PSI - Issue 23

I.A. Volkov et al. / Procedia Structural Integrity 23 (2019) 281–286 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

283

3

c С can be chosen, which corresponds to zero creep rate:

Among the equipotential surfaces, a surface with radius

(0) ij ij c F S S C    c c c

S

2 0;

,

c ij      ij

c

(3)

ij

where c ij S and ij   are a set of stressed states corresponding (with a certain allowance) to zero creep rate. It is assumed that

  1 c c ij ij S S C C 2

   

1

 

0,           0 , с с c с

t

2 ,

  

  

2

   



 , ;



 , ;

c о dt     c

c

c c ij ij e e

с с с С С Т  

c c c T    

;

;

с 

;

 

с 

(4)

0,

3



c

where с С and c  are experimentally determined functions of temperature Т . The evolutionary equation for the coordinates of the creep surface center will have the form Volkov et al (2016):

1 ij ij c g e g      2 , c c c c c ij

(5)

where 1 2 c g > 0 are experimentally determined material parameters. Concretizing relation (2), the law of orthogonality can be represented as from (6) whence the expression for с  will assume the following form Volkov et al (2016): c g and

   

c c ij ij S S C

 





2 2 3 3 c u e

   c с

 ,

  

c

e

Т S

c     с с ij с S

S

;





c ij

c

c

c c ij ij S S C 

.

с 

 

c 

(6)

ij

ij

С

c

с

From (7), for the three parts of the creep curve by Volkov et al (2016), the expression for с  will be written as:

  1 C                         1   2 , 0 , , , с с c I c c c II c c c c III

0,

0,

 

c 

  

(7)

  2

,

  

  3

,

c

c

c

c

е

ust

3 2

(0)         11 (1) 11 1 с с с е е 

е

с

  / 1 ; c r

;

с 



II

11

;

I  

с 

III с с      II

where

are obtained from

(1)

11

с

е

3 2

с

(1)

  

c       

11

 

с

11

11

experiments with laboratory specimens in uniaxial stressed states by Volkov et al (2016). Quantities that are not found in equations (7) are defined: (0) с  and (1)

с  are value of с  in the initial and final с е are boundaries of the parts of the

points of the first part of the creep curve of the material;   1 11

с е ,   2 11

с е and   3 11

creep curve for a uniaxial stressed state;   11

с nach е is creep strain rate at an initial time,   11

с ust е is creep strain rate along

the steady-state creep part (the second part of the creep curve);  is damage degree of the material; 2 3 с с С   is creep strength in a uniaxial stressed state; c r is material parameter by Volkov et al (2016). Equations (1) – (7) describe the transient and steady-state parts of the creep curve at different stress levels and the main effects of the creep process under alternating stress. At the stage of the development of defects scattered over the volume, the effect of damage on the physical-