PSI - Issue 33

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

939

7

4.3. Case of zero pressures If the internal and external pressures are equal to zero (

0 r R p p   ) then the solution of the problem has the

following simple form:

h h 

.

t



0

  

  

  

  

E T  

E T  









R R R T T  

 

 

 

th   

th

exp

exp

a m 

a m

T T 

r 



R R

r

r

r

r

2(1 )  

2(1 )  

Here,

sign sign

sign T      sign .

;

m m

T

R

r

Since in this case the hoop stresses on the internal and external surfaces remain constant during the corrosion (in the framework of our model), the maximal normal stress criterion is not applicable for the assessment of the lifetime. Therefore, the lifetime of the pipe can be defined as the time when its thickness reaches a given minimal value, for example, * 0 / 2 h h  . Figure 4 demonstrates evolution of the pipe wall thickness with time for different sets of temperatures at zero pressures, 0 r R p p   . The parameters involved are 0 400 r  [mm], 0 420 R  [mm], 0.16 r R a a   [mm/year], 0.0008 r R m m   [mm / (year MPa)],  1 0.003[ C ] r R       , 0 C th th r R T T    , 50 C R T   , r T changes from 0 to 100 C  . Table 2 shows the lifetimes of the pipe for different T  at fixed 50 C R T   , other parameters being the same as for Fig. 4. As can be seen from Fig. 4 and Table 2, the larger the difference | | T  is, the shorter is the life, because the larger | | T  causes the larger thermal stresses that accelerate the corrosion due to the mechanochemical effect. Moreover, in these situations, the lifetime of the pipe is always shorter at negative T  than at positive at fixed | | T  . The difference in the lifetimes at equal | | T  can be explained by the fact that the internal temperature r R T T  accelerates corrosion more than the internal temperature r R T T  at fixed R T .

Fig. 4. Evolution of the pipe wall thickness with time at different temperatures and zero pressures.