Characteristic strength and Weibull modulus of selected infrared-transmitting materials

Abstract

The results of fracture testing are usually reported in terms of a measured strength s M5s i6Ds i, where s i is the average of the re- corded peak stresses at failure, and Ds i represents the standard devia- tion. This ''strength'' does not provide an objective measure of the intrin- sic strength since s M depends on the test method and the size of the volume or the surface subjected to tensile stresses. We first clarify is- sues 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 equibi- axial 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 s C—i.e., the effective strength of a uniformly stressed 1-cm 2 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 flex- ural strength data thus amounts to obtaining the parameters s C and m, which is best done by directly fitting estimated cumulative failure proba- bilies to the appropriate failure-probability expression derived from Weibull's theory. Ring-on-ring fracture testing performed at four mechani- cal test facilities on five lots of Raytran™ 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 orien- tations, and on Oxyfluoride™ glass validates the procedure and demon- strates that, in many instances, the wide divergence of measured strengths can be attributed to the size of the stressed area. © 2002 Society