PSI - Issue 43

Sergiy Kotrechko et al. / Procedia Structural Integrity 43 (2023) 228–233 Author name / Structural Integrity Procedia 00 (2022) 000 – 000

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The obtained dependences describe the process of CN formation at the microscale, so they contain a significant number of microscopic parameters. The values of these parameters, at best, can be estimated by the order of magnitude, therefore, the obtained dependences can't be used directly in LA. However, the importance of these dependences is that they physically substantiate the effect of plastic strain and temperature on the rate of crack nuclei generation, as well as enable to ascertain the regularities of this effect and evaluate it by the order of ρ magnitude. The non- monotonic dependence of ρ on the plastic strain value is a characteristic feature of the CN formation in polycrystalline metals. This reflects the peculiarity of change in the incompatibility of plastic strains at grain boundaries during the polycrystal deformation. It grows to a certain value of macroplastic strain C e , and then begins to decrease. According to the model proposed, the growth of temperature should cause a monotonic decrease in the value of ρ. This is due to the thermally activated relaxation processes at the grain boundaries. In terms of the current model, this means a decrease in the value r t (dependence (5)) against the background of increasing the critical value of normalized stress of CN formation C t (dependence (4)). Theoretical dependences of ρ on the magnitude of plastic strain a nd temperature are shown in Fig. 1. The following values of microscopic parameters were used in their building: b m = 0.1; r = 10 -6 m ; d = 10  10 -6 m; d max = 30  10 -6 m; C  = 7 GPa ( G C 0 1 .   , where 70GPa  G is the iron carbide shear modulus (Kotrechko (2013)).) In the first approximation, the mean value of may be estimated by the value of thermally activated component of the yield strength Y Y    : ( )   C C C e T Y  ln . exp 2 3 1 0 5 +  = , (6) where e  is the plastic strain rate; С 1 , С 2 , С 3 are the constants, which values for typical ferritic steels are: С 1 = 1033 MPa, С 2 = 0.0068 K -1 , С 3 = 0.000415 K -1 (Kotrechko (2002)); e  = 10 -4 s - 1 . The equivalent stress value  was calculated as: n e where n is strain hardening exponent (value n = 0.05 was used); 0 2 .  is yield strength: ( )   C C C e T a  ln exp . 2 3 1 0 2 +  =  + , (8) where a  is athermal component of 0 2 .  (in the calculations a typical value a  = 470 MPa was utilized). 3. Experimental verification In accordance with the data shown in Fig. 1, the effect of plastic strain magnitude and temperature on the value of ρ is not additive one. The maximum influence on ρ is observed at strains close to critical one C e . At large strains, sensitivity of ρ to changes in temperature dec reases. As noted above, the direct use of the above model in LA implies significant difficulties. This is due to the need to determine the values of microscopic parameters. Therefore, Kotrechko et al. (2021) proposed approximation dependences to describe the effect of temperature and plastic strain on the CN density. The employment of these dependences makes it possible to predict more accurately the slope of the temperature dependence of fracture toughness and its scatter limits (Fig. 2). It should be emphasized that not accounting for the considered effect associated with a change in the CN density, gives rises not only to an error in the absolute value of Jc K , but also to an error in the values of the failure probability. Moreover, if the error in Jc K is tens of percent, the degree of overestimation of the fracture probability may be 2-4 times (Fig. 3, red arrows indicate the error in the value of fracture probability).       =    0 2 . 0 002 . , (7)