4.3 Article

Characteristic strength, Weibull modulus, and failure probability of fused silica glass

Journal

OPTICAL ENGINEERING
Volume 48, Issue 11, Pages -

Publisher

SPIE-SOC PHOTO-OPTICAL INSTRUMENTATION ENGINEERS
DOI: 10.1117/1.3265716

Keywords

failure probability; flexural strength; fused silica; stressed area; surface finish; Weibull statistics

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The development of high-energy lasers has focused attention on the requirement to assess the mechanical strength of optical components made of fused silica or fused quartz (SiO2). The strength of this material is known to be highly dependent on the stressed area and the surface finish, but has not yet been properly characterized in the published literature. Recently, Detrio and collaborators at the University of Dayton Research Institute (UDRI) performed extensive ring-on-ring flexural strength measurements on fused SiO2 specimens ranging in size from 1 to 9 in. in diameter and of widely differing surface qualities. We report on a Weibull statistical analysis of the UDRI data-an analysis based on the procedure outlined in Proc. SPIE 4375, 241 (2001). We demonstrate that (1) a two-parameter Weibull model, including the area-scaling principle, applies; (2) the shape parameter (m similar or equal to 10) is essentially independent of the stressed area as well as the surface finish; and (3) the characteristic strength (1-cm(2) uniformly stressed area) obeys a linear law, sigma(C) (in megapascals) similar or equal to 160-2.83 X (PBS) over bar (in parts per million per steradian), where (PBS) over bar characterizes the surface/subsurface damage of an appropriate set of test specimens. In this light, we evaluate the cumulative failure probability and the failure probability density of polished and superpolished fused SiO2 windows as a function of the biaxial tensile stress, for stressed areas ranging from 0.3 to 100 cm(2). (C) 2009 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3265716]

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