PSI - Issue 40

Vladlen Nazarov et al. / Procedia Structural Integrity 40 (2022) 348–353 Vladlen Nazarov / Structural Integrity Procedia 00 (2022) 000 – 000

351

4

   

   

exp rupt app rupt

 N

t t

min

lg

(10)

 

1

where N is number of experiments, exp rupt t is rupture time in experiment. For minimization target condition has been used by the algorithm Lasdon (1974) of nonlinear optimization Generalized Reduced Gradient Method (GRG2) by the Solver Add−in in Microsoft Excel. 4. Experimental data and analysis of minimum total errors The effects of strength anisotropy on creep rupture have been had in the test results Kowalewski (1996) and Stanzl (1983) have been obtained on tubular specimens under tension and torsion. The effect of several approximations for the same experimental data has been observed Nazarov (2014a) for an anisotropic material . Experimental data Kowalewski (1996) and Stanzl (1983) have been obtained in tubular specimens either only under torsion, or only under tension, or under torsion and tension. The peculiarity of the description of the experimental data Kowalewski (1996) and Stanzl (1983) is that in the diagram, instead of one dependence of the rupture time on the equivalent stress, there are three different dependences of the rupture time on the equivalent stress. This work is an extension of the study Nazarov (2019), where the analysis has carried out only for experimental data have been obtained at simultaneous torsion and tension of tubular specimens. Additional experimental data (Table 1) have been obtained either by biaxial tension Kobayashi et al. (2017) of plane specimens, or from tests Himeno et al. (2016) of tubular specimens under the influence of internal pressure and axial force.

Table 1. Summary table of publications of experimental data for two different plane stress states. Reference Material Temperature ( o C)

Principal stresses

0 1 2     0 3  

Himeno et al. (2016)

9Cr1MoVNb (steel)

650

Kobayashi et al. (2017)

304 (steel)

650

Dyson et al. (1977)

Nimonic 80A (nickel alloy)

750

0 1   0 2   0 3  

Cane (1981)

2.25Cr1Mo (steel)

565

Nazarov (2014a)

copper (after annealing)

264

The minimum total errors and parameters of complex equivalent stresses shown below (Table 2).

Table 2. Minimum total errors and parameters of complex equivalent stresses (criterion values are the smallest and they are underlined).

Minimum total errors

Parameters

Reference

1 eq 

2 eq 

max 2 

1 

2 

max 

mises 

Himeno et al. (2016)

0.9

0.8

0.9

0.6

0.9

0.3

−

Kobayashi et al. (2017)

1.5

1.3

1.5

1.3

1.5

0.0

−

Dyson et al. (1977)

4.3

4,3

6.6

1.6

1.7

0.5

0.6

Cane (1981)

1.6

2.5

3.2

0.7

0.7

0.7

0.8

0.5

0.3

0.0

0.0

Nazarov (2014a)

0.6

0.5

0.3