PSI - Issue 42

Florian Garnadt et al. / Procedia Structural Integrity 42 (2022) 1113–1120

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F. Garnadt et al. / Structural Integrity Procedia 00 (2019) 000–000

3.4. Crack growth laws

The crack growth for the fatigue part of the cycle is computed based on the Paris law given in Eq. 3 and the crack growth during the dwell time due to creep is computed based on the Nikbin-Smith-Webster (NSW) model in Eq. 4, Nikbin et al. (1986). The sum of both portions gives the result for creep-fatigue crack growth. It is assumed that no crack growth occurs in the dwell time in compression and no crack growth occurs due to oxidation. Both crack growth laws base on standardized independent tests with the same material and temperature conducted in previous investigations. The creep rupture strain in Eq. 4 is assumed to be 20% and time invariant. d a d N fat. = 4E − 07 ∆ K 1 MPa √ m 2 . 3 1 mm cycle (3) d a d N cr. = 3 10 ε cr f ( C t ) avg 1000 N / mm h 0 . 85 1 mm h t h , tension (4) By the insertion of the computed crack tip loadings and the integration of the crack growth laws, the ECG from notches under creep-fatigue loading is known and the cycle number can be used to determine the notch support factor defined by Eq. 1. In addition to the described computations, the ECG cycle number is measured in tests to be used for validation. Therefore, two independent techniques, (1) the load drop correlation (LDC) and (2) the alternating current potential drop (ACPD) technique, are applied. The first is based on the measured load drop over cycle number during the strain controlled experiments and the computed load drop over crack depth based on FE simulations. More details about the LDC are given in Kontermann et al. (2016). The second uses the principle of an increasing electrical resistance for a growing crack, which is measured over the number of cycles. After the test, the crack depth is measured and linearly correlated with the measured potential signal. The results of both techniques show negligible deviations as long as the crack geometry is concentric as assumed, which is the case for the majority of the tests. 4. Measurement of ECG The resulting measured notch support factors for the round bar specimens with two di ff erent notch shapes are given in Fig. 5 (a) for two di ff erent loading levels and with and without dwell times. Thus, notch support is higher for the sharp notch due to the higher stress gradient and is slightly higher for the lower loading level. Besides the additional creep crack growth, the described impact of dwell times on crack closure and thus a higher fatigue crack tip loading in the loading part of the cycle lead to a higher crack growth rate and reduces notch support significantly. The validation of the computed by the measured notch support factors shows Fig. 5 (b). All results are in a scatter band of ± 2. Additionally, the results of two tests with cruciform specimens with a borehole in the center under uniaxial and biaxial loading, as shown in Fig. 5 (c), are plotted to demonstrate the transferability of the modelling approach for ECG. For more information about the testing principle behind please refer to Erbe et al. (2022). It seems that the linear relationship between notch support factor and normalized stress gradient known from ap plication diagrams in literature is suitable to capture this notch support e ff ect even for di ff erent specimen geometries, round bar and cruciform specimen, and fatigue or creep-fatigue loading conditions. However, the slope of the linear relationship is a function of dwell times. Please note that all the described e ff ects are considered within the computa tional approach implicitly. 5. Results, validation and transferability

6. Application example

To give an example for the applicability in lifetime assessment procedures of components, the modelling approach was applied to a component-like structure representing a borehole in a thick-walled casing of a steam turbine. The