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The results of fracture testing are usuaJly documented in terms of a measured strength, M ? where designates the arithmetic average of the recorded peak stresses at failure, and io represents the standard deviation. This "strength" '7M does not provide an objective measure of the intrinsic strength since M depends on the test method and the size of the volume or the surface subjected to tensile stresses. In this paper, we take advantage of Weibull's the- ory of fracture for providing an improved description of the failure statistics of sapphire test specimens subjected to biaxial stresses. For that purpose, we make use of the results of "ring-on-ring" flexural testing that was carried out over a period of 18 years at mechanical test facilities operated by the Southern Research Institute (SoRI), the University of Massachusetts (UMass), and the University of Dayton Research Institute (UDRI). Experiments were conducted, at room temperature, on test specimens supplied by two vendors and included mechanically polished as well as compressively coated specimens in the form of planar disks of different crystallographic orientation. Since equibiaxial flexure testing has now been adopted as the preferred method for assessing the strength of ceramics, we describe the failure probability in terms of a characteristic strength—i. e. , the effective strength for a 1-cm2 uniformly stressed area—, which allows one to evaluate the effective strength under different experimental conditions if the Weibuil modulus is available. The characteristic strengths (oc) and Weibull moduli (m) are predicated on a two-parameter model and validate the applicability of the area scaling law. Specifically, we conclude that: (a) The characteristic strength of polished c-plane sapphire is of the order of 975 MPa (140 kpsi) and the Weibull modulus is close to 3.4. (b) The strength of r-plane sapphire is substantially lower (oc 550 MPa 80 kpsi), but so is the scatter (m 4.1). And (c) strongly adhering compressive coatings can augment the strength by as much as 60 %,in accord with predictions based on simple fracture-mechanical considerations.
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