Issue 36

M. Arsic et alii, Frattura ed Integrità Strutturale, 36 (2016) 27-35; DOI: 10.3221/IGF-ESIS.36.03 33 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:     2 1 2 2 1 1 , log log log min n z c i F C C C S C a       (5) 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 , F C C C    0;   1 2 2 , F C C C    0 (6) In this way, system of equations for calculation of coefficients C 1 and C 2 is obtained:     1 2 1 1 1 2 1 1 1 log log log log log log log log n n zi ci i i n n n zi zi zi ci i i i n C C S a C S C S S                (7) 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: 3.15 18960 c z a S   (8) i S zi, [MPa] a ci [mm] log S zi log a ci (log S zi ) log S zi log a ci 1 195 1.125 2.2898831 0.0511525 5.2435646 0.1171332 2 226 0.723 2.3535816 -0.1408617 5.5393463 -0.3315295 3 249 0.591 2.3958992 -0.2284125 5.7403329 -0.5472533 4 282 0.351 2.4509785 -0.4546928 6.0072956 -1.1144422 5 315 0.250 2.4982637 -0.6020599 6.2413215 -1.500414 Σ 11.988606 -1.3748744 28.771858 -3.3801961 Table 4 : Values for solving the equation system (7).