PSI - Issue 14

432 A.N. Savkin et al. / Procedia Structural Integrity 14 (2019) 429–434 Author name / Structural Integrity Procedia 00 (2018) 000–000 from the analytical dependence K th = f ( *  ), substituting it into Eq. (3). Thus, a known loading history made it possible to determine Δ K eff , K max and K th at each cycle for fatigue life estimation (Savkin et al. (2016). The constant amplitude loading was carried out with Р max = 1750 N, R = 0.7, N = 10 4 . The level of overload is 1.5 times higher in comparison with the subsequent constant amplitude loading. The factors с , m, p , q и K c are constant and are known, and the loading history introduced determines the change Δ K, K max and Δ K th . Summation of crack length increments on each cycle of loading history allows to determine the fatigue crack life: 4

a a 

0

f

N



f

dN da

m

n

  

  

j    1 1 i

ij

(4) where a f is the critical crack length; a 0 is the initial crack length; n is the loading history cycles number; m is the number of iterations of loading sequence; (da/dN) ij is the crack growth rate and increment on i -th cycle of j -th iteration of loading sequence. The blocks of spectra MiniFALSTAFF, MiniTWIST, SAETRANS differ from the original quazi-random sequences, because negative loads were truncated to zero. Thus, all tests were carried out without compressive loading. The load value was P max1 = 2500 N, P max2 = 3000 N and P max3 = 3500 N. 4. Test results and discussion The test simulation under constant amplitude loading with overload-underload (curve 1) and underload-overload (curve 2) sequences overlapping is shown on Fig. 3.

Fig. 3. The local near-tip stress σ * (a), threshold SIF К th (b) and fatigue crack length (c) under cyclic loading with overload-underload (1) and underload-overload (2)

The overload unit of loading block, consisting of underload-overload, slows the crack growth by 6 times compared to the block with underload-overload sequence, which is close to the results obtained in the experiment. Here, the change of SIF K th (Fig. 3 b) as a function of the calculated near-tip stress σ* is shown in these tests (Fig. 3 a). The crack growth rate slowing with the underload-overload sequence in comparison with overload-underload is associated with the local near-tip stress σ* decreasing and threshold SIF K th increasing.