PSI - Issue 33

I.A. Evstafeva et al. / Procedia Structural Integrity 33 (2021) 933–941 Author name / Structural Integrity Procedia 00 (2019) 000–000

937

5

 

  

  

  

E T  

E T  









R R R T T  

 

 

 

th    

th

exp

exp

;

R R r A a m p m    

r r R r a m p m

T T 

r 



R

r

r

2(1 )  

2(1 )  









 

th T T m pR    

 

 

exp

exp

.

th

R c M m pR  

T T 



r 



R R R

r

c

r

r

Solution (6) has the form, which is absolutely the same as the solution for a pipe under pressure, based on the classical thin-shell theory (see, e.g., Karpunin et al. (1975)), with the only constants A and M being different. At the same time, this solution reflects the effects of thermal stresses and the effect of the internal and external pressures (not only their difference). 4. Calculation results and discussion Let the lifetime of the tube be defined as the time when the maximal hoop stress, max{| ( ) |,| ( ) |} r R   , reaches a given strength limit   , i.e. when the maximal relative stress, * /   , reaches unity. 4.1. Comparison with the available solutions and effect of hydrostatic pressure Since other solutions for a pipe under pressure are available, let us compare them with the solution presented here (at equal internal and external temperatures). Let us assess the evolution of maximal hoop stress with time using three models: the first one is the solution of Karpunin et al. (1975) based on the classical thin shell theory, the second one is the exact solution of Pronina (2011) based on the Lame solution for a thick-walled tube, and the third is the solution presented here. The following data are used for the calculations. The initial radii of the pipe are 0 400 r  [mm], 0 420 R  [mm]. The corrosion kinetics parameters used in Eqs. (1) and (2) are 0.16 r R a a   [mm/year], 0.0008 r R m m   [mm / (year MPa)],  1 0.003[ C ] r R       , 20 C th th r R T T    . The temperatures of the internal and external surfaces are 30 C r R T T    . The strength limit is 300    MPa and sign sign     . Figure 2 demonstrates the effect of hydrostatic pressure min{ , } r R p p p  on the lifetime of the tube, when the absolute value of the difference between the internal and external pressures is constant: 3 p   [MPa] for all sets of input data. Curves 1–8 correspond to the next sets of internal and external pressures [MPa]: 15, 12 R r p p   (curve 1); 9, 6 R r p p   (curve 2); 3, 0 R r p p   (curve 3); 0, 3 R r p p   (curve 4); 6, 9 R r p p   (curve 5); 12, 15 R r p p   (curve 6); 50, 53 R r p p   (curve 7); 100, 103 R r p p   (curve 8).

Fig. 2. Evolution of the maximal relative stress with time for different pressures at

3 p   and

0 T   .