Grants and Contracts per year
Grants and Contracts Details
Description
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
surfaceenhancement techniques such as shot peening, low plasticity burnishing, etc.) on critical
components of aircraft engines to improve their highcycle 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 secondorder 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 online 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.
Status  Finished 

Effective start/end date  7/15/04 → 6/30/08 
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Projects
 1 Finished

Microstructures and Residual Stress in Polycrystalline Materials: Their Nondestructive Characterization and effects on Mechanical Properties: Support for Scott Godefrey
Man, C. S.
7/15/04 → 6/30/08
Project: Research project