PSI - Issue 16

Yaroslav Ivanytskyi et al. / Procedia Structural Integrity 16 (2019) 126–133 Yaroslav Ivanytskyi et al. / Structural Integrity Procedia 00 (2019) 000 – 000

128

3

where α, g , r – material constants,

v R – a coefficient reflecting the influence of a complex stressed state on the

investigated material:

2

 3 1            ,    3 2 1 2 h  eq  

R

(5)

v

where h  – hydrostatic stresses,  – Poisson's coefficient. One of the important factors that significantly effects on the characteristics of creep and long-term durability is working hydrogen-containing environments, which causes hydrogenation of the metal and change in its characteristics. There are two possible ways to consider the influence of hydrogen on constructive element. In the first case, during calculations one can use known formulas (1) – (5), which defines that the constants of the material depend not only on temperature, but also on hydrogen concentration. This method is inconvenient, because it is necessary to have values of many constants of a material, which is determined experimentally in hydrogen, which is rather difficult to calculate the durability. The second way is proposed in the works by Lokoshchenko and Fomin (2015, 2018). In order to take into account the influence of hydrogen in the kinetic theory of Kachanov-Rabotnov, a second structural parameter is introduced: hydrogen concentration C(t). Then the Kachanov-Rabotnov-Lokoshchenko kinetic equations are written as

n

cr

d

S

ij 



  

  





C

3

eq

ij

,

(6)

m t f

A

t

,



    

1

dt

C

2 1

 

eq

0

  1 1 ru 



  

 

d

C



m t f

(7)

B

, , t 



2



    



dt

C

 

0

where С – hydrogen concentration; С 0 – initial value of hydrogen concentration; material constants A, B, n, m, q 2 ,  ,  depend only on temperature. The form of functions    0 , 1, 2,3, 4 i f C C t i  is as follows (Lokoshchenko and Fomin, 2018):     0 0 / , 1 i i f C C t a C t C    , where i a are determined experimentally and depend on both temperature and concentration of hydrogen. The abovementioned models, which are widely used in many studies, contain a lot of material parameters that need to be determined experimentally. Therefore, it is important to build an appropriate model of damage accumulation by creep and material hydrogenation that can be used without loss of accuracy. The number of uncertain parameters in the damage accumulation model can be reduced if the energy approach is used to model the process.

2. The energy approach of the damage accumulation kinetics

The measure of energy damage is taken as the ratio of energy of elastic-plastic deformation of the local volume of the material to its critical value (I vanyts’kyi et al. (2015), Qin et al. (2018), Chang et al. (2018))   H W W c ω x, y, z,t  , (8)

where W – current value of deformation energy

0 t

  cr ij 









,

x, y, z,t

x, y, z, τ

x, y, z, τ dτ

(9)

W

 



eq