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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.
A γ-analogue of the superalloy CMSX-4 that does not contain the strengthening γ′ -phase and only consists of the γ-solid solution of nickel has been designed, solidified as single-crystals of different orientations, and tested under creep conditions in the temperature range between 1150 and 1288 °C. The tests have revealed a very high creep anisotropy of this alloy, as was previously found for CMSX-4 at supersolvus temperature of 1288 °C. This creep anisotropy could be explained by the dominance of 〈011〉{111} octahedral slip. Furthermore, the analysis of the creep data has yielded a high value of the creep activation energy, Qc≈442 kJ/mol, which correlates with the high activation energy of Re diffusion in Ni. This supports the hypothesis that dislocation motion in the γ-matrix of Re-containing superalloys is controlled by the diffusion of the Re atoms segregating at the dislocation core. The Norton stress exponent n is close to 5, which is a typical value for pure metals and their alloys. The absence of γ′ -reprecipitation after high-temperature creep tests facilitates microstructural investigations. It has been shown by EBSD that creep deformation results in an increasing misorientation of the existing low angle boundaries. In addition, according to TEM, new low angle boundaries appear due to reactions of the a/2 〈011〉 mobile dislocations and knitting of new networks.
Initially, as-cast and homogenized single crystals of nickel-base superalloy CMSX-4 are subjected to hot isostatic pressing at 1288 °C. Two series of experiments are conducted: under the same pressure of 103 MPa but with different durations, between 0.5 and 6 h, and under different pressures, between 15 and 150 MPa, but for the same time of 0.5 h. The porosity annihilation is investigated metallographically and by high-resolution synchrotron X-ray tomography. The obtained experimental results are compared with the predictions of the vacancy model proposed recently in the group. Herein, the model is further refined by coupling with X-ray tomography. The model describes the evolution of the pore arrays enclosed in the 3D synchrotron tomograms during hot isostatic pressing and properly predicts the time and stress dependences of the pore annihilation kinetics. The validated model and the obtained experimental results are used for selecting the optimal technological parameters such as applied pressure and processing time
The cyclic crack tip opening displacement ΔCTOD is a promising loading Parameter to quantify the crack propagation under thermomechanical fatigue (TMF). In this work, suitable techniques are investigated and compared for an accurate calculation of ΔCTOD under TMF loading using a viscoplastic temperature dependent material model.
It turned out that collapsed special crack tip elements give the best results. An efficient FEM-technique is developed to simulate the incremental crack growth by successive remeshing, whereby the deformations and internal state variables are mapped from the old mesh onto the new one. The developed techniques are demonstrated and discussed for two-dimensional examples like TMF-specimens. Recommendations are made regarding important numerical control parameters like optimal size of crack tip elements, length of crack growth increment in relation to plastic zone size and ΔCTOD value.
Results of an extended TMF test program on grade P92 steel in the temperature range of 620 °C - 300 °C, comprising in-phase (IP) and out-of-phase (OP) tests, partly performed with symmetric dwells at Tmax/Tmin, are presented. In contrast to previous studies, the low-strain regime is also illuminated, which approaches flexible operation in a power plant with start/stop cycles. At all strain amplitudes, the material performance is characterized by continuous cyclic softening, which is retarded in tests at lower strains but reaches similar magnitudes in the course of testing. In the investigated temperature range, the phase angle does not affect fatigue life in continuous experiments, whereas the IP condition is more detrimental in tests with dwells. Fractographic analyses indicate creep-dominated and fatigue-dominated damage for IP and OP, respectively. Analyses of the (micro)hardness distribution in the tested specimens suggest an enhanced microstructural softening in tests with dwell times for the low- but not for the high-strain regime. To rationalize the obtained fatigue data, the fracture-mechanics-based D_TMF concept, which was developed for TMF life assessment of ductile alloys, was applied. It is found that the D_TMF parameter correlates well with the measured fatigue lives, suggesting that subcritical growth of cracks (with sizes from a few microns to a few millimeters) governs failure in the investigated range of strain amplitudes.
The elastic properties of the single-crystal nickel-base superalloy CMSX-4 used as a blade material in gas turbines were investigated by the sonic resonance method in the temperature interval between room temperature and 1300 °C. Elastic constants at such high temperatures are needed to model the mechanical behavior of blade material during manufacturing (hot isostatic pressing) as well as during technical accidents which may happen in service (overheating). High reliability of the results was achieved using specimens of different crystallographic orientations, exciting various vibration modes as well as precise measurement of the material density and thermal Expansion required for modeling the resonance frequencies by finite element method. Combining the results measured in this work and literature data the elastic constants of the gamma and gamma' phases were predicted.
This prediction was supported by measurement of the temperature dependence of the gamma'fraction.
All data obtained in this work are given in numerical or analytical forms and can be easily used for different scientific and engineering calculations.
Mit Hilfe des HIP-Verfahrens („Hot Isostatic Pressing“) werden Poren in der einkristallinen Nickel-Basis Superlegierung CMSX-4 kontinuierlich geschrumpft und dadurch die nach der Erstarrung und der Wärmebehandlung vorhandene Porosität stark reduziert. In diesem Beitrag werden experimentelle und numerische Untersuchungen zu den Mechanismen der Porenschrumpfung zusammengefasst. Es zeigt sich, dass das Verformungsverhalten während Kriechversuchen bei der HIP-Temperatur durch Versetzungsgleitung auf oktaedrischen Ebenen dominiert wird.
Dagegen zeigen Messungen der Porositätsabnahme und Simulationen des Porenschließens, dass die Kinetik der Porenschrumpfung durch das Phänomen der Leerstellendiffusion zwischen Poren und Kleinwinkelkorngrenzen („Low Angle Boundary“, LAB) bestimmt wird. Im Gegensatz führt die klassische Kristallviskoplastizität zu einer systematischen Überschätzung dieser Kinetik. Der scheinbare Widerspruch lässt sich auflösen, wenn man bedenkt, dass auf der Skala der Poren Versetzungsquellen nicht gleichmäßig verteilt sind, wie in der konventionellen Kristallplastizität implizit angenommen wird. Stattdessen wird in einem weiterführenden Modell davon ausgegangen, das Kleinwinkelkorngrenzen (LABs) als Versetzungsquellen fungieren, während die Scherspannungen sehr stark in der Nähe der Poren lokalisiert sind, was die Emission von Versetzungen deutlich reduziert.
Mit Hilfe des HIP-Verfahrens („Hot Isostatic Pressing“) werden Poren in der einkristallinen Nickel-Basis Superlegierung CMSX-4 kontinuierlich geschrumpft und dadurch die nach der Erstarrung und der Wärmebehandlung vorhandene Porosität stark reduziert. In diesem Beitrag werden experimentelle und numerische Untersuchungen zu den Mechanismen der Porenschrumpfung zusammengefasst. Es zeigt sich, dass das Verformungsverhalten während Kriechversuchen bei der HIP-Temperatur durch Versetzungsgleitung auf oktaedrischen Ebenen dominiert wird.
Dagegen zeigen Messungen der Porositätsabnahme und Simulationen des Porenschließens, dass die Kinetik der Porenschrumpfung durch das Phänomen der Leerstellendiffusion zwischen Poren und Kleinwinkelkorngrenzen („Low Angle Boundary“, LAB) bestimmt wird. Im Gegensatz führt die klassische Kristallviskoplastizität zu einer systematischen Überschätzung dieser Kinetik. Der scheinbare Widerspruch lässt sich auflösen, wenn man bedenkt, dass auf der Skala der Poren Versetzungsquellen nicht gleichmäßig verteilt sind, wie in der konventionellen Kristallplastizität implizit angenommen wird. Stattdessen wird in einem weiterführenden Modell davon ausgegangen, das Kleinwinkelkorngrenzen (LABs) als Versetzungsquellen fungieren, während die Scherspannungen sehr stark in der Nähe der Poren lokalisiert sind, was die Emission von Versetzungen deutlich reduziert.
Single crystal superalloys usually contain pores of sizes 5-10 micro-m after casting and heat treatment. These pores can be reduced under compression by combined creep and diffusion in a subsequent treatment called Hot Isostatic Pressing (HIP). The paper presents a methodology to simulate pore shrinkage under HIP conditions in two dimensions (2D).
At the scale of the pores, which is also the scale of the sub-grains (<50 micro-m) the dislocation sources cannot be assumed to be homogeneously distributed. Thus, the applicability of classical crystal plasticity is questionable. In this case, the transport of dislocations under an applied stress from the location where they are nucleated must be explicitly modelled. This is done by solving the transport equations for the dislocation densities and the elasticity equations in 2D. The dislocations are assumed to be nucleated at Low Angle Boundaries. They glide or climb through the sub-grains with a stress dependent velocity.
The transport equations are solved by the Flux-Corrected Transport method, which belongs to the predictor-corrector class of algorithms. In the first step, an artificial diffusion is introduced, which suppresses spurious oscillations of the solution. In a second step, the solution is corrected in such a way that no additional extremes appear and that the extremes do not grow. The algorithm is validated by simulating the transport of simple distributions with a constant velocity field.
With the dislocation velocities and the computed dislocation densities, the inelastic shear rate at the slip system level is computed by integrating the Orowan equation. In the 2D-setting, three slip systems are considered. The contributions of these slip systems are summed up to obtain the total inelastic strain rate. Dislocation glide and climb and the coupling of climb with vacancies diffusion are considered.
The resolution of the equilibrium equations from the inelastic strains turned out to be prone to numerical instabilities. As an alternative, the stresses are directly computed from the distribution of geometrically necessary dislocations following the method presented in. The resulting boundary value problem is solved by the Least-Square Finite Element method.
Examples of simulations are presented for a representative region under creep tension and for a pore shrinking under external pressure.