Adhesion between a viscoelastic material and a solid surface

In this paper, we present a qualitative analysis of the dissipative processes during the failure of the interface between a viscoelastic polymer, characterized by a weak adhesion, and a solid surface. We reassess the viscoelastic trumpet model (de Gennes, P.-G. C. R. Acad. Sci. Paris 1988, 307, 1949), to express the viscous energy dissipated in the bulk as a function of the rheological moduli of the material, involving the local frequencies of solicitation during crack propagation. We deduce from this integral expression the adhesion energy for different kind of materials: (i) we show that, for a cross-linked polymer, the dissipation had been underestimated at low velocities. Indeed, the interface toughness G(V) starts from a relatively low value, G(0), due to local processes near the fracture tip, and rises up to a maximum of order G(0)(mu(infinity)/mu(0)) (where mu(0) and mu(infinity) stand for the elastic modulus of the material, respectively at low and high strain frequencies). This enhancement of fracture energy is due to far-field viscous dissipation in the bulk material, and begins for peel-rates V much lower than previously thought. (ii) For a polymer melt, the adhesion energy is predicted to scale as 1/V. In the second part of this paper, we compare some of these latest theoretical predictions with experimental results about the viscoelastic adhesion between a poly(dimethylsiloxane) polymer melt and a glass surface. In particular, the expected dependence of the fracture energy vs separation rate is confirmed by the experimental data, and the observed changes in the concavity of the crack profile are in good agreement with our simple model. More generally, beyond the qualitative an simple picture sued for our approach, we expect our theoretical treatment to apply for relatively weak viscoelastic adhesives, for which the crack-tip dissipative term G(0) is weakly dependent on the fracture velocity.