Rheology of Peeling

Abstract

The dependence of the peeling strength on the peeling rate is treated in this paper rheologically. First we showed experimentally that the time-temperature superposition principle is applicable to the S-type curve of the peeling strength vs, the rate for the amorphous polymer films (Vinylite) of various plasticizer (DBP) contents above glass transition temperature (Tg). The dependence of the shift factor aT on the temperature obeyed the W. L. F. equation giving reference temperature Ts considerably lower than Tg+50°, where Tg is measured dilatometrically. This means that the fractional free volume at Tg is larger than 0.025, in our case showing 0.037. This discrepancy is explained by the theory of Ferry and Stratton on the increase of fractional free volume due to the extension of polymers of Poisson's ratio less than 1/2. The apparent activation energy at Ts evaluated from the dependence of log aT on temperature, are 46.5-33kcal/mol for samples of plasticizer contents 0-40%, which are reasonable values for the viscous flow of the polymer segments. From these experimental results we conclude that the dependence of the peeling strength on the rate is substantially rheological in character, and that the course of peeling is not governed by the electrostatic mechanism as proposed by Deryagin et al.Secondly, we derived a theoretical formula relating to the peeling strength to the rate of peeling in adhesive tapes, assuming that the adhesive layer is deformed locally only at the peeling end, and its rhelogical behavior is described by the simple Voigt model. It is also assumed for simplicity that the shape of the bend at the peeling end is regarded as a part of a circle of radius R, which is determined by the peeling force P as R=√EoI/P, and that the deformation is vertical to the adherend surface. If the peeling proceeds steadily with velocity v, we may represent the initial and proceeding stage after time t of peeling with two circles whose centers are at (O, R) and (vt, R). Then the elongation of the adhesive layer at the origin, y, is given as a function of v, R, and t, with its time derivative, dy/dt, as a function of v, R, and y. Introducing this into Voigt's equation and integrating the equation dW=fdy from f=0 to f=fb where fb means the critical surface force, we obtain work of deformation, Wd, at the adhesion break. In the work of deformation, elastic energy We must be reserved. Put Wd'=Wd-We, then the sum of Wa, work of adhesion, and Wd' equals to the work done by the applied force, that is Wa+Wd'=P(1-cosθ), where θ is peeling angle. Carrying necessary calculation with some reasonable approximations, we obtain the following equation in the case of L-peeling (θ=π/2), P-C1P1/4v+C2P1/2v2=Wa, C1=2√2h1/2/3(EoI)1/4·(fb/E)3/2η, C2=2/(EoI)1/2(η/E)2fb, where Eo is Young's modulus of polymer film which determines the curvature at the peeling end, I, its moment of inertia, h, the thickness of the adhesive layer, η and E, viscosity coefficient and Young's modulus of the adhesive. This equation represents well the S-type curve of logP vs.