Adhesive fracture mechanics

Abstract

Recently Williams, Malyshev and Salganik and others have applied the concepts of fracture mechanics to predict adhesive fracture. The specific adhesive fracture energy, γ_a, is defined as the energy released per unit of new surface created on separation of dissimilar materials. Williams has elucidated the similarity between adhesive and cohesive fracture from the standpoint of a Griffith energy balance analysis. One finds that for either cohesive or adhesive fracture, crack instability (where the crack has a characteristic dimension,a) is predicted by a general equation of the form$\sigma _{cr} = k\sqrt {E\gamma /a}$ wherek=f [geometry and loading] and includes all loading and geometric factors,E and γ are Young's modulus and specific fracture energy, respectively, and σ_cr is the applied load at incipient failure.

Within the fracture mechanics interpretation the adhesive fracture energy γ_a is viewed as a fundamental property of the adhesive system. It is important to note, however, that it may depend on surface preparation, curing conditions, absorbed monolayers, etc. It is, therefore, essential that if γ_a is used to predict adhesive fracture for different geometries, then the surface preparation must be identical with that for the test specimen.

If γ_a is a system parameter, then it would be possible to predict fracture by conducting an energy balance analysis of the configuration, utilizing values of γ_a, Young's modulus, and Poisson's ratio as determined from separate simple test specimens.

There is, however, a need to establish that γ_a is a system parameter which is independent of geometry. One can in principle perform a number of tests on several specimen configurations or, more effectively, several tests on a single specimen which changes configuration between successive tests. In this latter case the surface and dissimilar materials remain constant. A specimen which is suitable for our purpose was developed by Williams and Jones by incorporating aspects of tests first suggested by Dannenburg and Salganik and Malyshev.

The test method considers a disk or plate which has been bonded to a substrate material except for a central portion of radiusa. When pressure,p, is injected into the unbonded region, the plate lifts off the substrate and forms a blister whose radius stays fixed until a critical pressure,p _cr, is reached. At this critical value the radius of the blister increases in size, signifying an adhesive failure along the interface.

An energy balance analysis is available for the circular blister specimen in the two limiting cases of a thick plate (Williams) or a very thick medium (Mossakovskii), each with an infinite outer radius. Having established the utility of this general test method, we have considered it necessary to extend the analysis and test calibration capability to other thicknesses for more general engineering applications, as for example, very thin membranes which are used in paint coatings.

An axisymmetric finite element numerical analysis was, therefore, conducted for specimens of different thickness and debond radii to establish the energy balance for the various arbitrary thicknesses. A continuous curve for arbitrary specimen thickness was then produced on a dimensionless plot ofp ² a/Eγ versush/a whereh is the specimen thickness. The region ofh/a over which the limiting case equations are valid was also established within the accuracy of the numerical analysis. Since many, if not most, bond geometries are not readily analyzed in closed form, the numerical procedures for energy balance analysis is included and may be used for analyzing geometries other than the blister test specimens.

Experiments were conducted over a broad range ofh/a and found to agree with the analytical elasticity solutions which assumed a constant (for given surface preparation, temperature, loading conditions, strain rate independence, etc.) value for γ_a. These experiments confirm that for this system at least γ_a is a constant independent of geometry.

Résumé

L'application par Williams, Malyshev, Salganik et autres de la mécanique de rupture pour prédire la rupture des adhésifs a conduit à définir γ_a, énergie spécifique de rupture, à élucider la similitude entre rupture d'adhésion et de cohésion au point de vue de l'analyse de l'équilibre énergétique de Griffith, et à prédire l'instabilité d'une fissure de dimension caractéristique “a” par une équation générale de la forme$\sigma _{cr} = k\sqrt {E\gamma /a}$, valable pour la rupture de cohésion ou d'adhésion.

En termes de mécanique de rupture, l'énergie de rupture d'adhésion γ_a est considérée comme une propriété fondamentale d'un système collé, mais elle dépend de la préparation de la surface, des conditions de polymérisation etc... Dès lors, il est essentiel de maintenir ces paramètres constants lorsque l'on examine différentes géométries. Dans ces conditions, moyennant la détermination de γ_a du module de Young, et du rapport de Poisson à l'aide d'essais simples et distincts, on doit pouvoir prédire la rupture par une analyse d'équilibre énergétique. Mais ceci implique que γ_a soit un paramètre du système indépendant de la géométrie.

Des expériences, conduites sur un type nouveau d'éprouvettes développé par Williams et Jones ont permis de conclure que γ_a était une constante indépendante de la géométrie, à tout le moins pour un type déterminé de système.

Zusammenfassung

Die Anwendung der Bruchmekanik durch Williams, Malyshev, Salganik und andere, um den Bruch von Klebstoffen vorauszusagen, hat zur Definition von γ_a geführt, sowie zur Erläuterung der Ähnlichkeit zwischen dem Adesiven- und dem Cohesivenbruch begründet auf die Analyse des Energiegleichgewichtes nach Griffith, sowie die Voraussagung der Unbeständigkeit eines Risses, mit karakteristischen Abmessungen “a”, durch eine allgemeine Gleichung des Typs$\sigma _{cr} = k\sqrt {E\gamma /a}$ gültig für Cohesiv oder Adesivbruch.

Auf dem Gebiet der Bruchmekanik wird die Energie γ_a des Adesifbruches als eine Grundeigenschaft des geklebten Systems angesehen, aber sie hängt von der Oberflächenvorbereitung, der Polymerisations Bedingungen und so weiter ab. Daher ist es ausschlaggebend diese Parametern konstant zu halten wenn man verschiedene Geometrien untersucht. Unter diesen Bedingungen, indem man γ_a, das Modul von Young und den Koefficient von Poisson mittels einfachen und unabhängigen Versuche bestimmt, muss es möglich sein mittels einer Energiegleichgewichtsanalyse den Bruch vorauszusagen. Dies bedingt dass γ_a ein von der Geometrie unabhängiger Parameter des Systems ist.

Versuche auf einem neuen Typ von Proben, entwickelt durch Williams und Jones, ermöglichten die Schlussfolgerung dass γ_a eine von der Geometrie unabhängige Konstante ist, wenigstens für ein gegebenes System.