PSI - Issue 32

A.Yu. Iziumova et al. / Procedia Structural Integrity 32 (2021) 93–100 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

98 6

3 2



  :



,

0

S

S

 





back      ys

(10)

back

back σ is the backstress tensor. Isotropic hardening:   0 , ys ys h peff      

(11)

2 3

  

 

 is the effective plastic strain,   h peff σ ε is the isotropic hardening

: ε ε

p p

peff ε



0 ys σ is the yield stress,

function. Non-linear kinematic hardening:

2 3

2

 

,

p

C









(12)

0

, back j

back

1

j



2 3

,

p C ε γ ε σ  

σ

(13)

, back j

, j peff back j

j

j C is the kinematic hardening modulus, j γ is the kinematic hardening parameter. Plastic work:

: . p A d    

(14)

A statistical thermodynamic model of the collective behaviour of mesodefects ensemble developed by Naimark (2003) was applied to determine the stored energy. According to this model, the stored energy is a function of the internal damage parameter calculating by Eq. (15)-(16).

 

  

1 

1

S F G p   

,

p



(15)

 

 

n

2

2

G с p









p

1

ys

1

Exp   

 

a

F

p p



n

,

с p



(16)

p



: p p p  , p τ is the characteristic relaxation time, F is the free energy, с , a ,

1 ys σ , n

: σ S S  ,

where

are material parameters. Stored energy

s E was calculated as: