The Schwickerath three point bending adhesion test is the basis of the International Standard ISO 9693:1999 procedure for assessing porcelain bonding to metals . It has also been used to evaluate the adhesion of porcelain to zirconia. The purpose of this paper is a fracture mechanics analysis of this test, which allows determination of the crack-length load-displacement and toughness dependence of cracks extending along or near the interface.
Linear elastic mechanics is used to develop expressions for the strain energy and compliance of Schwickerath geometry specimens as a function of crack extension along or near the interface. From the derivative of the compliance as a function of crack growth the strain energy release rate ( G , N/m) is determined.
The energy release rate for interface crack extension of Schwickerath geometry specimens is determined. It is found that a simple relationship between the minima of the force–displacement response and the strain energy release rate G exists. Further development enables the predicted force–displacement response as a function of crack length to be derived for different values of G . Experimental results of porcelain bonded to zirconia with and without notches of various lengths machined along the interface verify the expressions and analysis developed.
With the fracture mechanics analysis developed in this paper it is possible to determine the quality of adhesion in Schwickerath specimens by the interface toughness in addition to the nominal interface shear bond strength. As the toughness of brittle materials has much less scatter than its strength, the interface toughness characterization of the adhesion should allow for a better distinction between the adhesion quality of bonding.
Adhesion assessment of bonded materials has a long history of various approaches being used to quantify this property . Considerable focus for quantifying such bonding was applied to porcelain bonding to metal especially during the development of veneered crowns for dental clinical application. One such test was developed by Schwickerath in the early 1980’s after investigating various bonded bilayer combinations . It consisted of a 25 × 3 × 0.5 mm bar with a 8 × 3 × 1.1 mm porcelain bonded specimen that was loaded in three point bending with the porcelain located on the tension side . Almost 20 years later this test was approved as an ISO standard and a value of 25 MPa for the nominal shear bond strength was assigned for materials to meet the standard.
The initial approach of Schwickerath was to develop a test that generated indirect loading of the bonded system. Other tests, such as the various shear bond strength tests, used a direct loading of the bonded specimen by a punch system often initiating fracture at the punch contact site (see for example ). Various groups developed some initial analysis of the Schwickerath test including and showed the basic relationship between the force–displacement response of the bonded and unbonded specimen. Subsequent work by Lenz et al. conducted a detailed finite element analysis (FEA) to calculate the stresses at the interface especially at the sharp edge of the bonded interface where crack initiation occurred . On the basis of this calculation an averaged stress at the edge of the notch was determined resulting in a factor linking fracture load and shear stress that was dependent upon the ratio of the elastic properties of the bonded system. The emphasis of the FEA was to determine a critical strength for quantifying adhesion.
The present work arose from a study that investigated the adhesion of various dental porcelain veneering materials to zirconia using the Schwickerath test . In the course of that work inadvertent overloading of some samples resulted in the stable debonding of the porcelain. Two additional features were evident upon examining the resultant force–displacement response; 1. the curves always passed through a minima which displayed far less scatter than the load to initiate cracking, the traditional measurement approach of the ISO test, and 2. complete debonding of the porcelain was observed well before the fracture load required for the supporting zirconia beam. In a subsequent investigation Kosyfaki and Swain explored the complete loading and unloading response of four different porcelain compositions fused to zirconia and developed a simple mechanics of materials analysis to determine the interfacial toughness.
This paper initially develops a more in-depth analysis of the deflection of the Schwickerath specimen under load as well as with a crack of varying dimension at the interface from the approach in . From these calculations the crack length dependence of the compliance is determined. The strain energy associated with such loaded structures is then determined based on Castigliano’s theorem and is used to calculate the strain energy release rate. In addition from the classic fracture mechanics relationship between compliance variation with crack length and for a known value of the interface toughness or strain energy release rate for a system the anticipated force–displacement response can be predicted. Complimentary experimental observations with un-notched and partially notched specimens confirm the analysis developed.