The JKR-DMT Transition in the Presence of a Liquid Meniscus and the Extension of the JKR Theory to Large Contact Radii
In the Hertz theory of frictionless contacting spheres, only compressive stresses in the contact area are assumed. In the JKR theory (Johnson et al., 1971) tensile stresses in the contact area are allowed, whereas in the DMT theory (Derjaguin et al., 1975) adhesion forces act around an unilateral contact. It was shown (Maugis and Barquins, 1978) that the problems of mechanics of contact with adhesion are fracture mechanics problems and that the Sneddon’s equations (Sneddon 1965) for axisymmetric frictionless punches are particularly suitable to derive the stress intensity factors (Maugis and Barquins, 1981; Barquins and Maugis, 1982; Maugis and Barquins, 1983). Using a Dugdale model for adhesion force (constant constraining stresses acting around the contact area in an annulus whose size is such that the total stress intensity factor cancels), Maugis (1992) has obtain a general theory with the the JKR and DMT theories as limiting cases. As a liquid meniscus at the edge of a contact is a perfect example of a Dugdale zone, this theory was used to study the change in profile of two crossed cylinders in contact when the size of a surrounding meniscus increases. On the other hand, recent experiments on adhesion of small particles on soft elastic substrates (Rimai et al.,1994) have revealed that the contact radius under zero load can be very large and does not vary as the particle radius to the 2/3 power as required by the JKR theory (which is restricted to small contact radii). These two last points are the subject of this presentation. The corresponding full papers are published elsewhere (Maugis and Gauthier-Manuel, 1994; Maugis, 1994).
KeywordsStress Intensity Factor Energy Release Rate Crack Opening Displacement Stress Intensity Factor1 Linear Elastic Fracture Mechanics
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