Temperature dependence of the ultrasonic transmission through electrical resistance heated imperfect metal–metal interfaces

Abstract

Because of surface roughness, the area of contact between real surfaces is less than the geometrical area. For this reason the known rules of acoustic reflection and transmission have to be modified for real interfaces. Ultrasonic transmission through imperfect interfaces is commonly described in terms of the contact stiffness model which assumes distributed springs between the surfaces in contact [Proc. R. Soc. Lond. A 202 244; J. Acoust. Soc. Am. 89 (1991) 503ff; J. Acoust. Soc. Am. 68 1516; J. Nondestr. Eval. 4 177; J. Geophys. Res. 94 (1989) 17681ff]. Several authors [Trans. ASME 123 8ff; J. Acoust. Soc. Am. 103 657ff; Ultrasonics 38 513] theoretically and experimentally show the pressure and frequency dependence of the ultrasonic transmission through such interfaces. Our paper will document, that the temperature of the interface has significant influence on the ultrasonic transmission as well. In the experimental approach, a CuSn8-rod was clamped between the electrodes of a resistance welding unit. Either longitudinally or transversally polarised ultrasonic pulses were generated by a transmitter built in the upper electrode. The transmitted ultrasonic signal was subsequently detected by the receiver integrated in the lower electrode. After the welding current was turned on, a strong decrease in ultrasonic transmission has been observed due to resistance heating of the interfaces between the welding electrodes and the rod. To explain this extraordinary strong temperature effect, a simple quasistatic analytical thermal–electrical model of the contacting area was used to give a rough estimation of the maximum interfacial temperature and the temperature distribution during the flow of the welding current. In a second step, the temperature dependence of the material data in the acoustic contact stiffness model was used to calculate the changes in ultrasonic transmission caused by the welding current. It is shown, that the observed decrease in ultrasonic transmission with increasing temperature is mainly caused by the temperature dependence of the elastic constants of the metals and is much stronger than expected for ideal interfaces. The calculated ultrasonic transmission is in very good agreement with the experimental data and seems to be interpreted correctly by the acoustic contact stiffness model.