PSI - Issue 40

V.N. Syzrantsev et al. / Procedia Structural Integrity 40 (2022) 411–417

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V.N. Syzrantsev et al./ Structural Integrity Procedia 00 (2022) 000 – 000

2 S        ;

V S S

where

0,1, 2,3 k  ;

3 10 / E     ; E - is the elastic modulus of the material sample

,0

,1

,2

k

k

k

k

( E =2.15  10 5 MPa). The coefficients’ values

,0 ,1 ,2 , , k k k S S S ,

0,1, 2,3 k  are presented in Table 1.

Table 1 – Coefficients’ values. k S k, 0

S k, 1

S k, 2

0 1 2 3

0.278 -0.098 -0.044

-0.435 -0.086 0.066

0.169 0.129 -0.025

1.465  10 -3

-2.068  10 -3

7.258  10 -4

The calibration dependencies for the FDS at different voltage amplitudes are shown in Fig. 4.

Fig. 4. Function  R(  ,N) :  1 =473 MPa ( ●● ) ;  2 =451.5 MPa ( ▲▲ ) ;  3 =430 MPa ( □□ ) ;  4 =408.5 MPa ( ◊◊ ) ;  5 =387 MPa ( ○○ ) ;  6 =365.5 MPa ( ∆∆ ) . The function (13) allows to calculate the  R value for the FDS. It is for the known N and parameters for the stages of the cyclogram blocks j j N N t   , j  1, j m  , in accordance with the rule of linear damage summation [Kapur (1977), Collins (1981)]:

m     

.

(14)

1 1 R N R t N      ( ) ( ,

)

( , R t N R t N        ) ( ,

)

 

1

j

j

j

j

2

j



( ) R N R    value is fixed during the pipeline service for the period of its

If the N value is unknown, but the

operation with the FDS, then the N value is determined from this equation:

m     

( , R t N R t N R            ) ( , )

( ,  

)

0

.

(15)

1 1 R t N 



1

j

j

j

j

2

j



The N value from the equation (15) allows solving the equation by the numerical method:

( , ) E R N R    

(16)

E  , which is equivalent to the loading cyclogram in terms of the damaging effect.

to calculate the mechanical stress