PSI - Issue 16

Mykola Stashchuk et al. / Procedia Structural Integrity 16 (2019) 252–259 Mykola Stashchuk et al. / StructuralIntegrity Procedia 00 (2019) 000 – 000

255

4

B

x l

v

2

1  

    , 0 x x  





p

x l x 

arccos

.

 



l

2





(7)

Using the equations (6), (7) and expression (5) we get according to Stashchuk and Dorosh (2016):

2

B

4       R Bpl

μ

π(1 )  

2 2

U

p l

(8)

ln

.



l

4 π(1 ) 

2 8μ

  

Correlation (8) is the generalization of the plastic energy of deformation for classical dislocation. When p = 0, the known formula (Stashchuk and Dorosh (2015)) for body energy with edge dislocation follows from here. The work in (4) is spent for the formation of new surfaces of the dislocation crack in the presence of residual half-unlimited insert in crystal body (Fig. 2) is calculated by Griffith (1920, 1924):

2 . F l  

(9)

where γ – specific surface energy. After substitutions of (8) and (9) into (4) the equation for the estimation of dislocation crack length l is received:

2 B Bp

μ

(1 )π  

2 p l

(10)

2 γ 0.



 

 

4 π(1 ) l  

2 4μ

Solution of (10) gives two correlations for crack length estimation:   2 2 2 πμ 4 γ 2 4γ 2 γ . π (1 ) eq l Bp Bp p v        2 2 2 πμ 4 γ 2 4γ 2 γ . π (1 ) cr l Bp Bp p v     

(11)

The first correlation corresponds to the value of equilibrium crack length, second – to value of nonequilibrium dislocation crack length. Let us note that it was obtained by Stashchuk and Dorosh (2015) that in the absence of pressure in the dislocation crack its length is determined by (10) when p = 0:

2

2

B

EB

μ

l

v

.





eq

2 16 π(1 )γ v 

8 π(1 )γ v 

For the criteria of the dislocation crack spontaneous propagation let us assume the condition for equation fulfillment . eq cr l l  (12)