Article Article
Contact and Non-Contact Resonance Spectroscopy Characterization of Additively Manufactured and Wrought Metallic Samples

Nonlinear resonance ultrasound spectroscopy (NRUS) is a growing NDT technique that tracks amplitude-dependent changes in resonance frequency to assess the presence of damage, such as dislocations and micro-cracks [1]. The amount of frequency shift with increasing amplitude is typically quantified with the nonclassical nonlinear parameter f [1]. NRUS has been used in metals to study fatigue damage [2], [3] , creep [4], stress corrosion cracking [5], thermal aging [6]–[8], and porosity [9]. Unlike linear techniques, nonlinear approaches are sensitive to the presence of micro-damage, which is of great interest to uncover early forms of damage, and help setting out adequate maintenance plans. Additionally, resonance approaches enable quick inspection of parts, irrespective of how complex the geometry is. A typical way of conducting NRUS tests is to bond a piezoelectric (PZT) disc to the sample. The PZT is used as a source and allows one to achieve large excitation amplitudes (nonlinear elastic regime with dynamic strain of order ~10-5). Unfortunately, the bond between the sample and the disc introduces additional elastic nonlinearity, and measurements must be repeated several times, with ungluing/regluing of the PZT in-between each test. Moreover, the intrinsic nonlinearity of the sample cannot be determined, and only relative differences in nonlinearity across a set of samples can be examined, that is, only relative measurements can be made. This makes consistent and repeatable measurements difficult to achieve [10]. Being able to conduct NRUS tests in a non-contact fashion would be transformational, making the measurements much faster, more reproducible, and absolute. Recently, air-coupled transducers have been used as an excitation source for NRUS tests on small metallic prismatic specimens [6]–[8], reaching dynamic strains of order ~2×10-6. A “candy can” cavity with multiple PZTs has also been used successfully as an excitation source to conduct nonlinear measurements [11], [12] . The cavity consists of a focusing chamber with an aperture for sample excitation. Combined with a time reversal technique, the cavity achieves higher incident pressure and narrower focus than commercial focused air-coupled transducers [11], [12]. If a high enough excitation can be achieved, it could likely be used as an excitation source for NRUS testing. Pulsed Nd:YAG lasers have also been used as a non-contact excitation source for resonance ultrasound spectroscopy (RUS) [13], [14]. Such laser could be used for NRUS testing as well, in combination with signal processing developed for impact-based NRUS, when a single hammer impact excitation is used for NRUS testing [15]–[17]. The objective of this study is to compare the NRUS parameters of additively manufactured (AM) and wrought cylindrical 316 stainless steel samples with four different heat treatments. We compare the results of four different excitation methods: in-contact piezoelectric discs, air-coupled transducers, a “candy can” cavity, and laser excitation.

DOI: 10.32548/RS.2022.023


[1] P. Johnson and A. Sutin, “Slow dynamics and anomalous nonlinear fast dynamics in diverse solids,” J. Acoust. Soc. Am., vol. 117, no. 1, pp. 124–130, Jan. 2005, doi: 10.1121/1.1823351.

[2] Y. Cheong, M. K. Alam, and C. Kim, “Nonlinear parameters for a diagnosis of micro‐scale cracks using a nonlinear resonant ultrasound spectroscopy (nrus),” AIP Conf. Proc., vol. 1211, no. 1, pp. 1439–1444, Feb. 2010, doi: 10.1063/1.3362237.

[3] T. Ohtani and Y. Ishii, “Nonlinear Resonant Ultrasound Spectroscopy (NRUS) applied to fatigue damage evaluation in a pure copper,” AIP Conf. Proc., vol. 1474, no. 1, pp. 203–206, Sep. 2012, doi: 10.1063/1.4749331.

[4] T. Ohtani, Y. Kusanagi, and Y. Ishii, “Noncontact nonlinear resonant ultrasound spectroscopy to evaluate creep damage in an austenitic stainless steel,” AIP Conf. Proc., vol. 1511, no. 1, pp. 1227–1233, Jan. 2013, doi: 10.1063/1.4789183.

[5] S. M. Hogg, B. E. Anderson, P.-Y. Le Bas, and M. C. Remillieux, “Nonlinear resonant ultrasound spectroscopy of stress corrosion cracking in stainless steel rods,” NDT E Int., vol. 102, pp. 194–198, Mar. 2019, doi: 10.1016/j.ndteint.2018.12.007.

[6] Steffen Maier, Jin-Yeon Kim, Marc Forstenhäusler, James J. Wall, and Laurence J. Jacobs, “Noncontact nonlinear resonance ultrasound spectroscopy (NRUS) for small metallic specimens,” NDT E Int., vol. 98, pp. 37–44, Apr. 2018, doi:

[7] K. M. S. Levy, J.-Y. Kim, and L. J. Jacobs, “Investigation of the relationship between classical and nonclassical ultrasound nonlinearity parameters and microstructural mechanisms in metals,” J. Acoust. Soc. Am., vol. 148, no. 4, pp. 2429–2437, Oct. 2020, doi: 10.1121/10.0002360.

[8] D. N. Fahse, K. M. Scott Levy, J.-Y. Kim, and L. J. Jacobs, “Comparison of changes in nonclassical (α) and classical (β) acoustic nonlinear parameters due to thermal aging of 9Cr–1Mo ferritic martensitic steel,” NDT E Int., vol. 110, p. 102226, Mar. 2020, doi: 10.1016/j.ndteint.2020.102226.

[9] J. Kober et al., “Assessing Porosity in Selective Electron Beam Melting Manufactured Ti–6Al–4V by Nonlinear Impact Modulation Spectroscopy,” J. Nondestruct. Eval., vol. 39, no. 4, p. 86, Nov. 2020, doi:


[10] Marcie A. Stuber Geesey, Bettina Aristorenas, Timothy J. Ulrich, and Carly M. Donahue, “Investigation of the nonlinearity of transducer acoustic couplants for nonlinear elastic measurements,” NDT E Int., vol. 104, pp. 10–18, Mar. 2019, doi:

[11] P.-Y. Le Bas, T. J. Ulrich, B. E. Anderson, and J. J. Esplin, “A high amplitude, time reversal acoustic non-contact excitation (trance),” J. Acoust. Soc. Am., vol. 134, no. 1, pp. EL52–EL56, Jul. 2013, doi: 10.1121/1.4809773.

[12] P.-Y Le Bas, M. C. Remillieux, L. Piezonka, J. A. Ten Cate, B. E. Anderson, and T. J. Ulrich, “Damage Imaging in a Laminated Composite Plate Using an Air-Coupled Time Reversal Mirror,” Appl. Phys. Lett., vol. 107, 2015, doi: 10.1063/1.4935210.

[13] D. H. Hurley, S. J. Reese, S. K. Park, Z. Utegulov, J. R. Kennedy, and K. L. Telschow, “In situ laser-based resonant ultrasound measurements of microstructure mediated mechanical property evolution,” J. Appl. Phys., vol. 107, no. 6, p. 063510, Mar. 2010, doi: 10.1063/1.3327428.

[14] D. H. Hurley, S. J. Reese, and F. Farzbod, “Application of laser-based resonant ultrasound spectroscopy to study texture in copper,” J. Appl. Phys., vol. 111, no. 5, p. 053527, Mar. 2012, doi: 10.1063/1.3692386.

[15] K. Van Den Abeele, P. Y. Le Bas, B. Van Damme, and T. Katkowski, “Quantification of material nonlinearity in relation to microdamage density using nonlinear reverberation spectroscopy: Experimental and theoretical study,” J. Acoust. Soc. Am., vol. 126, no. 3, pp. 963–972, Sep. 2009, doi: 10.1121/1.3184583.

[16] J. N. Eiras, J. Monzó, J. Payá, T. Kundu, and J. S. Popovics, “Non-classical nonlinear feature extraction from standard resonance vibration data for damage detection,” J. Acoust. Soc. Am., vol. 135, no. 2, pp. EL82–EL87, Feb. 2014, doi: 10.1121/1.4862882.

[17] J. Jin, W. Xi, J. Riviere, and P. Shokouhi, “Single-Impact Nonlinear Resonant Acoustic Spectroscopy for Monitoring the Progressive Alkali–Silica Reaction in Concrete,” J. Nondestruct. Eval., vol. 38, no. 3, p. 77, Aug. 2019, doi: 10.1007/s10921-019-0614-5.

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