PSI - Issue 13

Jacopo Schieppati et al. / Procedia Structural Integrity 13 (2018) 642–647 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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where W 0 is the elastically stored energy and h 0 the height of the specimen in the unstrained condition. For practical purpose, it is easier to calculate the tearing energy using the mechanical energy U calculated from the load displacement curve divided by the uncracked area A uncr . Further explanations of the procedure can be found in

Stadlbauer et al. (2013). 2.3. Thermal conductivity

Thermal conductivity measurements were carried out using two different methods. In a first step, a guarded heat method was conducted using a DTD300 machine by TA instruments. Secondly, a laser flash method (LFA) was implemented with a LFA467 Hyperflash by Netzsch. However, the actual measurement from the LFA method is thermal diffusivity. The thermal conductivity can be retrieved by knowing the density and specific heat. The specific heat was measured with a DSC6000 by Perkin Elmer while the density was measured using a XS205 Dual Range Analytical Balance by Mettler Toledo. The measurements for thermal conductivity were carried out between 30 °C and 130 °C, for every 10 °C. For the measurements carried out with the first method, specimens with thickness of 2 mm were used, while for the second method 1 mm thick samples provided a higher reproducibility. Rubbers subjected to cyclic loading present high-energy dissipation due to molecular frictions, which results in a significant heat generation in the material as reported by Medalia (1991). This effect, in combination with the low thermal conductivity of elastomers, leads to a considerable increase of temperature of rubber components. The temperature could reach regions leading even to thermal failure. The degree of heat build-up strongly depends on the stiffness of the material, on the frequency of oscillation and on the loading amplitude, Gent (2012). During fatigue crack growth tests, the evolution of the surface temperature was monitored and the results of one of the tests are reported in Fig. 1. From the plots in Fig. 1(a), it is possible to notice that the temperature increased fast in the first six thousand cycles, while afterwards a plateau value was reached around 27 °C. It is worth to notice that a slight increase of the temperature was recorded around the crack tip (grey area in the plots), which is more evident in Fig. 1(b). This increase in temperature is related to higher viscoelastic dissipations near the crack tip as suggested by Persson and Brener (2005). With increasing crack length and passing the IR sensor, the surface temperature dropped since no strain is applied in the monitored region. Even though the temperature variation is limited, the small changes reported should be considered relevant since they originated from specimens with low thickness (4 mm). To measure the fatigue crack growth rate, tests were carried out at different frequencies in order to verify the impact of this parameter on both, surface temperature and crack growth rate. As depicted in Fig. 2(a) higher frequencies result in a rising surface temperature. As reported by Gent (2012), the heat generated per second is given by the energy dissipated per cycle multiplied by the frequency. Therefore, the increasing frequency leads to a higher amount of heat, which cannot be transferred to the surrounding environment, resulting in a rising temperature. Moreover, the frequency also impacts the crack growth rate as depicted in Fig. 2(b), with faster crack growth rates for lower frequency. Gent (2012) reported that for non-crystallizing rubbers as NBR, the frequency has a stronger effect than for crystallizing rubbers, especially at a frequency lower than 0.2 Hz. The reported results reveal a variation of one order of magnitude in the crack growth rate with a change of frequency of one order of magnitude even at frequencies higher than 0.2 Hz. Therefore, further analyses of these results were implemented to characterize this specific behavior in detail. In a first step, the reported behavior was explained considering the rising temperature at higher frequency suggesting a higher energy dissipation, resulting in a lower available energy for crack propagation, i.e. lower crack growth rate. For the verification of this hypothesis, the dissipated and the elastically stored energy during cycling loading were analyzed. Fig. 3(a) summarizes the hysteresis curves at 1000 cycles for different frequencies. The curve shapes seem similar and the only evident variation is the increasing slope with higher frequencies, correlating to a stiffer material behavior at higher strain rates. In order to compare the dissipated and stored energies at the different frequencies, their percentages with respect to the input of mechanical energy were calculated and plotted as a function of the number of cycles in Fig. 3(b). As depicted, the differences in the percentage of dissipated energy are very small and they maintain constant along the duration of the tests at different frequencies. This fact suggests that the energy dissipation is not responsible for the observed differences in the crack growth rate. 3. Results and discussion 3.1. Fatigue crack growth