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Approximation of the crack driving force for cracks at notches under static and cyclic loading
(2017)
The work deals with the efficient calculation of the elastic-plastic crack driving force (J-integral for monotonic loading andΔJ-integral under cyclic loading) for short cracks at notches as essential parameter for the reliable static and fatigue assessment of notched structures. The J- or ΔJ-integral is calculated based on analytical solutions for stress intensity factors, estimated by means of well-known weight function solutions in the case of cracks under power-law stress distributions. A plasticity-correction function is applied to the stress intensity factors to obtain the final expression of the crack driving force. The comparison between analytical solutions and finite element calculations in case of cracks at the weld toe in welded joints shows good agreement.
Pulsed thermography is a well-known non-destructive testing technique and has proven to be a valuable tool for evaluation of material defects. Material defects are often simulated by flat-bottom holes (FBH) or grooves. Typically, analytical 1D models are used to determine the defect depth of FBHs, grooves or delaminations. However, these models cannot take into account lateral heat flows, or only to a limited extent (semi-empirical model). Their applicability is therefore limited by the FBHs aspect ratio (diameter to remaining wall thickness), to ensure that the heat flow above the defect can still be described one-dimensionally. Additionally, the surfaces of semi-transparent materials have to be blackened to absorb the radiation energy on the surface of the material. Without surface coatings, these models cannot be used for semi-transparent materials. Available 1D analytical models for determination of sample or layer thicknesses also do not take into account lateral heat flows.
Here, we present an approach for quantitative determination of the geometry of FBHs or grooves in semi-transparent materials by considering lateral heat flow. For this purpose, the results of a numerical 2D model are fitted to experimental data, e.g., to determine simultaneously the defect depth of a FBH or groove and its diameter or width, respectively. The model considers semi-transparency of the sample within the wavelength range of the excitation source as well as of the IR camera and thermal losses at its surfaces. Heat transport by radiation within the sample is neglected. It supports the use of an arbitrary temporal shape of the heating pulse to properly describe the measurement conditions for different heat sources.
Iterative numerical 2D-modeling for quantification of material defects by pulsed thermography
(2018)
Pulsed thermography is a well-known non-destructive testing technique and has proven to be a valuable tool for examination of material defects. Typically, analytical 1D models are used to determine the defect depth of flat-bottom holes (FBH), grooves or delamination. However, these models cannot take into account lateral heat flows, or only to a limited extent. They are therefore limited by the FBHs aspect ratio (diameter to remaining wall thickness), to ensure that the heat flow above the defect can still be described one-dimensionally. Here, we present an approach for quantitative determination of the geometry for FBH or grooves. For this purpose, the results of a numerical 2D model are fitted to experimental data, e.g., to determine simultaneously the defect depth of a groove or FBH and its diameter of width. The model takes lateral heat flows into account as well as thermal losses. Figure 1 shows the temperature increase of a pulsed thermography measurement at three different locations on the sample. The numerical model is fitted to the experimental data (red lines) to quantify the groove. The numerical simulation matches the experimental data well.
Turbine blades often contain cylindric holes used to generate an air film that protects the blade alloy from the hot gases. These cooling holes of diameter around one mm are drilled by laser through the thickness of the blades. Unfortunately, the resulting stress concentration and the drilling-induced damage are known to favor crack initiation from the holes. It is thus necessary to assess the impact of these cooling holes on the structural integrity of the blades. Since cracks initiate very readily, the fatigue life of the components is mainly controlled by the propagation of the cracks in the stress gradient induced by the holes.
For this purpose, displacement controlled high-temperature LCF (Low-Cycle-Fatigue) tests were performed with center hole specimens of a coarse-grained Nickel base Superalloy. The tests were stopped after a defined load drop. In addition, crack propagation tests with Double Edge Notch specimens were performed. Moreover, specimens with different hole surface finishes were investigated, which showed a detrimental effect of the hole surface roughness. In parallel, an evaluation of the LCF tests based on a fracture mechanics-based model (Madia et al., Eng. Fract. Mech., 2018) has been applied. Thereby, the specimen life is controlled by the crack propagation time until failure. Crack growth is controlled by a modified NASGRO equation accounting for large-scale yielding and a progressive build-up of crack closure. The initial crack size has been derived from the measurements of defects around the borehole. A reasonable agreement between predicted and measured lifetimes is observed if one keeps in mind the large uncertainty regarding the effective shape of the cracks.
The scatter of fatigue crack growth data can become significant for coarse grained materials. By using a probabilistic description of crack propagation as the foundation of a lifetime prediction model, lifetime scatter of laboratory specimens can be reproduced. However, the lifetime of real components is subjected to additional scattering factors such as surface condition or uncertainty regarding direction and shape of emerging cracks. These factors need to be addressed in order to exploit the advantages of probabilistic description, i.e. the reduction of unnecessary conservatisms.
High temperature LCF (Low-Cycle-Fatigue) tests were performed with center hole specimens of a coarse-grained Nickel base Superalloy. In addition, crack propagation tests with Double Edge Notch specimens were performed. A procedure to detect the shape of the starting crack that combines the potential drop method and induction thermography was developed. The geometry and the number of notches were varied. Moreover, specimen with different hole surface finishes were investigated, which showed a detrimental effect of the roughness of the hole surface.
The results have been compared to predictions of a probabilistic tool for the estimation of lcf lifetime that has been calibrated beforehand on laboratory specimens with and without notches. In parallel, a fracture mechanics-based lifetime model was developed, which includes the initial crack size as a critical parameter. Thereby, the influence of the large grain size (>1mm), and the shape of the starting crack at the notch were considered.
Acknowledgements
The investigations are conducted as part of the joint research program COOREFLEX-Turbo in the frame of AG Turbo. The work is supported by Siemens AG and the Bundesministerium für Wirtschaft und Technologie (BMWi) as per resolution of the German Federal Parliament under grant number 03ET7071E.