PSI - Issue 39

Nina Selyutina et al. / Procedia Structural Integrity 39 (2022) 157–160 Author name / Structural Integrity Procedia 00 (2019) 000–000

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hysteresis loop associated with the experiment, we considered the characteristic of the hysteresis loop width, defined as the difference between the maximum and minimum strains at zero stress cycle. Two effects of the stabilisation of plastic deformation during low-cycle deformation can be distinguished. In both cases, the material accumulates plastic deformation cycle after cycle. In the first case, the width of the hysteresis loop during low-cycle deformation in new cycles can be so small that the material is elastically deformed in subsequent cycles. Furthermore, when the new plastic deformation decreases, the deformation energy does not change. In the other case, the deformation energy increases with each new cycle of the stabilisation of the width of the hysteresis loop. The stabilisation effect with the final elastic stage has been observed on steel 50 (Makarov et al. 2015) and DP 500 steel ( Moćko et al. 2016). Moreover, the theoretical modelling of the stabilisation effect for these steels based on the structural–temporal approach of cyclic loading is shown in our studies (Selyutina and Petrov 2020; Selyutina et al. 2021). This paper experimentally investigates the effect of plastic deformation stabilization at zero cycle loading is as an example steel C45E and the dependence of the hysteresis loop’s width on the number of cycles depending on changes in the amplitude. 2. Experimental details The material of the tests is carbon steel 45 and its mechanical components (weight percentage, %) are C 0.48, Mn 0.59, Si 0.3, P 0.022, S 0.019, Cr 0.07, Ni 0.06, Cu 0.03. A testing machine Shimadzu AG- 50 kNX was used for quasi static tensile tests. Low-cycle fatigue experiments were carried out on an Instron Electropuls E3000 setup with a loading frequency of 0.5 Hz. Then, experimental samples were prepared from a round bar with a diameter of 6 mm, corresponding to Russian standards (GOST 1050-88, GOST 1051-73 and 7417-75), with the chemical composition shown in Table 1. Each sample had a diameter d = 3 mm and a distance between shoulders l = 25 mm for the quasi static tests and d = 1.3 mm and l = 16.6 mm for the low- cycle fatigue tests. Prepared samples were quenched at 840 ºC and polished before the mechanical tests. The specimens were tested in two strain-controlled modes in a zero-deformation cycle ( ε min = 0): (i) a constant strain amplitude ε a = 0.6% and a loading rate of 0.5%/s, (ii) a constant strain amplitude ε a = 0.6% and a loading rate of 0.55%/s, and (iii) a constant strain amplitude ε a = 0.7% and a loading rate of 0.65%/s;. The deformation dependence of true stress was calculated from the output data of stress ( σ s ) and stroke strain ( ε s ) using the Instron software, according to the force characteristics of the entire sample and the displacement, which was defined as the distance between the grips that captured the sample. In further calculations of stress-strain dependences, true strains ε = ln(1 + ε s ) and true stresses σ = σ s (1 + ε s ) were used. 3. Results Results of the static tests for carbon steel C45E before and after quenching at 840 ◦C, obtained from the experimental data for the four samples, are shown in Fig. 1. The static yield strength was 430 MPa for the static specimens after quenching at 840 ºC. The hysteresis strain width stabilised with a constant strain amplitude of 0.6% and different velocity of loading (Fig. 2), and it stabilised earlier for a higher loading velocity at the same strain amplitude (Fig. 2b). Fig. 3 shows the hysteresis loops of steel C45E at 100 and 2050 cycles, as well as the width of the hysteresis loop for two loading regimes: strain amplitude 0.6% and loading strain rate 0.5%/s, and strain amplitude 0.7% and loading strain rate 0.65% /s. The hysteresis loops at the beginning of the stabilization effect and at the stage of hardening under low-cycle deformation are different (Fig. 3a). Moreover, the cycles for stable plastic deformation ranged from 100 to 950 cycles with a constant strain amplitude of 0.6% and from 75 to 280 cycles with a constant strain amplitude of 0.7%. The duration of the stability of the hysteresis strain width decreases with increasing amplitude. Thus, the stability of the hysteresis strain width depends on strain amplitude and velocity of loading. Revealing the experimentation of the stabilisation regime for various materials improves the quality of the assessment of the strength and resources of a structure subjected to cyclic loading.