Issue 46

A. Kostina et alii, Frattura ed Integrità Strutturale, 46 (2018) 332-342; DOI: 10.3221/IGF-ESIS.46.30 337 The sample is considered as a perfectly elastic isotropic solid which has no energy dissipation. The coating is considered as a visco-elastic material subjected to the Maxwell’s model or as isotropic elastic solid with a material damping describing by an isotropic loss factor. The crack tip is simulated as an area with an initial strain localization and, as a consequence, with a large number of microdefects. (a) (b) Figure 1 : (a) A relative error versus maximum size of the element. (b) Temperature rise at edge crack tip (solid line – results presented in [5], dashed line – results of the developed model). Figure 2 : Schematic representation of the two-layered specimen. Figure 3 : Finite-element mesh of the two-layered specimen. It is supposed that the specimen is laid on some surface during the loading process. Therefore, fixed constrained boundary conditions were set to the lower boundary. The initial temperature of the sample is assumed to be 293.15 K. Convective heat flux with a heat transfer coefficient equal to 6 W/(m 2 *K) was applied to all boundaries of the specimen except for the lower. The lower boundary is assumed to be thermally insulated. Fig. 4 presents results of continuous ultrasonic excitation of the sample by a point load applied to the side of the sample opposite to a crack location obtained by two models: material damping and visco-elastic Maxwell’s model. The loading direction was perpendicular to the crack plane, the applied loading frequency was 20000 Hz, the duration of the loading was 1 second. It can be concluded that the crack location can be sharply visible in both models. The main difference is that damping model also made visible the point of load application. Fig. 5 shows evolution of the temperature rise during the loading process. The maximum value of the temperature is observed at the crack tip. On the initial stage of the excitation, the rate of the temperature rise is quite large. At subsequent stages of excitations, it is observed a decrease in the temperature rise rate induced by the attenuation of the wave. These results are confirmed by Fig. 6 (a). It can be seen that there is only a slight increase in the temperature rise value in the end of the excitation process at the crack tip. Moreover, fig. 6 (a) shows that the applied load and the used values of material parameters give the same temperature rise at the crack tip. This result can be interpreted as the equivalence of the damping model and visco-elastic model under the considered conditions. Numerical simulation has shown also that the choice of material parameters for both models affect the sensitivity of the obtained results to the applied load. A decrease in the isotropic loss factor value and relaxation time value by an order of magnitude gives a sensitivity of the temperature rise by the loading magnitude. Fig. 6 (b) presents results of ultrasonic excitation of the end face of the specimen by various surface loads. The graphs show that the sensitivity of the damping model is slightly larger than the Maxwell’s model. However, values of the isotropic loss factor and relaxation time given in the Tab., 2 are insensitive to the applied load.