Formulas for the strains, the stresses, and the curvature of multilayered optical windows

Claude A. Klein

doi:10.1117/12.379329

3 March 2000 Formulas for the strains, the stresses, and the curvature of multilayered optical windows

Claude A. Klein

Author Affiliations +

Proceedings Volume 3902, Laser-Induced Damage in Optical Materials: 1999; (2000) https://doi.org/10.1117/12.379329
Event: Laser-Induced Damage in Optical Materials: 1999, 1999, Boulder, CO, United States

Abstract

Optical windows consisting of layers of different materials created at elevated temperatures usually exhibit substantial residual stresses. These stresses are cause by intrinsic strains, in addition to thermal strains that originate from the bonding of the layers, which generates internal forces and moments that must be balanced to achieve mechanical equilibrium. For isotopically elastic structures, this leads to planar contraction or elongation accompanied by spherical deformation, thus resulting in a partial relaxation of the stresses. There is a vast amount of literature relating to this topic. Analytical solutions have been proposed for thin films on a thick substrate, but a closed-form solution for multiple layers of arbitrary thickness has only been available since 1987 and has not yet been fully exploited. It is the purpose of this contribution to take advantage of Townsend's model for deriving 'user-friendly' formulas that properly describe the strains, the stresses, and the curvature of chemically vapor-deposited multilayered optical window blanks; interfacial shear stresses do not alter the curvature or the normal stress distribution off the edges and are beyond the scope of this paper.

Citation Download Citation

Claude A. Klein "Formulas for the strains, the stresses, and the curvature of multilayered optical windows", Proc. SPIE 3902, Laser-Induced Damage in Optical Materials: 1999, (3 March 2000); https://doi.org/10.1117/12.379329

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