PSI - Issue 42

Florian Garnadt et al. / Procedia Structural Integrity 42 (2022) 1113–1120 F. Garnadt et al. / Structural Integrity Procedia 00 (2019) 000–000

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2. Methodology of investigations

The objective of the investigations is to quantify the impact of notches on the number of cycles to crack initiation and growth up to a technical relevant crack depth. Therefore, a round bar specimen with and without notch is compared at the same local loading level for same crack depths. In standardized LCF tests using cylindrical specimens with a constant diameter of 8 mm along the test section, a typical load drop criterion of 5% indicates crack initiation with crack depths of about 1 mm. To make the cycle numbers for the di ff erent investgated specimen geometries comparable, a crack depth of 1 mm is used to define a criterion for evaluation in this paper. Furthermore, early crack growth (ECG) is defined as short crack growth from 0.2 to 1 mm crack depth. The initial crack depth of 0.2 mm is chosen, because it is still measurable in a robust way during the experiments and it is a distinct starting point for the ECG model. The cycle number for ECG ( N 1mm − N 0 . 2mm ) in the typical LCF specimen without notch is negligible small as shown in Garnadt et al. (2021). Therefore, it can be assumed that the cycle numbers for 0.2 mm, 1 mm and 5% load drop ( N 0 . 2mm = N 1mm = N 5% ) are equal. In the case of the investigated specimens with notch, the cycle number for ECG is clearly pronounced due to the stress gradient raised by the notch and the reduced crack growth rate. The number of cycles for crack initiation up to 0.2 mm is assumed to be equal in the case of the specimens with and without notch. Based on the aforementioned definitions a notch support factor for a crack depth of 1 mm is given by Eq. 1. The methodology of the investigations is a comparison of the notch support for di ff erent notch geometries and cycle shapes as shown in Fig. 2 by both an experimental and a simulation-based approach. Thus, a model for ECG based on FE simulations was developed and a systematic experimental study was conducted. The notch geometries in Fig. 2 (a) are characterized by the stress concentration factor K t , I and the normalized stress gradient χ ∗ I based on the first principle stress following an elastic stress analysis. The cycle shapes in Fig. 2 (b) di ff er by a dwell time of three minutes at maximum and minimum load to investigate the impact of superimposed creep. To be able to compare the ECG for di ff erent geometries and loading conditions, it is necessary to apply the same local loading level. As a definition of the local loading, the local equivalent strain range at the notch root based on the von Mises hypothesis is used. In the experiments, it is not possible to control this strain. Therefore, the global axial strain range at the position of the side-extensometer with a reference length of 15 mm is used. To figure out the necessary global strain range for a specific local strain range, FE simulations were performed using the cyclic flow curve at midlife cycle as a material model for the elastic-plastic behaviour. Furthermore, the impact of di ff erent materials at di ff erent temperatures was investigated, e.g., Kontermann et al. (2016); Garnadt et al. (2021). In this paper, the results are limited to the 9%-Cr cast steel 9Cr-2Mo-1Co-VNbB at a temperature of 600 ◦ C. n 1mm = 1 + ( N 1mm − N 0 . 2mm ) with notch ( N 5% ) without notch (1)

3. Computation of ECG

This section describes the computation of the ECG cycle number used in this paper independent from the specimen geometry. First, the simulation procedure based on finite element analysis (FEA) is explained, which is the basis for the evaluation of the crack tip loading. Second, the e ff ects of plasticity and visco-plasticity in terms of crack closure will be considered due to the high local loading in the vicinity of the notch and the high temperature. Third, the resulting crack tip loading will be used to compute the crack growth rates by independently determined crack growth laws.

3.1. FE simulation procedure

The simulation of the strain controlled cyclic loading of the specimens with notch is based on FEA. Therefore, the symmetry properties of the specimen are used to reduce the size of the problem. Fig. 3 (a) shows the modelled section of the round bar specimen with notch as an example. The assumed crack path and crack geometry, which was validated by the experiments, is a concentric crack extension along the circumference at the notch root perpendicular to