PSI - Issue 57

Martin Matušů et al. / Procedia Structural Integrity 57 (2024) 327 – 334 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

332 6

̇ − = + 1 , = −

(1)

Here,  represents a difference of temperatures measured on a loaded specimen T loaded and on a reference non loaded specimen T ref , which is placed nearby the examined loaded specimen, see Fig. 2a. The reference specimen acts like a sensor of ambient temperature. It helps to eliminate its fluctuations in surroundings of both specimens, and the potential temperature sensor drift. The first term represents the inner energy based on the derivative of stabilized temperature. The second term on left represents heat conduction as a function of a specific time constant  , that relates to the time to cool the surface temperature of the loaded specimen, loading of which was stopped, to the ambient temperature or to temperature of the reference specimen. t S represents the energy term related to the thermoelastic effect and 1 d is a dissipation, that includes hysteresis of plastic deformation [11]. In real measurements, the equation is integrated over time due to the fact that the used infrared thermal camera records the action in a frame rate lower than the load frequency imposed by the testing equipment. The thermoelastic effect can therefore be neglected.

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 ofobserved temperature difference in correspondence with the load amplitudes related to various fatigue domains. In our case, we are using the stabilized temperature to characterize the materialresponse to cyclic loading, so the time dependent first term is equal to zero. Then we can simplify Eq. (1) to: ̃ = ̃ 1 , ̃= ̃ 1 (2) where wave marks above the variables represent integration of the variables over time. Temperature evolution during cyclic loading typically follows three distinct phases, as shown in Fig. 4, left. The first phase is characterized by the initial incline R 0 , which typically lasts between 5,000 to 7,000 cycles for this material and for this specimen design. The second phase is marked by a stabilized temperature difference. The final phase characterized by the inclination R y is the quick transition to the failure of the specimen. To further investigate stabilized temperature in the second phase, a step self-heating (S-H) test was pursued to monitor the stabilized temperature response to various subsequently increasing load amplitudes. This test is designed to monitor the temperature response to stress values from below the fatigue limit up to the stress amplitudes that would lead to the numbers of cycles in the LCF region. The S-H experiment was designed with the focus on defining the number of cycles to reach the stabilized temperatures on specific stress amplitudes. At last, the test block length was derived from the tests on a single load amplitude, which were used for the definition of S-N curves. The conclusion is that the transition to the stabilized temperature of the Phase 2 occurs around 5000 to 6000 cycles with our testing conditions. The load block duration