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The prediction of crack propagation in coarse grain RR1000 using a unified modelling approach
Abstract
The polycrystalline nickel-base superalloy RR1000 is used as turbine rotor material in Rolls-Royce aero engines and has to withstand a wide variety of load and temperature changes during operation. In order to maximize the potential of the material and to improve component design, it is of great interest to understand, and subsequently be able to accurately model the crack propagation caused by thermo-mechanical fatigue conditions. In this work, experimental data is analysed and used to inform unified modelling approaches in order to predict the crack propagation behaviour of RR1000 under a variety of stress-controlled thermo-mechanical fatigue conditions.
... As the aim of this paper is to quantify the effect of scatter in constitutive parameters to the obtained scatter in the predicted fatigue crack initiation life, the material data and response of the coarse-grained version of the powder-processed γ ′ -strengthened polycrystalline nickelbase superalloy RR1000 has been investigated, see e.g. Engel et al. [30]. The constitutive behaviour and the TMF crack initiation life, using a fatigue damage accumulation model, under a flight representative load cycle of this material has previously been modelled with success, see Leidermark et al. [20]. ...
For critical component application, such as aerospace turbine rotors, it is imperative to be able to make accurate in-service material behaviour and component life predictions for both design and monitoring of component life. The development of such predictive capability is dependent on the quality of the experimental data from which the material parameters are derived. This paper shows the effect that scatter which may be present within experimental data, manifesting itself within the constitutive parameters derived from this data, has on the resulting fatigue crack initiation life of the nickel-based superalloy RR1000. Industrial relevance was added to this investigation by the use of flight representative thermomechanical fatigue loading cycles and state of the art material behaviour and fatigue crack initiation models used within the finite element simulations conducted. The effect of the ‘scatter in’ to the modelling approach on the outcoming predictions is made via a Monte-Carlo analysis. This analysis consisted of running the same simulation several times, but with the experimentally determined and validated ‘baseline’ constitutive parameters varied via correction factors built into the model, for each run via a singular value decomposition procedure. It was found that small ‘scatter in’ has only a very localised ‘scatter out’ effect on the crack initiation predictions under the flight representative loading.
... It has been a long-term ambition to predict the fatigue life of ductile alloys, for which it is the short crack growth that dominates in many cases. Much progress (Barabash et al., 2008;Engel et al., 2020;Ghonem, 2010;Pang and Reed, 2008;Sangid et al., 2011;Texier et al., 2019) has been made on correlating the crack growth (including both growth path and rate) to the detailed microstructure (including morphology, grain size, crystallographic orientation, etc.) near the crack (approximately 1-10 grains surrounding). A particular microstructural quantity, namely the stored energy density which depends upon local GND density (Wan et al., 2014;Xu et al., 2021b), has been found to be a useful mechanistic driver in both fatigue crack nucleation (Chen et al., 2017) and growth (Wilson and Dunne, 2019). ...
A non-local method for the establishment of geometrically necessary dislocation (GND) based on a non-local domain integral has been developed and incorporated into crystal plasticity finite element (CPFE) formulations. The proposed non-local GND method has been validated through a four-point bending case, where the mesh sensitivity of the traditional GND method has been substantially diminished by virtue of the applied non-local domain integral. A comprehensive parametric study has been conducted to investigate the non-local domain effect on the GND calculation. The application of the non-local GND method has resembled the experimental observation of the GND density distribution near a crack tip, and improved the stress field compared to the local method. The improvement on the accuracy of predicting a microstructural driving force at crack tips reveals the necessity of applying the non-local GND method in predicting material fatigue life.
... Currently, a work at the universities is focused on characterisation of tertiary γ́precipitates, their size and distribution variations in all the IP specimens. The main hypothesis is that tertiary γ́size and volume fraction are responsible for difference in the TMF IP crack growth rates, namely smaller size and lesser amount of tertiary γ́precipitates are associated with higher crack growth rates [19]. ...
The current paper presents work on identification and evaluation of a range of factors influencing accuracy and comparability of data generated by three laboratories carrying out stress-controlled thermo-mechanical fatigue crack growth tests. It addresses crack length measurements, heating methods and temperature measurement techniques. It also provides guidance for pre-cracking and use of different specimen geometries as well as Digital Image Correlation imaging for crack monitoring. The majority of the tests have been carried out on a coarse grain polycrystalline nickel-base superalloy using two phase angles, Out-of-Phase and In-Phase cycles with a triangular waveform and a temperature range of 400-750 oC.
The high-temperature deformation behavior and fracture mechanism of Fe–Ni-Cr superalloy under high strain rates from 1 to 100 s⁻¹ were studied by hot tensile experiments at a temperature range of 900–1150 °C. The results manifest that the high strain rate has significant influence on the microstructure evolution and local instability fracture behavior of the superalloy. At high strain rates, the flow behavior of the alloy shows obvious dependence on the strain rate and temperature. With the increase of strain rate, a higher ratio of low-angle and low-energy grain boundaries can be obtained while keeping fine and uniform equiaxed grain microstructure, yet the control window of hot deformation microstructure of the alloy is obviously narrowed. After deforming at temperatures of 950–1000 °C and strain rates of 10–50 s⁻¹, the fine equiaxed grains with average grain size less than 10 μm can be controlled at high deformation rates. Under high strain rates and higher deformation temperature, it has been found that the plastic strain induced by recrystallization nucleation and growth at the original high angle grain boundary (HAGB) of the alloy is not enough to coordinate the rotation of the original grain and the sliding of the original HAGB during deformation, resulting in intergranular cracking. This is the fundamental reason for the abnormal change of thermal deformation power dissipation behavior, higher strain rate sensitivity, flow instability and fracture when the alloy is hot deformed at high strain rates.
The presented methodology in this study is addressed to in-phase (IP) and out-of-phase (OOP) loading cycles in stationary and transient thermo-mechanical fields. The subject of the numerical and experimental study is a single edge notch tension (SENT) specimen produced from a high-temperature nickel-based alloy ХН73М. In order to determination a local thermo-mechanical stress-strain rate and displacement fields a new algorithm for the multi-physics numerical calculations developed and implemented incorporates Maxwell 3D, Fluent and Transient Structural modules of ANSYS 2021R1. The employment of proposed algorithm to represent the cyclic history associated with the TMF conditions in the experiments, multi-physics finite element (FE) modelling of the stress, strain and displacement fields in the SENT specimen was performed. Additionally, time dependent non-uniform temperature fields were determined with the same cyclic variations and magnitudes as in the experimental OOP and IP cycling. As a complement to the FEM computations, the infra-red thermography temperature distribution measurements was implemented for the TMF state in the experiments in the SENT specimen. The comparison multi-physics FE-analysis and direct measurements shown in the present study is intended to contribute to a better understanding of the different mechanisms driving TMF crack growth and the address the outstanding questions associated with basic methodology.
In this article, machine learning is used to predict lifetime under isothermal low-cycle fatigue and thermo-mechanical fatigue loading, both of which represent the most complex loadings that couple creep, fatigue and oxidation damage. A uniaxial fatigue and fatigue-creep dataset, which was obtained for temperatures of between 300∘C and 600∘C for a low-alloy martensitic steel, is utilized in this study. Two different machine learning based approaches to lifetime prediction are demonstrated. The first approach is based only on a shallow neural network, whereas the second approach is proposed as a combination of a sequence learning based model - either long short-term memory network or gated recurrent unit - with the shallow neural network. A good correlation between the experiment and the prediction suggests that lifetime under complex thermo-mechanical loading can be reasonably predicted via the proposed machine learning based damage models.
The current paper describes TMF crack growth behaviour in an advanced nickel-based superalloy. Changes in behaviour are examined which occur as a function of the phase angle between applied stress and temperature. The fractography of the failed specimens reveals changes from transgranular to intergranular growth between high and low phase angle tests as a result of the onset of high temperature damage mechanisms. More targeted testing has also been undertaken to isolate the contributions of these mechanisms, with specific transitions in behaviour becoming clear in 90° diamond cycles, where dynamic crack growth and oxidation strongly interact.
Plasticity-induced, roughness-induced and oxide-induced crack closures are reviewed. Special attention is devoted to the physical origin, the consequences for the experimental determination and the prediction of the effective crack driving force for fatigue crack propagation. Plasticity-induced crack closure under plane stress and plane strain conditions require, in principle, a different explanation; however, both types are predictable. This is even the case in the transition region from the plane strain to the plane stress state and all types of loading conditions including constant and variable amplitude loading, the short crack case or the transition from small-scale to large-scale yielding. In contrast, the prediction of roughness-induced and oxide-induced closures is not as straightforward.
The influence of microstructure on the dwell fatigue crack growth behaviour of an advanced nickel-based superalloy was investigated at a temperature of 700 °C. Microstructural variations were induced by heat treatment variables: different cooling rates of quenching from super-solvus solution heat treatment, 0.7 and 1.8 °C s−1, and an addition of a high temperature stabilisation heat treatment (2 h at 857 °C) between the solution treatment and the final ageing treatment. With a one hour dwell introduced at the peak load of the fatigue cycle, such different microstructural conditions can lead to a difference of up to two orders of magnitude in crack growth rates in air, when compared to those obtained under baseline fatigue loading. By performing such dwell fatigue and baseline fatigue tests in vacuum, it is confirmed that such increases in crack growth rates under dwell fatigue loading in air are mainly environmentally related. Transmission electron microscopy (TEM) was utilised to analyse both crack tip oxides and associated deformation mechanisms in the matrix. A novel mechanism taking into account competing interactions of crack tip oxidation (leading to increases in crack growth rates) and stress relaxation (leading to decreases in crack growth rates) is outlined.
The microstructural evolution of γ′ has been investigated in a series of advanced nickel-base superalloys, produced via the powder metallurgy route. The size, morphology and distribution of γ′ within the microstructure has been found to be highly sensitive to the rate of cooling from the supersolvus solutioning temperature. Precipitate morphologies and the resulting γ′ particle size distributions, were correlated to the various cooling rates, ranging from 6 to 600°C/min. Cooling rates below about 60°C/min resulted in a bimodal distribution of γ′, while rates above 60°C/min were able to suppress the formation of tertiary γ′ and yield a unimodal distribution of γ′ in this set of alloys. Following the supersolvus heat treatment, the effect of ageing these various microstructures at 800°C was assessed. While characteristic precipitate coarsening was observed in microstructures containing a bimodal distribution of γ′, anomalous coarsening to a critical size followed by the splitting of the γ′ precipitates, was observed in specimens initially containing a unimodal distribution of γ′.
This paper summarises Rolls-Royce's efforts in developing a production capable and industrially robust process for the production of dual-microstructure components. This has been possible through the use of process modeling, full-scale validation trials, detailed microstructural assessment through a variety of destructive and non-destructive methods and mechanical property evaluation. This paper reports the fundamental underlying relationships between thermal history and microstructural evolution and how these directly influence mechanical properties. This work has enabled a deeper understanding of the opportunities and difficulties faced in the application of this technique for producing dual microstructures, and how the technique can be scaled up from the research laboratory to full production capacity.
To study the effect of γ′ precipitate size on the deformation behaviour of a polycrystalline nickel-based superalloy, model microstructures with a unimodal γ′ size distribution were developed and subjected to loading experiments at 750 °C. Neutron diffraction measurements were carried out during loading to record the elastic lattice strain response of the γ and γ′ phase. A two-site elasto-plastic self-consistent model (EPSC) assisted in the interpretation of the elastic lattice strain response. In addition, the microstructures of the deformed specimens were analysed by (scanning) transmission electron microscopy (STEM). Excellent agreement was found between the EPSC and STEM results regarding a joint deformation of the γ and γ′ phase in the fine γ′ microstructures and for low plastic strains in the medium γ′ microstructures. With increasing γ′ size and increasing degree of plastic deformation, both experimental methodologies revealed a tendency of the two phases to deform independently.
a b s t r a c t This paper presents the formulation of a phenomenological model to predict the crack growth in single crystal superalloy at high temperature. The proposed model relies on an extensive experimental study performed on AM1 single crystal superalloy at temperatures ranging from 650 °C to 950 °C. Tests carried out in fatigue and creep–fatigue regimes investigate the effects of time on crack growth rates. The crack growth model follows the framework of classical linear elastic fracture mechanics. Time effects at high temperature are captured by creep–fatigue and oxidation–fatigue interactions. The specific model formu-lation for nonisothermal conditions is attractive for identifying parameters on a large temperature domain and for predicting complex Thermo-Mechanical Fatigue (TMF) tests. Model predictions are then compared with a large set of experimental results including TMF tests. The application of this model, which accounts for a better understanding and modeling of physical phenomena such as the environ-mental or creep effects on crack growth rate, should improve the prediction of crack growth regime in single crystal superalloys that are used to design critical components such as turbine blades.
Understanding the relationship between deformation mechanisms and microstructure is essential if one wants to fully exploit the potential of advanced nickel base superalloys and develop future alloys. In the present work, the influence of the lattice misfit between gamma and gamma' has been studied by means of in-situ loading experiments using neutron diffraction in combination with crystal plasticity modelling on RR1000 and Alloy 720Li. Both alloys were processed to generate three simplified uni-modal gamma' microstructures to allow determination of gamma' responses and experiments were carried out at 750 degrees C. The results showed that a positive misfit strain increases the level of load partitioning from gamma to gamma' during plastic deformation introduced by uniaxial tensile loading.
A line integral is exhibited which has the same value for all paths surrounding the tip of a notch in the two-dimensional strain field of an elastic or deformation-type elastic-plastic material. Appropriate integration path choices serve both to relate the integral to the near tip deformations and, in many cases, to permit its direct evaluation. This averaged measure of the near tip field leads to approximate solutions for several strain-concentration problems. Contained perfectly plastic deformation near a crack tip is analyzed for the plane-strain case with the aid of the slip-line theory. Near tip stresses are shown to be significantly elevated by hydrostatic tension, and a strain singularity results varying inversely with distance from the tip in centered fan regions above and below the tip. Approximate estimates are given for the strain intensity, plastic zone size, and crack tip opening displacement, and the important role of large geometry changes in crack blunting is noted. Another application leads to a general solution for crack tip separations in the Barenblatt-Dugdale crack model. A proof follows on the equivalence of the Griffith energy balance and cohesive force theories of elastic brittle fracture, and hardening behavior is included in a model for plane-stress yielding. A final application leads to approximate estimates of strain concentrations at smooth-ended notch tips in elastic and elastic-plastic materials.
The current paper describes TMF crack growth behaviour in an advanced nickel-based superalloy. Changes in behaviour are examined which occur as a function of the phase angle between applied stress and temperature. The fractography of the failed specimens reveals changes from transgranular to intergranular growth between high and low phase angle tests as a result of the onset of high temperature damage mechanisms. More targeted testing has also been undertaken to isolate the contributions of these mechanisms, with specific transitions in behaviour becoming clear in 90° diamond cycles, where dynamic crack growth and oxidation strongly interact.
The threshold in the alternating range of stress intensity factor for fatigue crack growth is investigated for 2024-T3 aluminum. Testing techniques provided displacement control at frequencies up to 1000 Hz. The thresholdis seen to decrease with increasing frequency at a fixed load ratio, dropping by nearly a factor of 2 from 342 to 832 Hz. The threshold is also observed to decrease with increasing load ratio in such a way that is tentatively explained by considerations of crack closure. Some confirmation of this is obtained from direct strain gage measurement of the closure stress intensity, K c , which agrees with that predicted from trends in the threshold data with respect to load ratio.
Single crystal nickel-based alloys are widely used as blade materials in aero-gas-turbines because of their excellent resistance to high temperature deformation. Coatings are applied in order to provide the blades with adequate protection against environmental degradation and loss of mechanical performance. The major cause of failure in current single crystal blades of aero-gas-turbines is thermally induced stresses, which result from thermal strains over the blade thickness caused by temperature gradients during heating and cooling cycles.
In this paper R-ratio effects on fatigue crack growth near threshold region of a metastable austenitic stainless steel (MASS) in two different conditions, i.e. annealed and cold rolled, is investigated. The authors present two approaches to correlate FCGR data for R=0.1, 0.3, 0.5, 0.7 and Kmax = 23MPa√m using a two-parameters approach (ΔK, Kmax and α in Kujawski’s model) and crack closure model (using Elber’s Kop and in Donald’s ACRn2 approaches). The Kop and ACRn2 were experimentally measured on a single edge tension specimens. The Kop measurements were performed using a modified method and based on ASTM standards. While the two driving force approaches correlate data well in the Paris region, they fail to correlate them in the threshold region. However, this correlation can be improved in the threshold region when a different α value from the Paris region is used. The authors indicated that two different mechanisms operate; one in the Paris region and another in the near threshold. Hence, they proposed to combine the two-parameter and crack closure approaches where ΔK is replaced by ΔKeff (estimated by a new method proposed in this paper), which is shown to correlate the FCGR data for different stress ratios for annealed steel. The correlation for cold rolled condition shows improvement with the new approach but is not as good as for the annealed one. The author further suggests to modify Kmax in the two-parameter approach.
The influences of elevated Co and Ti levels on the mechanical properties of the Ni-base superalloy RR1000 have been investigated. Following heat treatment, the modified alloys had the typical γ-γ′ microstructure, with γ′ precipitate sizes comparable to similarly heat treated RR1000, but with a slightly higher volume fraction. The modified alloys exhibited a higher proof stress than RR1000 across the entire 20 to 800°C temperature range investigated. Superior creep rupture lives, when compared to RR1000, were observed in the modified alloys at 700°C, but not at 750°C, where extensive precipitation of topologically close packed σ phase occurred on the grain surfaces. The formation of this deleterious phase was linked to Cr and Mo enrichment of the c matrix, caused by the elevated Co and Ti additions.
The paper deals with the development of a fatigue crack growth model for high temperature complex loading and application to turbine disc conditions. The proposed model is based on an extensive experimental study performed on Astroloy at 650 C, which comprises fatigue with or without hold times, special tests with holds at intermediate loads, fast-slow or slow-fast triangular waves, sequence tests... The crack growth model is built up in the framework of classical Linear Elastic Fracture Mechanics. Its structure is quite simple and is supported by previously developed fatigue crack growth models and a companion study made at Ecole des Mines de Paris (EMP) for the oxidation processes on Astroloy.
Fatigue crack growth in structure components, which is subjected to variable amplitude loading, is a very complex subject. Studying of fatigue crack growth rate and fatigue life calculation under spectrum loading is vital in life prediction of engineering structures at higher reliability. The main aim of this paper is to address how to characterize the load sequence effects in fatigue crack propagation under variable amplitude loading. Thus, a fatigue life under various load spectra, which was predicted, based on the Austen, Forman and NASGRO models. The findings were then compared to the similar results using FASTRAN and AFGROW codes. These models are validated with the literature-based fatigue crack growth test data in 2024-T3 Aluminium alloys under various overload, underload, and spectrum loadings. With the consideration of the load cycle interactions, finally, the results show a good agreement in the behaviour with small differences in fatigue life compare to the test data.
The effects of positive stress ratios on the fatigue crack growth behavior of a forged, mill-annealed Ti-6Al-4V alloy (with a duplex α + β microstructure) are discussed. Differences between fatigue crack growth rates at low and high stress ratios are shown to be due largely to crack closure. A 1% offset procedure is shown to collapse “closure corrected” low stress ratio data with the “closure-free” high stress ratio data. A three parameter multiple regression model is developed for the prediction of the fatigue crack growth rate as a function of stress ratio, crack closure and stress intensify factor range for Ti-6Al-4V. The micromechanisms of fatigue crack growth in the near-threshold and Paris regimes are elucidated via crack tip transmission electron microscopy (TEM) and scanning electron microscopy (SEM). Crack tip TEM shows that Stage II fatigue crack growth in Ti-6Al-4V is crystallographic in nature. Stage II cracks are shown to unzip along intersecting slip bands that are induced as a result of shear localization. The unzipping crack growth mechanism observed in polycrystalline Ti-6Al-4V is shown to be consistent with Neumann's “alternating slip” model for the information of striations in single crystals. © 1997 Acta Metallurgica Inc.
Results of an investigation are presented, which indicate that a fatigue crack, propagating under zero-to-tension loading may be partially or completely closed at zero load. An analysis of the stress distribution acting on the fracture surfaces shows that the local compressive stress maxima may exceed the yield stress of the material. Fractographic evidence is presented to show that crack closure may influence the shape of the striation pattern on the fracture surfaces.RésuméOn présente les résultats d'une recherche indiquant qu'une fissure due à la fatigue, se propageant sous une charge allant de zéro à la tension qui peut être partiellement ou complètement refermée à la charge zéro. Une analyse de la distribution de la tension agissant sur les surfaces de fracture, montre que les maxima de la force locale de compression, peuvent dépasser la tension limite du matériau. La preuve fractographique est présentée dans le but de montrer que la fermeture de la fissure peut influencer la forme du modèle de striation sur les surfaces de fracture.ZusammenfassungEs werden die Ergebnisse einer Untersuchung dargelegt, die daraufhindeuten, dass ein unter Ursprungsbelastung wachsender Ermündungsbruch im unbelasteten Zustand teilweise oder ganz gescholssen sein kann. Eine Analyse der auf der Bruchfläche vorhandenen Spannungsverteilung zeigt, dass die örtlichen Druckspannungshöchstwerte die Fliessgrenze des Werkstoffes übertreffen können. Es wird fraktographisches Beweismaterial geliefert um zu zeigen, dass ein Schliessen des Risses die Form des Markierungsmusters auf den Bruchflächen beeinflussen kann.
A substantial fraction of the mysteries associated with crack extension might be eliminated if the description of fracture experiments could include some reasonable estimate of the stress conditions near the leading edge of a crack particularly at points of onset of rapid fracture and at points of fracture arrest. It is pointed out that for somewhat brittle tensile fractures in situations such that a generalized plane-stress or a plane-strain analysis is appropriate, the influence of the test configuration, loads, and crack length upon the stresses near an end of the crack may be expressed in terms of two parameters. One of these is an adjustable uniform stress parallel to the direction of a crack extension. It is shown that the other parameter, called the stress-intensity factor, is proportional to the square root of the force tending to cause crack extension. Both factors have a clear interpretation and field of usefulness in investigations of brittle-fracture mechanics.
Clad 2024-T3 and 7075-T6 sheet specimens were loaded at three different load amplitudes and three different mean loads. It turned out that the mean stress had an important influence on the crack propagation rate. The crack growth rate in the 7075 specimens was three to four times as large as in the 2024 specimens.
In support of Douglas Aircraft Co. structural damage tolerance analysis, crack propagation rates were measured in humid air from 10−8 to 10−3 mm/cycle of several high strength martensitic steels at stress ratios of R = 0.1 and R = 0.5. Increasing the stress ratio was found to decrease the threshold stress intensity. Increasing the tensile yield material strength in these quench and tempered steels resulted in a nearly linear inverse relationship with the threshold stress intensity. The threshold stress intensity appeared to be independent of the fracture toughness of the alloy steel.
Mechanical behaviour of a nickel-based superalloy, RR1000, has been investigated at 650 °C under cyclic and dwell loading conditions. The microstructural characteristics of the alloy have been studied using scanning electron microscopy (SEM) and transmission electron microscopy (TEM), and the distribution patterns of the dislocations and slip planes have been compared between samples tested under fatigue and creep–fatigue loading conditions. Constitutive behaviour of the alloy was described by a unified constitutive model, where both cyclic plastic and viscoplastic strains were represented by one inelastic strain. The results show that the precipitation state is very stable at 650 °C and only minor differences exist in the dislocation arrangements formed under pure fatigue and combined creep and fatigue conditions. Hence, a unified constitutive model seems to be justified in describing and predicting the constitutive behaviour in both cases.
The concept of oxide-induced crack closure is utilized to explain the role of gaseous and aqueous environments on corrosion
fatigue crack propagationat ultralow, near-threshold growth rates in bainitic and martensitic 2 1/4 Cr-1 Mo pressure vessel steels. It is shown that at low load ratios, near-threshold growth
rates are significantly reduced in moist environments (such as air or water), compared to dry environments (such as hydrogen
or helium gas), due to the formation of excess corrosion deposits on crack faces which enhances crack closure. Using Auger
spectroscopy, it is found that at the threshold stress intensity, ΔKo, below which cracks appear dormant, the maximum thickness of excess oxide debris within the crack is comparable with the
pulsating crack tip opening displacement. The implications of this model to near-threshold fatigue crack growth behavior,
in terms of the role of load ratio, environment, and microstructure are discussed.
Mechanisms for fatigue crack closure under plane strain conditions have recently been identified at very low (near-threshold)
stress intensities in terms of effects of excess corrosion deposits or fracture surface roughness in promoting premature closure
of the crack. In the present paper, a geometric model is presented for crack closure induced by fracture surface roughness.
This model specifically addresses the contribution from both Mode I and Mode II crack tip displacements in addition to considering
the nature of the fracture surface morphology. The implications of this model are briefly discussed in light of the roles
of grain size, yield strength, microstructure, and crack size in influencing near-threshold fatigue behavior in engineering
alloys.
The resulting strengthening by two distinct coexisting dispersions of coherent ordered γ′ (Ni3Al, Ti) precipitates (one coarse and one fine) has been investigated using double-aged polycrystalline Nimonic PE 16. It is shown that, if the two classes of γ′ particles exist as randomly intermixed distributions, then the superposition of their individual yield stress increments Δτ1 and Δτ2 to the measured total yield stress increment Δτ0 can be empirically described by Δτ0α = Δτ1α + Δτ2α For various combinations of strong γ′ particles mixed among (shearable) weak particles the superposition exponent α varies between 1 (linear addition) and 2 (pythagorean addition) depending on the particle's specific obstacle strength. The experimental findings are compatible with earlier computer simulation results and with theoretical suggestions. After prolonged double aging, however, a particle-size-modulated γ′ duplex microstructure develops. It consists of well-defined regions which contain predominantly one class of γ′ precipitations only. For those regionally distributed obstacles, the experimental data exhibit a clear tendency to follow a rule of mixing given by Δτ0 = A1Δτ1 + A2Δτ2 where A1 and A2 are area fractions.
This paper presents some of our recent results from an ongoing collaborative research programme on creep-fatigue behaviour of two advanced nickel base superalloys for turbine disc applications. The role of creep, fatigue and oxidation in crack growth has been investigated at 650°C under typical loading waveforms at selected loading frequencies. Load-line deflections were monitored in selected tests under static and long dwell loading conditions. Scanning electron microscopy was adopted to identify the fracture mode and to facilitate the evaluation of oxidation.The results show that mixed time and cycle dependent crack growth seems to be the predominant crack growth mode in the two PM nickel alloys studied. Whilst limited creep may be present at the crack tip, particularly under static and long dwell loading conditions, oxidation appears to be the predominant mechanism for crack growth under the test conditions examined.
The deformation mechanisms under tensile loading in a 45 vol.% γ′ polycrystalline nickel-base superalloy have been studied using neutron diffraction at 20 °C, 400 °C, 500 °C, 650 °C and 750 °C with the results interpreted via (self-consistent) polycrystal deformation modelling. The data demonstrate that such experiments are suited to detecting changes of the γ′ slip mode from {1 1 1} to {1 0 0} with increasing temperature. Between room temperature and 500 °C there is load transfer from γ′ to γ, indicating that γ′ is the softer phase. At higher temperatures, opposite load transfer is observed indicating that the γ matrix is softer. At 400 °C and 500 °C, an instantaneous yielding increment of about 2% was observed, after an initial strain of 1.5%. This instantaneous straining coincided with zero lattice misfit between γ and γ′ in the axial direction. Predicted and experimental results of the elastic strain response of the two phases and different grain families showed good agreement at elevated temperatures, while only qualitative agreement was found at 20 °C.
The effect of R (minimum load/maximum load) on fatigue crack growth in tests on CrMoV steels at 550°C was investigated under oxidising conditions. Most results were described adequately by linear elastic fracture mechanics using just the tensile loading to calculate stress intensity amplitude ΔK. Crack growth rates in air and under vacuum were decreased by loading at R = 0 compared with tests at R = −1 or R > 0 especially near the threshold ΔK0 · R = −1 tests produced upper bound crack growth rates for any conditions.Crack growth in air was faster than under vacuum except at low amplitudes, so that for tests in air at 10−2 Hz and R = 0 the threshold amplitude was higher than under vacuum. Higher frequencies (e.g. 1 Hz), an inert environment and compressive or raised mean tensile stresses all lowered ΔK0. These effects are interpreted in terms of the cyclic crack tip displacement being reduced by shear lips at the crack surface, and oxide filling.Limited creep ratcheting per cycle in these creep-ductile steels was found not to increase crack growth rates.
The evolution during heat treatment of the as-forged microstructure of the high strength superalloy UDIMET 720Li has been studied. Particular emphasis has been placed on the characterisation of γ′ precipitation kinetics using optical and transmission electron microscopies (TEM) and subsequent image analysis. The observations are interpreted using thermodynamic, phase transformation and precipitate hardening theories. The results have implications for the gas turbine manufacturers. Through a better understanding of the evolution of the microstructure during ageing, a heat treatment of 24 h at 700°C is proposed, which is believed to be optimal. This allows full advantage to be taken of the properties of the alloy, whilst reducing the costs and time associated with the heat treatment schedules. Moreover, the data presented allows the variation in properties across a U720Li forging to be estimated.
An improved theory is proposed for the crack-growth analysis of cyclic-loaded structures. The theory assumes that the crack tip stress-intensity-factor range, ΔK, is the controlling variable for analyzing crack-extension rates. The new theory, however, takes into account the load ratio, R, and the instability when the stress-intensity factor approaches the fracture toughness of the material, Kc . Excellent correlation is found between the theory and extensive experimental data. A computer program has been developed using the new theory to analyze the crack propagation and time to failure for cyclic-loaded structures.
The practice of attempting validation of crack-propagation laws (i.e., the laws of Head, Frost and Dugdale, McEvily and Illg, Liu, and Paris) with a small amount of data, such as a few single specimen test results, is questioned. It is shown that all the laws, though they are mutually contradictory, can be in agreement with the same small sample of data. It is suggested that agreement with a wide selection of data from many specimens and over many orders of magnitudes of crack-extension rates may be necessary to validate crack-propagation laws. For such a wide comparison of data a new simple empirical law is given which fits the broad trend of the data.
The development of a dual microstructure heat treated Ni-base superalloy for turbine disc applications
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International Journal of Fatigue 137 (2020) 105652