Some Studies on Microtexture and Acoustoelasticity in Polycrystalline Media

DMS奖摘要奖#：0103979PI：MAN，致新研究所：肯塔基大学项目：应用数学项目经理：凯瑟琳·马夫里普利斯题目：多晶介质中微结构和声弹性的一些研究用肉眼看，金属薄板的抛光表面看起来是一个均匀的连续体。在金相师的显微镜下，蚀刻后的同一表面显示出潜在的多晶结构。许多材料，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方向，并被称为晶界的界面分开。最近，随着取向成像显微镜的出现，全面绘制多晶体中的晶界和单个晶向已经成为可能。有关颗粒取向的细节，例如相邻颗粒的错误取向，称为微观织构。微织构对多晶材料的力学行为有很大的影响(例如，对背向散射超声噪声的体积，在足够高的水平下，超声对飞机发动机中的材料缺陷检测完全无用；2号发动机中未被检测到的冶金缺陷是1989年美联航DC-10坠毁的罪魁祸首)。本项目的主要目标如下：(I)重新检验材料科学家提出的几个理论结构的数学基础和性质，这些理论结构描述了不同程度的细节和复杂性；(Ii)描述在成形操作中微观织构对金属薄板机械各向异性的影响；。(Iii)研究微观织构对应力多晶声弹性行为的影响；。(Iv)进一步发展一项早期研究，该研究涉及利用瑞雷波的频散来无损检测飞机发动机关键部件的表面残余应力，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