Dislocation motion in the early stages of high-temperature low-stress creep in a single-crystal superalloy with a small lattice misfit

Dislocation configurations at different creep stages (1100 °C and 137 MPa) in a superalloy TMS-75(+Ru) were studied in transmission electron microscopy (TEM) and the movement path of these creep-produced dislocations could be fully illustrated. Due to the small value of γ/γ′ lattice misfit, these dislocations cannot glide in the horizontal γ matrix channels by cross slip, but they mainly move by climbing around the γ′ cuboids. In the primary stage, the dislocations first move by slip in the γ-matrix channels. When they reach the γ′ cuboids, they move by climbing along the γ′ cuboid surfaces. In the secondary creep stage, dislocation reorientation in the (001) interfacial planes happens slowly, away from the deposition orientation of 〈110〉 to the misfit orientation of 〈100〉. The velocity of the reorientation is lower and a perfect γ/γ′ interfacial dislocation network cannot be formed quickly. This factor results in a large creep rate of the alloy during the secondary creep stage. The path for dislocation motion during the early creep stages consists of the following sequences: (i) climbing along the γ′ cuboid surface, (ii) deposition onto the (001) γ/γ′ interfacial plane, and (iii) reorientation from the 〈110〉 direction to the 〈100〉 direction.     

Rotary bending high-cycle fatigue behavior of DD32 single crystal superalloy containing rhenium

Smooth and notched specimens of single crystal superalloy DD32 were subjected to rotary bending high-cycle fatigue (HCF) loading at different temperatures. The experimental results demonstrate that fatigue strengths of the smooth and notched specimens reach the maxima and the minimum notch sensitivity displays at 760 °C. DD32 alloy exhibits excellent HCF properties compared to SRR99 alloy under the same test condition. As for the smooth specimens, slip bands moving through γ and γ′ phases as well as dislocation bowing are the main deformation modes. As for the notched specimens, the deformations are carried out by dislocation loop bowing and shearing of PSBs mode at intermediate temperatures; at 900 °C, the minimum fatigue strength results from dislocation climbing deformation and the degradation of γ′ precipitates. The fine secondary γ′ precipitates advantage the recovery of dislocations and further deformation of the fatigue specimens.     

Dislocation configurations and internal stresses in the creep of Nimonic 91

The internal stress, σ_i, developed during the creep of Nimonic 91 was determined as a function of applied stress, σ_a, using the strain transient dip technique. Transmission electron microscope observations of thin films of crept specimens showed Orowan dislocation loops to exist aroundγ′ phase particles at low stresses with partial dislocation loops around faultedγ′ particles at high stresses. The numbers of loops per specimen volume were counted and the resulting internal stress calculated. The results indicate that a significant part of the mechanically measured internal stress can be attributed to Orowan loops aroundγ′ particles which are stabilized against climb by the superlattice fault resulting from partial penetration of theγ′ particle by the dislocation. The variation of internal stress with applied stress can be accounted for qualitatively by the variation of loop density with stress at low stresses and the initiation of relaxation processes involving partial or complete shearing ofγ′ particles by loops at high stresses. It is suggested that creep in Nimonic 91 is dependent on the magnitude of the effective (σ_a-σ_i) and that the internal stress is determined largely by the density of dislocation loops aroundγ′ particles.     

Microstructures in Al-richγ-TiAl strained in the domain of temperature of flow stress anomalies

The plastic behaviour of single-phaseγ-TiAl poses a certain number of fundamental problems as to the origin of the flow stress anomaly and to how this is related to dislocation properties. Understanding these questions is of significant interest in the investigations of flow stress anomalies in intermetallics and in other materials. Also, it may reveal useful in the study of theγ-based lamellar alloys. The present contribution accounts for an investigation of mechanical properties and microstructural organization conducted in Al-richγ-TiAl single crystals oriented to activate single slip. Three separate topics are addressed.

The concept of directional binding energy and analysis of the phenomena involving surface and grain boundary: Part I Theory

The concept of directional binding energy (DBE) is proposed to describe the binding energy of the crystal and the ideal direction of the antiaction force against the surface tension, which derives the grain-boundary energy and also energy ratio (γ_gb/γ_s). It may provide a simple and lucid way to analyse the surface energy, grain-boundary energy and energy ratio from the correlative view point. It has been found that the grain-boundary energy can be derived only from the conceptual approach of DBE, irrespective of the dislocation model, which also makes it possible to determine the energy ratio with the misorientation angle. That is, the energy ratio (γ_gb/γ_s) is proportional to the misorientation angle, 2 sin (k′θ/2) where k′ is a constant and θ is the misorientation angle. This revised version was published online in November 2006 with corrections to the Cover Date.     

A simple application of the Bailey-Orowan creep model to Fe-39.8 at % AI and γ/γ′-α

A method which allows calculation of recovery rates and work hardening coefficients for creep from simple constant velocity compression experiments is described. Stressing rates and straining rates are computed from the measured load-time curves, and these quantities are then fitted to the universal form of the Bailey-Orowan equation for creep. The techniques were applied to B2 crystal structure Fe-39.8 at % Al intermetallics and the directionally solidified eutectic alloyγ/γ′-α compression tested between 1200 and 1400 K. The recovery rates were found to be functions of nominal strain rate, stress, and temperature; the hardening coefficients were dependent only on temperature. Hardening coefficients for the aluminides are small (<0.002 of the elastic modulus) and are believed to be due to the lack of dislocation barriers. A more typical value for the hardening coefficient (∼ 0.05 of the elastic modulus) was observed inγ/γ′-α. Recovery rates and hardening coefficients can be described in terms of stress and temperature, and the equations used to estimate creep rates.     

Electronic Damping of Dislocations and Kinetic Phenomena in Superconductors Under Plastic Deformation

Interaction of a moving screw dislocation with conduction electrons is considered in the conventional pure superconductors. At temperaturesT≪T _c , both “slow” dislocations are considered, which interact only with thermally excited quasiparticles, and “fast” dislocations which also break the Cooper pairs. Near the critical temperature, two limiting cases are considered depending on the relation between Meissner penetration depth and anomalous skin-layer depth for the dislocation-induced electromagnetic field. Power dissipation dependence on temperature and dislocation velocity is obtained. Due to low field intensity in the short-wave part of spectrum, the superconducting state is shown not to be destructed by a moving dislocation in a broad range of temperatures. Non-equilibrium states of electronic system created by the dislocation field are analyzed in the paper. With this purpose, Eliashberg’s kinetic equation for a multi-mode excitation source is used. Dislocation field is shown to reduce the order parameter whenT≪T _c , or stimulate superconductivity when(T−T _c )/T _c≪ 1. Damping reduction due to stimulation effect is discussed. Power dissipation dependence on the dislocations concentration in non-equilibrium state is obtained.     

L1<Subscript>2</Subscript>-phase cutting during high temperature and low stress creep of a Re-containing Ni-base single crystal superalloy

In the present study, we investigate dislocation processes in a Ni-base single crystal superalloy (LEK94) after high temperature and low stress creep. Specimens were creep deformed at 240 MPa and 980 °C to a strain of 20%. We use diffraction contrast transmission electron microscopy (TEM) to show that two γ-channel dislocations with different Burgers vectors combine and form a super dislocation that shears the γ′-particle. This type of cutting event has now been observed for three single crystal superalloys with different alloy chemistry (CMSX-4, CMSX-6 and LEK94 in the present work) and we therefore conclude that it represents a generic elementary dislocation process which governs high temperature (around 1000 °C) and low stress (around 240 MPa) creep. The present paper provides microstructural evidence for this type of cutting processes and discusses the results in the light of previous work published in the literature.     

The influence of interfacial dislocation arrangements in a fourth generation single crystal TMS-138 superalloy on creep properties

The morphologies of (001) / interfacial dislocation networks are studied through TEM observations. The lattice misfit has an important relation with creep property for superalloy during high temperature creep deformation. The fourth generation superalloy TMS-138 possesses superior creep properties based on its fine interfacial dislocation networks. The networks have two typical characteristics: closely spaced dislocations and stable square morphology during creep deformation. Such arranged dislocations can effectively prevent the slipping dislocations in the phase from moving through the / interface and improve drastically the creep resistance in the fourth generation superalloy TMS-138.     

Force between two parallel screw dislocations and application to linear screw dislocation pileups—Gauge theory results

An analytic expression for the force between two parallel screw dislocations, derived earlier on the basis of the gauge theory of dislocations, has been used to investigate the static distribution of a given numberN of parallel screw dislocations confined between two immobile dislocation obstacles. It is shown that in the limit of a continuous distribution of dislocations the equilibrium condition leads to a Fredholm integral equation of first type which does not admit any nontrivial solution. Implication of this result is discussed. For a finite number of dislocations, the ratio (η) of the obstacle separation to the core radius is an important parameter governing the nature of solution of the discrete equation. It is found that for a givenN, there is a critical valueη _c below which there does not exist any solution.     

Microstructural evolution during creep of a hot extruded 2D70Al-alloy

Microstructural evolution during creep of a hot extruded Al–Cu–Mg–Fe–Ni (2D70) Al-alloy was investigated in this study using transmission electron microscopy (TEM). The samples for creep test were carried out two-stage homogenization, followed by extruding. The creep ultimate strength dropped and the temperature increased gradually from 312 to 117 MPa and from 423 to 513 K, respectively. The microstructural observation for the crept samples showed that the S′ phase coarsened with increased creep temperature and the aging precipitates transformed from S″ phase to S′ phase during creep process. Meanwhile, excess solute atoms in supersaturated solid solution dynamically precipitated to further form finer S′ phase and S″ phase, which pinned the dislocations and impeded the dislocation movements. Large amount of dislocations piled up around the micron-scale Al₉FeNi phase, and a lot of dislocation walls were generated along 〈220〉 orientation. S phase accumulates around these defects. The interaction between dislocations and precipitates was beneficial for the improved performances at elevated temperature.     

A microanalytical study of the early stages of recrystallization in the nickel-base superalloy APK1

Analytical electron microscopy has been used to investigate the composition of various microstructural features in a powder-produced nickel-base superalloy. Specifically, it is shown that in the early stages of recrystallization the strain-free grains are depleted in theγ′-forming elements (i.e. titanium and aluminium). This observation is consistent with the hypothesis that recrystallization in this alloy is initiated in the immediate vicinity of large intergranularγ′ particles. It is also shown that the composition ofγ′ can be written as (Ni, Co)₃ (Al, Ti, Cr).     

Unidirectional solidification of Ni-Mo-Al eutectic alloys

The composition triangle of the Ni-Mo-Al ternary system contains a monovariant trough between theγ′ (Ni₃Al)-α(Mo) pseudobinary eutectic and a guessedγ(Ni)-γ′ (Ni₃Al)-α(Mo) ternary eutectic. Alloys with compositions on this trough were directionally solidified at various growth rates. The microstructure of the alloys consists of fine Mo fibres of rectangular cross-section in an Ni₃Al/Ni matrix. The determined crystallographic relationship does not correspond to an interface of low lattice mismatch. The eutectic trough strongly extends towards increasing Mo contents so that the volume fraction of the Mo fibres varies between 18 and 25% dependent on composition. It was not possible to determine the position of a ternary eutecticγ-γ′-α because the liquidus temperatures along the trough are almost equal and the distribution of the three phases is strongly dependent on the growth rate.     

Identification of singular interfaces with Δ<Emphasis Type="Bold">g</Emphasis>s and its basis of the O-lattice

This article identifies singular interfaces according to singularity in terms of structural defects, including dislocations and ledges. Defect singularities are defined by the elimination of one or more classes of defects, which must be present in the vicinal interfaces. In addition to the three commonly classified structural interfaces, a new type of interface—the CS-coherent interface—is introduced. Singularities in dislocation and ledge structures have been integrated in the study of orientation relationships (OR). The dislocation structures are determined through the O-lattice theory, originally proposed by Bollmann. The basic concepts of the O-lattice and related formulas from the original theory and extended studies are briefly reviewed. According to the theory, singular interfaces exhibiting singularity in the dislocation structures have been identified. An interface that is singular with respect to the interface orientation must be normal to at least one Δg, a vector connecting two reciprocal points from different lattices. An interface that is singular also with respect to the OR must obey one or more Δg parallelism rules. The selection of proper Δgs for different preferred states of interfaces are explained. Identification of singular interfaces with measurable Δgs provides a convenient and effective approach to the interpretation of the observed facets and ORs. The ambiguity about the selection of the deformation matrix (A) for the O-lattice calculation and the advantage of the O-lattice approach over the approach using the Frank–Bilby equation for the calculation of the interfacial dislocations are clarified. Limitations of the present approach and further study are discussed.     

Stress-Rupture Characterization in Nickel-Based Superalloy Gas Turbine Engine Components

Today’s gas turbine engines utilize high volume fraction gamma prime (γ′) strengthened alloys for turbine airfoils, which typically operate at temperatures greater than ∼0.5T _m of the alloy. At these temperatures and at stresses below yield, time-dependent deformation (creep) of the airfoil can occur and, if left unabated, can result in complete separation of the airfoil. This process is commonly referred to as stress rupture. Insufficient cooling air, unintentional interruptions of cooling air as well as abnormal engine operating conditions are typical causes of stress-rupture failures in gas turbine blade components. Stress-rupture fractures are generally heavily oxidized, tend to be rough in texture, and are primarily intergranular and/or interdendritic in appearance compared to smoother, transgranular fatigue type fractures. Often, gross plastic yielding is visible on a macroscopic scale. Commonly observed microstructural characteristics include creep voiding along grain boundaries and/or interdendritic regions. Internal voids can also nucleate at carbides and other microconstituents, especially in single crystal castings that do not possess grain boundaries. Other signs of overtemperature include partial resolutioning of the γ′ strengthening precipitates, with the remaining volume fraction of γ′ commonly used to estimate blade metal temperatures. This article highlights the visual, fractographic, and metallographic characteristics typically encountered when analyzing stress rupture of turbine airfoils. An erratum to this article can be found at     

Misfit dislocations and stress in In<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Ga<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>As/GaAs heterostructures

We have estimated the elastic properties of In_{1 − x} Ga _x As/GaAs heterostructures and the characteristics of misfit dislocations in such heterostructures: misfit dislocation spacing, Burgers vector length in various interfaces, surface density of dangling bonds, film/substrate interface energy, critical film thickness below which pseudomorphic growth is possible without misfit dislocations, elastic strain energy of the film-substrate system, average elastic strain of a thin-film island as a function of its radius, thermal stresses induced by the thermal-expansion and lattice mismatches between the layers in contact, and crack length in the film.     

The pre-wetting transition at antiphase boundaries: an atomistic modeling study of Ni<Subscript>3</Subscript>Al

Using an embedded-atom model for Ni–Al alloys, we have examined interfacial properties of the Ni/Ni₃Al system, concentrating on properties of the antiphase boundaries. These interfaces between domains of the γ′ phase can undergo a pre-wetting transition as the region of the antiphase boundaries disorders and then transforms into a metastable γ phase. In order to understand more about this transition, we have performed detailed thermodynamic, compositional, and structural analyses of this system using semi-grand canonical Monte-Carlo simulations, with particular interest in composition profiles and segregation. We will discuss our studies in the context of previous treatments of these interfaces.     

Effect of coherency on coarsening of second-phase precipitates in Cu-base alloys

The effects of matrix/precipitate interface states on coarsening of Co and γ-Fe precipitates in a Cu–4 wt.%Co and a Cu–2 wt.%Fe alloy aged at 500 and 700 °C have been examined by transmission electron microscopy (TEM) observations, electrical resistivity measurements, and length-change measurements. Analyses of TEM images show that the average radius for coherent/semi-coherent transition is 6–12 nm for the Co precipitates and 10–20 nm for the γ-Fe precipitates. The coarsening rates of the Co and γ-Fe precipitates are unchanged by the transitions in coherency of the precipitates. The interface energies γ of coherent Co and γ-Fe precipitates are estimated from data on coarsening alone as 0.15 and 0.27 J m⁻². From length-change measurements of the Cu–Co and Cu–Fe alloys during aging, the estimates of the isotropic misfit strains of Co and γ-Fe precipitates are −0.018 and −0.016 for the coherent interfaces and −0.013 and −0.012 for the semi-coherent interfaces. Free energy analyses for the coarsening of Co and γ-Fe precipitates reveal that the values of γ of semi-coherent Cu/Co and Cu/γ-Fe interfaces are 0.24 and 0.34 J m⁻².     

A1-L1<Subscript>2</Subscript> interfacial free energies from data on coarsening in five binary Ni alloys,informed by thermodynamic phase diagram assessments

The data on coarsening of γ′-type precipitates (Ni₃X, with the L1₂ crystal structure) in Ni–Al, Ni–Ga, Ni–Ge, Ni–Si, and Ni–Ti alloys are re-evaluated in the context of recent (TIDC) and classical (LSW) theories of coarsening, with the objective of ascertaining the best values possible of interfacial free energies, σ, of the γ/γ′ interfaces in these five alloy systems. The re-evaluations include fitting of the particle size distributions, reanalyzing all the available data on the kinetics of particle growth and kinetics of solute depletion, and using thermodynamic assessments of the binary alloy phase diagrams to calculate curvatures of the Gibbs free energies of mixing. The product of the work is two sets of interfacial free energies, one set for the analysis using the recent TIDC theory and the other for the analysis using the classical LSW theory. The TIDC-based analysis yields lower values of σ by about a factor of 2/3. All the interfacial energies are considerably larger, by factors ranging from ~4 to 10, than those previously reported, which were for the most part calculated from data on coarsening assuming ideal-solution thermodynamics. In the TIDC theory the width of the interface, δ, is allowed to increase with particle size, r. A simple equation relating σ to the ratio of the gradient energy and δ is used to show that σ can remain constant even though δ increases with r. Published work supporting this contention is presented and discussed.     

Long term coarsening of γ′ precipitates in a Ni-base superalloy

The mechanical properties of a Ni-based superalloy strongly depend on the distribution and size of the precipitate particle γ′ phase: Ni₃(Al, Ti). Such particles grow during the initial heat treatment and it is very important to predict the kinetic growth owing to their technological application at high temperatures. In this work, we performed analysis of particle coarsening in IN-713C during long ageing times at constant temperature, given an initial size and volume fraction distribution of the γ′ precipitate phase, and the evaluation of two different heat treatments through the microstructure analysis and γ′ morphology. We found that for short ageing times, t < 2500 h, the coarsening can be approximated by a linear volumetric growth as predicted by Lifshitz, Slyozov and Wagner (LSW) theory. For a time greater than 2500 h the growth rate of γ′ precipitate shows an asymptotic behaviour in both heat treatments. This revised version was published online in November 2006 with corrections to the Cover Date.