Some Studies on Microtexture and Acoustoelasticity in Polycrystalline Media

DMS Award AbstractAward #： 0103979 PI： 文智星学院： 剑桥大学课程： 应用数学项目经理：Catherine Mavriplis职务：多晶介质中的微织构和声弹性的研究用肉眼看，金属片的抛光表面是一个均匀的连续体。在金相显微镜下，蚀刻后的同一表面显示出下面的多晶结构。许多物质，包括金属、冰和岩石，都是微小晶体或颗粒的集合体，它们在空间中呈现不同的取向，并被称为晶界的界面分隔开。随着取向成像显微镜的出现，多晶体中晶粒边界和单个晶粒取向的综合映射最近成为可能。关于晶粒取向的细节，例如，相邻晶粒的取向差称为微观织构。微观织构可以对多晶材料的机械行为产生强烈的影响（例如，1989年联合航空公司一架DC-10型飞机坠毁的罪魁祸首是2号发动机中未被发现的冶金缺陷。（i）重新审查材料科学家提出的几种理论结构的数学基础和性质，这些理论结构用于以不同的细节和复杂程度描述微观结构;（ii）描述在成形操作中微观织构对金属板材的力学各向异性的影响;（iii）研究微观织构对受应力多晶体的声弹性行为的影响;（iv）进一步发展早期的研究，即利用瑞利波的频散对表面残余应力层进行无损检测，这是赋予飞机发动机的关键部件，以提高其高周疲劳性能。日期：2001年5月18日

DMS Award AbstractAward #: 0103979PI: Man, Chi-Sing Institution: University of KentuckyProgram: Applied MathematicsProgram Manager: Catherine MavriplisTitle: Some Studies on Microtexture and Acoustoelasticity in Polycrystalline MediaTo the naked eye, the polished surface of a metal sheet appears as a homogeneous continuum. Under the metallographer's microscope the same surface reveals, after etching, an underlying polycrystalline structure. Many materials, including metals, ice and rocks, are aggregates of tinycrystals or grains, which assume different orientations in space and are separated by interfaces called grain boundaries. Comprehensive mapping of grain boundaries and individual grain orientations in polycrystals has recently become possible with the emergence of orientation imaging microscopy. Details about grain orientations, e.g., the misorientations of neighboring grains, are called microtexture. Microtexture could exert a strong influence on the mechanical behavior of polycrystalline materials (e.g., on the volume of backscattered ultrasonic noise, whichat sufficiently high levels renders ultrasound totally useless for material flaw detection in aircraft engines; an undetected metallurgical defect in the No. 2 engine was the culprit for the crash of a United Airlines DC-10 in 1989).The main objectives of the present project are as follows: (i) to reexamine the mathematical foundations and properties of several theoretical constructs which have been proposed by material scientists for describing microtexture in various degrees of detail and sophistication; (ii) to delineate the effects of microtexture on the mechanical anisotropy of sheet metals in forming operations; (iii) to study the effects of microtexture on the acoustoelastic behavior of stressed polycrystals; (iv) to develop further an earlier study that concerns using the dispersion of Rayleigh waves for the nondestructive inspection of surface layer of residual stress, which is imparted on critical components of aircraft engines to enhance their high-cycle fatigue performance.Date: May 18, 2001