Biaxial flexural strength of optical window materials

Abstract

The design of high-energy laser windows critically depends on the availability of appropriate numbers for the allowable tensile stress. Relying on a modulus of rupture in conjunction with a safety factor usually results in overestimating the required thickness, which degrades the optical performance. The primary purpose of this paper is to clarify issues relating to Weibull's theory of brittle fracture and make use of the theory to assess the results of equibiaxial flexure testing that was carried out on laser-window material candidates. Specifically, we describe the failure-probability distribution in terms of the characteristic strength σ C --i.e., the effective strength of a uniformly stressed 1-cm 2 area---and the shape parameter m , which reflects the dispersion of surface-flaw sizes. A statistical analysis of flexural strength data thus amounts to obtaining the parameters σ C and m , which is best done by directly fitting estimated cumulative failure probabilities to the appropriate expression derived from Weibull's theory. In this light, we demonstrate that (a) at the 1% failure-probability level, fusion-cast CaF 2 and OxyFluoride Glass perform poorly compared to CVD-ZnSe; (b) available data for fused SiO 2 and sapphire confirm the area-scaling principle, thus validating Weibull's theory; and (c) compressive coatings enhance the characteristic strength but degrade the shape parameter, which mitigates their benefit. In Appendix, it is shown that four-point bending data for fusion-cast CaF 2 do not obey a simple two-parameter model but are indicative of a bimodal surface-flaw population.