Single Crystal Nickel Base Research Articles

Equivalent and simplification of nickel-based single crystal plates with film cooling holes

The mechanical properties of orthotropic material thin-walled plate with close-packed film cooling holes were studied based on the equivalent solid material concept. The equivalent principals of plane stress conditions, plane strain conditions, generalized plane strain conditions and general stress conditions were considered. A simplification method for square and triangular penetration patterns was presented. Extensive numerical simulation results covering different ligament efficiencies, penetration patterns and stress conditions were provided for the directionally solidified superalloy and nickel-based single crystal superalloy to verify the feasibility of equivalent principals and simplification method. Three crystal orientations [001], [011] and [111] of nickel-based single crystal superalloy were analyzed. The stress concentration factors were obtained for the mechanical behavior analysis of cooled blade. The values of equivalent error are all less than 10% when the ligament efficiency is larger than 0.4. The tensile deformation, Mises equivalent stress and stress distribution under the same stress level show the crystal orientation correlation. The tensile deformation of three crystal orientations is: [001] > [011] > [111]. The maximum Mises equivalent stress of [001] orientation and [011] orientation around the film cooling hole are basically the same, and they are all less than [111] orientation. The maximum and minimum values of stress concentration factors are 3.49 and 1.82 respectively.

Effect of Squareness of Initial γ′ Precipitates on Creep-Rupture Life of a Ni-Base Single Crystal Superalloy at 760/982 °C

An approach to determination of squareness of initial γ′ precipitates (S2D) is proposed to evaluate its effect on creep-rupture life (tr) of nickel-base single crystal (SC) superalloys. It is found that the 760/982 °C rupture life varied with the change in regional S2D caused by redistribution of W when 1st-step aging temperature changed in full heat treatment on superalloy DD83 investigated. The longest creep-rupture life occurred at the highest value/the lowest difference in S2D in the interdendritic regions/between the typical dendritic regions in DD83. It is also found that S2D is a weighted function of the area fraction (F2D), spacing (h), and size (d) of γ′ precipitates and is closely related to tr in a series of SC superalloys. In addition, the variation of S2D with F2D (here, thermodynamic mole fraction is approximately expressed by F2D) through lattice misfit (δ) in the SC superalloys with F2D ranging from ~ 60 to 75 pct is well correlated. Therefore, to reveal and to better understand these relationships and correlations may help to optimize the phase variables in order to achieve a long rupture life of SC superalloys. In addition, functions to reveal the interrelationships of F2D, volume fraction (F3D), S2D, and cuboidness (S3D) of initial γ′ precipitates are derived considering their shape changes. All of these are hoped to be helpful in practical applications and in understanding the true meaning of the related variables.

Low cycle fatigue modeling for nickel-based single crystal superalloy

The low cycle fatigue (LCF) characteristics of nickel-based single crystal (SC) superalloy have been experimentally and numerically investigated. The effects of crystallographic orientation, load ratio and stress concentration are studied. In order to model the effect of crystallographic orientation, a new orientation factor, which is relevant to the yield strength, is constructed. On the other hand, a new asymmetrical loading factor is introduced to describe the effect of load ratio. The LCF model for SC superalloy smooth specimen is established with these new damage parameters. The effect of the strain gradient on the LCF life of SC superalloy is further studied, which is applied to the evaluation of the LCF life of SC superalloy notched specimen. The LCF model proposed is validated by the experimental data of SC superalloy DD3 and PWA1480.

Orientation Dependence of Low Cycle Fatigue Properties of a Ni-based Single Crystal Superalloy DD10

Low cycle fatigue (LCF) properties of a nickel-based single crystal (SX) superalloy DD10 with different orientation deviation angles from the [001] axis were investigated at 760 °C with an invariable total strain amplitude of 1.4%. Results reveal that the LCF behaviors of DD10 exhibit a strong orientation-dependence. The fatigue life decreases apparently with the increment of the orientation deviation angle. For specimens with the same orientation deviation angle from the [001] axis, those on the [001]-[011] boundary exhibit a longer fatigue life than ones on the [001]-[ 1 ¯ 11] boundary. It is found that the orientation-dependence of fatigue life stems from the difference of accumulated plastic deformation per cycle. On the other hand, both of total stress amplitude and plastic strain amplitude show a reverse orientation-dependence compared with the fatigue life. However, the orientation deviation shows no influence on the model of fatigue crack initiation and subsequent propagation.

Effect of Secondary Orientation on the Mechanical Behavior of a Unit Cell Model with a Film-cooling Hole in Single Crystal

A 3D unit cell model with a hole has been set up to analyze the stress and strain distribution near the hole of nickel-based single crystal. The emphasis is placed on the influence of secondary orientation on the mechanical behavior of cell model. The crystallographic slip theory was applied to calculate the elasto-plastic deformation. The results show that, the maximum Mises stress and the maximum resolved shear stress are strongly dependent on the secondary orientation. The minimum plastic strain energy density criterion predicts that the optimal orientation of the hole is <100> crystallographic orientation. In addition, the secondary orientation has limited influence on the stress distribution near the hole. But the influence of the secondary orientation on the plastic strain energy density distribution around the hole is obvious.

Experimental and Numerical Modeling of the Stress Rupture Behavior of Nickel-Based Single Crystal Superalloys Subject to Multi-Row Film Cooling Holes

The stress rupture behavior of nickel-base single crystal superalloys is a primary issue facing aero-engine design, which has been studied for more than 40 years. To a large degree, it is the existence of film cooling holes with the introduction of air cooling techniques that adds the extra challenge to the problem. Using both experimental and numerical methods, we explore here the stress rupture behavior of nickel base single crystal plate specimens subject to multi-row film cooling holes. As the numerical simulation part, finite element analysis using Abaqus was performed. Numerical results reveal that the existence of film-holes causes stress concentration and transforms local stress from uniaxial to multi-axial. For the stress distribution of different types of specimens, we defined a stress multiaxiality factor to quantitatively characterize the degree of the stress complexity and examined its effect on the rupture behaviors of the specimens along with the true stress concentration factor. The test was also carried out and results indicated that the creep rupture lives of one- and two-row specimens turn out to be longer than those of non-hole specimen. However, the three- and four-row configuration showed the opposite trend. Among the geometric parameters of film-hole configuration, film-hole row spacing is a predominant one influencing the creep rupture properties. Numerical results agree well with the fracture positions and shapes of specimens.

New polycrystalline MC-reinforced nickel-based superalloys for use at elevated temperatures (T &gt; 1100°C)

In some high temperature applications, there is a constant need of refractory alloys able to resist oxidation by hot gases, hot corrosion by various melts and creep deformation. The best superalloys are currently the g/g’ nickel-based single crystals but they cannot be exposed to 1200°C and more without losing their mechanical resistance. New principles of conventionally cast polycrystalline nickel alloys, combining good resistance against both hot gas oxidation and melts corrosion are explored in this work. Among them, the most promising system involves a reinforcement by HfC carbides. The studied alloy has kept its chromia-forming behaviour which allows good resistance against both oxidation resistance and corrosion by melts. Interesting for a nickel-based alloy containing no g’ precipitates, its creep resistance at 1200°C still remains to be improved to allow using it at so high temperature.

A constitutive equation for the S–N fatigue behavior of metal single crystals and validation by the physical definition of fatigue endurance limit

A phenomenological constitutive equation for the stress–life (S–N) fatigue behavior of metal single crystals is presented and is validated on the basis of physical definition of fatigue endurance limit. The constitutive equation is developed here on the basis of probabilistic arguments for fatigue fracture in cyclic loading. The physical endurance limit for fatigue is taken as the stress amplitude corresponding to the critical resolved shear stress for dislocation slip initiation in ductile single crystals. It is shown that the constitutive equation is surprisingly compact and very flexible to accurately describe a wide range of S–N behaviors, as found in fatigue of nickel-based superalloy single crystals as well as in Fe and Zn single crystals. The S–N constitutive equation is also expanded by the superposition of the mean stress effect and the cyclic effect in fatigue. A remarkable outcome of this is a master S–N fatigue equation that yields S–N curves for any mean stress, on the basis of the S–N parameters for fully reversed fatigue behavior. The application of the presented equations to characterize the S–N behavior of polycrystalline materials is quite promising.

Development of a model for simulation of micro-twin and corresponding asymmetry in high temperature deformation behavior of nickel-based superalloy single crystals using crystal plasticity-based framework

Development of reliable computational models to predict the high temperature deformation behavior of nickel-based superalloys is in the forefront of materials research. These alloys find wide applications in manufacturing of turbine blades and discs of aircraft engines. The microstructure of these alloys consists of the primary γ′-phase, and the secondary and tertiary precipitates (of Ni3Al type) are dispersed as γ′-phases in the gamma matrix. It is computationally expensive to incorporate the explicit finite element model of the γ-γ′ microstructure in a crystal plasticity-based constitutive framework to simulate the response of the polycrystalline microstructure. Existing models in literature do not account for these underlying micro-structural features which are important for simulation of polycrystalline response. The aim of this work is to develop a physically motivated multi-scale approach for simulation of high temperature response of nickel-based superalloys. At the lower length scale, a dislocation density-based crystal plasticity model is developed which simulates the response of various types of microstructures. The microstructures are designed with various shapes and volume fractions of γ′-precipitates. A new model for simulation of the mechanism of anti-phase boundary shearing of the γ′-precipitates, by the matrix dislocations, is developed in this work. The lower scale model is homogenized as a function of various micro-structural parameters, and the homogenized model is used in the next scale of multi-scale simulation. In addition, a new criterion for initiation of micro-twin and a constitutive model for twin strain accumulation are developed. This new micro-twin model along with the homogenized crystal plasticity model has been used to simulate the creep response of a single crystal nickel-based superalloy, and the results have been compared with those of experiment from literature. It was observed that the new model has been able to model the tension–compression asymmetry as observed in single crystal experiments.

Effects of secondary orientation on crack closure behavior of nickel-based single crystal superalloys

The crack closure behavior of a nickel-based single crystal (SC) superalloy was studied based on in-situ SEM fatigue tests. Specimens in two different secondary orientations were tested at 600°C. A model considering the anisotropy of SC superalloys was developed to analyze crack closure behavior. The results show that specimens in two orientations exhibit different cracking modes. For specimen [001]/[010], roughness-induced crack closure effect is dominant in crack closure behavior and crack closure effect is constant during crack propagation process. However, for specimen [001]/[110], plasticity-induced crack closure effect is dominant in crack closure which becomes enhanced as crack grows.

Simulation of Material Stress–Strain Curve and Creep Deformation Response of Nickel Based Superalloys Using Crystal Plasticity Based Finite Element Models

Development of reliable computational models at the micro-scale to understand the material deformation behavior has been gaining worldwide attention. These are increasingly being used in order to design new materials as well as characterize material behavior at different length scales. In this work, a microstructure-sensitive crystal-plasticity-based model has been developed in order to understand the deformation behavior of nickel-based superalloys at different temperature and stress levels. As the microstructure of these alloys consist of primary \( \gamma \) matrix with embedded secondary and tertiary \( \gamma^{\prime} \) precipitates, the stress–strain as well as the creep deformation behavior at different temperatures depend upon the micro-structural features. The mechanical and creep strength of these alloys are sensitive to volume fraction, shape and size of the precipitates and their resistance to the dislocation motion. All these strengthening features has been incorporated into a dislocation density based crystal plasticity model and implemented in a finite element code. The responses of different microstructures have been homogenized as a function of different geometrical features of the precipitates and their distribution in the matrix. The homogenized model has been used to simulate the stress–strain behavior of a nickel-based alloy single crystal at 800 °C as well as the creep strain versus time behavior at 700 °C and 820 MPa of axial stress. The results have been compared with experimental data. It has been concluded that a multi-scale approach is necessary in order to take into account of the micro-structural information in the deformation response of materials and the dislocation-density based model is suitable for such simulations. The model has also been able to simulate the tension–compression asymmetry in the creep-deformation behavior of single crystals as observed in experiments.

Anisotropic Life Prediction for Single Crystal Nickel-Base Flat Plate with a Hole

The material properties of single crystal (SC) superalloys are orientation-dependent. To fully exploit the material capacity, the life modeling needs to consider the anisotropy. In the present study the life modeling of SC nickel-base superalloys is considered by employing the modified Mücker's anisotropic theory in which a Hill type function is utilized for describing the anisotropic failure. Strain-controlled low cycle fatigue (LCF) experiments of SC nickel-base superalloys at different crystallographic orientations (i.e. [00, [01 and [11) under high temperatures (i.e. 760°C) are carried out to verify the modeling availability for the modified Mücker's anisotropic theory. Further, based on the stress-strain field obtained by the anisotropic elastoplastic constitutive model coupled with the finite element method (FEM), the modified Mücker's anisotropic theory is employed to predict the fatigue life for SC flat plate with a hole.

Crystallographic analysis for fatigue small crack growth behaviors of a nickel-based single crystal by in situ SEM observation

Small fatigue crack growth behaviors of a nickel-base single crystal (SX) are studied by in situ observations with scanning electron microscope (SEM). Two different crack propagation modes are identified, i.e., cracks at room temperature and 300°C prefer non-crystallographic propagation mode, while those at a higher temperature of 600°C propagate preferentially along crystallographic slip systems, besides, evident “small crack anomaly” has been partly found. Further computation of crack growth rate reveals that conventional Paris law is found no longer capable of characterizing the crystallographic crack propagation behaviors. Subsequently, with the help of finite element analysis (FEA), the crack tip stress fields are reconstructed and resolved shear stresses in each octahedral slip systems are calculated. It is found that the maximum resolved shear stress intensity parameter, first proposed by Chen and Liu, is able to characterize the growth behaviors of those small cracks.

Microstructure-sensitive creep models for nickel-base superalloy single crystals

Microstructure-sensitive creep models have been developed for Ni-base superalloy single crystals. Creep rupture testing was conducted on fourteen single crystal alloys at two applied stress levels at each of two temperatures, 982 and 1093°C. The variation in creep lives among the different alloys could be explained with regression models containing relatively few microstructural parameters. At 982°C, γ−γ′ lattice mismatch, γ′ volume fraction, and initial γ′ size were statistically significant in explaining the creep rupture lives. At 1093°C, only lattice mismatch and γ′ volume fraction were significant. These models could explain from 84% to 94% of the variation in creep lives, depending on test condition. Longer creep lives were associated with alloys having more negative lattice mismatch, lower γ′ volume fractions, and finer γ′ sizes. The γ−γ′ lattice mismatch exhibited the strongest influence of all the microstructural parameters at both temperatures. Although a majority of the alloys in this study were stable with respect to topologically close packed (TCP) phases, it appeared that up to ∼2vol% TCP phase did not affect the 1093°C creep lives under applied stresses that produced lives of ∼200–300h. In contrast, TCP phase contents of ∼2vol% were detrimental at lower applied stresses where creep lives were longer.

Yield Criterion and Crack Tip Plastic Zone of Nickel-Based Single Crystal

A modified Hill yield criterion considering tension-shear stress coupling was given and material parameters of nickel-based single crystal in this criterion was determined by the Least Square Method. Crack tip plastic zones of nickel-based single crystal plate were analyzed by using this modified yield criterion and the plastic zones corresponding to mixed mode I, II crack, were derived. The crack tip plastic zones of nickel-based single crystal were compared to that of isotropic material. The influences of tension-shear stress coupling, compound ratio of mixed mode I, II crack and temperature on crack tip plastic zones were discussed. The results obtained in this paper indicate that the increasing rate of crack tip plastic zones with compound ratio in the plane stress condition is greater than that in the plane strain condition for nickel-based single crystal and the temperature has greater influence on the size of crack tip plastic zones.

Influence of composition on microstructural parameters of single crystal nickel-base superalloys

Abstract Fourteen nickel-base superalloy single crystals containing a range of chromium (Cr), cobalt (Co), molybdenum (Mo), and rhenium (Re) levels, and fixed amounts of aluminum (Al) and tantalum (Ta), were examined to determine the effect of bulk composition on basic microstructural parameters, including γ′ solvus, γ′ volume fraction, topologically close-packed (TCP) phases, γ and γ′ phase chemistries, and γ–γ′ lattice mismatch. Regression models describing the influence of bulk alloy composition on each of the microstructural parameters were developed and compared to predictions by a commercially-available software tool that used computational thermodynamics. Co produced the largest change in γ′ solvus over the wide compositional range explored and Mo produced the biggest effect on the γ lattice parameter over its range, although Re had a very potent influence on all microstructural parameters investigated. Changing the Cr, Co, Mo, and Re contents in the bulk alloy had an impact on their concentrations in the γ matrix and to a smaller extent in the γ′ phase. The software tool under-predicted γ′ solvus temperatures and γ′ volume fractions, and over-predicted TCP phase volume fractions at 982 °C. However, the statistical regression models provided excellent estimations of the microstructural parameters and demonstrated the usefulness of such formulas.

High-temperature creep and the defect structure of nickel-based superalloy single crystals after hot isostatic pressing

The influence of hot isostatic pressing on the high-temperature creep of single crystals of a nickel-based superalloy containing rhenium and ruthenium is studied. The microstructural damages caused by the development of creep have been studied. Hot isostatic pressing is found to weakly influence the life and creep of the superalloy at 1150°C. The distribution of deformation pores over the length and cross section of failed samples has been studied. A high pore concentration is shown to exist at the sites of severe plastic deformation.

Fluid Flow and Defect Formation in the Three-Dimensional Dendritic Structure of Nickel-Based Single Crystals

Fluid flow within the dendritic structure at the solid–liquid interface in nickel-based superalloys has been studied in two directionally solidified alloy systems. Millimeter-scale, three-dimensional (3D) datasets of dendritic structure have been collected by serial sectioning, and the reconstructed mushy zones have been used as domains for fluid-flow modeling. Flow permeability and the influence of dendritic structure on flow patterns have been investigated. Permeability analyses indicate that the cross flow normal to the withdrawal direction limits the development of flow instabilities. Local Rayleigh numbers calculated using the permeabilities extracted from the 3D dataset are higher than predicted by conventional empirical calculations in the regions of the mushy zone that are prone to the onset of convective instabilities. The ability to measure dendrite surface area in 3D volumes permit improved prediction of permeability as well.

In situ synchrotron X-ray imaging of high-cycle fatigue crack propagation in single-crystal nickel-base alloys

Fatigue crack propagation in single-crystal nickel-base superalloys was studied in situ with synchrotron X-ray imaging in a very high-cycle regime. Experiments were performed at ambient temperature with a newly developed portable ultrasonic fatigue instrument. The fatigue apparatus produced stable fatigue crack propagation with positive mean stresses for specimens as thin as 150 μm at a loading frequency of 20 kHz. Fatigue cracks propagated in a mixed-mode crystallographic manner along {1 1 1} slip planes. Phase-contrast imaging permitted analysis of the interaction of the crack front with microstructural features. Three-dimensional linear elastic finite-element analyses were performed to investigate the driving forces for crack propagation in the sheet specimen geometry. For the experimental conditions examined, fatigue crack growth is driven by the resolved shear and normal stresses on the active crack tip slip systems. An octahedral stress intensity is proposed as the relevant driving force for crack growth which determines the fatigue crack growth plane in nickel-base single crystals at room temperature.

Oxide‐Assisted Degradation of Ni‐Base Single Crystals During Cyclic Loading: the Role of Coatings

The role of oxidation‐induced layers in the failure process of aluminide‐coated nickel base single crystals subject to high‐temperature fatigue cycling has been investigated experimentally and via finite element analysis. Isothermal strain‐controlled compressive fatigue experiments (R=−∞) with 120 s holds in compression were conducted at 982° and 1093°C. Surface‐initiated cracks containing a layer of alumina progressively grew through the coating layers into the superalloy substrate, ultimately causing failure. Growth stresses in the oxide provided a driving force for extension of the oxide into the softer coating and substrate layers. Finite element modeling shows the rate of growth of the oxide‐filled cracks is sensitive to the strength of the constituent layers and the magnitude of the oxide growth strains. Implications for design of failure‐resistant coating–substrate systems are discussed.