PSI - Issue 7

7

Stanislav Žák et al. / Procedia Structural Integrity 7 (2017) 254 – 261 Stanislav Žák et al. / Structural Integrity Procedia 00 (201 7 ) 00 – 000

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approach by Plank and Kuhn, 1999 and Richard, 1981 (ii) numerical approach - without notch (i) numerical approach - notched specimen

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65 I I / MPa.mm 1 / 2 70

K

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1.5

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z / mm

Fig. 4. Comparison of numerical results and original approach for CTS specimen

The original approach was compared with two types of numerical simulations: (i) using the CTS specimen in Fig. 1, (ii) using the same specimen but containing just a crack of the length a p (instead of the notch and the crack). The comparison shows a good match between the original equation and the numerical simulation for the specimen without the notch – see Fig. 4. On the other hand, the function K II ( z ) for experimental geometry shows a decrease of SIF value as expected due to notch influence described by e.g. Hassan and Radhi (2013) or Sapora et al. (2014). Nevertheless, this phenomenon has no impact on normalized k II values because the results for smooth and tortuous crack fronts were obtained by considering the same specimen geometries: (i) notch ( a ) + precrack (Δ a ) for the numerical computation and (ii) crack ( a + Δ a ) for the analytical one. There is a very good agreement between the results obtained from analytical and numerical models, as can be seen from the data displayed in Table 1. Indeed, the averaged values of k II / K II differ by less than 5%.

Table 1. Comparison of numerical and analytical model.

R L = 1.078

R L = 1.261

k II / K II - analytical model

0.9270 0.8981 3.12 %

0.7912 0.7588 4.10 %

k II / K II – numerical model (mean value) Relative deviation between models

Considering the results in Tab. 1, the correction of the value of previously measured effective fatigue threshold Δ K IIth, eff = 1.5 MPa.m 1/2 for the cyclic ratio R = 0.1 in the polycrystalline ARMCO iron (Vojtek et al. (2015)) can be done by the determination of the linear roughness R L,Fe of precrack fronts on the fracture surfaces of broken specimens. This analysis will be performed using the stereophotogrammetrical data that were obtained immediately after the fatigue experiments by tilting the fractured samples in the scanning electron microscope. The corrected value can then be compared with the theoretical value K IIe = 0.7 MPa.m 1/2 , related to the emission of dislocations in the cracked iron single crystal, as obtained (by averaging over possible slip systems) from multiscale quasicontinuum models (Vatne et al. (2013)). With respect to the results of dislocation models of fatigue crack propagation (Riemelmoser et al. (2001)), this value is about 1.3 times lower than that of Δ K IIth,eff . Let us give here just a rough prediction of the corrected value by assuming the real linear roughness R L,Fe ≈ 1.2. According to Tab. 1, the geometrical shielding would reduce the threshold to K IIth, eff ≈ 1.2 MPa.m 1/2 . When taking the factor of 1.3 into account, this corrected value leads to K IIe ≈ 0.9 MPa.m 1/2 closely approaching the theoretical emission threshold.