PSI - Issue 42

Matěj Mžourek et al. / Procedia Structural Integrity 42 (2022) 457 – 464 Matěj Mžourek / Structural Integrity Procedia 00 (2019) 000 – 000

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low enough for volume in the entire cross section to satisfy the stress condition, the Volume - h crit curves become nearly linear with a common intersection point. In such case, the ratio of volumes in Eq. (2) is nearly unaffected by the h crit parameter and obtained estimations of fatigue strengths are insensitive to the value of h crit .

1000

A01 A03 A51

A02 A04 A52

a)

b)

1000

100

100

1 Volume [mm 3 ] 10

10

0.1 Volume [mm 3 ] 1

0.1

A01 A03 A51

A02 A04 A52

0.01

0.01

0

0.2

0.4

0.6

0.8

1

0.001

h crit [mm]

n [-]

0.8

0.85

0.9

0.95

1

Fig. 6. a) Critical volumes for various values of n via the V-model , b) Critical volumes for various values of h crit , via the V*-model , stress threshold parameter is kept constant ( n = 0.971)

Obtained fatigue data is used to obtain optimal values of parameters m , n and h crit . Dye penetrant tests did not confirm cracks in the critical region in the majority of A04 smooth specimens, and one A04 specimen broke in the threaded head during loading. The A04 fatigue data points were thus excluded from the optimization routine, as the anticipated and required type of failure of the specimens – cracking in the central part – could not be confirmed at this time, though more investigation are being made to detect possible internal cracks. S-N curves obtained for all 5 other geometry types described in Sec. 2 have been used to obtain the parameters listed in Table 4.

Table 4. Regression analysis results – optimized parameters and error value (sum of squares of errors of logarithms of fatigue strengths) Model n [-] h crit [mm] m [-] Error [-] V*-model 0.971 0.064 0.086 5.54 V-model 0.972 - 0.059 6.22 A-model 0.972 - 0.145 7.21

The V*-model provides the lowest error of the three models. The optimal value of n is consistent across all three models, and equals to roughly 1/ K t,A02 (the value of K t,A02 found through FEM is 1.03). As has been shown, the V ( n ) function features a sudden steep drop for the specimens with an elongated central section at n = 1/ K t . Near this value of n , a local minimum of the error generated by the model given by Eq. (2) can be found, but the optimized parameters cannot be expected to provide optimal results for data sets with different specimen geometries, as the value of the parameter is clearly dictated by geometry of the used specimens. This was tested via running the non-linear regression on fatigue data obtained from the notched A51 + A52 specimens only. The final values of the optimized parameters were vastly different than those listed in Table 4. As the S-N curves differ in slope (see Fig. 3.), it is expectable that the vertical shifts of the S-N curves via Eq. (1) alone will not provide satisfactory results. Expanding the model with a parameter that allows slope modification could improve the results to a large degree.