Article Article
Variations of Classical and Nonclassical Ultrasound Nonlinearity Parameters during Heat-Induced Microstructural Evolution in an Iron-Copper Alloy

This research demonstrates and compares the potential of two nonlinear ultrasound techniques, second harmonic generation (SHG) and nonlinear resonant ultrasound spectroscopy (NRUS). This research examines a set of thermally aged iron-copper (Fe-1.0% Cu) alloy specimens, which are used as surrogate specimens for radiation damage. It is found that both SHG and NRUS are sensitive to the growth of the copper precipitates, while the changes in the respective nonlinearity parameters are due to different mechanisms. This research demonstrates the potential use of both of these nonlinear ultrasound techniques.



Barbu, A., T.N. Le, N. Lorenzelli, F. Maury, and C.H. de Novion, 1991, “Formation of Copper-Rich Precipitates by Electron Irradiation or by Thermal Treatment in Model Iron-Based Alloys,” Annales de Chimie, Vol. 16, Science des Materiaux, Paris, France, pp. 325–331

Barsoum, M.W., M. Radovic, T. Zhen, P. Finkel, and S.R. Kalidindi, 2005, “Dynamic Elastic Hysteretic Solids and Dislocations,” Physical Review Letters, Vol. 94,

Bentahar, M., H. El Aqra, R. El Guerjouma, M. Griffa, and M. Scalerandi, 2006, “Hysteretic Elasticity in Damaged Concrete: Quantitative Analysis of Slow and Fast Dynamics,” Physical Review B, Vol. 73, /10.1103/PhysRevB.73.014116

Blackstock, J.J., and G.J. Ackland, 2001, “Phase Transitions of Copper Precipitates in Fe–Cu Alloys,” Philosophical Magazine A, Vol. 81, pp. 2127–2148,

Breazeale, M.A., and D.O. Thompson, 1963, “Finite‐Amplitude Ultrasonic Waves in Aluminum,” Applied Physics Letters, Vol. 3, pp. 77–78,

Cantrell, J.H., 2003, “Fundamentals and Applications of Nonlinear Ultrasonic Nondestructive Evaluation,” Ultrasonic Nondestructive Evaluation, CRC Press, pp. 377–448

Cantrell, J.H., and W.T. Yost, 2000, “Determination of Precipitate Nucleation and Growth Rates from Ultrasonic Harmonic Generation,” Applied Physics Letters, Vol. 77, pp. 1952–1954, /1.1311951

Cantrell, J.H., and W.T. Yost, 2001, “Nonlinear Ultrasonic Characterization of Fatigue Microstructures,” International Journal of Fatigue, Vol. 23, pp. 487–490,

Cantrell, J.H., and X.-G. Zhang, 1998, “Nonlinear Acoustic Response from Precipitate-Matrix Misfit in a Dislocation Network,” Journal of Applied Physics, Vol. 84, pp. 5469–5472,

Cantrell, J.H., 2004, “Substructural Organization, Dislocation Plasticity and Harmonic Generation in Cyclically Stressed Wavy Slip Metals,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Vol. 460, pp. 757–780, /rspa.2003.1181

Charleux, M., F. Livet, F. Bley, F. Louchet, and Y. Bréchet, 1996, “Thermal Ageing of an Fe-Cu Alloy: Microstructural Evolution and Precipitation Hardening,” Philosophical Magazine A, Vol. 73, pp. 883–897,

Chen, J., T. Yin, J.-Y. Kim, Z. Xu, and Y. Yao, 2017, “Characterization of Thermal Damage in Sandstone Using the Second Harmonic Generation of Standing Waves,” International Journal of Rock Mechanics and Mining Sciences, Vol. 91, pp. 81–89,

Espinoza, C., D. Feliú, C. Aguilar, R. Espinoza-González, F. Lund, V. Salinas, and N. Mujica, 2018, “Linear Versus Nonlinear Acoustic Probing of Plasticity in Metals: A Quantitative Assessment,” Materials, Vol. 11,

Haupert, S., G. Renaud, J. Rivière, M. Talmant, P.A. Johnson, and P. Laugier, 2011, “High-Accuracy Acoustic Detection of Nonclassical Component of Material Nonlinearity,” The Journal of the Acoustical Society of America, Vol. 130, pp. 2654–2661,

Hikata, A., B.B. Chick, and C. Elbaum, 1965, “Dislocation Contribution to the Second Harmonic Generation of Ultrasonic Waves,” Journal of Applied Physics, Vol. 36, pp. 229–236,

Hikata, A., F.A. Sewell, Jr., and C. Elbaum, 1966, “Generation of Ultrasonic Second and Third Harmonics due to Dislocations. II,” Physical Review, Vol. 151, pp. 442–449,

Hu, S.Y., Y.L. Li, and K. Watanabe, 1999, “Calculation of Internal Stresses around Cu Precipitates in the BCC Fe Matrix by Atomic Simulation,” Modelling and Simulation in Materials Science and Engineering, Vol. 7, pp. 641–655,

Hurley, D.C., D. Balzar, and P.T. Purtscher, 2000, “Nonlinear Ultrasonic Assessment of Precipitation Hardening in ASTM A710 Steel,” Journal of Materials Research, Vol. 15, pp. 2036–2042, /JMR.2000.0292

Hurley, D.C., and C.M. Fortunko, 1997, “Determination of the Nonlinear Ultrasonic Parameter b Using a Michelson Interferometer,” Measurement Science and Technology, Vol. 8, pp. 634–642, /0957-0233/8/6/009

Kim, G., C.-W. In, J.-Y. Kim, K.E. Kurtis, and L.J. Jacobs, 2014, “Air-Coupled Detection of Nonlinear Rayleigh Surface Waves in Concrete—Application to Microcracking Detection,” NDT & E International, Vol. 67, pp. 64–70,

Levy, K.M.S., 2019, “Investigation of Classical and Nonclassical Nonlinearity in Metals” (dissertation), Georgia Institute of Technology, Atlanta, GA

Li, Y., S. Hu, and C.H. Henager, Jr., 2019, “Microstructure-Based Model of Nonlinear Ultrasonic Response in Materials with Distributed Defects,” Journal of Applied Physics, Vol. 125,

Maier, S., J.-Y. Kim, M. Forstenhäusler, J.J. Wall, and L.J. Jacobs, 2018, “Noncontact Nonlinear Resonance Ultrasound Spectroscopy (NRUS) for Small Metallic Specimens,” NDT & E International, Vol. 98, pp. 37–44,

Marino, D., J.-Y. Kim, A. Ruiz, Y.-S. Joo, J. Qu, and L.J. Jacobs, 2016, “Using Nonlinear Ultrasound to Track Microstructural Changes Due to Thermal Aging in Modified 9%Cr Ferritic Martensitic Steel,” NDT & E International, Vol. 79, pp. 46–52,

Matlack, K.H., H.A. Bradley, S. Thiele, J.-Y. Kim, J.J. Wall, H.J. Jung, J. Qu, and L.J. Jacobs, 2015, “Nonlinear Ultrasonic Characterization of Precipitation in 17-4PH Stainless Steel,” NDT & E International, Vol. 71, pp. 8–15,

Matlack, K.H., J.-Y. Kim, J.J. Wall, J. Qu, L.J. Jacobs, and M.A. Sokolov, 2014, “Sensitivity of Ultrasonic Nonlinearity to Irradiated, Annealed, and Re-Irradiated Microstructure Changes in RPV Steels,” Journal of Nuclear Materials, Vol. 448, pp. 26–32, .2014.01.038

Matlack, K.H., J.J. Wall, J.-Y. Kim, J. Qu, L.J. Jacobs, and H.-W. Viehrig, 2012, “Evaluation of Radiation Damage Using Nonlinear Ultrasound,” Journal of Applied Physics, Vol. 111,

Muller, M., A. Sutin, R. Guyer, M. Talmant, P. Laugier, and P.A. Johnson, 2005, “Nonlinear Resonant Ultrasound Spectroscopy (NRUS) Applied to Damage Assessment in Bone,” The Journal of the Acoustical Society of America, Vol. 118, pp. 3946–3952,

Ostrovsky, L.A., and P.A. Johnson, 2001, “Dynamic Nonlinear Elasticity in Geomaterials,” La Rivista del Nuovo Cimento, Vol. 24, pp. 1–46,

Othen, P.J., M.L. Jenkins, and G.D.W. Smith, 1994, “High-Resolution Electron Microscopy Studies of the Structure of Cu Precipitates in a-Fe,” Philosophical Magazine A, Vol. 70, pp. 1–24, /01418619408242533

Payan, C., T.J. Ulrich, P.Y. Le Bas, T. Saleh, and M. Guimaraes, 2014, “Quantitative Linear and Nonlinear Resonance Inspection Techniques and Analysis for Material Characterization: Application to Concrete Thermal Damage,” The Journal of the Acoustical Society of America, Vol. 136, pp. 537–546,

Remillieux, M.C., R.A. Guyer, C. Payan, and T.J. Ulrich, 2016, “Decoupling Nonclassical Nonlinear Behavior of Elastic Wave Types,” Physical Review Letters, Vol. 116,

Ruiz, A., N. Ortiz, A. Medina, J.-Y. Kim, and L.J. Jacobs, 2013, “Application of Ultrasonic Methods for Early Detection of Thermal Damage in 2205 Duplex Stainless Steel,” NDT & E International, Vol. 54, pp. 19–26,

Scott, K., J.-Y. Kim, and L.J. Jacobs, 2018, “Signal Processing Methods for Second Harmonic Generation in Thin Specimens,” NDT & E International, Vol. 95, pp. 57–64,

Scott, K., J.-Y. Kim, J.J. Wall, D.-G. Park, and L.J. Jacobs, 2017, “Investigation of Fe-1.0% Cu Surrogate Specimens with Nonlinear Ultrasound,” NDT & E International, Vol. 89, pp. 40–43, /j.ndteint.2017.03.009

Smallman, R.E., and A.H.W. Ngan, 2014, “Chapter 10 - Surfaces, Grain Boundaries and Interfaces,” Modern Physical Metallurgy (8th ed.), ed. R.E. Smallman and A.H.W. Ngan, Butterworth-Heinemann, Oxford, pp. 415–442,

TenCate, J.A., D. Pasqualini, S. Habib, K. Heitmann, D. Higdon, and P.A. Johnson, 2004, “Nonlinear and Nonequilibrium Dynamics in Geomaterials,” Physical Review Letters, Vol. 93, /PhysRevLett.93.065501

Vandenbossche, L.P., M.J. Konstantinović, A. Almazouzi, and L.R. Dupré, 2007, “Magnetic Evaluation of the Hardening and Softening of Thermally Aged Iron–Copper Alloys,” Journal of Physics D: Applied Physics, Vol. 40,

Zhu, J., T. Zhang, Y. Yang, and C.T. Liu, 2019, “Phase Field Study of the Copper Precipitation in Fe-Cu Alloy,” Acta Materialia, Vol. 166, pp. 560–571,


Usage Shares
Total Views
96 Page Views
Total Shares
0 Tweets
0 PDF Downloads
0 Facebook Shares
Total Usage