-dimensional transversely isotropic half-space problem. By using equilibrium conditions and Griffith's criterion, the adhesion force and resistant moment to rolling are determined as functions of contact geometries and material properties of the contacting solids. Detailed discussions on the adhesion force and resistant moment are presented for some specific cases, revealing adhesion behaviors that have not been predicted by previous models. As the most generalized solution to the discussed problem, our results would have extensive applications in predicting the adhesion behavior between solids undergoing sophisticated mechanical loadings.
Issue Section:
Research Papers
References
1.
Hertz
, H.
, 1882
, “Ueber Die Berührung Fester Elastischer Körper (on the Contact of Elastic Solids)
,” J. Reine Angew. Math.
, 92
, pp. 156
–171
.2.
Johnson
, K. L.
, Kendall
, K.
, and Roberts
, A. D.
, 1971
, “Surface Energy and Contact of Elastic Solids
,” Proc. R. Soc. London, Ser. A
, 324
, pp. 301
–313
.10.1098/rspa.1971.01413.
Griffith
, A. A.
, 1921
, “The Phenomena of Rupture and Flow in Solids
,” Philos. Trans. R. Soc. London, Ser. A
, 221
, pp. 163
–198
.10.1098/rsta.1921.00064.
Chaudhury
, M. K.
, and Whitesides
, G. M.
, 1991
, “Direct Measurement of Interfacial Interactions Between Semispherical Lenses and Flat Sheets of Poly(Dimethylsiloxane) and Their Chemical Derivatives
,” Langmuir
, 7
, pp. 1013
–1025
.10.1021/la00053a0335.
Dutrowski
, R. C.
, 1969
, “Hertzian Contact and Adhesion of Elastomers
,” ASME J. Lubr. Technol.
, 91F
, pp. 732
–737
.10.1115/1.35550316.
Horn
, R. G.
, Israelachvili
, J. N.
, and Pribac
, F.
, 1987
, “Measurement of the Deformation and Adhesion of Solids in Contact
,” J. Colloid Interface Sci.
, 115
, pp. 480
–492
.10.1016/0021-9797(87)90065-87.
Chaudhury
, M. K.
, and Owen
, M. J.
, 1993
, “Correlation Between Adhesion Hysteresis and Phase State of Monolayer Films
,” J. Phys. Chem.
, 97
, pp. 5722
–5726
.10.1021/j100123a0438.
Shanahana
, M. E. R.
, and Michelb
, F.
, 1991
, “Physical Adhesion of Rubber to Glass: Cross–Link Density Effects Near Equilibrium
,” Int. J. Adhes. Adhes.
, 11
, pp. 170
–176
.10.1016/0143-7496(91)90019-E9.
Chen
, Y. L.
, Helm
, C. A.
, and Israelachvili
, J. N.
, 1991
, “Molecular Mechanisms Associated With Adhesion and Contact Angle Hysteresis of Monolayer Surfaces
,” J. Phys. Chem.
, 95
, pp. 10,736
–10,747
.10.1021/j100179a04110.
Dominik
, C.
, and Tielens
, A. G. G. M.
, 1995
, “Resistance to Rolling in the Adhesive Contact of Two Spheres
,” Philos. Mag. A
, 72
, pp. 783
–803
.10.1080/0141861950824380011.
Heim
, L. O.
, Blum
, J.
, Preuss
, M.
, and Butt
, H. J.
, 1999
, “Adhesion and Friction Forces Between Spherical Micrometer-Sized Particles
,” Phys. Rev. Lett.
, 83
, pp. 3328
–3331
.10.1103/PhysRevLett.83.332812.
Baney
, J. M.
, and Hui
, C. Y.
, 1997
, “A Cohesive Zone Model for the Adhesion of Cylinders
,” J. Adhes. Sci. Technol.
, 11
, pp. 393
–406
.10.1163/156856197X0077813.
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.
, 80
, pp. 30
–37
.10.1063/1.36281914.
Zhupanska
, O. I.
, and Ulitko
, A. F.
, 2005
, “Contact With Friction of a Rigid Cylinder With an Elastic Half-Space
,” J. Mech. Phys. Solids
, 53
, pp. 975
–999
.10.1016/j.jmps.2005.01.00215.
Kendall
, K.
, 1975
, “Rolling Friction and Adhesion Between Smooth Solids
,” Wear
, 33
, pp. 351
–358
.10.1016/0043-1648(75)90288-416.
She
, H.
, Malotky
, D.
, and Chaudhury
, M. K.
, 1998
, “Estimation of Adhesion Hysteresis at Polymer/Oxide Interfaces Using Rolling Contact Mechanics
,” Langmuir
, 14
, pp. 3090
–3100
.10.1021/la971061m17.
She
, H.
, and Chaudhury
, M. K.
, 2000
, “Estimation of Adhesion Hysteresis Using Rolling Contact Mechanics
,” Langmuir
, 16
, pp. 622
–625
.10.1021/la990798418.
Chen
, S.
, and Gao
, H.
, 2007
, “Bio-Inspired Mechanics of Reversible Adhesion: Orientation-Dependent Adhesion Strength for Non-Slipping Adhesive Contact With Transversely Isotropic Elastic Materials
,” J. Mech. Phys. Solids
, 55
, pp. 1001
–1015
.10.1016/j.jmps.2006.10.00819.
Yao
, H.
, Chen
, S.
, Guduru
, P. R.
, and Gao
, H.
, 2009
, “Orientation-Dependent Adhesion Strength of a Rigid Cylinder in Non-Slipping Contact With a Transversely Isotropic Half-Space
,” Int. J. Solids Struct.
, 46
, pp. 1167
–1175
.10.1016/j.ijsolstr.2008.10.01120.
Barnett
, D. M.
, and Lothe
, J.
, 1973
, “Synthesis of the Sextic and the Integral Formalism for Dislocations, Greens Function and Surface Waves in Anisotropic Elastic Solids
,” Phys. Norv.
, 7
, pp. 13
–19
.21.
Ting
, T. C. T.
, 1996
, Anisotropic Elasticity
, Oxford University Press
, New York
.22.
Chen
, S. H.
, and Gao
, H. J.
, 2006
, “Non-Slipping Adhesive Contact of an Elastic Cylinder on Stretched Substrates
,” Proc. R. Soc. London, Ser. A
, 462
, pp. 211
–228
.10.1098/rspa.2005.155323.
Anderson
, T. L.
, 2005
, Fracture Mechanics: Fundamentals and Applications
, Taylor & Francis
, Boca Raton, FL
.24.
Hwu
, C.
, 1993
, “Fracture Parameters for Orthotropic Biomaterial Interface Cracks
,” Eng. Fract. Mech.
, 45
, pp. 89
–97
.10.1016/0013-7944(93)90010-P25.
Rice
, J. R.
, 1988
, “Elastic Fracture Mechanics Concepts for Interfacial Cracks
,” J. Appl. Mech.
, 55
, pp. 98
–103
.10.1115/1.317366826.
Kendall
, K.
, 1975
, “Kinetics of Contact Between Smooth Solids
,” J. Adhes.
, 7
, pp. 55
–72
.10.1080/0021846750807889727.
Barquins
, M.
, 1988
, “Adherence and Rolling Kinetics of a Rigid Cylinder in Contact With a Natural Rubber Surface
,” J. Adhes.
, 26
, pp. 1
–12
.10.1080/0021846880807127128.
Fischer
, K. E.
, Aleman
, B. J.
, Tao
, S. L.
, Daniels
, R. H.
, Li
, M. E.
, Buenger
, M. D.
, Nagaraj
, G.
, Singh
, P.
, Zettl
, A.
, and Desai
, T.
, 2009
, “Biomimetic Nanowire Coatings for Next Generation Adhesive Drug Delivery Systems
,” Nano Lett.
, 9
, pp. 716
–720
.10.1021/nl803219f29.
Alon
, R.
, Hammer
, D. A.
, and Springer
, T. A.
, 1995
, “Lifetime of the P-Selectin-Carbohydrate Bond and its Response to Tensile Force in Hydrodynamic Flow
,” Nature
, 374
, pp. 539
–542
.10.1038/374539a030.
Dongye
, C.
, and Ting
, T. C. T.
, 1989
, “Explicit Expressions of Barnett-Lothe Tensors and Their Associated Tensors for Orthotropic Materials
,” Q. Appl. Math.
, 47
, pp. 723
–734
.Copyright © 2013 by ASME
You do not currently have access to this content.
