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The sudden exposure to a supersonic flight environment subjects a missile window, or missile dome, to intense convective heat loads stemming from the rise in temperature of the boundary layer. The thermal response of the window then results in temperature gradients through the thickness, which generate transient stresses that may exceed the tensile strength of the material, thus causing thermal shock induced fracture. Since most of the materials that possess favorable optical properties in the infrared (IR) are relatively weak brittle solids, the problem of selecting window/dome materials and assessing their performance on a fly-out trajectory requires a careful evaluation of the window's ability to withstand thermally induced shocks. In this context, it is essential to keep in mind that the transient stress intensity depends on the nature of the heat flow as characterized by the Biot number (Bi). The allowable heat flux depends not only on intrinsic material properties but also on the heat-transfer coefficient if the condition Bi greater than 1 holds, or the thickness of the window if the condition Bi less than 1 applies. In a first approximation, the thermal shock performance of a 'thick' window will be controlled by the figure of merit (FoM)Bi greater than 1 equals RH, i.e., the Hasselman parameter for strong shocks; in a thermally thin regime, however, the appropriate figure of merit is (FoM)Bi less than 1 equals sigmafnR'H with n equals 1/2 for flat plates and n equals 2/3 for hemispherical shells, and not the Hasselman parameter R'H for mild shocks. Judging from the results of thermal shock testing performed elsewhere, we conclude that in a laminar flow environment the allowable heat flux on a thermally thin IR dome can be expressed as follows: Qlim equals 2R'H/L, where L is the dome thickness. This expression provides a direct means of obtaining the Mach altitude failure line for a dome of given thickness and given radius, if the initial wall temperature is known. Furthermore, it then becomes straightforward to assess the thermal shock resistance capability of a thickness-optimized IR dome either in terms of the allowable heat load or, more simply, the allowable stagnation temperature.
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