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

127

2

1. Introduction

Many elements of modern constructions have been operating for a long time at increased temperatures. During their operation, there is a creep of the material with accumulation of irreversible deformation and damage, which leads later to a crack. One of the important factors that significantly affects the characteristics of creep and long term durability is the hydrogen-containing environment (Student et al. (2003), Babii et al. (2007)). In modelling of damage accumulation for a complex stressed state there are three main types of criterion equations with one durability variable: the criterion equations of Kachanov-Rabotnov (Kachanov (1967), Rabotnov (1969), Liu Murakami equation (Hayhurst and Felce (1986); Liu and Murakami (1998); Murakami et al. (2000), and Lemaitre equations (Lemaitre (1979, 1984, 1985)). Classical criterial equations of Kachanov-Rabotnov for uniaxial tension provide a relative specimen method for assessing durability at creep. An analogue of these equations for a complex stress state was later proposed in many papers (Rabotnov (1969), Hayhurst and Felce (1986); Hyde et al. (1996)). They can be written as follows

n

cr

d

S









3

ij

eq

ij

m

A  

t

,

dt d B 

2 1

   

 

eq

(1)

  ru 



m

t

,



   1 1





dt

 

 

where eq S   – components of creep deformation, deviator stresses and equivalent Mises stresses;  – material durability parameter. Parameter  depends on the magnitude of the fracture tensile stress, which is calculated according to the ratio   1 ru I eq        , (2) main stress and equivalent stresses on the fracture. In the Liu-Murakami model (Murakami and Liu (1995), Liu and Murakami (1998); Murakami et al. (2000)), an attempt is made to solve the problem of large values for velocity of components of creep deformation and durability parameter  , , cr ij ij where I  – maximum main stress. Formula for ru  contains parameter α, which indicates the effect of the largest

   

   

2





1     

cr

d



2 1 n 

3 2

ij

1 A S   n

m

3 2

t

exp

,





eq ij

dt

eq n    

1 3



(3)





  2 q

B

1 1 exp     

 

d





  ru 



 q t  2



m

exp



dt

q

2

where A, B, n, m, q 2 ,  ,  – material constants. It should also be noted that the destructive stress  ru has the same appearance, as in the model of Kachanov-Rabotnov. The Lemaitre criterion equation (Lemaitre (1979, 1984, 1985)) for a complex stress state can be written as follows:

  1 1  





r

eq   





1 1 1 v R               t g 



,

(4)