PSI - Issue 59

3

Anna Uhl et al. / Procedia Structural Integrity 59 (2024) 538–544 A. Uhl et al. / Structural Integrity Procedia 00 (2019) 000 – 000

540

1 4 1 

  

2 4 (2 ) (2 ) (2 ) A A A K K K     

2

.







(1)

 

2 A

2 A

3 K K

5

7

K

K



K

A

A

p

Writing the equation (1) in the form of a finite series, then after some transformations we get:

( 1) (2 ) n K  

n

1 4

 

.



A 

(2)

1

(2 1) 

n A

n K



K

P

0

n



Analyzing the resulting expression, we can determine that when 2 A K  corresponding to a surface with an arbitrary curvature, the distribution of orientation of surface elements and the local curvature of individual sections of the fracture surface does not affect the unambiguousness of the correlation between A K і P K . This result can be interpreted as follows: if we consider the first term in equation (2) to take into account the chaotic surface topography, then the higher-order terms can be considered as corrections for the deviation of the analyzed surface from a completely arbitrary fracture surface. It should be noted that when 1 A K  , which corresponds to the case of "ideal flat fracture surface", then 2 P K  .

а) b) Fig. 1. а) microrelief of the stepped plate type; b) "ideal" 3D stepped fracture surface of brittle fracture

A K for any normal section

When designing a hemispherical "ideal" surface on a base, the roughness index

2 A K  , (Fig. 2). Then,

ABCE will be

( ) ABC r AEC r  

sin     ( ) 2 sin 2   .

( ) 

K



(3)

P

2  

and in the case of orientations of the sectional surface within 0

the average integral value is equal to

 

2



( 2) d  

0   . Comparing the relationship betw/een the average roughness profile and the corresponding roughness index of the section for the "ideal" stepped surface from equation (1) and the corresponding values of A K і P K for a hemispherical surface, it can be argued that fracture surfaces with arbitrary curvature and stepped surfaces are statically equivalent at the global level. However, they may be quite different "locally" (Yasniy et al., 2011). ( ) ( ) p p K K   d     . If, ( ) d     , then for a hemisphere 2 P K