Prediction of crystallographic cracking planes in single-crystal nickel-base superalloys
Introduction
In today’s world, gas turbines are crucial in the energy generation sector, as their start-up and shut-down times are relatively short, making them perfect candidates for balancing the power grid with respect to inherently intermittent renewable energy sources like wind and solar power [1]. However, more pronounced cyclic loading conditions mean an increased risk for fatigue (primarily thermomechanical fatigue) in critical components. Furthermore, gas turbines are designed to work with very high gas temperatures in order to achieve a good thermal efficiency [2], as increasing the gas temperature in power generating gas turbines lowers the fuel consumption; therefore also lowering costs and reducing pollution [3]. These high temperatures result in high requirements on the materials in the hottest regions. One of the critical regions in a gas turbine is the first turbine stage, where the highest temperatures are present for rotating parts. The turbine blades in this region are often cast in single-crystal form of nickel-base superalloys due to their excellent properties at high temperatures.
The complex material behaviour of single-crystal nickel-base superalloys, like the elastic and plastic anisotropy, makes the modelling of these materials rather complicated. It has been shown that the anisotropy, which is closely linked to the crystallographic structure, has a considerable impact on the yield [4], [5], low-cycle fatigue [6], [7], thermomechanical fatigue [8], [9], [10] and creep behaviour [11], [12], to mention a few examples. Thus, the crystallographic structure needs to be accounted for in the modelling context. The same holds true for the fracture mechanical behaviour, where the distinct crystallographic slip planes are potential critical planes for crack initiation [13] and crack growth. Antolovich et al. [14] observed that nickel-base superalloys in single-crystal form show two distinct types of fracture. The first one is characterised by fracture on the {111}-planes, where the -precipitates are sheared. The second fracture type is characterised by cracking normal to the loading direction, i.e. Mode I, and shows a microscopically rough surface, where the crack tends to avoid the -precipitates instead of shearing them.
Fatigue cracks in single-crystal nickel-base superalloys tend to switch from Mode I to crystallographic cracking, where the crack grows along one of the internal crystallographic slip planes [15], [16], [17], [18]. Insufficient knowledge of how to handle the crystallographic cracking behaviour leads to large safety margins and conservative designs, which in turn decreases efficiency. Hence, it is important to establish a parameter describing the crack driving force in these materials that accounts for the observed behaviour. Furthermore, the transition from Mode I to crystallographic cracking is also important, as the latter is associated with a higher crack propagation rate [19].
Previous research [16], [20], [21], [22] points out the importance of the crystallographic orientation, including the misalignments, as the deviation from the ideal crystallographic orientation, formed during the casting process, has a non-negligible influence on the stress distribution, and thus on the mechanical behaviour and fatigue life. This is important for the industry, where the crystallographic orientations in single-crystal components at stress raising features are generally unknown, due to the rarely controlled secondary orientation in the casting process. Different fracture mechanics approaches for single-crystal superalloys are available in the literature, where Resolved Shear Stresses (RSSes) are commonly used in single-crystal crack growth modelling applications [15], [23], [24]. Telesman and Ghosn [18], as well as Gell and Leverant [25], proposed that the RSSes on the respective crystallographic slip plane can be used to predict the crystallographic fracture plane. Telesman and Ghosn [18] presented an octahedral stress intensity factor parameter that couples a Resolved Shear Stress Intensity Factor (RSSIF) with a Resolved Stress Intensity Factor (RSIF) based on the normal stress acting on the corresponding slip plane. Their work and most of the previous research was done in terms of two-dimensional (2D) analyses, due to its simpler nature. Tinga [15], Ranjan and Arakere [26] and Qiu et al. [27] presented frameworks with RSSIFs in a three-dimensional (3D) context based on the anisotropic Stress Intensity Factors (SIF) derived by Sih et al. [28]. However, these anisotropic SIFs are restricted to the special case where locally the plane perpendicular to the crack front must be a plane of material symmetry. This is not valid for most crack front shapes or when a deviation from the ideal crystallographic orientation is present.
Another approach was proposed by Sabnis et al. [29], where a microdamage model is used to predict the crack initiation and crack growth. The anisotropic continuum damage mechanics model couples crystal plasticity with damage induced on the crystallographic planes and predicts a realistic crack path in a four-point bending specimen. However, they state that their constitutive model is insufficient for a quantitative comparison with experiments.
In this paper, two different models are presented and evaluated in order to find a reliable prediction of the first global crystallographic cracking plane. The models include the calculations of anisotropic SIFs resolved on the crystallographic planes in a 3D context for arbitrary crack front shapes and crystallographic orientations based on the work of Hoenig [30]. An equivalent RSIF parameter is proposed based on these anisotropic SIFs, which is used to predict the active global crystallographic cracking planes after a transition from Mode I cracking. Validation of the models has been done by isothermal crack growth testing at 500°C for two different specimen geometries, where the crystallographic misalignments, due to the casting procedure, have been taken into account.Furthermore, no fatigue crack growth rate data is presented or used in this work.
The presented methodology is applicable to arbitrary 3D Finite-Element (FE) simulation contexts and crystallographic orientations. This aspect is of high importance for industrial applications, where a physical-inspired model, such as this, can be used to more accurately predict the crack growth in single-crystal components, and thus increase the efficiency of the design as well as the maintenance intervals. The authors are not aware of similar research using 3D-calculations of RSIF parameters based on anisotropic SIFs for arbitrary crack front shapes and crystallographic orientations.
Section snippets
Material
The investigated material is a single-crystal nickel-base superalloy of face-centred cubic structure (FCC) developed by Siemens Industrial Turbomachinery AB, similar to the alloy described by Reed et al. [31]. Its main alloying elements, in order of decreasing wt%, are as follows: Ni-Cr-Ta-Co-Al-W-Mo-Si-Hf-C-Ce.
As the specimens are cast in only one single grain they possess anisotropic properties, where the elastic stiffness constants for 500°C are presented in Table 1. The temperature of 500°C
Resolved stress intensity factor parameters
In this section, a general framework for RSIFs acting on arbitrary material planes in anisotropic materials is defined. Hence, anisotropic SIFs are employed to describe the stress field around the crack tip and used in the two proposed crack driving force models to evaluate the RSIFs on arbitrary material planes. The anisotropic SIFs and ) can be evaluated in different ways. The approach in this work has been by using the Linear Elastic Fracture Mechanics (LEFM) M-Integral [38], [39]
Crack driving force models
Adopting the above defined general framework of RSIFs for the application of FCC single-crystal nickel-base superalloys, the arbitrary material planes are chosen to be the crystallographic slip planes. Two different crack driving force models have been evaluated and compared to the results from the performed experiments. The difference between the models lies in the choice of the evaluation direction , and its impact on the RSIF calculations, cf. Eq. (10). The evaluation directions will be
Simulations
Simulations for the two specimen geometries were performed in the FE-environment Abaqus V6.12 [42] and paired with the crack growth tool FRANC3D V7.0.8 [43]. All simulations were performed in a 3D-context. In order to handle the anisotropic constitutive behaviour an elastic anisotropic material description was used. The crystallographic orientation corresponding to the specimens in the experiments were accounted for in the material model, as discussed earlier. The two initial FE-models were
Predictions and discussion
In this section the above described equivalent RSIF parameter is evaluated according to the two presented models. As explained in Section 2.4, the scatter due to the measurements of the dendrites was accounted for by the computed ranges of the possible crystallographic orientations. These, in turn, gave a scatter band for the calculated parameter values, from which one crystallographic orientation corresponds to the mean of the measured angles, and the others correspond to the scatter
Conclusions
From the presented results the following can be concluded:
- 1.
The developed crystallographic crack driving force parameter can successfully predict the active crystallographic cracking plane at the transition from a Mode I crack.
- 2.
The crystallographic orientation of the material with respect to the geometry is of major importance when computing the crystallographic crack driving force parameters.
- 3.
Model 1 and 2 are promising candidates for predicting the crystallographic crack propagation rate and
Acknowledgements
This research has been funded by the Swedish Energy Agency and Siemens Industrial Turbomachinery AB through the Research Consortium of Materials Technology for Thermal Energy Processes, Grant No. KME-702, the support of which is gratefully acknowledged. The authors would also like to thank Dr. Paul Wawrzynek at Fracture Analysis Consultants Inc. for valuable discussions and support and Johanna Simonsson at Siemens Industrial Turbomachinery AB for her laboratory work.
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