共格沉淀析出过程的模拟Ⅰ--微观结构演化

采用相场模型对共格沉淀析出过程微观结构演化进行模拟研究.模拟结果表明,应力场的存在将会对相变过程中析出相形态产生显著的影响,通过界面能与弹性应变能的相互竞争析出相在不同阶段呈现不同的形态如模量结构、网格结构、三明治多畴结构、沉淀宏观点阵结构以及板条状等;此外,点阵错配度中等(2%～4%)时,粒子的粗化过程将出现应力诱导反向粗化现象,这种粗化现象取决于粒子的点阵错配度与体积分数.     

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.     

Contributions from elastic inhomogeneity and from plasticity to γ′ rafting in single-crystal Ni–Al

Directional coarsening (rafting) of γ′ precipitates in single-crystal Ni–Al alloys under external load is investigated by three-dimensional computer simulations. Contributions from modulus mismatch between the precipitate and matrix phases and from channel plasticity are considered. The simulation technique is based on a phase field model that captures spatiotemporal evolution of precipitate microstructure in elastically anisotropic and inhomogeneous systems. Channel plasticity is incorporated in the model through the introduction of an effective plastic strain that is formulated based on dislocation contents in the γ channels. Experimental data on lattice misfit, elastic moduli, applied stress and dislocation density in γ channels are used as model inputs. The driving force for rafting is monitored continuously by tracking the change in chemical potential difference between different types of γ channels after an external stress is applied until rafting completes. Quantitative comparisons of the rafting driving force and rafting completion time obtained from the simulations confirm the dominant role of channel plasticity, indicating that the rafting direction is determined by channel plasticity rather than by modulus inhomogeneity. However, elastic inhomogeneity also makes a significant contribution to the driving force for rafting, especially during the first several hours after the external load is applied.     

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.     

含共格畸变的立方合金粗化机制的原子层面计算机模拟研究

基于微观相场动力学模型，编制了包含共格畸变能的二元立方合金沉淀过程微观组织演化的计算机模拟程序，开展了不同共格畸变能作用下，溶质浓度为20at％的二元镍基合金的粗化机制的计算机模拟。研究发现：共格畸变能为零时，粗化遵循LSW机制，仅仅由颗粒的尺寸大小决定：随着共格畸变能的增大，粗化过程遵循混合机制，由沉淀颗粒的大小和位向（颗粒间的相对位置）共同决定；当共格畸变增大到一定程度时，粗化过程纯粹由颗粒间的位向决定，处于弹性“软”方向上的颗粒优先长大，而处于弹性“软”方向外的颗粒将消失掉。     

A model for evolution of shape changing precipitates in multicomponent systems

Recently the authors introduced a concept of shape factors to extend an already established model for the growth and coarsening kinetics of spherical precipitates in multicomponent multiphase environments to needle- and disc-shaped geometries. The geometry of the precipitates is kept in the original version of the concept to be self-similar with a given fixed aspect ratio. In the present treatment, the aspect ratios of individual precipitates are treated as independent evolving parameters. The evolution equations of each precipitate, described by its effective radius, mean chemical composition and the aspect ratio, are derived by application of the thermodynamic extremal principle. The driving force for the evolution of the aspect ratio of the precipitate stems from the anisotropic misfit strain of the precipitate and from the orientation dependence of the interface energy. The model is used for the simulation of the precipitation of Ti₃AlN and Ti₂AlN in Ti–Al–0.5 at.% N matrix.     

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.     

Coarsening of ordered intermetallic precipitates with coherency stress

The morphological evolution and coarsening kinetics of ordered intermetallic precipitates with coherency stress were studied using a diffuse-interface phase-field model in two dimensions (2D). The emphasis is on the effects of precipitate volume fraction. The average aspect ratio of the precipitates in the microstructure is found to increase with time and decrease with volume fraction. Contrary to all the existing coarsening theories but consistent with a number of experimental measurements on the coarsening kinetics of ordered γ′ precipitates in Ni-base superalloys, we found that the coarsening rate constant from the cubic growth law decreases as a function of volume fraction for small volume fractions (≲20%) and is constant for intermediate volume fractions (20–50%). From the simulation results, we infer that the two length scales in a stress-dominated coherent two-phase microstructure, the average precipitate size and average spacing between arrays of aligned precipitates, follow different growth exponents. It is demonstrated that as the volume fraction increases, the precipitate size distributions become broader and their skewness become increasingly positive.     

Effect of Thermal Aging on Coarsening Kinetics of γ′ in Alloy 617

The effect of thermal aging on coarsening kinetics of alloy 617, a candidate material for heat exchanger of the very high temperature reactor, was experimentally studied at 750 and 950 °C for up to 5300 h. Formation of various precipitates such as μ-phase, M₂₃C₆ and γ′ phases and significant coarsening of the γ′ phase have been observed in the microstructure of the aged samples. Experimental observation was compared to alloy thermodynamic calculation and γ′-phase precipitation kinetics simulation. Thermal aging effect on the microstructural evolution and mechanical behavior of alloy 617 was then discussed based on experimental and microstructural modeling results.     

Coarsening of γ′ in Ni-Al alloys aged under uniaxial compression: III. Characterization of the morphology

The morphological evolution of γ′ precipitates during coarsening at 640 °C under applied compressive stress in the range 0–150 MPa was investigated in a monocrystalline Ni-Al alloy containing nominally 13.36 at. % Al. The strain was primarily elastic. The microstructures were examined by transmission electron microscopy, primarily in the section (100) perpendicular to the applied stress. The aspect ratio of a γ′ precipitate, as well as a shape parameter which provides a measure of how cuboidal it is, were used to characterize the γ′ morphology. As the stress increases precipitates of a given size generally tend to become more non-equiaxed and their interfaces are more planar, though this depends on the γ′ volume fraction. The applied compressive stress also promotes the coalescence of γ′ precipitates. This tendency is more pronounced the higher the γ′ volume fraction and appears to be its main influence on directional coarsening during elastic deformation.     

共格沉淀析出过程的微观结构演化相场法模拟

用铜模吸铸法制备了Zr(65-x)Cu17.5Ni10Al7.5Fex(x=0,1,2,3,4,5,at％)块体合金,利用X射线衍射仪(XRD)、透射电镜(TEM)、同步热分析(DSC)、万能试验机和扫描电镜(SEM)研究了Fe对Zr基合金的非晶形成能力、热稳定性及力学性能的影响.结果表明:适量添加Fe元素有利于提高该合金的非晶形成能力和热稳定性,当Fe含量为x=2时,其内部结构为完全非晶结构,并且此成分具有较高的GFA和热稳定性(△Tx=58 K).Fe元素的适量加入也有利于提高该合金的强度和塑性,其中x=2的块体非晶合金的抗压强度σf、断裂应变εf和塑性应变εp分别高达2338 MPa、12.4％和2.0％.     

Ni75Cr16.4Al8.6合金粗化过程标度行为的微观相场研究

基于微观相场模型,研究Ni75Cr16.4Al8.6的粗化后期演化过程。结果表明：L12相和DO22相的标度函数曲线图表明合金沉淀在粗化阶段均表现出标度行为,不加应变能时DO22相结构函数因子和标度函数峰值均大于L12相;加入应变能后,两相的结构函数因子和标度函数的峰值均变小,反映了应变能对两相沉淀粗化过程的阻碍影响;相对于L12相,DO22相减小幅度更大,L12相结构函数因子和标度函数峰值大于DO22相,应变能对DO22相的阻碍作用更大。     

Phase field modeling of channel dislocation activity and γ′ rafting in single crystal Ni–Al

Dislocation-precipitate interaction and directional coarsening (rafting) of γ′ precipitates in single crystal Ni–Al alloys under external load are investigated by three-dimensional computer simulations. The simulation technique is based on an integrated phase field model that characterizes simultaneously the spatiotemporal evolution of both precipitate microstructure and dislocations. The initial configurations consisting of cuboidal γ′ particles and dislocations in γ channels are constructed according to experimental observations and phase field simulations of the dislocation filling process in the γ channels. For a given state (sign and magnitude) of the lattice misfit and external load commensurate with experimental values, the predicted morphologies of the rafted γ′ precipitates and the rafting kinetics agree well with experimental observations. This indicates that plasticity plays a dominant role in the rafting process as compared to elastic modulus mismatch between γ and γ′ phases, which has been ignored in the present simulations. The spatial variation of chemical potential of solute atoms caused by the coupling between channel dislocations and misfit stress is evaluated from concentration and stress distributions, from which diffusion fluxes in the γ channels are analyzed.     

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.     

共格沉淀析出过程的模拟Ⅱ--外加应力场的影响

采用相场模型对外加应力场对共格沉淀析出过程的微观结构演化进行模拟研究,在外加应力场作用下,非均匀弹性模量系统沉淀相的析出过程发生重大的变化,粒子沿弹性软方向呈各向异性析出,这种各向异性生长与外加应力、点阵错配度的符号以及非均匀模量差的符号有关。采用双级时效模拟方式时,外加应力场对析出相的成核及生长阶段均有影响,只是影响程度与析出相自身的点阵错配度有关。对适当的体系采用应力时效的方式可能是实现除分子束外延技术之外的一种全新的制备超晶格微结构的方法。     

Mechanism and modeling of saw-tooth structure formation in the L12–L10 two-phase system

The strain-accommodating mechanism of formation of the saw-tooth microstructure in the L1₂+L1₀ two-phase ordered system is proposed. To describe the atomic scale kinetics of ordering and decomposition in this system, the master equation, which explicitly incorporates the effect of the transformation strain, is formulated. It is used to simulate the precipitation of the L1₀ phase from the L1₂ parent phase in the Co–Pt alloy. The computer simulation shows that the decomposition occurs heterogeneously on antiphase boundaries of the L1₂ structure if the composition is near the solubility limit of the L1₂ phase. It eventually produces the saw-tooth microstructure. The decomposition transforms the (010) antiphase boundary into a layer of the single-variant tetragonal L1₀ phase separating the L1₂ antiphase domains. Later, the strain accommodation transforms this single-variant L1₀ phase layer into the saw-tooth pattern. The simulation results are in excellent qualitative and quantitative agreement with our TEM images of Co_38.5Pt_61.5.     

不同弹性畸变程度下Ni75Al14Mo11合金沉淀过程的多尺度模拟

基于微观相场模型和第一性原理方法模拟了Ni75Al14Mo11合金在不同弹性畸变能常数下的相变过程。当弹性畸变能从无到有时,沉淀相形貌由椭圆状变为块状,分布由不规则随机排列变为沿弹性"软"方向规则排列,具有一定方向性;弹性畸变能对短程DO22有序相的析出有抑制作用,并且对沉淀粗化过程的影响要大于对析出过程的影响;弹性畸变能对沉淀相的有序化及原子簇聚的影响并不是随着其增加而简单的起抑制或促进作用,而是与其取值范围有关。在相同的外界条件下,Ni、Al元素形成Ni3Al要比Ni、Mo元素形成Ni3Mo容易,导致Ni75Al14Mo11合金在1073 K时效下较易析出Ni3Al。     

Microscopic phase-field simulation coupled with elastic strain energy for precipitation process of Ni-Cr-Al alloys with low Al content

The precipitation process of Ni-Cr-Al alloy with low Al content was studied at atomic scale based on the microscopicphase-field kinetic model coupled with elastic strain energy.The aim is to investigate the effect of elastic strain energy onprecipitation mechanism and morphological evolution of the alloy.The simulation results show that in the early stage of precipitation,D022 phase and L12 phase present irregular shape,and they randomly distribute in the matrix.With the progress of aging,L12 phaseand D022 phase change into the quadrate shape and their orientations become more obvious.In the later stage,L12 phase and D022phase present quadrate shape with round corner and align along the[100]and[010]directions,and highly preferential selectedmicrostructure is formed.The mechanism of early precipitation of L12 phase in Ni-17%Cr-7.5%Al(mole fraction)alloy is the mixedstyle of non-classical nucleation growth and spinodal decomposition and the D022 phase is the spinodal decomposition.Themechanisms of early precipitation of L12 phase and D022 phase in Ni-12.5%Cr-7.5%Al alloy are both the non-classical nucleationand growth.The coarsening process follows the rule of preferential selected coarsening.     

Effect of boron and carbon addition on microstructure and mechanical properties of the aged gamma-prime strengthened alumina-forming austenitic alloys

The goal of this work was to understand the effects of aging at 800 °C on the microstructures and mechanical properties of two recently-developed AFA stainless steels based on Fe-14Cr-32Ni-3Nb-3Al-2Ti (wt.%), one of which contained small additions of boron and carbon. To that end both the size distributions and growth kinetics of the B2, Laves phase, L1₂ precipitates present were quantified. While the lattice parameter, morphology, size and coarsening behavior of the L1₂ precipitates was the same in both AFA alloys, the B and C enhanced the grain boundary coverage by both Laves phase and B2-NiAl precipitates, but suppressed their coarsening. These interstitial additions also suppressed the formation of twins and discontinuous precipitation, which were observed in the B and C-free material. It is shown that the yield strength at 700 °C is largely controlled by the size of the L1₂ precipitates, with the largest strengthening effect obtained after aging for 2.4 h for both AFA alloys. Longer aging time led to a loss of strength mainly due to the coarsening of the L1₂ precipitates.