Lattice strain evolution during creep in single-crystal superalloys

In situ neutron diffraction studies are carried out to characterize the micromechanical deformation occurring during tensile creep of a typical single-crystal nickel-based superalloy, CMSX-4. The loading responses of the matrix γ phase and the precipitate γ′ are distinct. Moreover, the behaviour in the tertiary creep regime (in which the γ′ phase remains intact) is qualitatively different from that in the primary creep regime (when γ′ is sheared). In tertiary creep, initial deformation of the matrix leads to a release of misfit between the phases in the (1 0 0), resulting in elastic compression of the γ in the loading direction. The load state then remains fairly constant during creep. During the initial stages of primary creep, elastic compression of the γ phase is observed until at around 2–4% creep strain this compression stabilizes as the (1 0 0) misfit is released. This is the point at which γ′ shearing is thought to begin. Subsequently, the load in the γ increases by around 200 MPa until a maximum is reached at around 8% creep strain. This load is then suddenly released, which may be due to the release of back-stress.     

Development of γ phase stacking faults during high temperature creep of Ru-containing single crystal superalloys

An unusual deformation mode involving the formation of intrinsic stacking faults in the γ matrix of experimental Ru-containing γ–γ′ superalloys with high Co and Re contents during high temperature creep at 950 °C/290 MPa has been observed. The morphology, distribution and dependence of these stacking faults on alloy chemistry has been investigated along with their formation mechanism. Additions of Re and Co substantially decrease the stacking fault energy of the γ matrix. The observed stacking faults in the γ matrix form by the dissociation of a/2〈1 1 0〉 matrix dislocations with Burgers vectors perpendicular to the loading direction in the early stages of creep. The dependence of creep properties on elemental additions that influence stacking fault energy is discussed.     

High-temperature and low-stress creep anisotropy of single-crystal superalloys

The high-temperature and low-stress creep (1293 K, 160 MPa) of the single-crystal Ni-based superalloy LEK 94 is investigated, comparing the tensile creep behavior of miniature creep specimens in [0 0 1] and [1 1 0] directions. In the early stages of creep, the [0 0 1]-direction loading shows higher minimum creep rates, because a greater number of microscopic crystallographic slip systems are activated, the dislocation networks at γ/γ′ interfaces accommodate lattice misfit better, and γ channels are wider. After the creep rate minimum, creep rates increase more strongly as a function of strain for [1 1 0] tensile loading. This may be related to the nature of rafting during [1 1 0] tensile creep, which results in a more open topology of the γ channels. It may also be related to more frequent γ′ cutting events compared with [1 0 0] tensile creep.     

Microstructures of Rene 142 nickel-based superalloy fabricated by electron beam melting

Rene 142, a commercial, columnar grained, gas turbine airfoil Ni-based superalloy, has been fabricated from a pre-alloyed, atomized powder by additive manufacturing using electron beam melting. Monolithic components having [0 0 1] oriented, columnar grain structures exhibited a creep-optimized 59% volume fraction of cuboidal, coherent, γ′-phase precipitates averaging 275 nm on the side, and with γ/γ′ channel widths ranging from 25 to 75 nm. Transmission electron microscopy, utilizing bright and dark field imaging of optimally oriented γ/γ′ interfaces showed prominent misfit coherency strains as δ-fringe patterns. Corresponding hardness measurements also indicated the possibility of creep strength comparable with the commercial alloy. The notable feature of this study was the monolithic development of desirable superalloy properties without conventional, multi-step heat treatments.     

CRSS of γ/γ′ phases from in situ neutron diffraction of a directionally solidified superalloy tension tested at 900 °C

Neutron diffraction was used to monitor elastic strains during in situ tension testing of a directionally solidified (DS) superalloy at 900 °C. Changes in misfit and thermal expansion coefficients of individual phases were obtained. In the γ phase, it is demonstrated that elastic strains saturate at 350 MPa, which is well below the yield strength of the alloy. This is interpreted as the onset of dislocation glide through less stressed vertical channels. The critical resolved shear stress (CRSS) of γ is found to be 143 ± 11 MPa, in agreement with a calculated CRSS that is dominated by Orowan bowing of dislocations through nanoscale-wide γ channels. This provides confirmation of Orowan bowing in plasticity/creep of the γ phase. Implications of CRSS and misfit in a “threshold stress” for creep and rafting are discussed. The CRSS of γ′ is found to be consistent with pairwise penetration of dislocations into γ′.     

Evolution of multivariant microstructures with anisotropic misfit: A phase field study

We study, in two dimensions, the effect of misfit anisotropy on microstructural evolution during precipitation of an ordered β phase from a disordered α matrix; these phases have, respectively, 2- and 6-fold rotation symmetries. Thus, precipitation produces three orientational variants of β phase particles, and they have an anisotropic (and crystallographically equivalent) misfit strain with the matrix. The anisotropy in misfit is characterized using a parameter t = ?_yy/?_xx, where ?_xx and ?_yy are the principal components of the misfit strain tensor. Our phase field simulations show that the morphology of β phase particles is significantly influenced by t, the level of misfit anisotropy. Particles are circular in systems with dilatational misfit (t = 1), elongated along the direction of lower principal misfit when 0 < t < 1 and elongated along the invariant direction when ?1 ? t ? 0. In the special case of a pure shear misfit strain (t = ?1), the microstructure exhibits star, wedge and checkerboard patterns; these microstructural features are in agreement with those in Ti–Al–Nb alloys.     

Creep deformation of fully lamellar TiAl controlled by the viscous glide of interfacial dislocations

Creep mechanisms of fully lamellar TiAl with a refined microstructure (γ lamellae: 100–300 nm thick, α₂ lamellae: 10–50 nm thick) have been investigated. A nearly linear creep behavior (i.e. the steady-state creep rate is nearly proportional to the applied stress) was observed when the alloy was creep deformed at low applied stresses (<400 MPa) and intermediate temperatures (650–810°C). Since the operation and multiplication of lattice dislocations within both γ and α₂ lamellae are very limited in a low stress level as a result of the refined lamellar microstructure, creep mechanisms based upon glide and/or climb of lattice dislocations become insignificant. Instead, the motion of interfacial dislocation arrays on γ/α₂ and γ/γ interfaces (i.e. interface sliding) has found to be a predominant deformation mechanism. According to the observed interfacial substructure caused by interface sliding and the measured activation energy for creep, it is proposed that creep deformation of the refined lamellar TiAl in the intermediate-temperature and low-stress regime is primarily controlled by the viscous glide of interfacial dislocations.     

Creep behaviour of a new air-hardenable intermetallic Ti–46Al–8Ta alloy

Creep behaviour of a new cast air-hardenable intermetallic Ti–46Al–8Ta (at.%) alloy was investigated. Constant load tensile creep tests were performed at initial applied stresses ranging from 200 to 400 MPa in the temperature range from 973 to 1073 K. The minimum creep rate is found to depend strongly on the applied stress and temperature. The power law stress exponent of the minimum creep rate is n = 5.8 and the apparent activation energy for creep is calculated to be Q_a = (382.9 ± 14.5) kJ/mol. The kinetics of creep deformation of the specimens tested to a minimum creep rate (creep deformation about 2%) is suggested to be controlled by non-conservative motion of dislocations in the γ(TiAl) matrix. Besides dislocation mechanisms, deformation twinning contributes significantly to overall measured strains in the specimens tested to fracture. The initial γ(TiAl) + α₂(Ti₃Al) microstructure of the creep specimens is unstable and transforms to the γ + α₂ + τ type during creep. The particles of the τ phase are preferentially formed along the grain and lamellar colony boundaries.     

Phase chemistry of the superalloy SC16 after creep deformation

The local chemical concentrations of the elements in the nickel-based single crystal superalloy SC16 were examined by atom probe field ion microscopy (APFIM) after standard heat treatment and after creep strain of 1.35% at 1223 K. The measurements were carried out along the [001] direction parallel to the applied creep stress. An enrichment of Al and a slight depletion of Ti in the γ′ precipitate near the γ′/γ interface were observed in both states, the as-prepared and the creep-deformed. The average chemical composition of the γ′ precipitates had hardly been changed during the creep deformation. However, the average Cr content decreased in γ channels perpendicular to the applied stress significantly. Its enrichment was detected near the interface. Contrary to Cr, the average Ni concentration increased in these γ channels and depleted near the interface. Both Ti and Ta seem to be depleted in γ channels near the interface after creep deformation. According to the results, the long range diffusion for directional coarsening of γ′ precipitates is suggested to take place mainly in γ channels.     

Phenomenological modeling of the effect of specimen thickness on the creep response of Ni-based superalloy single crystals

Isothermal creep tests on single-crystal Ni-based superalloy sheet specimens show a thickness-dependent creep response that is known as the thickness debit effect. A size-dependent creep response at similar length scales has also been observed in a wide variety of other materials. We focus on Ni-based single-crystal superalloys and present a phenomenological nonlinear parallel spring model for uniaxial creep with springs representing the bulk and possible surface damage layers. The nonlinear spring constitutive relations model both material creep and evolving damage. The number of springs and the spring creep and damage parameters are based, as much as possible, on recent experimental observations of the thickness debit effect under two creep test conditions: a low-temperature, high-stress condition, 760 °C/758 MPa, and a high-temperature, low-stress condition, 982 °C/248 MPa. The bulk damage mechanisms accounted for are the nucleation of cleavage-like cracks from pre-existing voids and, at the higher temperature, void nucleation. The surface damage mechanisms modeled at the higher temperature are an oxidation layer, a γ′-precipitate-free layer and a γ′-precipitate-reduced layer. Model results for the creep response and for the thickness debit effect are in close quantitative agreement with the experimental results. In addition, the model predicts qualitative features of the failure process that are in good agreement with experimental observations. The simplicity of the model also allows parameter studies to be undertaken to explore the relative roles of bulk and surface damage as well as the relative roles of cleavage-like cracking and void nucleation in the bulk.     

Tensile creep of directionally solidified NiAl–9Mo in situ composites

Well-aligned Mo fiber-reinforced NiAl in situ composites were produced by specially controlled directional solidification. The creep behavior parallel to the growth direction was studied in static tensile tests at temperatures between 900 °C and 1200 °C. A steady-state creep rate of 10^?6 s^?1 was measured at 1100 °C under an initial applied tensile stress of 150 MPa. Compared to binary NiAl and previously investigated NiAl–Mo eutectics with irregularly oriented Mo fibers, this value demonstrates a remarkably improved creep resistance in NiAl–Mo with well-aligned unidirectional Mo fibers. A high-resolution transmission electron microscope investigation of the NiAl/Mo interface revealed a clean semi-coherent boundary between NiAl and Mo, which enabled an effective load transfer from the NiAl matrix to the Mo fibers, and thus leads to the remarkably increased creep strength. The stress exponent, n, was found to be between 3.5 and 5, dependent on temperature. The activation energy for creep, Q_c, was measured to be 291 ± 19 kJ mol^–1, which is close to the value for self-diffusion in binary NiAl. Transmission electron microscopy observations substantiated that creep occurred by dislocation climb in the NiAl matrix. The Mo fiber was found to behave in a quasi-rigid manner during creep. A creep model for fiber-reinforced metal matrix composites was applied for an in-depth understanding of the mechanical behavior of the individual components and their contribution to the creep strength of the composite.     

Effects of rhenium addition on the temporal evolution of the nanostructure and chemistry of a model Ni–Cr–Al superalloy. II: Analysis of the coarsening behavior

The temporal evolution of the nanostructure and chemistry of a model Ni–8.5 at.% Cr–10 at.% Al alloy with the addition of 2 at.% Re was studied using transmission electron microscopy and atom-probe tomography in order to measure the number density and mean radius of the γ′ (L1₂) precipitates and the chemistry of the γ′-precipitates and the γ (fcc)-matrix. In this article, the coarsening behavior of the γ′-precipitates is discussed in detail and compared with the Umantsev–Olson model for multi-component alloys. In addition, the experimental results are evaluated with PrecipiCalc™ simulations. The results show that the diffusivities of the solute elements play a major role in the coarsening behavior of the γ′-precipitates and that the addition of Re retards the coarsening kinetics and stabilizes the spheroidal morphology of the precipitates by reducing the interfacial energy.     

Nondestructive evaluation of creep and fatigue damages in nickel-base superalloys using a scanning blue laser microscope

A new nondestructive evaluation method for detecting both creep and fatigue damages of Ni-base superalloy used in advanced gas turbine systems has been proposed by applying a scanning blue laser microscope. The change of the microtexture in a grain of the alloy due to creep and fatigue damages can be observed clearly by using this microscope. The reflectance of the γ′ (Ni₃Al) phase of the alloy was found to be less than that of the γ (Ni-base alloy) phase, when a laser beam of wavelength shorter than 500 nm was radiated to the alloy. Since the microtexture of the alloy varies significantly during damage progress, it is possible to evaluate the damages quantitatively and nondestructively by observing the change of the microtexture using the laser beam with wavelength 410 nm.     

Modelling and analysis of the oxidation influence on creep behaviour of thin-walled structures of the single-crystal nickel-base superalloy René N5 at 980 °C

Creep test results of thin-walled specimens of the single-crystal nickel-base superalloy René N5 at 980 °C under vacuum as well as under air show different creep properties depending on material thickness and atmosphere. The differences in creep strength and strain were analysed based on a creep-oxidation model. The model specifies the primary and secondary creep stages of thin-walled specimens by a sequence of layers. The model takes different zones affected by oxidation into account. Four layers were experimentally observed and considered in the model: oxide layer, γ′-free layer, γ′-reduced layer and the two-phase substrate in the sample as centre. Material parameters for growth laws of each layer were identified both by experimental analyses and by thermodynamic simulations. The final creep-oxidation model characterizes the creep behaviour of samples with small thicknesses and low initial stress with high accuracy.     

Effects of rhenium addition on the temporal evolution of the nanostructure and chemistry of a model Ni–Cr–Al superalloy. I: Experimental observations

The temporal evolution of the nanostructure and chemistry of a model Ni–8.5 at.% Cr–10 at.% Al alloy, with the addition of 2 at.% Re, aged at 1073 K from 0.25 to 264 h, was studied. Transmission electron microscopy and atom-probe tomography were used to measure the number density and mean radius of the γ′ (L1₂ structure)-precipitates and the chemistry of the γ′-precipitates and the γ (face-centered cubic)-matrix, including the partitioning behavior of all alloying elements between the γ- and γ′-phases and the segregation behavior at γ/γ′ interfaces. The precipitates remained spheroidal for an aging time of up to 264 h and, unlike commercial nickel-based superalloys containing Re, there was not confined (nonmonotonic) Re segregation at the γ/γ′ interfaces.     

Kinetics of austenitization under uniaxial compressive stress in Fe–2.96 at.% Ni alloy

Differential dilatometry has been employed to study the kinetics of the massive ferrite (α) → austenite (γ) transformation upon isochronal heating (i.e. austenitization) of the substitutional Fe–2.96 at.% Ni alloy subjected to a range of applied constant uniaxial compressive stresses. A phase-transformation model, involving site saturation, interface-controlled (continuous) growth and incorporating an impingement correction for an intermediate of the cases of ideally periodically and of ideally randomly dispersed growing particles, has been employed to extract the interface-migration velocity of the α/γ interface and the transformation-induced deformation energy taken up by the specimen. The value obtained for the energy corresponding with the elastic and plastic deformation associated with the accommodation of the α/γ volume misfit depends on the austenite fraction and increases distinctly with an increase in the applied uniaxial compressive stress, which is compensated by, in particular, an increase in the chemical driving force corresponding to an increase in the onset temperature. The opposite effects of an applied uniaxial compressive stress on the α → γ transformation and on the γ → α transformation can be discussed as the outcome of constrained plastic deformation due to transformation-induced strain.     

Creep mechanisms in Ti–3Al–2.5V alloy tubing deformed under closed-end internal gas pressurization

Creep tests were carried out on Ti–3Al–2.5V alloy tubing in the temperature range of 723–873 K under closed-end internal pressurization. The data thus obtained were analyzed to obtain the mechanistic creep parameters (stress exponent and activation energy). Transitions in creep mechanisms were noted as the stress exponent varied from a lower value of 1 through 2 to a higher value of 5 with increasing stress where the activation energy assumed values of 232 and 325 kJ mol⁻¹, respectively. The creep mechanisms were elucidated in the light of standard creep models supported by the substructures studied by transmission electron microscopy. Newtonian viscous creep (n = 1) at lower stresses was identified to be in accordance with a slip band model named after Spingarn and Nix. Grain boundary sliding with n = 2 was noted in an intermediate stress region while climb of edge dislocations was observed to control creep at higher stresses. Microstructural observations along with parametric variations of creep rates were useful in identifying the underlying deformation mechanisms.     

Coarsening of a multimodal nickel-base superalloy

The coarsening of γ′-Ni₃Al precipitates in the nickel superalloy Ni115 has been examined and compared to the results of a numerical model based on LSW coarsening theory. Ni115 has a γ′ fraction of around 60%, and at the coarsening temperatures of interest the γ′ distribution is bimodal, with two populations ～5 nm and ～90 nm in radius. It is found that during the initial transient (around 2000 h at 800 °C), the fine γ′ dissolve, leading to a rapid increase in the mean radius followed by a plateau. At long times, the expected steady-state unimodal t^1/3 coarsening is observed. The model reproduces these features in form and approximately in magnitude, a first for LSW model-experiment comparisons in nickel superalloys.     

Tensile creep of Mo–Si–B alloys

Multiphase Mo–Si–B alloys containing a Mo solid solution matrix and brittle Mo₃Si and Mo₅SiB₂ (T2) intermetallic phases are candidates for ultra-high-temperature applications_. The elevated temperature uniaxial tensile response at a nominal strain rate of 10^?4 s^–1 and the tensile creep response at constant load between 1000 °C and 1300 °C of a (i) single phase solid solution (Mo–3.0Si–1.3B in at.%), (ii) two-phase alloy containing ～35 vol.% T2 phase (Mo–6Si–8B in at.%) and (iii) three-phase alloy with ～50 vol.% T2 + Mo₃Si phases (Mo–8.6Si–8.7B in at.%) were evaluated. The results confirm that Si in solid solution significantly enhances both the yield strength and the creep resistance of these materials. A Larson–Miller plot of the creep data showed improved creep resistance of the two- and three-phase alloys in comparison with Ni-based superalloys. The extent of Si dissolved in the solid solution phase varied in these three alloys and Si appeared to segregate to dislocations and grain boundaries. A stress exponent of ～5 for the solid solution alloy and ～7 at 1200 °C for the two multiphase alloys suggested dislocation climb to be the controlling mechanism. Grain boundary precipitation of the T2 phase during creep deformation was observed and the precipitation kinetics appear to be affected by the test temperature and applied stress.     

Misfit strain–film thickness phase diagrams and related electromechanical properties of epitaxial ultra-thin lead zirconate titanate films

The phase stability of ultra-thin (0 0 1) oriented ferroelectric PbZr_1–xTi_xO₃ (PZT) epitaxial thin films as a function of the film composition, film thickness, and the misfit strain is analyzed using a non-linear Landau–Ginzburg–Devonshire thermodynamic model taking into account the electrical and mechanical boundary conditions. The theoretical formalism incorporates the role of the depolarization field as well as the possibility of the relaxation of in-plane strains via the formation of microstructural features such as misfit dislocations at the growth temperature and ferroelastic polydomain patterns below the paraelectric–ferroelectric phase transformation temperature. Film thickness–misfit strain phase diagrams are developed for PZT films with four different compositions (x = 1, 0.9, 0.8 and 0.7) as a function of the film thickness. The results show that the so-called rotational r-phase appears in a very narrow range of misfit strain and thickness of the film. Furthermore, the in-plane and out-of-plane dielectric permittivities ε₁₁ and ε₃₃, as well as the out-of-plane piezoelectric coefficients d₃₃ for the PZT thin films, are computed as a function of misfit strain, taking into account substrate-induced clamping. The model reveals that previously predicted ultrahigh piezoelectric coefficients due to misfit-strain-induced phase transitions are practically achievable only in an extremely narrow range of film thickness, composition and misfit strain parameter space. We also show that the dielectric and piezoelectric properties of epitaxial ferroelectric films can be tailored through strain engineering and microstructural optimization.