Studies in Mathematics and Mechanics of Textured and Prestressed Solids

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DMS-9803441Chi-Sing ManThe objectives of this project are: (1) to develop a systematic mathematical procedure by which the quantitative effects of crystallographic texture on the material tensors (e.g., the fourth-order elasticity tensor, the sixth-order acoustoelastic tensor, etc.) of weakly-textured polycrystalline solids can be fully delineated; (2) to develop an acoustoelastic theory for using surface acoustic waves in nondestructive evaluation of residual stress and/or other material parameters (e.g., elastic constants, texture coefficients, etc.) in thin-film coated anisotropic solids. The systematic procedure to be developed in the first investigation will be based on the theory of group representations and the theory of invariants. The Stroh formalism and, in particular, Barnett and Lothe's surface impedance method will be used in the second study.Explicit formulae which would result from the first investigation will bear on all applications involving weakly-textured solids (e.g., metal forming operations, ultrasonic measurement of stress in structural metals) where delineating effects of texture-induced anisotropy is essential. Thin films of advanced coating materials, which are increasingly sprayed, deposited, or grown on substrates to increase their resistance to high temperatures, corrosion, or abrasive wear, often carry residual stresses as a by-product of the production process. The second investigation will provide a theoretical basis for using laser ultrasonics and acoustic microscopy to obtain information on surface stress for quality controlof thin-film coatings.