The objective of this proposal is to develop new theoretical foundations and numerical algorithms of physics-based stochastic methodology for predicting fatigue durability and reliability of functionally graded materials (FGMs). The proposed effort will be based on: (1) new level-cut Poisson random fields for stochastic modeling of heterogeneous microstructure; (2) new, computationally efficient, level set methods for both micro- and macro-structural fatigue durability analyses; and (3) innovative dimension-reduction methods for second-moment and reliability analyses of FGM subject to random loads, material properties, and geometry. From a fundamental point of view, the project will advance a largely uncharted research area that is concerned with physics-based, multi-scale, stochastic methodology capturing realistic microstructural features, micro- and macro-scale fatigue damage, and resultant cascading effects on stochastic mechanical performance of FGM. To the best knowledge of the PI, no probabilistic models of FGM are known to have been developed. As such, the development of the proposed methodology constitutes a new and significant advance towards the achievement of more realistic fatigue-durability simulation of FGMs.
The proposed research will find many high-technology applications involving material performance and structural integrity evaluations under super-high temperatures and large temperature gradients. Potential applications include thermal barrier coating in aircraft propulsion, shape memory alloys in space vehicles, high-performance ballistic components, fast-breeder nuclear reactor pressure vessels, microelectronic devices, bio-engineered implants, and others. Indeed, the research proposed here will positively impact a number of areas of national significance, such as civil and military infrastructure, advanced materials, and information technology. The transfer and dissemination of knowledge created by this project will take place through continued collaboration with industries, organization of symposia on FGM reliability in ASME conferences, peer-reviewed journal publications, presentations and publications at major conferences and institutions, and student education. The partnership with two government and industrial laboratories will enable sharing of important knowledge and experimental data and implementation of the basic methods developed in this project to resolve large-scale industrial problems. The educational goals comprise recruitment of a Ph. D. student from underrepresented minority, implementation of software tools from this project in upgrading courses in The University of Iowa's principal engineering programs, and authoring a comprehensive textbook.
