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  Cornell University

MAE Publications and Papers

Sibley School of Mechanical and Aerospace Engineering

New article: Understanding Local Deformation in Metallic Polycrystals Using High Energy X-rays and FInite Elements

Article:  Miller MP, Dawson PR (2014)  “Understanding Local Deformation in Metallic Polycrystals Using High Energy X-rays and FInite Elements”, Current Opinion in Solid State & Materials Science, 18 (5): 286-299


Abstract:  A methodology for understanding the stress and elastoplastic deformation responses within a loaded polycrystal is presented along with illustrative examples. High energy synchrotron X-rays are used to penetrate bulk metallic samples and produce diffracted intensity from each deforming crystal – revealing the evolving internal structure. A virtual representation of the microstructure is constructed using the finite element method (FEM) to simulate the evolution of the elastoplastic deformations, stress fields, and lattice orientations within the deforming crystals as the polycrystal is loaded. Simulations are compared directly to experimental diffraction data. In the case of powder experiments, lattice strain pole figures (SPFs) measured experimentally are compared to SPFs calculated by projecting X-rays through the finite element mesh. During in situ loading experiments, the stress states are found to differ from one crystal to the next and to vary from the stress being applied at the macroscale. A SPF/FEM-based methodology for quantifying residual stress fields within processed polycrystalline components is described. SPFs were measured at many points within a shrink-fit sample. Finite element discretizations of both the sample and orientation space of each diffraction volume were used to formulate an optimization for the distribution of the stress tensor within the sample. A different experiment, one in which the X-ray beam and the crystals are closer to the same size, is used to investigate the aggregate crystal by crystal. The Debye-Scherrer rings reduce to a set of spots associated with each crystal within the diffraction volume. This method is demonstrated by tracking deformation of four grains within a deforming BCC titanium aggregate loaded in situ within the elastic regime to determine the single crystal elastic moduli. Plastic deformation can also be investigated by monitoring the size and shape of individual diffraction spots. Each spot contains geometrically exact information regarding the internal structure of the crystal. Instead of reconstructing the crystal structure by inverting the diffraction data, virtual diffraction experiments are performed on the finite element mesh and the resulting simulated diffraction patterns are compared directly to the experimental results. Once the experimental/simulation methodology is validated, the approximation of the subgrain distribution of stress and lattice orientation from the finite element model can be used to construct theories for failure phenomena such as microcrack initiation. As opposed to other methods of discretizing a polycrystalline aggregate, the finite element framework enables a seamless transition to analyses associated with mechanical design. (C) 2014 Published by Elsevier Ltd.

Funding Acknowledgement:  Office of Naval Research; Air Force Office of Scientific Research; National Science Foundation; Department of Energy; DOE Office of Science by Argonne National Laboratory

Funding Text:  The authors acknowledge the students, post-docs and other researchers who have worked on these projects. Their names appear on the author lists of the cited papers. The research was funded by agencies including the Office of Naval Research, the Air Force Office of Scientific Research, the National Science Foundation and the Department of Energy. Specific agencies and award numbers can be found in the individual papers. High energy diffraction experiments were conducted at the Cornell High Energy Synchrotron Source (CHESS), which is supported by the National Science Foundation and at the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory.

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