Inhomogeneity of misfit stresses in nickel-base superalloys: Effect on propagation of matrix dislocation loops

It is shown experimentally that, during annealing and creep under low applied stresses, matrix dislocation loops frequently cross-glide. The periodic length of the zigzag dislocations deposited in the interfaces is equal to that of the γ/γ′-microstructure. Initially, the zigzag dislocations move in the (001) interface by a combination of glide and climb but then they stop near the γ′-edges and align along ?100?. Reactions of such dislocations lead to the formation of square interfacial networks consisting of ?100? oriented edge dislocations. The complex dislocation movement is explained by the inhomogeneity of the misfit stresses between γ- and γ′-lattices. The tensile components of the stress tensor drive the dislocations through the channel, whereas the shear components near the γ′-edges cause the zigzag movement and the ?100? alignment. The total effect is the most efficient relaxation of the misfit stresses. The results are relevant, especially for single-crystal superalloys of the newest generations, which have an increased γ/γ′-misfit due to the high level of refractory elements.     

Dissociation of a 〈100〉 edge superdislocations in the γ ′-phase of nickel-base superalloys

Dissociation of a〈100〉 edge superdislocations in Ni₃Al, the hardening γ′-phase of nickel-base superalloys, was investigated using molecular dynamics simulations and theory of elasticity. It was shown that these dislocations dissociate either symmetrically or asymmetrically when they are close to the 〈011〉 orientation. The symmetric dissociation, called Hirth lock, has the lowest energy. The reasons for the dissociation are the strong energy reduction due to the core splitting and the relaxation of elastic strains within the dissociation area. The dissociation of a〈100〉 edge superdislocations is the reason for their alignment in 〈011〉 orientation in the γ′-rafts of superalloys. However, the dissociation does not block the movement of the dislocation because they penetrate the γ′-rafts by climbing. Under loading conditions, typical for creep tests of nickel-base superalloys at high temperatures (≥1000°C), the Hirth lock slightly expands but remains stable. The asymmetric configuration is less stable and can transform into the lower energy Hirth lock.     

Decorrelated movements of Shockley partial dislocations in the γ-phase channels of nickel-based superalloys at intermediate temperature

In nickel-based superalloys with high volume fraction of γ′ precipitates, dislocations have to experience high curvatures in order to enter narrow channels by glide in the {111} planes of the fcc γ matrix. Observations of in situ dynamic sequences performed in a transmission electron microscope on several industrial superalloys have shown the occurrence of decorrelated movements of Shockley partial dislocations, originating from perfect dislocation dissociation. By evaluating the effective stress acting on each one of these partial dislocations, as well as their respective flexibility, the possible occurrence of such movements for some particular dislocation characters and channel widths is accounted for. These movements can play an important role in the creep behaviour of these materials in the low deformation rate regime.     

High-temperature creep of single-crystal nickel-based superalloy: microstructural changes and effects of thermal cycling

Creep tests were performed on MC2 single crystal superalloy at 950°C/200?MPa and 1150°C/80?MPa under isothermal and thermal cycling conditions with a tensile axis along the [0?0?1] direction. It was found that the thermal cycles strongly affect the creep behavior at 1150°C but not at 950°C. This was related to the repetitive precipitation and dissolution of small γ′ rafts at the higher temperature, as revealed by quantitative characterization of the γ/γ′ microstructure. The dislocation microstructure exhibits similar trends in all the tested conditions, with a very high activity of a[1?0?0]-type dislocations climbing through the rafts. Such climbing dislocations constitute a recovery process for the deformation active system. It appears that the density of a[1?0?0] dislocations, and not their climb velocity or diffusion rate, is the key parameter for the control of creep rate. The thermal cycles, which imply the creation and subsequent dissolution of rafts, provided new dislocations, which explains the acceleration of creep observed under such conditions.     

Observations of glide and decomposition of a⟨101⟩ dislocations at high temperatures in Ni-Al single crystals deformed along the hard orientation

Ni-44 at.% Al and Ni-50 at.% Al single crystals were tested in compression in the hard d001 ¢orientation. The dislocation processes and deformation behaviour were studied as a function of temperature, strain and strain rate. A slip transition in NiAl occurs from a?111? slip to non-a?111? slip at intermediate temperatures. In Ni-50 at.% Al single crystals, only a?010? dislocations are observed above the slip transition temperature. In contrast, a a?101?{101} glide has been observed to control deformation beyond the slip transition temperature in Ni-44 at.% Al. a?101? dislocations are observed primarily along both ?111? directions in the glide plane. High-resolution transmission electron microscopy observations show that the core of the a?101? dislocations along these directions is decomposed into two a?010? dislocations, separated by a distance of approximately 2 nm. The temperature window of stability for these a?101? dislocations depends upon the strain rate. At a strain rate of 1.4 210^?4 s^?1, a?101? dislocations are observed between 800 and 1000 K. Complete decomposition of a?101? dislocations into a?010? dislocations occurs beyond 1000 K, leading to a?010? climb as the deformation mode at higher temperatures. At lower strain rates, decomposition of a?101? dislocations has been observed to occur along the edge orientation at temperatures below 1000 K. Embedded-atom method calculations and experimental results indicate that a?101? dislocations have a large Peierls stress at low temperatures. Based on the present microstructural observations and a survey of the literature with respect to vacancy content and diffusion in NiAl, a model is proposed for a?101?{101} glide in Ni-44 at.% Al, and for the observed yield strength versus temperature behaviour of Ni-Al alloys at intermediate and high temperatures.     

Molecular dynamics simulation of the structural evolution of misfit dislocation networks at γ/γ′ phase interfaces in Ni-based superalloys

The structural evolution of misfit dislocation networks at γ/γ′ phase interfaces in Ni-based single crystal superalloys under tensile loading and temperatures is simulated by molecular dynamics. From the simulation, we find that, with increasing load or temperature, the patterns of dislocation networks on the (100), (110) and (111) phase interfaces change from regular to irregular or disappear. Under the same load and temperature, the dislocation networks of the different phase interfaces show different degrees and patterns of damage. The density and stability of the dislocation networks decrease with increasing temperature. When the interfacial dislocation networks become more regular, the γ/γ′ interfaces become more stable. The simulated results are supported by related experimental findings. Moreover, based on MD simulations, the averaged stress–strain responses for different phase interfaces under loading are presented. The results indicate that the combined influences of temperature and load play an important role for the structure evolution of misfit dislocation networks at γ/γ′ phase interfaces of Ni-based superalloys.     

Creep deformation of single crystals of new Co–Al–W-based alloys with fcc/L12 two-phase microstructures

The creep deformation behaviour of single crystals of Co–Al–W-based alloys with γ?+?γ′ two-phase microstructures has been investigated in tension under a constant stress of 137?MPa in air at 1000°C as a function of the γ′ solvus temperature and the volume fraction of the γ′ phase. When described by the creep strain rate versus time curve, the creep deformation of Co–Al–W-based alloys consists of transition and accelerating regions without a steady-state region, as observed in many modern nickel-based alloys. However, the creep strength of the present Co–Al–W-based alloys is comparable with nickel-based superalloys of the first generation but is much weaker than those of the second and higher generations. Unlike in nickel-based superalloys, the so-called p (parallel)-type raft structure, in which the γ′ phase is elongated along the tensile axis direction, is formed during creep in Co–Al–W-based alloys, being consistent with what is expected from the positive values of lattice misfit between the γ and γ′ phases. As a result, of the alloys investigated, the best creep properties are obtained with the alloy possessing the highest volume fraction (85%) of the γ′ phase, which is far larger than usual for nickel-based superalloys (55–60%).     

Discrete dislocation simulations of precipitation hardening in superalloys

The low-temperature yield stress of a nickel-based superalloy, containing up to 40% Ni₃A1 precipitates (γ′), is calculated by discrete dislocation simulations. A pair of screw or 60°(a/2) ?110? dislocation glides under external stress across a {111} plane of γ phase, intersected by a random distribution of either spherical or cubic γ′ precipitates. The stress is raised until the dislocations can cut or bow round all the obstacles. In this paper the emphasis is on the cutting regime which is prevalent when the precipitates are small and/or have low antiphase-boundary (APB) energies. From a large number of simulations in the cutting regime, the effects of size, shape, volume fraction and APB energy are found to be as follows: The yield stress is proportional to the square root of the volume fraction of γ′. The yield stress depends weakly on the precipitate size in the size range 20–400?nm, for APB energies of 150, 250 and 320?mJ?m^?2. The yield stress depends linearly on the APB energy for APB energies up to 320?mJ?m^?2 in the size range 50–200?nm. At a precipitate size of 100?nm, cubes are weaker obstacles than equivalent spheres by about 25% for an APB energy of 320?mJ?m^?2; however, the shape effect on strengthening decreases with decreasing APB energy and decreasing precipitate size. When a coherency stress (from a lattice parameter mismatch of 0.3%) is added, the yield stress increases by about 10%. When solid-solution strenthening is added, it is potent when the solute is in the γ matrix, but much less potent when the solute is in γ′. When the γ′ precipitates are larger than 400?nm across and the APB energy greater than 250?mJ?m^?2, significant Orowan looping occurs. The yield stress drops inversely as the precipitate size and becomes insensitive to the APB energy but sensitive to the shear modulus. Many of these results from the full simulations differ from the analytical models of strengthening in superalloys but they can be rationalized from the results of simulations on simple homogenized precipitate structures.     

Climb via vacancy diffusion of edge dislocations in 2D dislocation microstructures

The prevention of strength degradation of components is one of the great challenges in solid mechanics. In particular, at high temperatures material may deform even at low stresses, a deformation mode known as deformation creep. One of the microstructural mechanisms that governs deformation creep is dislocation motion due to the absorption or emission of vacancies, which results in motion perpendicular to the glide plane, called dislocation climb. However, the importance of the dislocation network for the deformation creep remains far from being understood. In this study, a climb model that accounts for the dislocation network is developed, by solving the diffusion equation for vacancies in a region with a general dislocation distribution. The definition of the sink strength is extended, to account for the contributions of neighbouring dislocations to the climb rate. The model is then applied to dislocation dipoles and dislocation pile-ups, which are dense dislocation structures and it is found that the sink strength of dislocations in a pile-up is reduced since the vacancy field is distributed between the dislocations. Finally, the importance of the results for modelling deformation creep is discussed.     

Numerical calculation of the rate of strain of interstitial solid solutions under irradiation. I. Model of radiation creep

A model of radiation creep of interstitial solid solutions is developed on the basis of the combined motion of dislocations, including their glide and climb past obstacles. The obstacles considered are forest dislocations and pileups of radiation-induced point defects. A computational formula for the rate of strain is derived which describes creep at high stresses, when the gliding dislocations overcome some of the barriers by force, and a method is described for determining the average distance traversed by a dislocation in the glide plane under the influence of the stress until it is stopped by barriers. The results are compared with those of other authors. It is shown that the formula obtained for the rate of strain goes over in particular cases to those given by the previously known SIPA, Gittus-Mansur, and glide-climb models of radiation creep. Zh. Tekh. Fiz. 69, 64–71 (January 1999)     

Peierls–Nabarro model for dislocations in MgSiO3 post-perovskite calculated at 120 GPa from first principles

We present here the first numerical modelling of dislocations in MgSiO₃ post-perovskite at 120?GPa. The dislocation core structures and properties are calculated through the Peierls–Nabarro model using the generalized stacking fault (GSF) results as a starting model. The GSFs are determined from first-principle calculations using the VASP code. Dislocation properties such as planar core spreading and Peierls stresses are determined for the following slip systems: [100](010), [100](001), [100](011), [001](010), [001](110), [001](100), [010](100), [010](001), ½[110](001) and ½[110](110). Our results confirm that the MgSiO₃ post-perovskite is a very anisotropic phase with a plasticity dominated by dislocation glide in the (010) plane.     

A crystal plasticity finite element model for flow stress anomalies in Ni3Al single crystals

This paper presents a dislocation density-based non-Schmid constitutive model to address the anomalous thermo-mechanical behaviour of the L1₂ intermetallic single-crystal Ni₃Al. Ni₃Al is used as a strengthening precipitate (γ′ phase) in Ni-based superalloys. Addressing such anomalous behaviour by accounting for temperature-dependent flow stress and hardening evolution, as well as orientation-dependent tension–compression asymmetry, is necessary for modelling superalloys across a range of temperatures. While hardening in cube-slip systems results from statistically stored dislocations (SSDs), hardening in octahedral slip systems is due to both SSDs and cross-slip dislocations (CSDs). The constitutive model incorporates hardening evolution due to SSDs and CSDs. Experimental data for Ni₃Al-type single crystals, available in the literature, are used to calibrate material parameters. Subsequently, results of crystal plasticity FEM simulations are compared with experimental data for several orientations under constant strain rate and creep loading conditions for a wide range of temperatures. The model is able to correctly predict the response of L1₂ intermetallic single crystals including features of anomalous flow stress and non-Schmid yield behaviour.     

Experimental and computational creep characterization of Al–Mg solid-solution alloy through instrumented indentation

Carefully designed indentation creep experiments and detailed finite-element computations were carried out in order to establish a robust and systematic method to extract creep properties accurately during indentation creep tests. Samples made from an Al–5.3?mol%?Mg solid-solution alloy were tested at temperatures ranging from 573 to 773?K. Finite-element simulations confirmed that, for a power-law creep material, the indentation creep strain field is indeed self-similar in a constant-load indentation creep test, except during short transient periods at the initial loading stage and when there is a deformation mechanism change. Self-similar indentation creep leads to a constitutive equation from which the power-law creep exponent n, the activation energy Q _c for creep, the back or internal stress and so on can be evaluated robustly. The creep stress exponent n was found to change distinctively from 4.8 to 3.2 below a critical stress level, while this critical stress decreases rapidly with increasing temperature. The activation energy for creep in the stress range of n = 3.2 was evaluated to be 123?kJ?mol^?1, close to the activation energy for mutual diffusion of this alloy, 130?kJ?mol^?1. Experimental results suggest that, within the n = 3.2 regime, the creep is rate controlled by viscous glide of dislocations which drag solute atmosphere and the back or internal stress is proportional to the average applied stress. These results are in good agreement with those obtained from conventional uniaxial creep tests in the dislocation creep regime. It is thus confirmed that indentation creep tests of Al–5.3?mol%?Mg solid-solution alloy at temperatures ranging from 573 to 773?K can be effectively used to extract material parameters equivalent to those obtained from conventional uniaxial creep tests in the dislocation creep regime.     

The interaction of dislocation loop and γ' precipitate in nickel based alloys

The nucleation and growth of interstitial loops during irradiation has a : ontrolling effect on the subsequent swelling behaviour of metals. In nickel based alloys containing ordered γ' precipitate (Ni₃Al, Ti), interactions occur between the nucleated loops and γ' particles. This effect has been studied in two nickel based alloys using a High Voltage Electron Microscope.

For the case of Nimonic 80A alloy containing 18% volume fraction : gamma;' precipitate, dislocation loop-particle interactions obeyed the developed isotropic elasticity theory.²'³'¹² Consequently, rather low dislocation densities were developed and the swelling resistance was high during electron irradiation. In Nimonic 115A alloy, loop nucleation and growth was dependent on the availability of interfacial dislocation surrounding the γ' particles.

With regard to the swelling behaviour of γ' hardened alloys, it : s concluded that several mechanisms contribute to make these materials resistant.

Coherency strains at the γ' particles reduce the density of : limbing dislocations.

The γ' precipitate affects the climb efficiency of the : ucleated dislocations by:

pinning the dislocation line, thus introducing a line tension force : hich opposes dislocation climb and reduces swelling;

reducing the available volume of material in which dislocation loops : an nucleate and grow.     

Diffusive fluxes associated with interfacial defeet motion and interaction

The diffusional flux associated with the motion of interfacial defects is described by an equation expressed in terms of the topological parameters which characterise defects, namely their Burgers vectors and step heights, the defect velocity and the concentration of each atomic species in the two adjacent crystals. This expression demonstrates that glide/climb behaviour of grain boundary defects is analogous to motion of dislocations in single crystals; climb motion results if a component of b is perpendicular to the interface plane. However, the situation is more complex in the case of interphase interface defects, but the present approach, which considers the step and dislocation portions of defects separately, enables a straightforward analysis. Several examples are illustrated to show the various possibilities, such as climb motion even when b is parallel to the interface, and glide motion when b is not. The latter case arises in martensitic transformation where the existence of an invariant-plane-strain relation at the interface leads to equal and opposite fluxes to the step and dislocation portions of transformation defects so that overall the motion is diffusionless.Interfacial processes involve the motion and interaction of defects. The present analysis facilitates the consideration of diffusive fluxes associated with defect interaction since the step and dislocation portions can be treated independently. A general expression is derived for the total flux arising, and a particular case, the interaction of transformation dislocations with crystal dislocations which have reached the interface during lattice-invariant deformation in martensite formation, is considered.     

Solute-diffusion-controlled dislocation creep in pure aluminium containing 0.026 at.% Fe

Pure aluminium containing about 200?at.ppm Fe in solution is shown to creep about 10⁶ times slower at 200°C than the same aluminium containing a negligible amount of iron in solution. The high creep resistance of the Al–200?at.ppm?Fe alloy is attributed to the presence of subgrain boundaries containing iron solute atoms. It is proposed that the opposing stress fields from subgrain boundaries and from the piled-up dislocations during creep are cyclically relaxed, by iron solute diffusion, to allow climb of the lead dislocation in the pile-up. The mechanism is a form of mechanical ratcheting. The model is applied to Al–Fe alloys and correctly predicts that the creep rate is controlled by the rate of iron solute diffusion and by a temperature dependence equal to the activation energy for iron diffusion, namely Q _c?=?221?kJ?mol^?1. Basic creep studies on solid-solution alloying with solute atoms that diffuse slowly in the lattice of aluminium (e.g. manganese, chromium, titanium and vanadium) appear worthy of study as a way of enhancing creep strength and of understanding creep mechanisms involving solute-atom-containing subgrain boundaries.     

Crystal plasticity and multiscale modelling of superalloy creep

A crystal plasticity approach for superalloy creep has been presented which employs a finite element-based representative volume element (RVE) methodology. The γ channels are assumed to undergo crystal slip and the γ′ particles to deform elastically. A range of superalloys has been studied. Thermocalc computations provide the γ′ volume fraction and an automated scheme for generating the resulting RVE has been developed. It has been shown that primary creep response in a wide range of superalloys over high stress, low temperature regimes is represented excellently by the model, by determination of just an activation energy and an alloying element density. It has been hypothesised that the transition from primary to secondary creep results from the development of geometrically necessary dislocations within the γ channels at the γ′ interfaces. Without the need of further material parameters, it has been shown that secondary creep rates over a broad range of stress and temperature can be accurately predicted, hence supporting the hypothesis. An empirical relationship has been established between the alloying element density and the atomic weight percentages of the alloying elements, using a range of superalloy data. It is hypothesised that a role of the alloying elements within the γ channels is to act as inhibitors of ribbon dislocation motion, hence leading to the large range of macro-level primary and secondary creep responses observed in the alloys with variations in constituent alloys. The empirical relationship established, when combined with the crystal RVE methodology, then allows the prediction of superalloy creep rates from knowledge of alloying constituents.     

Dislocation dynamics in multiwalled carbon nanotubes at high temperatures

Dislocation dynamics dictate the mechanical behavior of materials. Dislocations in periodic crystalline materials have been well documented. On the contrary, dislocations in cylindrical carbon nanotubes, particularly in multiwalled carbon nanotubes (MWCNTs), remain almost unexplored. Here we report that a room temperature 1/2<0001> sessile dislocation in a MWCNT becomes highly mobile, as characterized by its glide, climb, and the glide-climb interactions, at temperatures of about 2000 degrees C. The dislocation glide leads to the cross-linking of different shells; dislocation climb creates nanocracks; and the interaction of two 1/2<0001> dislocations creates kinks. We found that dislocation loops act as channels for mass transport. These dislocation dynamics are drastically different from that in conventional periodic crystalline materials due to the cylindrical, highly anisotropic structures of MWCNTs.     

Shearing of γ′ precipitates in Ni-base superalloys: a phase field study incorporating the effective γ-surface

An extended phase field model of dislocations in Ni-base superalloys is presented. It incorporates the recently developed effective γ-surfaces for both matrix and precipitate phases, obtained from atomistic simulations. These novel γ-surfaces feature extrinsic stacking faults as additional local minima. Thus, they offer an increased number of available dislocation dissociation pathways within the phase field system. The new model has been used to simulate a variety of mechanisms for γ′ precipitate shearing proposed in literature. A critical assessment is made based on the modelling observations.