PSI - Issue 23

I.A. Volkov et al. / Procedia Structural Integrity 23 (2019) 316–321 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

319

4

effective stresses by Volkov, Igumnov (2017):

 

G G

К К



          F

         F

  1 1 6 12 / (9 8 ) ij K G K G         

,

 

,

   4 1 / 4 3 G G K   

 

ij

ij

ij

1

2

 



where G , К are effective moduli of elasticity determined using McKenzie’s formulas . Variable ij  is determined in a similar way:   1 ij ij F     .

2.2. Evolutionary equations of fatigue damage accumulation It is postulated that the rate of the damage accumulation process for low-cycle fatigue (LCF) is described by the following evolutionary equation by Volkov, Коrotkikh (2008) or Bodner, Lindholm (1976) or Lemaitre (1985) or Volkov, Igumnov (2017):         1 2 3 4 f f f W f W     , (2) 1...4 i  account for: voluminosity of stressed state (   1 f  ), degree of accumulated damage (   2 f  ), accumulated relative energy of damage spent on the nucleation of defects (   3 f W ) and rate of change of the damage energy (   4 f W ). In equation (2): where functions i f ,

      

W W 

0,

,





а

, W e f W W W W     ( ) / , p

  3      1 f   1

  

2

1

ij ij

а

f

3

f

3      W W 

exp( ),



  f W W W  4

3 ,

а

1

2

ij  W de  

,

/ ,

p

ij

f

16

3

1





2

1





3      W W 

3   1



3 ,

а

9

where  is parameter of voluminosity of stressed state ( the stage of nucleation of scattered defects under LCF, and f W is value of the energy corresponding to the formation of a macroscopic crack. The duration of the microdefect nucleation phase will be related with the value of parameter a W . When microdefects attain the dimensions comparable with the average distance between them, the process of linkage starts (breakage of the remaining continuous gaps between the defects). No detailed model of merging of cavities was constructed in the present paper; to account for this process, the kinetic equation (due to its term   2 f  ) was formulated so that, when damage degree reached its value 1 3   , relation   1 f    took into account the avalanche-like increase of the damage degree value. / u     ), a W is value of damage energy at the end of

2.3. Strength criterion of the damaged material

1 f     is taken as the criterion of the end of

The condition when damage degree  reaches its critical value

the stage of growth of scattered microdefects.

3. Numerical results Specimens of the 12Х18Н9 stainless steel were experimentally studied in the Laboratory for Testing Physical Mechanical Properties of Structural Materials, Research Institute for Mechanics, Nizhny Novgorod Lobachevski