Biomaterials ] (]]]]) ]]]–]]] Analysis of tensile bond strengths using Weibull statistics Michael F. Burrow a, *, David Thomas a , Mike V. Swain b , Martin J. Tyas a a School of Dental Science, The University of Melbourne, Victoria 3010, Melbourne, Australia b Faculty of Dentistry, University of Otago, 310 Great King Street, Dunedin, New Zealand Received 30 November 2003; accepted 26 January 2004 Abstract Tensile strength tests of restorative resins bonded to dentin, and the resultant strengths of interfaces between the two, exhibit wide variability. Many variables can affect test results, including specimen preparation and storage, test rig design and experimental technique. However, the more fundamental source of variability, that associated with the brittle nature of the materials, has received little attention. This paper analyzes results from micro-tensile tests on unfilled resins and adhesive bonds between restorative resin composite and dentin in terms of reliability using the Weibull probability of failure method. Results for the tensile strengths of Scotchbond Multipurpose Adhesive (3 M) and Clearfil LB Bond (Kuraray) bonding resins showed Weibull moduli (m) of 6.17 (95% confidence interval, 5.25–7.19) and 5.01 (95% confidence interval, 4.23–5.8). Analysis of results for micro-tensile tests on bond strengths to dentin gave moduli between 1.81 (Clearfil Liner Bond 2 V) and 4.99 (Gluma One Bond, Kulzer). Material systems with m in this range do not have a well-defined strength. The Weibull approach also enables the size dependence of the strength to be estimated. An example where the bonding area was changed from 3.1 to 1.1 mm diameter is shown. Weibull analysis provides a method for determining the reliability of strength measurements in the analysis of data from bond strength and tensile tests on dental restorative materials. r 2004 Elsevier Ltd. All rights reserved. Keywords: Tensile bond test; Weibull analysis; Resin adhesives 1. Introduction The testing of adhesion to dentin and enamel is an area on which researchers have expended a tremendous amount of energy. However, when these results are extrapolated to the clinical situation, it appears that a weak correlation exists between successful laboratory bonding and clinical success. It is well known amongst researchers that bond strength outcomes, whether tensile, shear or micro-tensile tests, show wide variations [1–5]. The common method of presenting bond strengths is a mean with standard deviation, however the coefficient of variation can be as much as 100%. This variability has been observed both within tests from a single laboratory and between tests from different laboratories [6]. Therefore, the determination of a good or poor adhesive requires a method that might be a better predictor of clinical performance prior to performing expensive, time-consuming clinical studies. The applicability of bond strength measurements to clinical performance of restorative materials has been well covered in the literature [7]. Work from the authors of the present paper has shown that tensile bond strength tests to dentin of resin- based adhesives exhibits wide variability [8–13]. Many variables can affect these test results [14], including variables associated with specimen preparation, hand- ling of materials and specimen storage which may be difficult to control. In contrast, variables that relate to test rig design and experimental technique can be controlled well. However, the more fundamental source of variability associated with the brittle nature of the materials has received little attention. Weibull probability of survival analysis has been developed as, among other things, an engineering design method for components made from such materials as ceramics [15]. Failure loads in ceramic components are determined by defect size, and are thus characteristic of the specimens, not the material. The defects have a size distribution and thus the failure loads are variable. An ARTICLE IN PRESS *Corresponding author. Tel.: +61-3-9341-0312; fax: +61-3-9341- 0339. E-mail address: mfburrow@unimelb.edu.au (M.F. Burrow). 0142-9612/$-see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.biomaterials.2004.01.060