Peel adhesion. II. A theoretical analysis

Abstract

The purpose of this analysis is to find a method of calculating the maximum stress at failure from the variation of the peel force with the thickness of the adhesive layer If the failure is in the binder/substrate interface, this maximum stress is the adhesive bond strength. In the model it is assumed that, among other things, both substrate and adhesive are Hookean, the stresses parallel to the symmetry axis of the sample and the shear stresses are negligible, and the deflection of the substrate prior to failure is small. The latter assumptions are very questionable but the assumption involving Hookean behavior is a good approximation. It is shown that the rate of deformation in the sample is in the 104 to 106%/min. range. At such high rates of deformation viscoelastic bodies are expected to approach Hookean behavior. Two separate equations are derived describing the variation of the peeling force with adhesive layer thickness. These equations also contain an additional variable, the slope angle of the substrate at the failure point. This variable can be eliminated by combining the two equations. The parameters in the final expressions are the moduli of the binder and substrate, thickness of the binder, width of the sample, and the maximum stress at the failure point. The theoretical analysis also defines the geometry of the sample and allows the estimation of the rate of strain in the adhesive and in the substrate. Furthermore, it predicts the existence of compressive stresses which develop prior to tensional stresses. These compressive and tensional stresses in the sample can be separately calculated, and it is possible to establish the size of the area where these stresses exist at steady state conditions. The measured peeling force is proportional to the difference between the sum of tensional and the sum of compressive stresses. Data obtained with cellophane substrates and acrylic binders at high peeling rates, where the force is rate independent and the failure is adhesive, are analyzed in terms of the theory. The rheological parameters calculated from peel test data are of the right order of magnitude and the shape of force/adhesive layer thickness plot is consistent with theoretical predictions. It is also shown that the magnitude of the compressive force in the glue line changes only to a small extent with the thickness of the adhesive layer and that the tensional force in the glue line is approximately proportional to the area under tension.