On the creep and phase stability of advanced Ni-base single crystal superalloys

The present article examines microstructure stability and creep resistance of a 5th generation superalloy, which has Cr content at 4.6 wt%, 6.4 wt% Re and 5.0 wt% Ru, in comparison with that of a 4th generation superalloy (3.2 wt% Cr, 5.8 wt% Re and 3.6 wt% Ru). The aim is to elucidate the implication of increasing Cr, Re and Ru contents for future alloy developments. Experimental results have concluded that high Re + Ru content could promote formation of hexagonal δ phase at 900 °C; additional Cr and Re could enhance the precipitation of TCP phase at 1100 °C. Although an increase in lattice misfit between γ and γ′ in the 5th generation superalloy could strengthen the alloy against creep deformation under conditions at high temperatures (≥1000 °C) and low stresses (≤245 MPa) whilst the microstructural stability remained, the tendency to raft should be avoided during creep at lower temperatures and higher stresses.     

Structural and microstructural phase evolution during mechano-synthesis of nanocrystalline/amorphous CuAlMn alloy powders

The formation mechanism of Cu–11.5Al–4Mn alloys by mechanical alloying (MA) of pure elemental powders was investigated. During milling, the powder sampling was conducted at predetermined intervals from 1 h to 96 h. The quantitative phase analyses were done by X-ray diffraction and the particles size and morphology were studied by scanning electron microscopy. Furthermore, the microstructure investigation and phase identification were done by transmission electron microscopy. Concerning the results, the nanocrystalline Cu solid solution were formed at short milling times and, by milling evolution, the austenite-to-martensite (2H) phase transformation occurred. Moreover, the formation of considerable amount of amorphous phase and its partial transformation to crystalline phases during the milling process were revealed. It was also found that, by milling development, the powder morphology changes from lamellar to semi-spherical and their size initially increases, then reduces and afterward re-increases.     

Coupling phase field with creep damage to study evolution and creep deformation of single crystal superalloys

A phase-field model coupling with elastoplastic deformation and creep damage has been built to study the microstructural evolution and deformation behavior for Ni-Al single crystal alloy during the whole creep processing.The relevant experiments were conducted to verify the model validity.The simulation results show that under the tensile creep at 1223 K/100 MPa,cubic γ'phases coarsen along the direction parallel to the axis of tensile stress during the first two creep stages;and spindle-shaped and wavy γ'phases are formed during tertiary creep,similar to the experimental results.The evolution mechanism ofγ'phases is analyzed from the perspective of changes of stress and strain fields.The island-like γ phase is observed and its formation mechanism is discussed.With the increase of creep stress,the directional coarsening of γ'phase is accelerated,the steady-state creep rate is increased and the creep life is decreased.The comparison between simulated and experimental creep curves shows that this phase-field model can effectively simulate the performance changes during the first two creep stages and predict the influence of creep stresses on creep properties.Our work provides a potential approach to synchronously simulate the creep microstructure and property of superalloys strengthened by γ'precipitates.     

Effects of Ni,Cr and W on the microstructural stability of multicomponent CoNi-base superalloys studied using CALPHAD and diffusion-multiple approaches

The alloying effects of Ni,W and Cr on the microstructural stability of CoNi-base alloys were investigated using a multicomponent diffusion multiple after being aged at 1000 ℃ for 1000 h.The diffusion multiple was carefully designed based on thermodynamic calculations.The relationships between alloy compo-sitions and microstructural characteristics were established over a large compositional range using this single sample,and the alloying effects of Ni,W and Cr on the elemental partitioning behaviors between γ and γ'two phases were thermodynamically analyzed using high-throughput calculation.The results together show that an increase of Ni content increases the γ'volume faction in the long-term aged microstructures.However,the higher Ni content leads to the precipitation of the x phase by promoting the partitioning of W from the γ'phase to the γphase.The decrease of W content dramatically reduces the γ'volume faction,but the addition of Cr can properly counteract this effect by promoting the partitioning of Al and Ti from the γphase to the γ'phase.This study will be helpful for accelerating the development of novel γ'-strengthened multicomponent CoNi-base alloys,as well as providing experimental data to improve the thermodynamic database.     

Effect of magnetic field on interfacial energy and precipitation behavior of carbides in reduced activation steels

This work investigated the influence of high temperature and high magnetic field on the carbide precipitation behavior in reduced activation steels. As-quenched steels are tempered at 923 K for 3 h with and without a 10 T magnetic field. The applied field can effectively prevent the directional growth of rod-shaped M₂₃C₆ carbides along martensite packet boundaries. The aspect ratio of M₂₃C₆ carbides decreased from 2.3 to 1.2 due to an increase of the carbide/ferrite interfacial energy under the high magnetic field. Applications of the Weiss molecular field theory to calculate the difference in interfacial energy caused by the high magnetic field, and of the Langer-Schwartz theory to model metal carbide (MC) precipitation behavior under the magnetic field were described. Results indicated that the density of MC decreased by nearly an order of magnitude and its mean size increased by 40% owing to an increase of 0.03 J/m² of the carbide/ferrite interfacial energy.     

A phase field model for stress‐based evolution of load‐bearing structures

We present a continuum‐type optimality algorithm for the evolution of load‐bearing solid structures with linear elastic material. The objective of our model is to generate structures with help of a sensitivity function accounting for equivalent stress. Similar to Evolutionary Structural Optimization, a threshold of equivalent stress is evaluated. However, we do not consider a material rejection ratio. The evolution process is governed by an Allen‐Cahn equation in the context of phase field modeling. The steady state of phase transition is the final geometry of the structure. The model accounts for the desired filling level, geometry of the design space, static loadings, and boundary conditions. Our variational approach drops conservation of mass and couples density as well as stiffness of the continuum by a sophisticated function to the phase field variable. Continuous regions of voids and material evolve from the initial state of homogeneously distributed material. The complexity of evolving structures depends on two numerical parameters, which we discuss in several examples.     

相场方法模拟氙枝晶生长研究

基于相场方法对纯物质的凝固过程进行了二维数值模拟.以氙为例,展示了界面形貌的演化过程,研究了相场参数对枝晶界面形貌的影响.结果表明,随着过冷度值的增加,晶核由一圆核逐渐发展为发达的枝晶,相应的枝晶稳态尖端速度明显加快;随着耦合系数的增大,晶核由一圆核发展为细长的枝晶,枝晶的稳态尖端速度呈单调递增趋势,界面的稳定性逐渐变差.     

Diffusion of lithium ions and diffusion-induced stresses in a phase separating electrode under galvanostatic and potentiostatic operations: Phase field simulations

Phase separation in an electrode of a lithium ion battery, which is a phenomenon where an active electrode material is separated into Li-rich and Li-poor phases, exists widely in many active materials and has significant impacts on the diffusion of lithium ions and diffusion-induced stresses. A phase field model is developed to study the phase separation. Firstly, the influences of various energies, such as the free energy of uniform Li-ion concentration, gradient energy and elastic energy, on phase separation are discussed. Secondly, the impacts of charge operation, e.g. galvanostatic and potentiostatic, on Li-ion diffusion and diffusion-induced stresses in a planar phase separating electrode are investigated. Calculations are also made for single phase electrodes based on Fick’s law for comparison. The obtained simulation results show that the Li-ion diffusion in a phase separating electrode depends significantly on the phase separating profile and movement of phase boundary, but it is not sensitive to charge operation. The diffusion-induced stresses also separate into high and low stress regions. Finally, based on the diffusion process and diffusion-induced stress, it is suggested that phase separation should be avoided for the sake of fast charging and mechanical reliability.     

Mechanical properties and microstructural evolution of Al 6061 alloy processed by multidirectional forging at liquid nitrogen temperature

Al–Mg–Si alloy was subjected to multidirectional forging (MDF) at liquid nitrogen temperature (LNT), to cumulative strains of 1.8, 3.6 and 5.4. The deformed microstructures were examined by optical microscopy under polarized light and transmission electron microscopy (TEM). The deformed samples showed the formation of dislocation cells structure with high dislocation density at lower strains. Composite structure consisting of lamellar morphology at deformation bands and equiaxed grain morphology was observed. Significant differences in microstructure of the deformed samples were observed with increasing strain at LNT. At cumulative strain of 5.4, the microstructure shows nearly equiaxed subgrain structure with an average size of 250 nm with high angle grain boundaries. The mechanical properties were studied through Vickers hardness testing machine and tensile tester. The hardness value of MDFed alloy at LNT has increased from 50 Hv to 115 Hv for cumulative strain of 5.4. Tensile strength has increased from 180 MPa to 388 MPa with 4.5% percentage of elongation to failure. The improvement in hardness and tensile strength of forged alloy is attributed to the formation of equiaxed sub-grain structures and the presence of high dislocation density.     

A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns

The numerical modeling of dynamic failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies and demands the formulation of additional branching criteria. This drawback can be overcome by a diffusive crack modeling, which is based on the introduction of a crack phase field. Following our recent works on quasi‐static modeling of phase‐field‐type brittle fracture, we propose in this paper a computational framework for diffusive fracture for dynamic problems that allows the simulation of complex evolving crack topologies. It is based on the introduction of a local history field that contains a maximum reference energy obtained in the deformation history, which may be considered as a measure of the maximum tensile strain in the history. This local variable drives the evolution of the crack phase field. Its introduction provides a very transparent representation of the balance equation that governs the diffusive crack topology. In particular, it allows for the construction of a very robust algorithmic treatment for elastodynamic problems of diffusive fracture. Here, we extend the recently proposed operator split scheme from quasi‐static to dynamic problems. In a typical time step, it successively updates the history field, the crack phase field, and finally the displacement field. We demonstrate the performance of the phase field formulation of fracture by means of representative numerical examples, which show the evolution of complex crack patterns under dynamic loading. Copyright © 2012 John Wiley & Sons, Ltd.     

热磁耦合下淬火考虑相变的温度场有限元分析

外加磁场淬火的温度场分布模拟是一个新的领域，研究了比热容在居里温度附近的突变，建立了外加磁场淬火时瞬态温度场和相变计算的数学模型；建立了包含磁场作用的热传导方程；建立了统一的有限元基本方程，得到热磁耦合作用下瞬态温度场的分布，并进行了测试。结果表明：外加磁场淬火后，冷却速度减小，冷却曲线变缓；工件的硬度略有上升。     

Solving thermal and phase change problems with the eXtended finite element method

 The application of the eXtended finite element method (X-FEM) to thermal problems with moving heat sources and phase boundaries is presented. Of particular interest is the ability of the method to capture the highly localized, transient solution in the vicinity of a heat source or material interface. This is effected through the use of a time-dependent basis formed from the union of traditional shape functions with a set of evolving enrichment functions. The enrichment is constructed through the partition of unity framework, so that the system of equations remains sparse and the resulting approximation is conforming. In this manner, local solutions and arbitrary discontinuities that cannot be represented by the standard shape functions are captured with the enrichment functions. A standard time-projection algorithm is employed to account for the time-dependence of the enrichment, and an iterative strategy is adopted to satisfy local interface conditions. The separation of the approximation into classical shape functions that remain fixed in time and the evolving enrichment leads to a very efficient solution strategy. The robustness and utility of the method is demonstrated with several benchmark problems involving moving heat sources and phase transformations. Received 20 May 2001 / Accepted 19 December 2001     

Implementation of a new strain split to model unilateral contact within the phase field method

A new orthogonal split of strain tensor into compressive and tensile parts is implemented within the phase field model to mimic unilateral contact condition with which any existing cracks and any crack propagation have to comply. The resulting phase field model offers several advantages as compared to other available schemes. First, it involves rigorous orthogonality between traction and compression parts. Second, it yields remarkably simple, new analytical expressions of the projectors which provide computational saving during the crack propagation simulation. Finally, it can be applied to arbitrary initial elastic anisotropic media, which is not the case of other available strain tensor split operators. A detailed comparison of the fracture responses predicted by the present model and other approaches is provided. It is shown that the present orthogonal decomposition is able to accurately predict experimental results and removes spurious effects found in other schemes for specific loads like compression.     

Micromagnetic investigation by a simplified approach on the demagnetization field of permanent magnets with nonmagnetic phase inside

A simplified analysis method based on micromagnetic simulation is proposed to investigate effects of nonmagnetic particles on the demagnetizing field of a permanent magnet. By applying the additivity law of the demagnetizing field, the complicated demagnetizing field of the real magnet could be analyzed by only focusing on the stray field of the reserved magnet. For a magnet with nonmagnetic particles inside, the particle size has no significant effect on the maximum value of the demagnetization field, but the area of the affected region by the particle is proportional to the particle size. A large particle produces a large affected area overlapped with those influenced by other particles, which leads to the large demagnetization field. With increasing the length of the particle along the magnetization direction, the demagnetization field on the pole surface increases. The pole surface with a convex shape will increase the demagnetization field. The demagnetizing field near the nonmagnetic particle will be further increased by the large macroscopic demagnetizing field near the pole surface. This work suggests some practical approaches to optimize the microstructure of permanent magnets.     

Effect of Hf additions on phase transformation,microstructural stability,and hardness of nanocrystalline 304L stainless steels synthesized by mechanical alloying

304L stainless steels with Hf additions were nanostructured by mechanical alloying (MA) and annealed at temperatures up to 1100 °C. The results showed that face-centered cubic (fcc) phase in 304L transformed to body-centered cubic (bcc) phase during MA. The in-situ studies revealed that bcc-to-fcc phase transformation completed after 105 min annealing at 900 °C for 304L, whereas Hf addition increased the required time and temperature for the complete transformation. The grain size of 304L stainless steel was ~10 nm after MA and remained ~167 and ~293 nm after annealing at 900 and 1100 °C, respectively, with Hf addition in comparison to 960 nm average grain size of base 304L stainless steel after annealing at 900 °C. The hardness of 304L increased from ~200 HV to 408 HV after MA and remained 329 HV after annealing at 1100 °C with Hf addition as opposed to 195 HV hardness of 304L.     

脉冲电场对FeMnSiCr形状记忆合金凝固组织及形状记忆效应的影响

研究了脉冲电场对FeMnSiCr合金凝固组织和形状记忆效应的影响.发现脉冲电场作用于FeMnSiCr合金凝固过程将使合金凝固组织的晶粒得到细化,分析认为柱状晶的存在使形状记忆效应明显提高.在脉冲电压为250V、频率为3Hz的条件下,贴近极冷区,FeMnSiCr合金的形状记忆效应最好.     

Simulation of the hydration kinetics and elastic moduli of cement mortars by microstructural modelling

The ability of the VCCTL microstructural model to predict the hydration kinetics and elastic moduli of cement materials was tested by coupling a series of computer simulations and laboratory experiments, using different cements. The novel aspects of this study included the fact that the simulated hydration kinetics were benchmarked using real-time measurements of the early-age phase composition during hydration by in situ X-ray diffraction. Elastic moduli are measured both by strain gauges (static approach) and by P-wave propagation (dynamic approach). Compressive strengths were measured by loading mortar prisms until rupture. Virtual samples were generated by VCCTL, using particle size distribution and phase composition as input. The hydration kinetics and elastic moduli were simulated and the numerical results were compared with the experimental observations. The compressive strength of the virtual mortars were obtained from the elastic moduli, using a power-law relation. Experimentally measured and simulated time-dependence of the major cement clinker phases and hydration product phases typically agreed to within 5%. Also, refinement of the input values of the intrinsic elastic moduli of the various phases enabled predictions of effective moduli, at different ages and different water-to-cement mass ratios, that are within the 10% uncertainty in the measured values. These results suggest that the VCCTL model can be successfully used as a predictive tool, which can reproduce the early age hydration kinetics, elastic moduli and mechanical strength of cement-based materials, using different mix designs.     

A study of nucleation, growth, texture and phase formation of electrodeposited cobalt layers and the influence of magnetic fields

Cobalt (Co) layers with a thickness of up to 50 nm have been electrodeposited under the influence of magnetic fields up to 10 T aligned perpendicular or parallel to the electrode surface. The crystallographic orientation and the phase composition of these layers have been investigated by X-ray diffraction and transmission electron microscopy. The layers consist mainly of the face centered cubic phase with a 〈111〉 orientation perpendicular to the electrode surface which results from the low surface free energy of these planes. An influence of magnetic fields on the crystallographic orientation has not been observed. It was found that magnetic fields affect the phase composition which results predominantly from the influence of the magnetic fields on the electrochemistry. The nucleation has been studied by in-situ scanning tunneling microscopy.     

Modeling the microstructural evolution and effect of cooling rate on the nanograins formed during the friction stir processing of Al5083

An analytical model is developed to study the effect of cooling rate on the final grain size of stirred zone of the Al5083 subjected to friction stir processing. The effect of cooling rate on the grain size of the stirred zone was investigated experimentally and numerically. A new microstructural evolution model was also suggested illustrating the mechanisms contributed in refining the microstructure. A new mechanism termed meta-dynamic recovery (MDRV) is introduced here in this regard. The simulation results also show that the rapid cooling rate resulted in superior mechanical properties through refining the microstructure of the stirred zone. However, decreasing the rotational speed and increasing the traverse speed of pin can also decrease the grain size of stirred zone.