Issue 68

S. Kotrechko et alii, Frattura ed Integrità Strutturale, 68 (2024) 410-421; DOI: 10.3221/IGF-ESIS.68.27



4



K

3 2 3 1 sin   

  

  





0 

2

2

2

2 4    Y



 



1 2 sin 



S

d

( А 2)

 

 

Y

4

2

4

After integration:





4

2 3.75 1 2 4  

K     



S

( А 3)

Y     

Y

Taking into account that:

 

l  

K

( А 4)

f

f

where f  is the macroscopic shear stress; f l is the shear crack half-length. Substituting ( А 4) into ( А 3) gives rise to:   2 4 2 3.75 1 2 4 f Y f Y S l                  

( А 5)

A PPENDIX B: E STIMATION OF THE CRACK SIZE AT WHICH ENERGY COSTS FOR FRACTURE AT THE CRACK FRONT ARE SIGNIFICANTLY LESS THAN THE COSTS FOR LOCAL PLASTIC DEFORMATION s noted above, at brittle fracture of bcc metals and alloys, low energy costs for fracture of the crystal structure ahead of the crack nuclei of submicroscopic sizes causes their avalanche growth. The excess of released elastic energy goes to form the local yielding region and to heat it. In the Eqn. (7), this effect is characterized by the difference:

A

E 

2 2 f f l



4   l

(B1)

f

This expression enables to estimate the crack length f l , at which the energy costs for fracture ahead of the crack tip, 4  , is quite negligible:

E 

2 f f l



4  

(B2)

where

2 4   E



l

(B3)

f

f

2 10 / J m   , at

0.9   , gives

 

GPa

0.7

Substitution of the upper limit for specific energy of failure,

72 E GPa  ,

,

f

rise to the following estimation - . This means that when the crack length approaches to the specimen size ( 2 m  f l 

f l 

2 mm

), the term 4  in the Eqn. (10) can

be neglected, i.e. almost all released energy is spent for plastic deformation ahead of the crack tip.

421