PSI - Issue 40

Vladlen Nazarov et al. / Procedia Structural Integrity 40 (2022) 334–340 Vladlen Nazarov / Structural Integrity Procedia 00 (2022) 000 – 000

338

5

n

  

  

1



dim max

0   n

0

A

A

 



(6)

1 max

1

1



n

  

  

2

2



dim max

0

0

A

A

n





 



(7)

2 max

2

2



Experimental data Nazarov (2014) had been obtained at tension (two experiments) and simultaneous torsion and tension (three experiments) of copper tubular specimens (the inner diameter is 14 mm, the outer diameter is 16 mm, the working length is 100 mm) at 264 o C have been used for the analysis of total errors for (6) and (7). Before the tests, the copper specimens have been annea led at 800°C. Heat treatment made it possible to obtain an equiaxed structure of copper, after which copper acquired the properties of an anisotropic material. The test results have been obtained under the condition that the normal stress  and the double tangential stress  2 contribute equally to the maximum tangential stress max  . For describing the secondary creep can to use formulas

2

2  

2

3

3





      



   







2







   

  

(8)







max

max

4

4

2

2

2

2







   

   

2

2



2 2    





  



(9)

max

max

2

loko  Lokoshchenko et al. (1986) and

leb  Lebedev (1996) have been

Two complex equivalent stresses considered Lokoshchenko et al. (2004)

max     [

] 0    

0.5

(10)



 





1 1 2 3  

   

loko

3 3

max

[1 ]

0 1   

(11)



 

 





leb

mises

max

The material parameters  and  have been calculated for the minimum total error  of the difference between the experimental rupture time exp rupt t and the approximate rupture time app rupt t

   

   

exp rupt app rupt

 N

t t

min

lg

(12)

 

1

where N is number of experiments. Minimization target condition (12) performed by the algorithm Lasdon et al. (1974) of nonlinear optimization Generalized Reduced Gradient Method (GRG2) by the Solver Add− in of Microsoft Excel at initial solution exp rupt app rupt t t  . In Lokoshchenko et al. (2004) it was concluded at which variant of the plane stress state one of the two complex equivalent stresses (10) and (11) should be used. The complex equivalent stress naz  have been proposed by Nazarov et al. (2020) for the sum of two maximum stresses

[1 ]2

0 1   

(13)



 

max    

naz

max