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# Note for OPTI 521 at UA

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This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 14 views.

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Date Created: 02/06/15
Strength of Glass Using Weibull Statistics Mir Salek Optomechanics Opti521 College of Optics University of Arizona Fall 2008 Glass is a brittle material therefore its tensile strength is mainly determined by the surface aw on it The rst aw which spreads under tensile stress would determine the tensile strength of the glass Since it is very dif cult to nd the exact size and features of the aws usually the strength of glass is expressed in terms of the probability of failure Weibull distribution function speci es the probability of failure of glass as a function of the tensile stress Pf l exp 24 0 Pf Probability of failure of Applied stress on characteiistic strength 632 of the specimens fail at this stress level In Weibull modulus 7 an indicator of the scatter of the data 50 and m which are the glass type dependent parameters in the above formula are determined Via empirical methods These two parameters are determined by tting the Weibull formula to 30 or more test specimens For example for Schott BAKl m 82 50 589 As a result the failure probability resulting from 1 ksi stress would be 26E8 However for Can m 3 50 5 and the probability of failure under the same stress would be 0936 The brittleness of glass and Weibull distribution imply many failure characteristics of the glass Since crack growth happens mainly under tensile stress glass is much stronger under compressive stress than tensile stress Most glasses can break at about 1 ksi of tensile stress but they usually can tolerate 50ksi of compressive stress Since glass strength is highly dependent on surface aw size and sharpness its strength can be enhanced considerably by ne abrasive grinding polishing or acid etching Also as glass gets larger there would be more cracks on it and as a result the size of the largest crack on average increases Weibull analysis assumes that the distribution of aw size and as a result probability of failure does not change with time In other words it ignores subcritical crack growth as a result of stress over time A more thorough analysis would determine the probability of failure as a function of stress applied over the period of the service of the glass as well as timetofailure as a function of applied stress over time References 1 Keith B Doyle Sigmadyne Inc Rochester NY Design strength of optical glass Proceedings of SPIE Vol 5176 Optomechanics 2003 P 14 2 D Vukobratovich S M Vukobratovich Introduction to Optomechanical Design Raytheon Systems Co Defense Systems Segment

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