Issue 46

A. Kostina et alii, Frattura ed Integrità Strutturale, 46 (2018) 332-342; DOI: 10.3221/IGF-ESIS.46.30 333 play a key role in the energy dissipation under ultrasonic loading. To increase the efficiency of application of ultrasonic vibrothermography method for layered structures it is necessary to develop an adequate mathematical model, which can predict the value of energy dissipation and give one an opportunity to optimize the monitoring procedure without expensive experimental program. If solids are perfectly elastic then there is no heat dissipation. Such solids are characterized by linear relation between stress and strain values during the whole process of excitation. Heat dissipation in elastic wave take place if stress and strain are not related by a proportional dependence during the period of vibration. In this case, the hysteresis effect and attenuation of the vibrational amplitude are observed. In viscoelastic media there are several sources of damping. The main of them are dissipation due to the nonlinear relation between stresses and strains, frictional rubbing of contact surfaces and thermoelastic damping [4]. The nature of thermoelastic damping is related to the fact that when the solid is subjected to the loading, the arising strain leads to the temperature increase. If the strain is homogeneous along the specimen, the change in the temperature value is distributed uniformly. Inhomogeneous strain distribution (for example, in the presence of the defect) leads to the local temperature gradients and irreversible processes due to heat conductivity. Therefore, the heat generation occurs in the specimen containing defects. In solids, thermoelastic effect is small compared to the other (inelastic) mechanisms of damping [4]. and it is neglected in this work. Heat generation in cracks can be explained by frictional heating arising from rubbing contact surfaces. Therefore, the crack can be considered as a local heat source. In recent years, much works have been done to simulate dissipation during the ultrasonic wave propagation. Rizi et al. [5] carried out numerical simulation of crack heating during ultrasound wave propagation. They have shown that crack length has a negligible effect on a hysteresis heating. Amount of heat dissipated by friction depends on the size of the crack, gap between crack surface, sliding velocity and contact pressure. In [6] thermal response of the crack is evaluated by numerical scheme based on the solution to the contact problem. The main feature of the proposed approach is simulation of the rough crack surfaces allowing the description of a non-uniformly distributed heating. S.R. Hiremath et al. [7] evaluated temperature rise and velocity in linear elastic plate with a crack. It has been shown that presence of the crack induces deviation of the wave velocity and temperature from their values obtained for the case of an ideal plate without crack. Analytic relation describing temperature rise in a flat-bottom hole during the ultrasonic excitation was obtained in [8]. The proposed solution was based on the concept of a local defect resonance. Calculations and experimental results confirm that the use of this concept strongly intensifies local vibrations and enhances efficiency of vibrothermography. An overview of the existing works shows that defect detection by thermosonic technique can be successfully modelled by a finite-element method. However, most of the considered works are devoted to the application of vibrothermography method to the crack location in a one-layered material. In this work, simulation of the thermosonic method is carried out for a two-layered material (steel specimen with a viscoelastic thin damaged coating). The effect of the loading frequency on the heat dissipation value as well as loading direction and location of the coating defects are investigated in the framework of this work. We have considered an ultrasonic excitation of a bi-metallic sample which include elastic body (steel) coated by viscoelastic media (copper). The steel is considered as a linear elastic solid while an inelastic thin layer with geometric shortcoming models the coating. A coupled thermo-mechanical model is used for the calculation of the heat dissipation. Internal losses in the considered system “elastic solid-viscoelastic coating” are induced by the dissipation of a mechanical energy. In this work, two models of energy dissipation are formulated (hysteretic damping model and visco-elastic Maxwell’s model). Results obtained by the model is compared to results reported in [5]. The obtained results can be used for an optimal choice of the ultrasonic vibrothermography parameters and substitution of expensive experimental procedures. M ATERIAL & METHOD he main idea of the thermosonic technique is to use high-frequency vibrations for local excitation of the defects. Coating defects are passive in the sense that they have a uniform temperature equal to the ambient temperature and require additional mechanical or thermal excitation in order to obtain a useful temperature signal. Therefore, the specimen with the damaged coating is subjected to the ultrasonic vibration with the loading frequency which usually lies in the range from 10000 to 60000 Hz. Cracks or other structural defects induce local heating of the specimen which is identified by the infrared thermography systems. However, the applicability of this technique to the real structures requires additional investigations. The numerical simulation is a powerful tool which can be used for an optimal choice of such technological parameters as loading frequency or loading direction for the structures with the specific geometry. T