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Chapter 12:
Applied Stress Determination
The previous chapters discussed methods to obtain the requisite values for strength and flaw growth factors. Once these are known, the missing link in solving the equations of fracture mechanics is the applied stress itself: σa. This is determined completely by analysis. Stress analysis of glasses and ceramics that exhibit linear elastic behavior prior to failure proceeds in the same fashion as for metals below their yield point. Table 12.1 summarizes some key structural properties of select glasses and ceramics. Of course, analysis of structures having various shapes (beams, plates, shells, and solids) and support conditions (simple, fixed, guided, etc.) would fill volumes, and indeed it has. Some key texts on this topic are herein referenced, but there are many choices. The following section presents the calculation of applied stresses for a few special cases that customarily occur in the design of optics for astronomical and ground-based telescopes, as well as for airborne cameras and for many other areas of ceramic applications, including wafer design. Accordingly, while this brief synopsis cannot transplant the need for texts, it may nonetheless transplant the need for extensive research on the usual cases one might encounter. These are circular plates (mirrors, windows, and lenses) that are uniformly and simply supported at the edge or at a number of points, typically three, internally or at an edge. The plates are subjected to gravitational, pressure, and thermal loading.
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