Abstract
The results of fracture testing are usually reported in terms of a measured strength σM = sigma;i∓&Deltaσi where σi is the average of the recorded peak stresses at failure, and ;&Deltaσi represents the standard deviation. This "strength" does not provide an objective measure of the intrinsic strength since σM depends on the test method and the size of the volume or the surface subjected to tensile stresses. We first clarify issues relating to the application of Weibull's theory of brittle fracture and then make use of the theory to assess the results of equibiaxial flexure testing carried out on selected IR-transmitting materials. Since equibiaxial flexure testing has now been adopted as the preferred method for measuring the strength of optical materials, we describe the failure-probability distribution in terms of a characteristic strength σC—i.e., the effective strength of a uniformly stressed 1-cm2 area—which enables us to predict the average stress at failure in a concentric ring configuration if the Weibull modulus m is available. A Weibull statistical analysis of flexural strength data thus amounts to obtaining the parameters σC and m, which is best done by directly fitting estimated cumulative failure probabilies to the appropriate failure-probability expression derived from Weibull's theory. Ring-on-ring fracture testing performed at four mechanical test facilities on five lots of RaytranTM materials [AlON, chemically vapor deposited (CVD) diamond, ZnSe, standard ZnS, and multispectral ZnS], on sapphire specimens cut in the a-, the c-, and the r-plane orientations, and on OxyfluorideTM glass validates the procedure and demonstrates that, in many instances, the wide divergence of measured strengths can be attributed to the size of the stressed area.
