PSI - Issue 6

Yu.V. Petrov et al. / Procedia Structural Integrity 6 (2017) 265–268 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

267

3

          



    

     ds

( ) s

t

1,

1

1,







t





y



    

     ds

( ) s

1

t

( ) t





(3)

, 1

1,



1





t





y

   

   





    

   

( ) s

1

t

ds







t





y

Equality ( ) 1  t  in (5) relates with the elastic deformation accumulation before the starting time t * of the macroscopic plastic flow. Gradual decrease of the relaxation function in the range 0 ( ) 1   t  corresponds to the material transition into the plastic stage of deformation. During the plastic stage of deformation, * t t  , the relaxation function satisfies the condition



      t t y    

     ds

t s ( ) ( )

1

(4)

1.



Let us define the actual stress ( ) t  in a deformed specimen by the following form ( ) 2 ( ) ( ), t t g t   

(5)

where is an “effective” shear stress that takes into account the plastic relaxation;  is a scalar 0   corresponds to the plastic deformation without hardening. Considering the stages of elastic and plastic deformations separately, we can obtain from (7) the following stress-strain relation in the case of a linear growth of strain ( ) ( ) t H t t     (the constant strain rate) parameter ( 1 0    ) characterizing the level of hardening; the case ( ) t ( ) g t G 1     

2 ( ), G t 

 * t t t t t 

,

    2

( ) ( ), t 

( ( )) t  



  

   

(6)

1





G

,





*





where we take into account that . On the basis of the relaxation model of plasticity (Petrov and Borodin (2015), Borodin et al. (2014), Selyutina et al. (2016), Borodin et al. (2016)) let us connect of deformation on the cycle with the additional condition for the unloading process:    ( ) / t t 

   

unl j

( ( ) t    ( ( )), t j

 t t

;

( ( )) t  



(7)

j

j

unl j

unl j

unl j

E

) ( ( ) t H 

 t t

),

,









j

j

( ( )) t j j   is a temporal dependence of stresses, ( ) t j  is temporal dependence of strain, unl

j t is an unloading

Where

time, unl

unl j t .

j  is a value of strain at

3. Discussion & Conclusion The calculated dependences of the accumulated residual deformations on the cycle number on the basis of experimental data Makarov et al. (2014) are represented in Fig. 1. Estimations for heat-treated steel μs 320   and combined strain-heat treated steel μs 140   were obtained. The characteristic relaxation times of steels depending on methods of treatment differ more than 2 times. It was also noted by Makarov et al. (2014), that the additional deformation treatment of steel-50 influenced on the internal structure of the material (by the thermal deformation