Issue 36

M. Arsic et alii, Frattura ed Integrità Strutturale, 36 (2016) 27-35; DOI: 10.3221/IGF-ESIS.36.03

Figure 9 : Relationship between critical crack length and fatigue strength.

Procedure of calculating coefficients C 1

and C 2

by the method of the minimal square deviations is based on the condition

that sum of obtained data square deviations from functional relation should be minimal:

n



 2









log log log C a  



, F C C

C S

min

(5)

z

c

1 2

2

1



i

1

Parameters C 1

and C 2 should be determined from following equation in order to get minimal value of function F(C 1 ,C 2 ):   1 2   1 2 



, F C C C 

, F C C C 





(6)

0;

0

1

2

In this way, system of equations for calculation of coefficients C 1

and C 2

is obtained:

n

n

       2 1 1 2 log log log log zi ci i i n n n zi S C  zi a S    

log n C C S 

1

(7)





log log S 

C

log

zi

ci

1







i

i

i

1

1

1

where “i” represents specimen number (from 1 to 5). Values needed to solve the equation system (7) are given in Tab. 4. Relation between critical length of short crack a c (given in meters) and fatigue strength S f,z (given in MPa) is:

z S 

3.15



a

18960

(8)

c

S zi,

[MPa]

a ci

[mm]

log S zi

log a ci

(log S zi

)

log S zi

log a ci

i

1 2 3 4 5

195 226 249 282 315

1.125 0.723 0.591 0.351 0.250

2.2898831 2.3535816 2.3958992 2.4509785 2.4982637 11.988606

0.0511525 -0.1408617 -0.2284125 -0.4546928 -0.6020599 -1.3748744

5.2435646 5.5393463 5.7403329 6.0072956 6.2413215 28.771858

0.1171332 -0.3315295 -0.5472533 -1.1144422 -1.500414 -3.3801961

Σ

Table 4 : Values for solving the equation system (7).

33