Issue 49

M. Bannikov et alii, Frattura ed Integrità Strutturale, 49 (2019) 383-395; DOI: 10.3221/IGF-ESIS.49.38

4 0 U p U    n

U

0

4 



kT

1

1

.

0

0

0

0

4 n 0





















exp(

)

4

4

4

4

4 0 U p U    n

4 0 U p U U p     0 4 0 n n

p 

kT







0

exp(

)

1

kT

kT

Then the kinetic coefficients will have the following form:

0 n  . U p 

0 i n ε G     , i U i

1...3 i  ,

 

4

4 

G

We introduce the notation:

1 0 n ε      , 1

2 ε      , 2 0 n p

3 p ε     , 3 0 n

4      , 0 n p 

1 2 n n n    ,

2 p n n n   . 3

The final determining equation is the fracture criterion. In the framework of the proposed model, we can enter a criterion based on the structural scaling parameter: 0 δ  (22) The meaning of this criterion is that the percentage ratio of the volume of material occupied by defects tends to 100%, which can be achieved by tending to zero the distance between defects or tending to infinity of the size of defects. The second option is impossible, and the first has a clear physical meaning. In the calculation, the condition (22) is not realizable due to the instability, as it is, therefore, we can replace it with a softer one: f δ  is the critical value [22], after which the avalanche-like growth of defects begins and the material is considered destroyed. This value is universal for all plastic materials for the proposed model. Critical value f δ δ  corresponds to critical value c p . Model Parameter Identification The identification of the parameters of the constructed model (15)-(19) was carried out in the uniaxial case: f δ δ  (23) where 0.4

2 ( G           p σ λ p  

)

(24)



F

0 n

p   

( ε     σ 

)

(25)





p



p



F

0 n

p ε  

( p     σ

)

(26)



p

p



p



F

δ p  

0 n

   

(27)





δ

2 p p 2 2

2

σp

F

2

c p c    

)   

3 4 c c p p

ln(

(28)

1

2

F

δ

G

2

m

391