PSI - Issue 16

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

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Using (13) the relation between B and the length of dislocation crack l is received, that is

2 π(1 )γ . μ l  

B



(19)

2 cr p B   into (15) it can be written that

After entering

l

B

γ

μ

l I

K

(20)

.

 

B

l 

2 π(1 ) 

Since the right crack tip in fact is responsible for fracture substitution of (19) into (20) gives the formulae for definition through shear modulus, surface energy and Poisson's critical pressure coefficient:

      2 1

l I K

.

(21)



4. Numerical results

Numerical calculations of full energy of a solid with a dislocation crack under pressure were carried out using (10) and (11). Dependences of full energy F+U of a body with dislocation crack on the dislocation crack length l for p =0, p < p cr , p=p cr and p>p cr are shown in Fig. 3. Calculations of F+U energy correspond to that for cylindrical body of a unit thickness with R = 10 -7 m. Such values were used for these calculations (Vladimirov (1984)): E = 2·10 11 Pа; γ = 0,01 · E a = 0,6 J/m 2 ; ν = 0,3; lattice parameter b = 3·10 – 10 m; Burgers vector module B = 3 b .

Fig. 3. Dependence of the solid energy F+U on dislocation crack length when ( a ) p =0; ( b ) p

p cr .