Coarsening kinetics of γ′ precipitates in cobalt-base alloys

The expeditious development of novel cobalt-base γ–γ′ alloys as possible next generation superalloys critically depends on achieving a comprehensive understanding of the coarsening kinetics of ordered γ′ precipitates. This paper discusses the coarsening of L1₂ ordered Co₃(W, Al) precipitates in a model ternary Co–10Al–10W (at.%) alloy during isothermal annealing at 800 and 900 °C. The experimentally determined temporal evolution of average size of the γ′ precipitates suggests classical matrix diffusion limited Lifshitz–Slyozov–Wagner coarsening at both temperatures. The γ′ coarsening rate constants have been determined using a modified coarsening rate equation for non-dilute solutions. Furthermore, using the Cahn–Hilliard formulation for interfacial energy, the γ/γ′ interfacial energies at the respective annealing temperatures have been correlated to the concentration profile across the interface that has been experimentally determined using atom probe tomography. The calculated interfacial energies are in comparable range with those observed in nickel-base superalloys. Additionally, this analysis has permitted, for the first time, the determination of the gradient energy coefficient for γ/γ′ interfaces in Co-base alloys, a critical input for phase-field and other simulation models for microstructural evolution.     

Predicting equilibrium shape of precipitates as function of coherency state

A general approach is proposed to predict the equilibrium shapes of precipitates in crystalline solids as function of size and coherency state. The model incorporates effects of interfacial defects such as misfit dislocations and structural ledges on transformation strain and on interfacial energy. Using α precipitation in α/β titanium alloys as an example, various possible equilibrium shapes of precipitates having different defect contents at interfaces are obtained by phase-field simulations. The simulation results agree with experimental observations in terms of both precipitate habit plane orientation and defect content at the interface. In combination with crystallographic theories of interfaces and experimental characterization of habit plane of finite precipitates, this approach has the ability to predict the coherency state (i.e. defect structures at interfaces) and equilibrium shape of finite precipitates.     

Coarsening kinetics of γ′ precipitates in the Ni–Al–Mo system

The effect of Mo on the microstructure evolution and coarsening kinetics of γ′ precipitates in the Ni–Al–Mo system is studied using phase-field simulations with inputs from thermodynamic, kinetic and lattice parameter databases. For alloys of different compositions, the precipitate morphology and the statistical information of precipitate sizes are predicted as a function of annealing time. It is observed that increasing Mo content leads to a change of the precipitate morphology from being cuboidal to spherical as well as a reduction in the coarsening rate. Comparison between simulated results and existing experimental microstructure morphologies and coarsening rates shows good agreements.     

Coarsening kinetics of γ′ precipitates in the commercial nickel base Superalloy René 88 DT

René 88 DT samples were subjected to different cooling rates after a supersolvus treatment, and aged for varying periods of time from 25 to 200 h at 760 °C. Primary and secondary γ′ precipitate sizes were measured after each heat treatment. Coarsening rate constants were calculated and reported based on the measured precipitate sizes. When describing the change in radius (r) as a function of time (t), fits between the experimental results and analysis were investigated for two types of functional relationships, r³ vs. t and r² vs. t. The experimental rate constants derived from this analysis were compared with analytical values deduced from two different models: volume diffusion and bulk diffusion through the interface. The applicability of the two mechanisms for γ′ coarsening is discussed based upon the comparison between the analytically derived and experimentally observed values of these rate constants.     

Phase-field simulation of coarsening of γ precipitates in an ordered γ′ matrix

The evolution of the microstructure and coarsening kinetics of disordered γ precipitates in an ordered monovariant γ′ matrix was studied using a diffuse-interface phase-field model in two dimensions. Specifically, we studied the morphological evolution, average precipitate size and size distribution as a function of time for a given temperature and for different concentrations. It was found that the coarsening kinetics for the average particle size are described by a t^1/3 power law with a rate constant that increases with the volume fraction of the γ phase. The particle size distribution scaled by the average particle size is time invariant. We find that the particle shapes are perturbed by elastic interaction and local distributions of γ particles. Comparison of the phase-field simulation results with experiments shows good qualitative agreements.     

Simulation of the coarsening behavior of intermetallic precipitates in Ni75AlxV25-x alloys

The coarsening behavior of L12 and D022 in Ni75AlxV25-x （x,at.%） alloys including coherent strain was investigated using the microscopic phase-field model. The simulation results indicate that the shape transition and spatial correlation of L12 and D022 are caused by the morphological-dependent anisotropic elastic interactions in the system. The coarsening process of the particles is by means of neighbor particles impingement and aggregation into larger ones. For the strain-induced interactions between the precipitates,the LSW theory is altered for the coarsening behavior of L12 and D022. In addition,the simulation reveals that the growth and coarsening of D022 present two obvious stages at lower Al concentration regions and proceed simultaneously at high Al concentration regions. The growth and coarsening processes of L12 at the same regions is reverse to those of D022.     

Disorder strengthening of ordered L12 alloys by face centered cubic (A1) precipitates

We present a new theory of strengthening (disorder strengthening) of a crystallographically ordered L1₂ matrix by spherical, coherent crystallographically disordered fcc (A1) precipitates. There are two versions of the theory, each involving different approximations for the length of the chord, inside the precipitate, subtended by the trailing dislocation in the super-dislocation pair. Each of these versions incorporates two other assumptions involving the statistics of dislocation-precipitate interactions, which determine the average spacing of the precipitates along the super-dislocation. All versions of the theory predict a peak-strength condition at small particle sizes, followed by an extended period of overaging in which the strength decreases slowly with increasing particle size. We compare the quantitative predictions of the theory with both computer-simulated and experimentally generated data on inverse Ni-base γ′-type superalloy matrices strengthened by γ precipitates. In all cases at least one version of the theory is in excellent agreement with the data. The predicted strengthening is significant, the order of 85–110 MPa in the computer simulated results and 40–80 MPa in model precipitation strengthened inverse superalloys containing small volume fractions (≤0.04) of γ precipitates. The results are discussed in light of the statistics of dislocation-precipitate interactions and the resistance of individual γ particles to shearing by the super-dislocation pair; this resistance depends on the ratio of maximum force required to break free of the precipitate and the line tension of the dislocation pair.     

Coarsening of γ (Ni–Al solid solution) precipitates in a γ′ (Ni3Al) matrix

The coarsening behavior of Ni–Al solid–solution precipitates in an Ni₃Al matrix was investigated in alloys containing 22.0–22.8 at.% Al aged at 650–800 °C for times exceeding 1800 h. The rate constant for coarsening increases with equilibrium volume fraction as predicted by the MLSW theory. The activation energy for coarsening, 314.1 ± 16.6 kJ mol⁻¹, agrees very well with results from conventional diffusion experiments. The particle size distributions are not in very good agreement with the predictions of any theory; possible reasons are discussed. The particles become more spherical with decreasing elastic self-energy. The results are consistent with the premise that a strong volume fraction effect is observed so long as diffusion in the matrix phase, and not through the precipitate–matrix interface, controls the kinetics.     

Exploring dendrite coherency with the discrete element method

The particulate discrete element method (DEM) is used to simulate crystal rearrangement during equiaxed solidification of Al alloys for a range of morphologies across the globular to equiaxed-dendritic transition. It is shown that DEM is able to capture the key experimental results reported in past dendrite coherency studies, namely: the marked increase in resistance to shear at a critical solid fraction, the influence of crystal morphology on dendrite coherency, and that dendrite coherency marks the onset of dilatancy. Dendrite coherency is shown to be the lowest solid fraction at which long-range interconnectivity in the force chain network develops during shear. It is further found that dendrite coherency depends on both the internal solid fraction within dendrite envelopes and the mean shape of envelopes at coherency. The potential to extend DEM to the simulation of mushy-zone mechanics in casting problems is then discussed.     

Effects of applied stress on coherent precipitates via a discrete atom method

Morphological evolution of coherent precipitates under an applied stress is analyzed by means of a discrete atom method, which is predicated upon Hookean atomic interactions and Monte Carlo diffusion, and mates no assumption of a specific shape. Precipitates having elastic constants different from those of the matrix phase art treated in dislocation-free, anisotropic elastic systems under a plane strain condition with a purely dilatational misfit. Under an applied tensile stress, soft particles with a positive misfit strain tend to become plates perpendicular to the applied stress axis, while hard particles elongate along the stress direction. If the elastic interaction between the applied stress and the coherency strain is strong enough, precipitates often split into smaller particles and then follow coarsening. Even in the absence of a coherency strain, particles are shown to undergo morphological evolution through Eshelby’s inhomogeneity effects. A particle shape depends on the following variables: the sign and magnitude of the coherency strain, the sense and magnitude of the applied stress, its stiffness relative to the matrix phase, and the magnitude of the interfacial energy.     

不同时效态7050铝合金时效成形中析出相对应力松弛行为的影响

铝合金时效成形方法结合了合金的蠕变松弛和析出强化作用,作为一种先进的整体壁板制造技术倍受航空制造业青睐。7xxx系铝合金在时效成形过程中的应力松弛行为受到合金内析出相与位错蠕变交互作用的影响从而制约着成形后零件质量与性能。本文采用设计的应力松弛试验研究了不同时效态(固溶态,欠时效态和峰时效态)7050铝合金内析出相对时效成形过程中应力松弛行为的影响,并通过位错热激活动力学参数计算和显微组织表征分析析出相与位错运动的交互作用。结果表明时效成形过程中析出相对位错热激活运动有明显地阻碍作用,因此含有不同尺度析出相铝合金的应力松弛行为表现不同,随着析出相尺度的增加合金应力松弛速率减缓,应力松弛极限增大。不同时效态7050铝合金位错激活体积计算和显微组织表征结果都证明了应力松弛过程中析出相增大对位错运动的阻碍作用也越显著。峰时效态7050铝合金的位错激活体积最大,时效成形后塑性应变的转化率最低。此外,时效成形过程中,7050铝合金内析出相对位错热激活的阻碍作用引起了槛应力现象,且随着析出相的增大槛应力也逐渐增大。     

X-ray elastic constant determination and residual stress of two phase TiAl-based intermetallic alloy

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Neutron diffraction studies of Zr-containing intermetallic hydrides with ordered hydrogen sublattice.: V. Orthorhombic Zr3CoD6.9 with filled Re3B-type structure

Zr₃CoD_6.9 deuteride (space group Cmcm; a=3.5959(1); b=10.9734(3); c=9.5961(3) Å) has been studied by high resolution powder X-ray and neutron diffraction. Rietveld profile refinements showed that it is isostructural to Zr₃FeD_6.7 with a filled Re₃B-type structure. D atoms occupy four types of interstitial positions. Deuterium sublattice is completely ordered and can be described as a spatial stacking of deformed cubes ZrD₈ and deformed cubes with an extra ninth vertex ZrD₉. The shortest interatomic distances are: Zr–D=2.044(5); Co–D=1.727(8); D–D=2.025(6) Å.     

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.     

Dendrite coherency point of A357 alloys

The dendrite coherency point was determined for A357 alloys using double-thermocouples technique. The effects of the cooling rate and different treatments such as grain refinement, modification, and superheat on the dendrite coherency point were investigated. The results show that the increase of the cooling rate and refinement significantly postpones the coherency point of A357 alloys. The morphology of silicon phase is modified, which slightly leads to lower solid fraction （fs） at the coherency point. But the fs^coh value decreases after superheat treatment at 850 ℃ for 30 min. The grain size plays a decisive role in the fs^coh value ofA357 alloys. The smaller the grain size is, the more the fs^coh value increases, which is beneficial to improving the final property of this alloy, while the secondary dendrite arm spacing and modification have almost no influence on fs^coh.     

Effects of coherency on diffusivity in multilayers

In coherent multilayers, the remote spacing of vacancy sources and sinks indicates that Darken’s equations no longer apply. Under these circumstances, after a transient, the diffusivity should drop to that of the slower diffusing component. The magnitude of this effect in comparison with other effects that can retard diffusivity such as sink efficiency and internal stress fields, is discussed.     

Coarsening dynamics of self-accommodating coherent patterns

The coarsening kinetics of self-accommodating coherent domain structures is investigated using computer simulations based on a continuum phase-field model. The domain structures are produced from coherent hexagonal to orthorhombic phase transformations. It is found that the long-range elastic interactions arising from the lattice accommodation among different orientation domains of the orthorhombic phase dominate the domain morphologies and the kinetics of domain coarsening. It is shown that the long-range elastic interactions result in several new features for the domain coarsening as compared to normal grain growth. For example, the domain growth rate is reduced significantly and the growth exponent becomes a function of the relative contribution of the elastic energy reduction to the total driving force. In general, the elastic interaction is in favor of fine domains. Although triple junctions are dominant in the microstructure, a significant amount of quadrojunctions exist throughout the domain coarsening process. The average number of sides of the domain is also reduced.     

Stereology of grain-boundary precipitates

Grain-boundary precipitates coexist with matrix precipitation in many alloys. Depending on the orientation of the sectioning plane, particle sections appearing in the matrix on a plane of polish will arise from both grain boundary and matrix participate particles. The errors associated with assuming that the only GBP particles on a section are the ones appearing on the grain-boundary traces are discussed and evaluated. The corrections required are shown to be small, but may nonetheless be important. In addition, a dimensionless grain-boundary affinity parameter has been derived that indicates the tendency of the precipitate to occur on the boundaries rather than the matrix.     

Deforming nanoporous metal: Role of lattice coherency

Nanoporous metals prepared by alloy corrosion may assume the form of monolithic, millimeter-sized bodies containing around 10¹⁵ nanoscale ligaments per cubic millimeter. Here, we report on the fabrication and mechanical behavior of macroscopic, crack-free nanoporous gold samples which exhibit excellent ductility in compression tests. Their yield stress is significantly lower than that expected based on scaling laws or on previous nanoindentation experiments. Electron backscatter diffraction imaging reveals a polycrystalline microstructure with grains larger than 10 μm which acquire a subdomain structure during plastic flow, but remain otherwise intact. We highlight the action of lattice dislocations which can travel over distances much larger than the ligament size. This results in a collective deformation of the many ligaments in each grain. Remarkably, the dislocation cores are partly located in the pore channels. The results suggest a critical view of the conversion between indentation hardness and yield stress in previous work.