Issue 46

A. Kostina et alii, Frattura ed Integrità Strutturale, 46 (2018) 332-342; DOI: 10.3221/IGF-ESIS.46.30 341 isotropic loss factor and visco-elastic Maxwell’s model. The application of both models is illustrated by numerical simulation of ultrasonic excitation of the steel specimen with a copper coating containing an edge crack. The obtained results have shown that the visibility of the crack depends on the loading method. The crack is highly visible when the applied load is perpendicular to the crack plane. Under such loading conditions, the Maxwell’s model and isotropic damping model can be considered as equivalent with regard to the temperature rise value. The emergence of the stationary wave blurs the visibility of the crack tip, because the maximum temperature values coincides with the antinodes of the wave. Under such loading case, Maxwell’s model gives more visible crack tip compared to the isotropic damping model. Both considered models are sensitive to the values of the material parameters. A sensitivity of the obtained results to the loading magnitude can be observed when the values of the isotropic loss factor and relaxation time value are small enough. The most pronounced is the dependence of the obtained results on the loading frequency. The increase in the loading frequency gives approximately twofold increase in the maximum value of the temperature rise at the crack tip. The optimal conditions for application of ultrasonic vibrothermography include relative high loading frequency and ultrasonic excitation perpendicular to the crack plane. A CKNOWLEDGMENTS his work is supported by the Russian Science Foundation (Grant No. 15-19-10056). R EFERENCES [1] Henneke, E.G., Reifsnider, K.L., and Stinchcomb, W.W. (1979). Thermography - an NDI method for damage detection, J. Met., 31, pp. 11–15. [2] Pye, C.J. and Adams, R.D. (1981). Detection of damage in fiber reinforced plastics using thermal fields generated during resonant vibration, NDT Int., 14(3), pp. 111–118. [3] Guo, X. and Vavilov, V.P. (2013). Crack detection in aluminum parts by using ultrasound excited infrared thermography, Infrared Phys. Technol., 61, pp. 149–156. [4] Truell, R., Elbaum, C. and Chick, B.B. (1969). Ultrasonic methods in solid state physics, New York and London, Academic Press. [5] Sabotkarin Rizi, A., Hedayatrasa, S., Maldague, X. and Vukhanh, T. (2013). FEM modeling of ultrasonic vibrothermography of a damaged plate and qualitative study of heating mechanisms, Infrared Phys. Technol., 61, pp. 101–110. [6] Plum, R. and Ummenhofer, T. (2011). Structural-thermal finite element simulation of vibrothermography applied to cracked steel plates, Quant. Infrared Thermogr. J., 8, pp. 201–220. [7] Hiremath, S.R., Mahapatra, D.R. and Srinivasan, S. (2012). Detection of crack in metal plate by thermo sonic wave based detection using FEM, J. Exp. Stroke Transl. Med., 1(1), pp. 12–18. [8] Solodov, I., Rahammer, M., Derusova, D. and Busse, G. (2015). Highly-efficient and noncontact vibro-thermography via local defect resonance, Quant. Infrared Thermogr. J., 12(1), pp. 98–111. [9] Findeisen, D. (2000). System dynamics and mechanical vibrations, Berlin, Springer. [10] Comsol. (2017). COMSOL Multiphysics User’s Guide, Version 5.3a. N OMENCLATURE  Density; u Displacement vector; t Time; σ Cauchy’s stress tensor; f Volumetric force vector;   F  Fourier transform of a function; T