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The effect of small-scale random defects such as microcracks or inclusions are critical to the prediction of material failure, yet including these in a fracture simulation can be difficult to perform efficiently. Typically, work has focused on implementing these through a statistical characterization of the micro- or meso-scales. This characterization has traditionally focused on the spatial distribution of faults, assuming the material is purely isotropic. At the macro-scale, many materials can be assumed to be fully isotropic and homogeneous, but at the small scale may show significant anisotropy or heterogeneity. Other materials may be effectively anisotropic in bulk, such as rock bedding planes. Statistical volume elements (SVE) are one homogenization methodology used to retain this heterogeneity or anisotropy when characterizing a material. Unlike a Representative Volume Element (RVE), the choice of SVE including size, boundary conditions applied, shape, and type, may affect the given material properties. In addition, the size which an RVE exists is well-studied for homogeneity, but there is less study of the isotropic limit. This work introduces a multi-scale methodology using SVEs to study material heterogeneity and anisotropy. Results are given for macroscopic fracture simulations using this SVE-based homogenization scheme. In addition, the rate of convergence to the RVE limit for both the homogeneous and isotropic limit of two types of SVE, Regular Square and Voronoi Square, are shown. This methodology shows promise for characterization of both isotropic and anisotropic materials.

A two-pole synchronous motor was recently rewound for the von Karman Gas Dynamics facility at Arnold Engineering Development Complex, Arnold Air Force Base, Tennessee. After installing the rewound rotor, unexpected vibration amplitudes were recorded during motor checkouts. To resolve this issue, an investigation was initiated to investigate the causes of the vibration issues. The investigation discovered that the original design used sleeve bearings rather than pressure dam bearings. A study was formed to determine the effect of changing the pressure dam bearings back to sleeve bearings. Because only one spare bearing shell existed, the bearing with the highest vibration amplitudes was chosen to be switched. A lateral rotordynamic analysis was performed to determine the impact of this switch, prior to performing the bearing swap. The rotordynamic model predicted that the rotor was operating near the second critical speed. Regardless of the bearing change, the second critical speed was not impacted. However, the determination was made to change the bearing to the sleeve bearing due to predicted lower vibration amplitudes. From the motor checkout runs, the model prediction was verified and the sleeve bearing was kept. Vibration amplitudes have been reduced, but issues still remain with the rotor operation near the second critical speed. Further analysis is required to successfully shift the rotor operation away from the second critical speed.