Studies in Mathematics and Mechanics of Textured and Prestressed Solids

本项目的目标是：(1)建立一个系统的数学程序，通过该程序可以充分描述晶体织构对弱织构多晶固体的材料张量（如四阶弹性张量、六阶声弹性张量等）的定量影响；(2)发展一种声弹性理论，用于使用表面声波无损评估薄膜涂层各向异性固体中的残余应力和/或其他材料参数（例如，弹性常数，织构系数等）。在第一个研究中发展的系统程序将基于群表示理论和不变量理论。Stroh的形式，特别是Barnett和Lothe的表面阻抗方法将在第二项研究中使用。从第一次调查中得出的明确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，结构金属应力的超声波测量），其中描述织构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，越来越多地被喷涂、沉积或生长在基材上，以增加其对高温、腐蚀或磨料磨损的抵抗力，通常作为生产过程的副产品携带残余应力。第二项研究将为利用激光超声和声学显微镜技术获取薄膜涂层表面应力信息以进行质量控制提供理论依据。

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.