Studies in Mathematics and Mechanics of Textured and Prestressed Solids

本计画的目标是：（1）发展一个系统的数学程序，借以定量地分析晶体学结构对材料张量的影响（例如，四阶弹性张量、六阶声弹性张量等）可以完全描绘弱织构多晶固体的结构;（2）开发声弹性理论用于在残余应力和/或其它材料参数的非破坏性评估中使用表面声波（例如，弹性常数、纹理系数等）在薄膜涂层各向异性固体中。 在第一次调查中开发的系统程序将基于群表示理论和不变量理论。在第二项研究中将使用斯特罗形式主义，特别是巴内特和洛特的表面阻抗方法。从第一项研究中得到的显式公式将适用于所有涉及弱织构固体的应用（例如，金属成形操作、结构金属中应力的超声波测量），其中描绘纹理诱导的各向异性的影响是必不可少的。先进涂层材料的薄膜越来越多地喷涂、沉积或生长在基材上，以提高其耐高温、耐腐蚀或耐磨损的能力，这些薄膜通常带有残余应力，作为生产过程的副产品。 第二项研究将为利用激光超声和声学显微镜获取薄膜表面应力信息以控制薄膜质量提供理论基础。

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.