PSI - Issue 41

Victor Rizov et al. / Procedia Structural Integrity 41 (2022) 103–114 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

109

7

2



 3

p



     ,

(41)

1

2

j

T

T

2



 3

q



     ,

(42)

1

2

j

T

T

where

1 cos

1

nT j T T 1

  

  









sin

nT

 j nT

 j nT







 1

,

(43)

T

T

T

j

j







  

  

j T



 m T   







j sin 1 

sin

j nT 





1

,

(44)

2

T

T



  

mT T 1

j T



  





  j sin 1 

 m T

sin

j T 









T

3

T

T



T

1

1 cos

  













    m T

sin

m T (1 ) sin

1

T

j nT 

j nT 

j





 



T

T

T

T

T

j

j





  

 1 cos    j

  

 m T



1





,

(45)

T

j

1 sin

  

   

T nT j T 1







cos

 j nT nT 

j nT 



 1

,

(46)

T

T

T

j

 

  

  

j T



 m T   







cos

1

cos

j

j nT 





 2



1

,

(47)

T

T



  

mT T 1

j T



  





  j cos 1 

 m T

cos

j T 

3 









T

T

T



T

1 1 sin

1 sin 1

  







 







 

cos

j nT 

j

T T m T T

j T 





 

T

T

j

j

j

 



  

  

   1

 m T





 m T



cos

1

j





.

(48)

T

T

( ) * E t , has to be

In order to take into account the effect of the temperature, the modulus of elasticity,

recalculated by using the following dependence (Narisawa (1987)):   E t T t T E T T * 1 0 0 0           ,

(49)

/(  T T 0 0

)

0 T E is the modulus at room temperature. Usually,

1 

ratio is equal to unit (Narisawa (1987)). The

where

factor, T  , is a function of the temperature and is determined by the formula (Narisawa (1987))     S B S A T C T T C T T       lg ,

(50)

where 101.6  B C (Narisawa (1987)). The quantity, S T , is a material property. By applying the compliance method, the strain energy release rate, G , for the longitudinal crack in the beam 8.86  A C and