PSI - Issue 33

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

935

3

2. Problem formulation Consider a linearly elastic isotropic thin-walled pipe exposed to mechanochemical corrosion on the inside and outside. Let the inner and outer radii of the pipe be denoted by ( ) r r t  and ( ) R R t  , respectively; 0 (0) r r  and 0 (0) R R  are the initial radii of the pipe at time 0 t  . The pipe is loaded with internal 0 r p  and external 0 R p  pressures and subjected to interior r T and exterior R T temperatures (Fig. 1).

Fig. 1. The pipe under pressure.

The rates of corrosion on the internal and external surfaces are supposed to be linearly dependent on an equivalent stress and exponentially dependent on temperature (see Dolinskii (1967), Naumova and Ovchinnikov (2000)):

dr dt





th r    r T T  

[

( )]exp

;

v

a m r 

r 

  

(1) (2)

r

r

r

dR a m R





R R R T T  



th

[

( )]exp

.

v



   

  

R

R R

dt

th r T ,

th R T are experimentally determined constants. As an equivalent stress,  , in

Here, r a , R a , r m ,

R m , r  , R  ,

the corrosion kinetics equations (1) and (2), we use principal stress with maximum absolute value, because it provides best fit to experimental data (see Pavlov et al. (1987)) and reflects the effect of both internal and external pressures (in contrast to the von Mises stress – see Sedova and Pronina (2015)). Add that

sign sign

sign ( ); sign ( ). r R  

m m



r



R

In this work, we consider situations when the maximal stress at both surfaces is the hoop stress. We disregard the temperature-dependency of material properties (which was addressed, e.g., by Naumova and Ovchinnikov (2000) and Dehrouyeh-Semnani et al. (2019)). It is required to obtain a closed-form solution in a relatively simple form, which allows one to assess the lifetime of the pipe.