International Science Index


Methods for Material and Process Monitoring by Characterization of (Second and Third Order) Elastic Properties with Lamb Waves


In accordance with the industry 4.0 concept, manufacturing process steps as well as the materials themselves are going to be more and more digitalized within the next years. The “digital twin” representing the simulated and measured dataset of the (semi-finished) product can be used to control and optimize the individual processing steps and help to reduce costs and expenditure of time in product development, manufacturing, and recycling. In the present work, two material characterization methods based on Lamb waves were evaluated and compared. For demonstration purpose, both methods were shown at a standard industrial product - copper ribbons, often used in photovoltaic modules as well as in high-current microelectronic devices. By numerical approximation of the Rayleigh-Lamb dispersion model on measured phase velocities second order elastic constants (Young’s modulus, Poisson’s ratio) were determined. Furthermore, the effective third order elastic constants were evaluated by applying elastic, “non-destructive”, mechanical stress on the samples. In this way, small microstructural variations due to mechanical preconditioning could be detected for the first time. Both methods were compared with respect to precision and inline application capabilities. Microstructure of the samples was systematically varied by mechanical loading and annealing. Changes in the elastic ultrasound transport properties were correlated with results from microstructural analysis and mechanical testing. In summary, monitoring the elastic material properties of plate-like structures using Lamb waves is valuable for inline and non-destructive material characterization and manufacturing process control. Second order elastic constants analysis is robust over wide environmental and sample conditions, whereas the effective third order elastic constants highly increase the sensitivity with respect to small microstructural changes. Both Lamb wave based characterization methods are fitting perfectly into the industry 4.0 concept.

[1] J. Krautkraemer and H. Krautkraemer, Werkstoffprüfung mit Ultraschall. Springer Berlin Heidelberg, Berlin and Heidelberg, 5. edition.
[2] H. Lamb, “On waves in an elastic plate,” Royal Society of London Proceedings, 1917.
[3] B. A. Auld, Acoustic fields and waves in solids, Vol. 2. R.E. Krieger, Malabar, 2. Edition, 1990.
[4] W. P. Rogers, “Elastic property measurement using rayleigh-lamb waves,” Research in Nondestructive Evaluation, 1995, 6(4):185–208.
[5] C. Potel et al., “Lamb wave attenuation in a rough plate,” Journal of Applied Physics, 104(7):074908, 2008.
[6] B. Pavlakovic et al., “Disperse: A general purpose program for creating dispersion curves,” In Thompson, D. O. und Chimenti, D. E., editors, Review of Progress in Quantitative Nondestructive Evaluation, Springer US, Boston and MA, 1997, pp. 185–192.
[7] P. Bocchini, A. Marzani, and E. Viola, “Graphical user interface for guided acoustic waves,” Journal of Computing in Civil Engineering, 25(3):202–210, 2011.
[8] K. Vignesh et al., “Non-destructive evaluation of elastic modulus in metals using lamb wave technique,” The e-Journal of Nondestructive Testing, 2015, 20(6).
[9] D. S. Hughes and J. L. Kelly, “Second-order elastic deformation of solids,” Phys. Rev., 92:1145–1149, 1953.
[10] F. D. Murnaghan, “Finite deformations of an elastic solid,” American Journal of Mathematics, 59(2):235–260, 1937.
[11] R. A. Toupin and B. Bernstein, “Sound waves in deformed perfectly elastic materials. acoustoelastic effect,” The Journal of the Acoustical Society of America, 33(2), 1961.
[12] D. D. Muir, “One-Sided Ultrasonic Determination of Third Order Elastic Constants using Angle-Beam Acoustoelasticity Measurements,” PhD thesis, Georgia Institute of Technology, Atlanta and Georgia, 2009.
[13] R. Meier, “Influences of stress and temperature on the time-of-flight of ultrasound in solid matter,” Master’s thesis, Universität Leipzig, Leipzig, 2008.
[14] K. S. Tarar et al., “Stress detection with guided acoustic ultrasonic waves by non-linear elastic and geometric effects,” In Proceedings of SPIE - The International Society for Optical Engineering, SPIE Proceedings, pages 729518–1 – 729518–8. SPIE, 2009.
[15] U. Amjad et al., “Determination of the stress dependence of the velocity of lamb waves in aluminium plates,” In Proceedings of SPIE - The International Society for Optical Engineering, SPIE Proceedings, pages 798410–1 – 798410–9. SPIE, 2011.
[16] N. Gandhi, “Determination of Dispersion Curves for Acoustoelastic Lamb Wave Propagation,” PhD thesis, Georgia Institute of Technology, Atlanta and Georgia, 2010.