A generalized cohesive zone model of the peel test for pressure-sensitive adhesives

Abstract

The peel test is a commonly used testing method for adhesive strength evaluation. The test involves peeling a pressure-sensitive tape away from a substrate and measuring the applied peel force. In the present study, a cohesive zone model, in which the adhesive fails cohesively, is proposed to analyze the mechanics of the peel test. The proposed model is capable of predicting the dependence of the peel force, as well as the traction distribution across the peel front, on factors such as the peel rate, the peel angle, the nature of the adhesive, the mechanical properties and geometries of the backing and the substrate.

Introduction

The adhesion between soft and stiff materials comprises an important component of many practical applications. One of the most important adhesion technologies is that of pressure-sensitive adhesives (PSAs). PSAs are used in pressure-sensitive tapes, labels, note pads and a wide variety of other products. Pressure-sensitive tapes are designed that, by applying a light pressure, PSAs forms a continuous layer to bond the tape to the adherend. The layer has to be soft enough to adhere to the adherend, whereas it has to be hard enough to offer a proper bond resistance. This special behavior requires PSAs exhibiting a viscoelastic character [1]. PSAs are viscoelastic, that is, their mechanical properties are time dependent. Creton and Leibler [2] studied the tack of PSAs on rigid substrates. The viscoelastic behavior was found to be accounted for a time-dependent elastic modulus. Hui et al. [3] extended their work to a rough surface with a Gaussian distribution of asperity heights.

The strength of the adhesive bond can be quantified with a peel test. A 120° peel test is illustrated schematically in Fig. 1, in which a thin flexible backing that has been bonded to a rigid surface is peeled away from the substrate. The peel test provides a measure of the strength of the adhesive bond. The test is commonly conducted by pulling the backing at a constant rate and measuring the peel force that is applied to rupture the adhesive bond. The peel force depends on factors such as the rate at which the backing is detached, the angle at which the detachment occurs, the nature of the adhesive, the mechanical and physical properties of the backing and the substrate, the temperature and humidity of the environment, and the conditioning process [4]. However, the interaction of these factors still remains unclear.

Kaeble [5] developed the fundamental theory of the peel test, which is based on the elementary beam bending theory. Kaelble and Reylek [6] succeeded in determining experimentally the stress distribution in the vicinity of the peel front. They demonstrated that the peel force is significantly affected by the process of cavitation and fibrillation of the adhesive. Niesiolowski and Aubrey [7] also suggested that the peel force and the stress distribution are affected by fibrillation significantly. Generally, the propagation of the peel front is accompanied by a process of cavitation and fibrillation of the adhesive [8]. The adhesive in the vicinity of the peel front is subjected to large hydrostatic tension due to the lateral constraint imposed by the adherends. For strong adhesives, the adhesive does not debond from the adherends. As a result, newly formed cavities grow perpendicular to the adherend surfaces. These cavities grow rapidly to a critical size at which the hydrostatic tension is used to extend an array of fibrils.

The fibrils are often modeled as deformable strings, that is, the fibrils are subjected to uniaxial extension. Gent and Petrich [9] calculated the peel force by summing tensile stresses in fibrils of the adhesive across the peel front. Gutpa [10] pointed out that it is difficult to represent the peel process with controlled deformation as the peel geometry is not known a priori. Christensen et al. [11], [12] quantified the deformation of the adhesive in photo images. They compared the theoretical peel forces with measurements and demonstrated the validity of the expression and the string assumption [13]. They also observed that the extension of a fibril in its longitudinal direction is accompanied by the extensive shrinkage in its transverse directions. Lin et al. [8] analyzed the failure of the adhesive in a 180° peel test. The peel force was found to be dependent on the adhesive thickness and the peel rate. However, the peel force does not represent the true strength of the adhesive bond. The measured peel force may represent a combination of the true strength of the adhesive bond and other work expended in the elastic and plastic deformation of the adherends. This can be understood by considering a 180° peel test, where work is being done not only to rupture the adhesive bond but also to bend the backing through 180° [1].

The flexibility, geometry and dimensions of the backing influence the peel force. Several authors [4], [14], [15], [16], [17] studied the influence of flexible backings on the peel force. Wei and Hutchinson [15] investigated the relationship between the peel force and the adhesive fracture energy in the presence of the plastic deformation of the peel arm. The macroscopic fracture energy was found to be the sum of the adhesive fracture energy and the plastic dissipation. However, the adhesive thickness was neglected in their analysis, whereas it is comparable with the backing thickness for pressure-sensitive tapes. In addition, the proposed traction–separation relation is incapable of characterizing the viscoelastic behavior of PSAs. Therefore, their model may not be appropriate for analyzing the mechanics of the peel test for pressure-sensitive tapes.

For certain applications, peel tests are performed on curved surfaces. For example, Vayeda and Wang [18] conducted a series of peel tests to evaluate the coating adhesion of plastically deformed sheet metal. Since the adhesive is much softer than the substrate, its flow properties strongly depend on the geometry of the substrate surface. As the flow of the adhesive is restricted by the substrate surface, the traction distribution across the peel front is also influenced by the geometry of the substrate surface.

The present study extends the work of Lin et al. [8] to analyze the mechanics of the peel test. A cohesive zone model, in which the adhesive fails by splitting of itself, is proposed. The cohesive zone is modeled as a continuous fibrillated region. The viscoelastic behavior of the adhesive is characterized by a Maxwell solid. The mechanical response of the adhesive in the presence of a curved substrate surface is considered. Governing equations and associated boundary conditions, which characterize the mechanics of the peel test, are derived. Numerical results are obtained under steady-state conditions. The model predicts the dependence of the peel force, as well as the traction distribution across the peel front, on factors such as the peel rate, the peel angle, the nature of the adhesive, the mechanical properties and geometries of the backing and the substrate.