Adherence and Fracture Mechanics

  • Daniel Maugis


Cohesion of solids is insured by a number of well-known forces (van der Waals, ionic, metallic, covalent) and their rupture occurs by propagation of a crack during which the bonds are broken one by one, like a zip fastener. The energy needed to break these bonds is 2γ per surface area (where γ is the surface energy of the material) and is taken from the potential energy of an applied load and/or the elastic energy stored in the body. Surface energy reflects the strength of bonds and rarely exceeds 2 J/m2.


Stress Intensity Factor Energy Release Rate Adherence Force Crack Opening Displacement Liquid Bridge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    S. J. Burns, J. C. Pollet, and C. Lun Chow, Nonlinear fracture mechanics, Int. J. Fract. 14, 311–326 (1978).CrossRefGoogle Scholar
  2. 2.
    C. Gurney and J. Hunt, Quasi-static crack propagation, Proc. R. Soc. London, Ser: A 299, 508–524 (1967).CrossRefGoogle Scholar
  3. 3.
    J. W. Hutchinson and P. C. Paris, Stability analysis of J controlled crack growth, in: Elastic-Plastic Fracture, ASTM STP 668, Philadelphia (1979).Google Scholar
  4. 4.
    D. Maugis and M. Barquins, Fracture mechanics and adherence of viscoelastic solids, in: Adhesion and Adsorption of Polymers (L. H. Lee, ed.), Part A, pp. 203–277, Plenum Press, New York (1980).CrossRefGoogle Scholar
  5. 5.
    G. I. Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture, Adv. Appl. Mech. 7, 55–129 (1962).CrossRefGoogle Scholar
  6. 6.
    D. McLean, Grain Boundaries in Metals, p. 299, Clarendon Press, Oxford (1957).Google Scholar
  7. 7.
    K. Kendall, The adhesion and surface energy of elastic solids, J. Phys. D 4, 1186–1195 (1971).CrossRefGoogle Scholar
  8. 8.
    P. C. Paris and G. C. Sih, Stress analysis of cracks, in: Fracture toughness Testing and its Applications, pp. 30–83, ASTM STP 381, Philadelphia (1965).CrossRefGoogle Scholar
  9. 9.
    K. L. Johnson, K. Kendall, and A. D. Roberts, Surface energy and the contact of elastic solids, Proc. R. Soc. London, Ser. A 324, 301–313 (1971).CrossRefGoogle Scholar
  10. 10.
    D. Maugis and M. Barquins, Fracture mechanics and the adherence of viscoelastic bodies, J. Phys. D 11, 1989–2023 (1978).Google Scholar
  11. 11.
    I. N. Sneddon, The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile, Int. J. Eng. Sci. 3, 47–57 (1965).CrossRefGoogle Scholar
  12. 12.
    M. Barquins and D. Maugis, Adhesive contact of axisymmetric punches on an elastic half-space: the modified Hertz-Huber’s stress tensor for contacting spheres, J. Mech. Theor. Appl. 1, 331–357 (1982).Google Scholar
  13. 13.
    D. Maugis and M. Barquins, Adhesive contact of a conical punch on an elastic half-space, J. Phys. (Paris), Lett. 42, L95–L97 (1981).CrossRefGoogle Scholar
  14. 14.
    D. Maugis and M. Barquins, Adhesive contact of sectionally smooth-ended punches on elastic half-spaces: theory and experiment, J. Phys. D 16, 1843–1874 (1983).CrossRefGoogle Scholar
  15. 15.
    K. Kendall, Shrinkage and peel strength of adhesive joints, J. Phys. D 6, 1782–1787 (1973).CrossRefGoogle Scholar
  16. 16.
    M. Barquins, Kinetics of the spontaneous peeling of elastomers, J. Appl. Polym. Sci. 29, 3269–3282 (1984).CrossRefGoogle Scholar
  17. 17.
    F. M. Orr, L. E. Scriven, and A. P. Rivas. Pendular rings between solids: meniscus properties and capillary force, J. Fluid Mech. 67, 723–742 (1975).CrossRefGoogle Scholar
  18. 18.
    M. A. Fortes, Axisymmetric liquid bridges between parallel plates, J. Colloid Interface Sci. 88, 338–352 (1982).CrossRefGoogle Scholar
  19. 19.
    E. A. Boucher, M. J. B. Evans, and S. McGarry, Capillary phenomena. XX. Fluid bridges between horizontal solid plates in a gravitational field, J. Colloid Interface Sci. 89, 154–165 (1982).CrossRefGoogle Scholar
  20. 20.
    D. N. Mazzone, G. I. Tardos, and R. Pfeffer, The effect of gravity on the shape and strength of a liquid bridge between two spheres, J. Colloid Interface Sci. 113, 544–556 (1986).CrossRefGoogle Scholar
  21. 21.
    R. A. Fisher, On the capillary forces in an ideal soil: corrections of formulae given by W. B. Haines, J. Agric. Sci. 16, 492–505 (1926).CrossRefGoogle Scholar
  22. 22.
    R. B. Heady and J. W. Cahn, An analysis of the capillary forces in liquid-phase sintering of spherical particles, Metall. Trans. 1, 185–189 (1970).Google Scholar
  23. 23.
    L. R. Fisher and J. N. Israelachvili, Direct measurement of the effect of menicus forces on adhesion: a study of the applicability of macroscopic thermodynamics to microscopic liquid interfaces, Colloids Surf. 3, 303–319 (1981).CrossRefGoogle Scholar
  24. 24.
    R. W. Coughlin, B. Elbirli, and L. Vergara-Edwards, Interparticle force conferred by capillary-condensed liquid at contact points. I. Theoretical considerations, J. Colloid Interface Sci. 87, 18–30 (1982).CrossRefGoogle Scholar
  25. 25.
    M. A. Erle, D. C. Dyson, and N. R. Morrow, Liquid bridges between cylinders, in a torus and between spheres, A.I.Ch.E.J. 17, 115–121 (1971).CrossRefGoogle Scholar
  26. 26.
    C. Mason and W. C. Clark, Liquid bridges between spheres, Chem. Eng. Sci. 20, 859–866 (1965).CrossRefGoogle Scholar
  27. 27.
    K. Hotta, K. Takeda, and K. Ilnoya, The capillary binding force of a liquid bridge, Powder Technol. 10, 231–242 (1974).CrossRefGoogle Scholar
  28. 28.
    J. S. McFarlane and D. Tabor, Adhesion of solids and the effect of surface films, Proc. R. Soc. London Ser. A 202, 224–243 (1950).CrossRefGoogle Scholar
  29. 29.
    W. J. O’Brien and J. J. Hermann, The strength of liquid bridges between dissimilar materials, J. Adhes. 5, 91–103 (1973).CrossRefGoogle Scholar
  30. 30.
    L. R. Fisher and J. N. Israelachvili, Determination of the capillary pressure in menisci of molecular dimensions, Chem. Phys. Lett. 76, 325–328 (1980).CrossRefGoogle Scholar
  31. 31.
    Healey, A. Trans. Inst. Rubber Ind. 1, 334 (1926).Google Scholar
  32. 32.
    H. K. Mueller and W. G. Knauss, The fracture energy and some mechanical properties of a polyurethane elastomer, Trans. Soc. Rheol. 15, 217–233 (1971).CrossRefGoogle Scholar
  33. 33.
    E. H. Andrews and A. J. Kinloch, Mechanics of adhesive failure, Proc. R. Soc. London, Ser. A 332, 385–399 (1973).CrossRefGoogle Scholar
  34. 34.
    A.N. Gent and J. Schultz, Effect of wetting liquids on the strength of adhesion of viscoelastic materials, J. Adhes. 3, 281–294 (1972).CrossRefGoogle Scholar
  35. 35.
    L. Mullins, Rupture of rubber, Part IX. Rôle of hysteresis in the tearing of rubber, Trans. Inst. Rubber Ind. 35, 213–222 (1959).Google Scholar
  36. 36.
    M. Barquins, Influence of the stiffness of testing machines on the adherence of elastomers, J. Appl. Polym. Sci. 28, 2647–2657 (1983).CrossRefGoogle Scholar
  37. 37.
    A. D. Roberts, Looking at rubber adhesion, Rubber Chem. Technol. 52, 23–42 (1979).CrossRefGoogle Scholar
  38. 38.
    M. Barquins and D. Maugis, Tackiness of elastomers, J. Adhes. 13, 53–65 (1981).CrossRefGoogle Scholar
  39. 39.
    D. Maugis, Adherence of solids, in: Microscopic Aspects of Adhesion and Lubrication (J. M. Georges, ed.), pp. 221–252, Elsevier, Amsterdam (1982).Google Scholar
  40. 40.
    G. P. Marshall, L. H. Coutts, and J. G. Williams, Temperature effects in the fracture of PMMA, J. Mater. Sci. 9, 1409–1419 (1974).CrossRefGoogle Scholar
  41. 41.
    R. M. Hill and L. A. Dissado, Relaxation in elastic and viscoelastic materials, J. Mater. Sci. 19, 1576–1595 (1984).CrossRefGoogle Scholar
  42. 42.
    O. Coussy, Unmodèle de viscoélasticité confinée en mécanique de la rupture. Propagation subcritique, C. R. Acad. Sci. Paris, Ser. II 302, 53–56 (1986).Google Scholar
  43. 43.
    R. S. Rivlin and A. G. Thomas, Rupture of rubber I. Characteristic energy for tearing, J. Polym. Sci. 10, 291–318 (1953).CrossRefGoogle Scholar
  44. 44.
    R. D. Margolis, R. W. Dunlap, and H. Markovitz, Fracture toughness testing of glassy plastics, in: Cracks and Fracture, pp. 391–408, ASTM STP 601, Philadelphia (1976).CrossRefGoogle Scholar
  45. 45.
    D. Maugis, Subcritical crack growth, surface energy, fracture toughness, stick-slip and embrittlement, J. Mater. Sci. 20, 3041–3073 (1985).CrossRefGoogle Scholar
  46. 46.
    T. Kobayashi and J. W. Dally, A system of modified epoxies for dynamic photoelastic studies of fracture, Exp. Mech. 17, 367–374 (1977).CrossRefGoogle Scholar
  47. 47.
    A. B. J. Clark and G. R. Irwin, Crack propagation behaviors, Exp. Mech. 6, 321–330 (1966).CrossRefGoogle Scholar
  48. 48.
    J. G. Williams, J. C. Radon, and C. E. Turner, Designing against fracture in brittle plastics, Polym. Eng. Sci. 4, 130–141 (1968).CrossRefGoogle Scholar
  49. 49.
    J. G. Williams, Fracture Mechanics of Polymers, Ellis Horwood, New York (1984).Google Scholar
  50. 50.
    S. Yamini and R. J. Young, Crack propagation in and factography of epoxy resins, J. Mater. Sci. 14, 1609–1618 (1979).CrossRefGoogle Scholar
  51. 51.
    D. W. Aubrey and M. Sherriff, Peel adhesion and viscoelasticity of rubber-resin blends, J. Polym. Sei., Polym. Chem. Ed. 18, 2597–2608 (1980).CrossRefGoogle Scholar
  52. 52.
    M. Barquins, B. Khandani, and D. Maugis, Propagation saccadée de fissure dans le pelage d’un solide viscoelastique, C. R. Acad. Sci. Paris, Ser. II 303, 1517–1519 (1986).Google Scholar
  53. 53.
    D. Maugis, Propagation saccadée de fissure en pelage, rôle de l’inertie, C. R. Acad. Sci. Paris, Ser. II304, 775–778 (1987).Google Scholar
  54. 54.
    D. Maugis and M. Barquins, Stick-slip and peeling of adhesive tapes, in: Adhesion 12 (K. W. Allen, Ed.), pp. 205–222, Elsevier, London (1988).CrossRefGoogle Scholar
  55. 55.
    N. Minorsky, Nonlinear Oscillations, Van Nostrand, New York (1962).Google Scholar
  56. 56.
    D. W. Jordan and P. Smith, Non-linear Ordinary Differential Equations, Clarendon Press, Oxford (1977).Google Scholar
  57. 57.
    A. Carré and J. Schultz, Polymer-aluminium adhesion IV. Kinetic aspects of the effect of a liquid environment, J. Adhes. 18, 207–216 (1985).CrossRefGoogle Scholar
  58. 58.
    T. A. Michalske and V. D. Frechette, Dynamic effect of liquids on crack growth leading to catastrophic failure in glass, J. Am. Ceram. Soc. 63, 603–609 (1980).CrossRefGoogle Scholar
  59. 59.
    S. M. Wiederhorn, Influence of water vapor on crack propagation on soda-lime glass, J. Am. Ceram. Soc. 50, 407–414 (1967).CrossRefGoogle Scholar
  60. 60.
    S. M. Wiederhorn, S. M. Freiman, E. R. Fuller, and C. J. Simmons, Effects of water and other dielectrics on crack growth, J. Mater. Sci. 17, 3460–3478 (1982).CrossRefGoogle Scholar
  61. 61.
    D. Maugis, Subcritical crack growth, surface energy and fracture toughness of brittle materials, in: Fracture Mechanics of Ceramics, Vol. 8 (R. C. Bradt, A. G. Evans, D.P.H. Hasselman, and F. F. Lange, eds.), pp. 255–272. Plenum Press, New York (1986).CrossRefGoogle Scholar
  62. 62.
    M. Barquins, Influence of dwell time on the adherence of elastomers, J. Adhes. 14, 63–82 (1982).CrossRefGoogle Scholar
  63. 63.
    M. Barquins, Adhesive contact and kinetics of adherence between a rigid sphere and an elastomeric solid, Int. J. Adhes. Adhesion 3, 71–84 (1983).CrossRefGoogle Scholar
  64. 64.
    M. Barquins and D. Wehbi, Study of adherence of elastomers by cyclic unloading experiments, J. Adhes. 20, 55–74 (1986).CrossRefGoogle Scholar
  65. 65.
    A. N. Gent and P. Vondracek, Spontaneous adhesion of silicone rubber, J. Appl. Polym. Sci. 27, 4357–4364 (1982).CrossRefGoogle Scholar
  66. 66.
    G. J. Lake and A. G. Thomas, The strength of highly elastic materials, Proc. R. Soc. London, Ser. A 300, 108–119(1967).CrossRefGoogle Scholar
  67. 67.
    A. N. Gent and R. H. Tobias, Threshold tear strength of elastomers, J. Polym. Sci., Polym. Phys. Ed. 20, 2051–2058 (1982).CrossRefGoogle Scholar
  68. 68.
    A. Carré and J. Schultz, Polymer-aluminium adhesion. II. Role of the adhesive and cohesive properties of the polymer, J. Adhes. 17, 135–156 (1984).CrossRefGoogle Scholar
  69. 69.
    A. Ahagon and A. N. Gent, Effect of interfacial bonding on the strength of adhesion, J. Polym. Sci., Polym. Phys. Ed. 13, 1285–1300 (1975).CrossRefGoogle Scholar
  70. 70.
    R. J. Chang and A. N. Gent, Effect on interfacial bonding on the strength of elastomers. I. Self-adhesion, J. Polym. Sci., Polym. Phys. Ed. 19, 1619–1633 (1981).CrossRefGoogle Scholar
  71. 71.
    A.N. Gent, The strength of adhesive bonds. An examination of interfacial chemistry, rheology of materials, and fracture mechanics, Adhes. Age 27–31 (Feb. 1982).Google Scholar
  72. 72.
    G. J. Lake and A. Stevenson, On the mechanics of peeling, in Adhesion 6 (K. W. Allen, ed.), pp. 41–52, Applied Science Publ., London (1982).Google Scholar
  73. 73.
    G.J. Lake, Influence of the strength of interfacial bonding on the fracture characteristics of adhesive joints, in: International Adhesion Conference Nottingham 1984, pp. 22.1–22.4, The Plastic and Rubber Institute (1984).Google Scholar
  74. 74.
    W. V. Titow, Solvent welding of plastics, in: Adhesion 2 (K. W. Allen, ed.), pp. 181–196, Applied Science Publ., London (1978).Google Scholar
  75. 75.
    K. Jud, H. H. Kausch, and J. G. Williams, Fracture mechanics studies of crack healing and welding of polymers, J. Mater. Sci. 16, 204–210 (1981).CrossRefGoogle Scholar
  76. 76.
    P. G. de Gennes, Sur la soudure des polymeres amorphes, C. R. Acad. Sci. Paris, Ser. B 291, 219–221 (1980).Google Scholar
  77. 77.
    P. G. de Gennes, The formation of polymer/polymer junctions, in: Microscopic Aspects of Adhesion and Lubrication (J. M. Georges, ed.), pp. 335–367, Elsevier, Amsterdam (1982).Google Scholar
  78. 78.
    P. G. de Gennes, Adhesion: une liste de questions, in: Adsorption and Adhesion (5ème école d’Eté Méditerranenne, ed.), pp. 1–10, Les Editions de Physique, Paris (1984).Google Scholar
  79. 79.
    S. Prager and M. Tirrell, The healing process at polymer-polymer interfaces, J. Chem. Phys. 75, 5194–5198 (1981).CrossRefGoogle Scholar
  80. 80.
    Y.-H. Kim and R. P. Wool, A theory of healing at a polymer-polymer interface, Macromolecules 16, 1115–1120(1983).CrossRefGoogle Scholar
  81. 81.
    E. J. Kramer, Microscopic and molecular fundamental of crazing, Adv. Polym. Sci. 52/53, 1–56 (1983).CrossRefGoogle Scholar
  82. 82.
    G. P. Marshall, L. E. Culver, and J. G. Williams, Craze growth in polymethylmethacrylate: a fracture mechanics approach, Proc. R. Soc. London, Ser. A 319, 165–187 (1970).CrossRefGoogle Scholar
  83. 83.
    H. R. Brown and I. M. Ward, Craze shape and fracture in poly(methylmethacrylate), Polymer 14, 469–474 (1973).CrossRefGoogle Scholar
  84. 84.
    G. P. Morgan and I. M. Ward, Temperature dependence of craze shape and fracture in polymethylmethacrylate), Polymer 18, 87–91 (1977).CrossRefGoogle Scholar
  85. 85.
    R. A. W. Frazer and I. M. Ward, Temperature dependence of craze shape and fracture in polycarbonate, Polymer 19, 220–224 (1978).CrossRefGoogle Scholar
  86. 86.
    G. L. Pitman and Î. M. Ward, Effect of molecular weight on craze shape and fracture toughness in polycarbonate, Polymer 20, 895–902 (1979).CrossRefGoogle Scholar
  87. 87.
    J. P. Berry, Fracture processes in polymeric materials. V. Dependence of the ultimate properties of poly(methylmethacrylate) on molecular weight, J. Polym. Sci. A 2, 4069–4076 (1964).Google Scholar
  88. 88.
    A. N. Gent and A. G. Thomas, Effect of molecular weight on the tensile strength of glassy plastics, J. Polym. Sci. 10, 571–573 (1972).CrossRefGoogle Scholar
  89. 89.
    R. P. Kusy and D. T. Turner, Influence of molecular weight of poly(methylmethacrylate) on fracture surface energy in notched tension, Polymer 17, 161–166 (1976).CrossRefGoogle Scholar
  90. 90.
    R. P. Kusy and M. J. Katz, Effect of molecular weight on the fracture surface energy of polymethylmethacrylate) in cleavage, J. Mater. Sci. 11, 1475–1486 (1976).CrossRefGoogle Scholar
  91. 91.
    R. P. Kusy and M. J. Katz, Generalized theory of the total fracture surface energy for glassy organic polymers, Polymer 19, 1345–1357 (1978).CrossRefGoogle Scholar
  92. 92.
    P. Prentice, Influence of molecular weight on the fracture of poly(methylmethacrylate) (PMMA), Polymer 24, 344–350 (1983).CrossRefGoogle Scholar
  93. 93.
    P. Prentice, The influence of molecular weight on the fracture of thermoplastic glassy polymers, J. Mater. Sci. 20, 1445–1454 (1985).CrossRefGoogle Scholar
  94. 94.
    K. E. Evans, A scaling analysis of the fracture mechanisms in glassy polymers, J. Polym. Sci. B, Polym. Phys. 25, 353–368 (1987).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Daniel Maugis
    • 1
  1. 1.Laboratoire des Materiaux et Structures (UMR 113)CNRS-LCPCParis Cédex 15France

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