PSI - Issue 6

Irina Stareva et al. / Procedia Structural Integrity 6 (2017) 48–55

53

Author name / Structural Integrity Procedia 00 (2017) 000 – 000

6

200  l m are shown in Fig. 3 for different

(0, ) t    and R a a  and

(0, ) r r t  for the tube with

The dependencies

zz

r R m m  .

corrosion kinetics constants r

Fig. 3: (a) the stresses; (b) the inner radii over time.

Let us assess the mechanochemical effect induced by own weight of the tubes with different lengths and find out if the synergetic growth of stress and corrosion rate affects the process of dissolution noticeably. For this purpose, compare the time * t to reach the residual thickness * h = 5 mm calculated by the following ways: (i) by the proposed numerical algorithm, (ii) by the formula

h z h

( ,0) * 

t

(5)

,

*



r a m 

a m

(0,0)

(0,0)





 

r

R R

0 0  t are used instead of equation (4) (i.e. ignoring

l g 

at the initial moment

where the maximum stresses

 (0,0)



the synergetic growth of stresses and corrosion rate), and (iii) by formula (5) with mechanochemical effect at all). These results are presented in Table 2 for 0.0005   r R m m mm/(year·MPa), other parameters being the same as before. The magnitude “er” indicates the relative error with respect to the numerical solution. It can be seen from the table that the mechanochemical effect is noticeable for only long enough tubes. Moreover, despite the fact that the stress grows very slowly with time, using the simple formula (5) ignoring the synergetic growth of stress and corrosion rate is not reasonable when the mechanochemical effect should be taken into account. 0   r R m m (i.e. ignoring 0.1   r R a a mm/year,

Table 2. The time to reach the residual thickness 5 mm (year) solution 12 m

25 m

50 m

100 m

200 m

74.6570775

74.2875571

73.5828767

72.1976029

69.523973

numerical solution formula (5)

t*

t* er t* er

74.8818

74.8079

74.6671

74.3902

73.8543

0.3%

0.7%

1.5%

3%

6.2%

0   r R m m

formula (5) for

75

75

75

75

75

0.5%

0.9%

1.9%

3.7%

7.3%