PSI - Issue 23

M.A. Artamonov et al. / Procedia Structural Integrity 23 (2019) 257–262 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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vector of the fatigue crack development from the origin. For each local site of the fracture the coordinates were determined. Therefore, it became possible to calculate the distance to origin and to measure the pitch of fatigue striations. The pitch of fatigue striation was measured by measuring the cluster of fatigue striations and averaging over the number of fatigue striations contained in this cluster. The obtained dependence of the FCG rate on the distance to origin makes it possible to calculate the number of the crack propagation cycles (N c ) (Fig. 1d). It is assumed that the rate of FCG from the origin to the first local fracture site, at which the formation of fatigue striations is observed, is equal to the minimum pitch of fatigue striations. In reality, it can be expected that the rate of FCG between the origin and the first local site is lower, and consequently the number of cycles is greater. This difference between the calculated and real number of cycles will be attributed to the period of the fatigue crack initiation. The transition from the first stage of crack growth to the stage of the fatigue striation formation for LCF runs quite fast. The distance from the origin to the site where the formation of fatigue striations begins lies in the range from 70 to 150 μm. The period of the fatigue crack initiation N o is obtained from the difference between the total lifetime N f and the number of the crack growth cycles N c . The fracture was used to determine the shape of fatigue crack at the initial and final points of the fatigue crack growth.

Fig. 1. Microstructure of the fracture surface during the tests at 550 o C. (a) General view of the fracture; (b) Site where the crack with the largest area was initiated; (c) Fatigue striations; (d) FCG rate and increment of the number of cycles versus the distance to origin.

Methods of calculation The purpose of calculation is to obtain the relations between range of the stress intensity factor ∆K and the size of crack for each specimen being investigated. The simulation of fractured specimen was carried out with the ANSYS software. The model for the finite element analysis is presented in Fig. 2a. The simulation took into account: temperature of testing, value of relative strain in the specimen, geometric dimensions of the crack at the points of the fatigue striation analysis, crack shape. The loading was defined as displacement corresponding to deformations during the tests under strain control. The calculation was performed in the elastic formulation with the individual value of Young's modulus for each specimen. The Young's modulus was obtained after the processing of hysteresis loops recorded during the test for each loading cycle. At the temperatures of 350 to 750 °C the hysteresis loop on the stress- strain diagram «collapses» and the material, having received hardening, is at the conditions of the elastic strain-stress state. However, at the temperature of 20 °C the «collapse» of loading diagram does not occur, the range of plastic deformations is held for