Resonance ultrasound spectroscopy (RUS) is a nondestructive technique that exploits the natural resonance behavior of a material to characterize its elastic properties. The traditional RUS approach utilizes an analytic approximation to determine resonance behavior given a guess set of elastic moduli. An optimization process is then used to fit elastic properties to experimentally measured resonance frequencies. This approach generally requires certain limiting assumptions to be made with respect to sample geometry, crystallographic orientation, and requires single crystal samples to obtain single crystal elastic properties. Toward the goal of developing a measurement process to obtain single crystal elastic properties on polycrystalline aerospace alloys without the aforementioned limitations, a framework has been developed to enable this process on samples with multiple grains, arbitrary sample shape, and without restrictions to crystallographic orientation. This framework utilizes off-the-shelf finite element method software and optimization routines, enabling rapid modeling and easy adaptation to different scenarios. Testing of this framework was performed on an amorphous specimen, a single crystal specimen, and preliminary results show promise on a nickel aluminide bicrystal, provided that the sample geometry, density, and crystallographic orientations are adequately characterized.
Anderson, O.L., E. Schreiber, and N. Soga, Elastic Constants and their Measurements, McGraw-Hill, New York, NY, 1973.
Auld, B.A., Acoustic Fields and Waves in Solids: Vol. 1, Wiley, New York, NY, 1973, p. 74.
Demarest, H.H., “Cube-resonance Method to Determine the Elastic Constants of Solids,” Journal of the Acoustical Society of America, Vol. 49, No. 3B, 1971, pp. 768–775.
Groeber, M.A., and M.A. Jackson, “DREAM.3D: A Digital Representation Environment for the Analysis of Microstructure in 3D,” Imaging Materials and Manufacturing Innovation, Vol. 3, No. 5, 2014, pp. 1–17.
Holland, R., “Resonant Properties of Piezoelectric Ceramic Rectangular Parallelepipeds,” Journal of the Acoustical Society of America, Vol. 43, No. 5, 1968, pp. 988–997.
Kaplan, G., T.W. Darling, and K.R. McCall, “Resonant Ultrasound Spec-troscopy and Homogeneity in Polycrystals,” Ultrasonics, Vol. 49, No. 1, 2009, pp. 139–142.
Kelly, C.T., Implicit Filtering, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2011.
Liu, G., and J.D. Maynard, “Measuring Elastic Constants of Arbitrarily Shaped Samples using Resonant Ultrasound Spectroscopy,” Journal of the Acoustical Society of America, Vol. 131, No. 3, 2012, pp. 2068–2078.
Marquardt, D., “An Algorithm for Least-squares Estimation of Nonlinear Parameters,” Journal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 2, 1963, pp. 431–441.
Marburg, S., “Discretization Requirements: How many Elements per Wavelength are Necessary?” Computational Acoustics of Noise Propagation in Fluids – Finite and Boundary Elements Methods, edited by S. Marburg and B. Nolte, Springer, Berlin, Germany, 2008, pp. 309–332.
Maynard, J., “Resonant Ultrasound Spectroscopy,” Physics Today, Vol. 49, No. 1, 1996, pp. 26–31.
Migliori, A., and J.L. Sarrao, Resonant Ultrasound Spectroscopy, Wiley, New York, NY, 1996.
Migliori, A., J.L. Sarrao, W.M. Visscher, T.M. Bell, M. Lei, Z. Fisk, and R.G. Leisure, “Resonant Ultrasound Spectroscopic Techniques for Measure-ment of the Elastic Moduli of Solids,” Physica B, Vol. 183, Nos. 1–2, 1993, pp. 1–24.
Miracle, D., “The Deformation of NiAl Bicrystals,” Technical Report, WL-TR-92-411, Wright Laboratory, Dayton, OH, 1990.
Miracle, D., “Physical and Mechanical Properties of NiAl,” Acta Metallur-gica et Materialia, Vol. 41, No. 3, 1993, pp. 649–684.
Ohno, I., “Free Vibration of a Rectangular Parallelepiped Crystal and its Application to Determination of Elastic Constants of Orthorhombic Crystals,” Journal of Physics of the Earth, Vol. 24, No. 4, 1976, pp. 355–379.
Plesek, J., R. Kolman, and M. Landa, “Using Finite Element Method for the Determination of Elastic Moduli by Resonant Ultrasound Spectroscopy,” Journal of the Acoustical Society of America, Vol. 116, No. 1, 2004, pp. 282–287.
Remmillieux M.C., T.J. Ulrich, C. Payan, J. Riviere, C.R. Lake, and P.-Y. Le Bas, “Resonant Ultrasound Spectroscopy for Materials with High Damping and Samples with Arbitrary Geometry,” Journal of Geophysical Research: Solid Earth, Vol. 120, 2015, pp. 4898–4916.
Siebörger, D, H. Knake, and U. Glatzel, “Temperature Dependence of the Elastic Moduli of the Nickel-base Auperalloy CMSX-4 and its Isolated Phases,” Materials Science and Engineering: A, Vol. 298, No. 1, 2001, pp. 26–33.
Visscher, W.M., A. Migliori, T.M. Bell, and R.A. Reinert, “On the Normal Modes of Free Vibration of Inhomogeneous and Anisotropic Elastic Objects,” Journal of the Acoustical Society of America, Vol. 90, No. 4, 1991, pp. 2154–2162.
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