PSI - Issue 33

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

938

6

In the framework of the classical thin shell theory (solution of Karpunin et al. (1975)), only one curve (the solid one) describes the evolution of stresses with time for all the sets of input data. At the same time, new solution presented in the paper demonstrates a perfect coincidence of the results with the exact solution of Pronina (2011) and reflects the effect of pressure values themselves (not only their difference). As seen from Fig. 2, the classical thin shell model gives underestimated lifetime for R r p p  and overestimated for < R r p p , that can lead to dangerous situations. Table 1 shows the relative error in the lifetime calculated using the classical thin shell model (compared to exact solution).

Table 1. Error in the lifetime calculated using classical thin shell model. r p 15 9 3 0 6

12 15

50 53

100 103 48.4

12

6

0

3

9

R p

Error (%)

4.99

2.75

0.49

0.66

2.97

5.33

21.48

As one can see, the error in the lifetime of the tube can reach about 50%, if

min{ , } r R p p p  is high enough.

4.2. Effect of the temperature difference Figure 3 demonstrates the effect of different temperatures at the internal and external surfaces on the lifetime of the tube at fixed | | 4 p   [MPa]. The following parameters are used in the calculations: 0 400 r  [mm], 0 420 R  [mm], min{ , } 0 r R p p  [MPa], min{ , } 20 C th th r R r R T T T T     , 0.16 r R a a   [mm/year], 0.0008 r R m m   [mm / (year MPa)],  1 0.003[ C ] r R       . Figure 3a is for r R p p  , while Fig. 3b is for R r p p  . As seen from Fig. 3, lifetimes of the pipe at | | 40 T   are shorter than at | | 20 T   . This is explained by the fact that the maximal initial stresses, 0 0 max{| ( ) | , | ( ) | } t t r R     , at | | 40 T   are larger than that at | | 20 T   , and therefore closer to the limiting value. Since the change of the sign of T  at fixed | | T  leads to a slight change in the lifetime, we can conclude that the change in the location of the maximal stress (from the inner to the outer surface) as well as acceleration of corrosion described by exponential multipliers   exp th r r r T T      and   exp th R R R T T      have only a small effect on the pipe lifetime (for the considered low temperatures). In cases when, at fixed p  and | | T  , the sings of p  and T  coincide, the lifetime is always shorter than in the opposite case (because in the first situations, maximum values of elastic stresses at the inner surface increase due to thermal stresses). Recall that r R p p p    , whereas R r T T T    . Note that if at 0 p   , the temperatures have a little effect on the corrosion rates and the initial stresses are relatively low, so that the dependencies of maximal stresses on time have time to get closer to their vertical asymptotes, then the lifetime of the pipe is mostly determined by the pressure values – see the paper of Pronina and Sedova (2021). a b

R p p  (a) and for r

R p p  (b).

Fig. 3. Evolution of the maximal relative stress with time for different temperatures at r