PSI - Issue 65

D.S. Bezverkhy et al. / Procedia Structural Integrity 65 (2024) 17–24 D. S. Bezverkhy and N. S. Kondratev / Structural Integrity Procedia 00 (2024) 000–000

22 6

The parameters of the constitutive multilevel model of the Inconel 690 nickel alloy are listed in Table 2, which also presents the relevant literature sources from which the values of the required parameters were determined. As a result of the identification procedure, there is a good quantitative correspondence with the stress-strain state diagram of the polycrystal, the first few stress peaks coincide, after which the stress reaches a stationary value (Fig. 6 (a)). Figure 6 (b) shows the cycles of changes in the volume fractions of recrystallized material and the change in the average size (diameter) of polycrystal grains, the results obtained are qualitatively consistent with the experimental data (Wang B. et al. (2013)).

Table 2. Parameters of a multilevel model (Bezverkhy D. S. & Kondratev N. S. ( in Print )) for Inconel 690 alloy

Parameter

Value

Source

Parameter

Value 50.694

Source

D 0 , μm

k 2

89.0

(Wang B. et al. (2013)) (Alers G. A. et al. (1960)) (Alers G. A. et al. (1960)) (Alers G. A. et al. (1960))

Identification Identification Identification 0.16 4 J 1 s 1 3 10 10 4 J 1 s 1 2.2510 11 Identification

c 1111 , GPa c 1122 , GPa c 1313 , GPa τ c 0 , MPa

HP

180.735 141.676 79.526

M HAG , m M LAG , m

K sub

1.0

Identification

150 0.75

Identification

n ρ 0 , m q lat

e gb , J / m 2 sub , J / m γ

100.0

(Blaizot J. et al. (2016))

(Rohrer G. S. et al. (2010)) (Zurob H. S. et al. (2006))

10 10

2

2

Identification

0.3

1.4

(Bronkhorst C. A. et al. (1992)) Θ II , MPa

7151.180 196.464

Identification Identification

χ

0.37

Identification Identification

Σ s , MPa

7

k 1

2510

(a)

(b)

Fig. 6. Polycrystal stress-strain state after the identification procedure (solid line) and experimental data (Wang B. et al. (2013)) (dots) (a); average polycrystalline grain size change and recrystallization cycles (b).

The following notations were used in Table 2: D 0 is the initial grain size (diameter), c ijmn are components of the elastic properties tensor in the basis of the crystallographic coordinate system, τ c 0 is the initial critical stress of the sliding system, n is the indicator of the material speed sensitivity, ρ 0 is the initial grain dislocation density, q lat , χ, k 1 , k 2 are parameters describing the material hardening, HP is a parameter describing the Hall–Petch effect, M HAG is the mobility of the high-angle boundary, M LAG is the mobility of the low-angle boundary, K sub is a material parameter, e gb is the grain boundary energy, γ sub is the subgrain boundary energy, Θ II and Σ s are macrolevel hardening parameters. The dynamic recrystallization process has a significant influence on the material response (Huang K. E. & Logé R. E. (2016), Alaneme K. K. & Okotete E. A. (2019)). Primary recrystallization consists of the low-defect grains formation in a deformed material and the subsequent migration of high-angle boundaries (or sections thereof), the