PSI - Issue 53

Martin Matušů et al. / Procedia Structural Integrity 53 (2024) 29 – 36 Author name / Structural Integrity Procedia 00 (2019) 000–000

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5

2.3. Thermal response The temperature evolution on the specimen surface was measured by an infrared thermal camera to investigate the thermal response of the dynamically loaded specimen. While the description of the temperature evolution is not the main focus of this paper, the research findings are presented briefly below. Main sources are [11] and [12]. � � � � �� � �� � , �� ������ �� ��� (1) The stabilized temperature increase  is retrieved as a difference between temperatures on the loaded specimen and on the unloaded reference specimen (placed nearby the loaded specimen). The reference specimen acts like an ambient temperature sensor that can eliminate fluctuations in specimen’s surroundings. Second term on the right of Eq. (1) represents heat conduction as a function of a time-dependent variable  that measures the time to cool the surface temperature to the ambient temperature or to temperature of the reference specimen. Thermoelastic effect is represented by t S , and 1 d is a dissipation that includes hysteresis of plastic deformation (see [11]). Eq. (1) is integrated over time because the infrared thermal camera records in a lower frame rate than the load frequency, The thermoelastic effect is therefore neglected. In our case, we are using the stabilized temperature to characterize the material response to dynamic loading, and so the time dependent variable is equal to zero. Thanks to that, we can simplify Eq. (1) to:

 





d 



, c d 

 

(2)

.

1

1

c





The wave symbol over the variable represents a value integrated over time. Temperature evolution during cyclic loading typically follows three distinct phases, see Fig. 4a. The first phase is characterized by an initial rate R 0 , which typically lasts between 5,000-7,000 cycles for this specific material in this set-up conditions. The second phase is marked by a stabilized temperature. The final phase is the failure of the specimen described by the rate R y .

a)

b)

Fig. 4. a) The temperature evolution during constant-amplitude cyclic loading leading to failure (at N f ) can be divided into three distinct phases. The area with grey background is equal to the limiting energy  . b) Evolution of observed temperature difference in correspondence with the load amplitudes related to various fatigue domains. The self-heating test based on sequential blocks of constant amplitude loading with increased amplitude is designed to monitor the temperature from the lower stresses below the fatigue limit up to the amplitude stress equal to the service life in the LCF region. Fig. 5 illustrates that the most noticeable differences are observed in the upper section of the SH test, where the stabilized temperature varies significantly among the series. The highest and lowest recorded temperatures were found in series 44 and 43, respectively, with series 42 and 41 exhibiting intermediate values. A significant temperature increase is observed beyond 90 MPa, although a closer examination of this trend reveals that the first response increase occurs around 65 MPa, as depicted in the close-up graph in Fig. 5.