Mode-mixity-dependent adhesive contact of a sphere on a plane surface

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 466, Issue 2117, 2010, Pages 1303-1325

  Waters, Julie F ^a   Guduru, Pradeep R ^a  

^a Brown University   (United States)

Author keywords

Contact mechanics; Interfacial work of adhesion; Mode mixity

Indexed keywords

BIOLOGICAL MATERIALS; ENERGY DISSIPATION; MECHANICS; SILICONES;

A-PLANE; ADHESIVE CONTACT; CONTACT AREAS; CONTACT MECHANICS; CONTACT PROBLEM; CRACK FRONTS; HALF-SPACE; MICROTRIBOMETER; MIXED MODE; MODE MIXITY; NORMAL LOADING; PHENOMENOLOGICAL MODELS; POLYDIMETHYLSILOXANE PDMS; POWER-LAW DEPENDENCES; RATE EFFECTS; RIGID SPHERE; SOFT ELASTOMERS; TANGENTIAL LOADING; WORK OF ADHESION;

ADHESION;

EID: 77952054376     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2009.0461     Document Type: Article

References (83)

1. Andrews, E. H. & Kinloch, A. J. 1973 Mechanics of adhesive failure. I. Proc. R. Soc. Lond. A 322, 385-399. (doi:10.1098/rspa.1973.0032)
2. Baney, J. M. & Hui, C.-Y. 1999 Viscoelastic crack healing and extension. J. Appl. Phys. 86, 4232-4241. (doi:10.1063/1.371351)
3. Barber, M., Donley, J. & Langer, J. S. 1989 Steady-state propagation of a crack in a viscoelastic strip. Phys. Rev. A 40, 366-376. (doi:10.1103/PhysRevA.40.366)
4. Barquins, M. 1984a Kinetics of the spontaneous peeling of elastomers. J. Appl. Polym. Sci. 29, 3269-3282. (doi:10.1002/app.1984.070291106) (Pubitemid 15423737)
5. Barquins, M. 1984b On a new mechanism in rubber friction. Wear 97, 111-114. (doi:10.1016/ 0043-1648(84)90086-3)
6. Barquins, M. 1985 Sliding friction of rubber and Schallamach waves-a review. Mater. Sci. Eng. 73, 45-63. (doi:10.1016/0025-5416(85)90295-2) (Pubitemid 16457122)
7. Barquins, M. 1992 Adherence, friction and wear of rubber-like materials. Wear 158, 87-117. (doi:10.1016/0043-1648(92)90033-5)
8. Barquins, M. & Courtel, R. 1975 Rubber friction and the rheology of viscoelastic contact. Wear 32, 133-150. (doi:10.1016/0043-1648(75)90263-X)
9. Barquins, M. & Roberts, A. D. 1986 Rubber friction variation with rate and temperature: some new observations. J. Phys. D Appl. Phys. 19, 547-563. (doi:10.1088/0022-3727/19/4/010)
10. Barquins, M., Maugis, D. & Courtel, R. 1975 Micro-glissements dans l'aire de contact d'une bille de verre et d'une plaque de caoutchouc au cours du deplacement preliminaire. C. R. Acad. Sci. B 280, 49-52.
11. Barthel, E. & Haiat, G. 2002 Approximate model for the adhesive contact of viscoelastic spheres. Langmuir 18, 9362-9370. (doi:10.1021/la025959+) (Pubitemid 35458197)
12. Barthel, E. & Roux, S. 2000 Velocity-dependent adherence: an analytical approach for the JKR and DMT models. Langmuir 16, 8134-8138. (doi:10.1021/la000474b)
13. Brown, H. R. 1993 Effects of chain pull-out on adhesion of elastomers. Macromolecules 26, 1666-1670. (doi:10.1021/ma00059a027)
14. Cao, H. C. & Evans, A. G. 1989 An experimental study of the fracture resistance of bimaterial interfaces. Mech. Mater. 7, 295-304. (doi:10.1016/0167-6636(89)90020-3)
15. Cattaneo, C. 1938 Sul contatto di due corp elastici: distribuzione local degli sforzi. Rend. Accad. Naz. Lin. 27, 342-348, 434-436, 474-478.
16. Chaudhury, M. K. 1999 Rate-dependent fracture at adhesive interface. J. Phys. Chem. B 103, 6562-6566. (doi:10.1021/jp9906482)
17. Chaudhury, M. K. & Whitesides, G. M. 1991 Direct measurement of interfacial interactions between semispherical lenses and flat sheets of poly(dimethylsiloxane) and their chemical derivatives. Langmuir 7, 1013-1025. (doi:10.1021/la00053a033)
18. Chaudhury, M. K., Weaver, T., Hui, C.-Y. & Kramer, E. J. 1996 Adhesive contact of a cylindrical lens and flat sheet. J. Appl. Phys. 80, 30-37. (doi:10.1063/1.362819)
19. Chen, S. & Gao, H. 2006a Generalized Maugis-Dugdale model of an elastic cylinder in non-slipping adhesive contact with a stretched substrate. Int. J. Mater. Res. 97, 584-593.
20. Chen, S. & Gao, H. 2006b Non-slipping adhesive contact between mismatched elastic spheres: a model of adhesion mediated deformation tensor. J. Mech. Phys. Solids 54, 1548-1567. (doi:10.1016/j.jmps.2006.03.001) (Pubitemid 43776860)
21. Chen, S. & Gao, H. 2006c Non-slipping adhesive contact of an elastic cylinder on stretched substrates. Proc. R. Soc. A 462, 211-228. (doi:10.1098/rspa.2005.1553)
22. Chen, S. & Gao, H. 2007 Non-slipping adhesive contact between mismatched elastic cylinders. Int. J. Solids Struct. 44, 1939-1948. (doi:10.1016/j.ijsolstr.2006.07.021) (Pubitemid 46161494)
23. Chen, S. & Wang, T. 2006 General solution to two-dimensional nonslipping JKR model with a pulling force in an arbitrary direction. J. Colloid Interf. Sci. 302, 363-369. (doi:10.1016/ j.jcis.2006.06.014)
24. Choi, S. T., Jeong, S. J. & Earmme, Y. Y. 2008 Modified-creep experiment of an elastomer film on a rigid substrate using nanoindentation with a flat-ended cylindrical tip. Scripta Mater. 58, 199-202. (doi:10.1016/j. scriptamat.2007.09.036) (Pubitemid 350110417)
25. de Gennes, P. G. 1996 Soft adhesives. Langmuir 12, 4497-4500. (doi:10.1021/la950886y)
26. Deruelle, M., Léger, L. & Tirrell, M. 1995 Adhesion at the solid-elastomer interface: influence of the interfacial chains. Macromolecules 28, 7419-7428. (doi:10.1021/ma00126a021)
27. Evans, A. G. & Hutchinson, J. W. 1989 Effects of non-planarity on the mixed mode fracture resistance of bimaterial interfaces. Acta Metall. 37, 909-916. (doi:10.1016/0001-6160(89) 90017-5)
28. Evans, A. G., Rühle, M., Dalgleish, B. J. & Charalambides, P. G. 1990 The fracture energy of bimaterial interfaces. Mater. Sci. Eng. A 126, 53-64. (doi:10.1016/0921-5093(90)90113-H)
29. Felder, E. & Barquins, M. 1992 Adherence of natural rubber sheets subjected to biaxial tensile strain. J. Phys. D Appl. Phys. 25, A9-A13. (doi:10.1088/0022-3727/25/1A/003)
30. Ferry, J. D. 1980 Viscoelastic properties of polymers, 3rd edn. New York, NY: John Wiley & Sons.
31. Galliano, A., Bistac, S. & Schultz, J. 2003 Adhesion and friction of PDMS networks: molecular weight effects. J. Colloid Interf. Sci. 265, 372-379. (doi:10.1016/S0021-9797(03)00458-2) (Pubitemid 37072078)
32. Gent, A. N. & Schultz, J. 1972 Effect of wetting liquids on the strength of adhesion of viscoelastic materials. J. Adhesion 3, 281-294. (doi:10.1080/00218467208072199)
33. Ghatak, A., Vorvolakos, K., She, H., Malotky, D. L. & Chaudhury, M. K. 2000 Interfacial rate processes in adhesion and friction. J. Phys. Chem. B 104, 4018-4030. (doi:10.1021/jp9942973)
34. Greenwood, J. A. 2004 The theory of viscoelastic crack propagation and healing. J. Phys. D Appl. Phys. 37, 2557-2569. (doi:10.1088/0022-3727/37/18/011)
35. Greenwood, J. A. & Johnson, K. L. 1981 The mechanics of adhesion of viscoelastic solids. Phil. Mag. A 43, 697-711. (doi:10.1080/01418618108240402)
36. Haiat, G., Phan Muy, M. C. & Barthel, E. 2003 The adhesive contact of viscoelastic spheres. J. Mech. Phys. Solids 51, 69-99. (doi:10.1016/S0022- 5096(02)00059-5) (Pubitemid 35282040)
37. Hui, C.-Y., Xu, D.-B. & Kramer, E. J. 1992 A fracture model for a weak interface in a viscoelastic material (small scale yielding analysis). J. Appl. Phys. 72, 3294-3304. (doi:10.1063/1.351451)
38. Hui, C.-Y., Baney, J. & Kramer, E. J. 1998 Contact mechanics and adhesion of viscoelastic spheres. Langmuir 14, 6570-6578. (doi:10.1021/ la980273w)
39. Hutchinson, J. W. & Suo, Z. 1992 Mixed mode cracking in layered materials. In Advances in applied mechanics, vol.29 (eds J. W. Hutchinson & T. Y. Wu), pp. 63-191. Boston, MA: Academic Press.
40. Jensen, H. M., Hutchinson, J. W. & Kim, K.-S. 1990 Decohesion of a cut prestressed film on a substrate. Int. J. Solids Struct. 26, 1099-1114. (doi:10.1016/0020-7683(90)90018-Q)
41. Johnson, K. L. 1985 Contact mechanics. Cambridge, UK: Cambridge University Press.
42. Johnson, K. L. 1996 Continuum mechanics modeling of adhesion and friction. Langmuir 12, 4510-4513. (doi:10.1021/la950889a)
43. Johnson, K. L. 1997 Adhesion and friction between a smooth elastic spherical asperity and a plane surface. Proc. R. Soc. Lond. A 453, 163-179. (doi:10.1098/rspa.1997.0010)
44. Johnson, K. L., Kendall, K., & Roberts, A. D. R. 1971 Surface energy and the contact of elastic solids. Proc. R. Soc. Lond. A 324, 301-313. (doi:10.1098/rspa.1971.0141)
45. Kendall, K. 1971 The adhesion and surface energy of elastic solids. J. Phys. D Appl. Phys. 4, 1186-1195. (doi:10.1088/0022-3727/4/8/320)
46. Kendall, K. 1973 Peel adhesion of solid films-surface and bulk effects. J. Adhesion 5, 179-202. (doi:10.1080/00218467308075019)
47. Kendall, K. 1975 Kinetics of contact between smooth solids. J. Adhesion 7, 55-72. (doi:10.1080/ 00218467508078897)
48. Kim, K.-S., McMeeking, R. M. & Johnson, K. L. 1998 Adhesion, slip, cohesive zones and energy fluxes for elastic spheres in contact. J. Mech. Phys. Solids 46, 243-266. (doi:10.1016/S0022- 5096(97)00070-7)
49. Lake, G. J. & Thomas, A. G. 1967 The strength of highly elastic materials. Proc. R. Soc. Lond. A 300, 108-119. (doi:10.1098/rspa.1967.0160)
50. Liechti, K. M. & Chai, Y. S. 1992 Asymmetric shielding in interfacial fracture under in-plane shear. J. Appl. Mech. 59, 295-304. (doi:10.1115/1. 2899520)
51. Lin, Y.-Y. & Hui, C.-Y. 2002 Mechanics of contact and adhesion between viscoelastic spheres: an analysis of hysteresis during loading and unloading. J. Polym. Sci. B Polym. Phys. 40, 772-793. (doi:10.1002/polb.10140) (Pubitemid 34428553)
52. Lin, Y.-Y., Hui, C.-Y. & Baney, J. M. 1999 Viscoelastic contact, work of adhesion and the JKR technique. J. Phys. D Appl. Phys. 32, 2250-2260. (doi:10.1088/0022-3727/32/17/316)
53. Lin, I.-K., Liao, Y.-M., Liu, Y., Ou, K.-S., Chen, K.-S. & Zhang, X. 2008 Viscoelastic mechanical behavior of soft microcantilever-based force sensors. Appl. Phys. Lett. 93, 251907. (doi:10.1063/1.3056114)
54. Maugis, D. 1987 Adherence of elastomers: fracture mechanics aspects. J. Adhes. Sci. Technol. 1, 105-134. (doi:10.1163/156856187X00120)
55. Maugis, D. 1992 Adhesion of spheres: the JKR-DMT transition using a Dugdale model. J. Colloid Interf. Sci. 150, 243-269. (doi:10.1016/0021-9797(92) 90285-T)
56. Maugis, D. & Barquins, M. 1978 Fracture mechanics and the adherence of viscoelastic bodies. J. Phys. D Appl. Phys. 11, 1989-2023. (doi:10.1088/0022-3727/11/14/011)
57. Meitl, M. A., Zhu, Z.-T., Kumar, V., Lee, K. J., Feng, X., Huang, Y. Y., Adeside, I., Nuzzo, R. G. & Rogers, J. A. 2006 Transfer printing by kinetic control of adhesion to an elastomeric stamp. Nat. Mater. 5, 33-38. (doi:10.1038/nmat1532) (Pubitemid 43049385)
58. Mindlin, R. D. 1949 Compliance of elastic bodies in contact. J. Appl. Mech. 16, 259.
59. Muller, V. M. 1996 Viscoelastic pull-off of a sphere from a flat surface. Colloid J. 58, 612-619.
60. Persson, B. N. J. & Brener, E. A. 2005 Crack propagation in viscoelastic solids. Phys. Rev. E 71, 036123. (doi:10.1103/PhysRevE.71.036123) (Pubitemid 40619799)
61. Perutz, S., Kramer, E. J., Baney, J., Hui, C.-Y. & Cohen, C. 1998 Investigation of adhesion hysteresis in poly(dimethylsiloxane) networks using the JKR technique. J. Polym. Sci. B Polym. Phys. 36, 2129-2139. (doi:10.1002/(SICI)1099-0488(19980915)36:123.0.<2129::AID-POLB11>CO;2-1)
62. Rand, C. J. & Crosby, A. J. 2006 Insight into the periodicity of Schallamach waves in soft material friction. Appl. Phys. Lett. 89, 261907. (doi:10.1063/1.2408640) (Pubitemid 46058001)
63. Rand, C. J. & Crosby, A. J. 2007 Friction of soft elastomeric surfaces with a defect. Appl. Phys. Lett. 91, 261909. (doi:10.1063/1.2828136)
64. Roberts, A. D. & Thomas, A. G. 1975 The adhesion and friction of smooth rubber surfaces. Wear 33, 45-64. (doi:10.1016/0043-1648(75)90223-9)
65. Saulnier, F., Ondarçuhu, T., Aradian, A. & Raphaël, E. 2004 Adhesion between a viscoelastic material and a solid surface. Macromolecules 37, 1067-1075. (doi:10.1021/ma021759t)
66. Savkoor, A. R. 1987 Dry adhesive contact of elastomers. Master's thesis, Delft University of Technology, Delft, The Netherlands.
67. Savkoor, A. R. 1992 Models of friction based on contact and fracture mechanics. In Fundamentals of friction: macroscopic and microscopic processes (eds I. L. Singer & H. M. Pollack), pp. 111-133. Dordrecht, The Netherlands: Kluwer Academic Publishers.
68. Savkoor, A. R. & Briggs, G. A. D. 1977 The effect of tangential force on the contact of elastic solids in adhesion. Proc. R. Soc Lond. A 356, 103-114. (doi:10.1098/rspa.1977.0123)
69. Schallamach, A. 1971 How does rubber slide? Wear 17, 301-312. (doi:10.1016/0043-1648(71)90033-0)
70. Schapery, R. A. 1975a A theory of crack initiation and growth in viscoelastic media. I. Theoretical development. Int. J. Fracture 11, 141-159. (doi:10.1007/BF00034721)
71. Schapery, R. A. 1975b A theory of crack initiation and growth in viscoelastic media. II. Approximate methods of analysis. Int. J. Fracture 11, 369-388.
72. Schapery, R. A. 1989 On the mechanics of crack closing and bonding in linear viscoelastic media. Int. J. Fracture 39, 163-189. (doi:10.1007/ BF00047448)
73. Schneider, F., Fellner, T., Wilde, J. & Wallrabe, U. 2008 Mechanical properties of silicones for MEMS. J. Micromech. Microeng. 18, 065008. (doi:10.1088/0960-1317/18/6/065008)
74. She, H., Malotky, D. & Chaudhury, M. K. 1998 Estimation of adhesion hysteresis at polymer/oxide interfaces using rolling contact mechanics. Langmuir 14, 3090-3100. (doi:10.1021/la971061m)
75. Shen, L., Glassmaker, N. J., Jagota, A. & Hui, C.-Y. 2008 Strongly enhanced static friction using a film-terminated fibrillar interface. Soft Mat. 4, 618-621. (doi:10.1039/b714737f) (Pubitemid 351304319)
76. Silberzan, P., Perutz, S., Kramer, E. J. & Chaudhury, M. K. 1994 Study of the self-adhesion hysteresis of a siloxane elastomer using the JKR method. Langmuir 10, 2466-2470. (doi:10.1021/ la00019a073)
77. Tang, S., Guo, T. F. & Cheng, L. 2008 Mode mixity and nonlinear viscous effects on toughness of interfaces. Int. J. Solids Struct. 45, 2493-2511. (doi:10.1016/j.ijsolstr.2007.12.010)
78. Vaenkatesan, V., Li, Z., Vellinga, W.-P. & de Jeu, W. H. 2006 Adhesion and friction behaviors of polydimethylsiloxane-a fresh perspective on JKR measurements. Polymer 47, 8317-8325. (doi:10.1016/j.polymer.2006.09.037) (Pubitemid 44708237)
79. VanLandingham, M. R., Chang, N.-K., Drzal, P. L., White, C. C. & Chang, S.-H. 2005 Viscoelastic characterization of polymers using instrumented nanoindentation. I. Quasi-static testing. J. Polym. Sci. B Polym. Phys. 43, 1794-1811. (doi:10.1002/polb.20454) (Pubitemid 41164822)
80. Varenberg, M., Peressadko, A., Gorb, S. & Arzt, E. 2006 Advanced testing of adhesion and friction with a microtribometer. Rev. Sci. Instrum. 77, 066105. (doi:10.1063/1.2214692) (Pubitemid 44000661)
81. Waters, J. F. 2009 Contact mechanics of biologically-inspired interface geometries. PhD thesis, Brown University, Providence, RI.
82. White, C. C., vanLandingham, M. R., Drzal, P. L., Chang, N.-K. & Chang, S.-H. 2005 Viscoelastic characterization of polymers using instrumented indentation. II. Dynamic testing. J. Polym. Sci. B Polym. Phys. 43, 1812-1824. (doi:10.1002/polb.20455) (Pubitemid 41164823)
83. Williams, M. L., Landel, R. F. & Ferry, J. D. 1955 The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J. Am. Chem. Soc. 77, 3701-3707. (doi:10.1021/ ja01619a008)