Microstructures and Residual Stress in Polycrystalline Materials: Their Nondestructive Characterization and Effects on Mechanical Properties

Many materials (e.g., metals and rocks) are polycrystalline: they are aggregates of tiny crystal- lites of various orientations, sizes, and shapes. The orientations of the crystallites, their stereology (i.e., how they are arranged in space) and their chemical composition determine the macroscopic mechanical properties of the polycrystal. A polycrystalline material may also be prestressed. For instance, a thin subsurface layer of compressive residual stress is arti¯cially imparted (e.g., by surface-enhancement techniques such as shot peening, low plasticity burnishing, etc.) on critical components of aircraft engines to improve their high-cycle fatigue behavior and material damage tolerance. Mathematical methods (e.g., homogenization) have been developed to relate macroscopic elastic and plastic properties of the polycrystal to its structure at the grain level. It turns out that for many purposes the macroscopic mechanical properties can be taken as functions of some coarsely de¯ned microstructural variables, which include the orientation distribution function (the ODF, which de¯nes crystallographic texture or the volume fraction of crystallites in each orientation) and the second-order fabric tensor (which gives a rough description of the average grain shape) among others. The objectives of this project are threefold: ² to derive mathematical formulae which relate the dispersion of Rayleigh waves to the presence of an inhomogeneous subsurface layer of stress and texture, with a view to nondestructive inspection of the residual stress induced by low plasticity burnishing; ² to derive explicit formulae of plastic potentials of sheet metals that include the ODF and the fabric tensor as independent variables (which quantitatively account for the e®ects of crystallographic texture and grain shape on plastic anisotropy); ² to develop a mathematical theory for determination of grain shape from measurements of ultrasonic attenuation. Broader Impacts. Part 1 of the project on nondestructive inspection of residual stress is contin- uation of work done in collaboration with a group at GE Aircraft Engines and a group at the Air Force Research Laboratory. All new ¯ndings will be disseminated to the PI's collaborators there. Part 2 supplements proposed joint research projects with colleagues at Materials Engineering, Uni- versity of Kentucky, which have Commonwealth Aluminum Concast, Inc. (CACI) as industrial partner. Part 3 has its ultimate goal to develop an ultrasound technique for on-line monitoring of grain shape in sheet metals, which will certainly have industrial applications. The PI will continue to o®er a course on \Quantitative Texture and Microtexture Analysis" at the University of Ken- tucky (in the past taken by graduate students from Mathematics and Materials Engineering). The contents of this course will be expanded to include the fabric tensor and its measurement during the course of the present project. Two graduate students will conduct their dissertation research under the framework of this project.