Unit-cell design for two-dimensional phase-field simulation of microstructure evolution in single-crystal Ni-based superalloys during solidification

Phase-field simulation serves as an effective tool for quantitative characterization of microstructure evolution in single-crystal Ni-based superalloys during solidification nowadays. The classic unit cell is either limited to γdendrites along 001 crystal orientation or too ideal to cover complex morphologies for γ dendrites. An attempt to design the unit cell for two-dimensional(2-D) phase-field simulations of microstructure evolution in single-crystal Ni-based superalloys during solidification was thus performed by using the MICRESS(MICRostructure Evolution Simulation Software) in the framework of the multi-phase-field(MPF) model,and demonstrated in a commercial TMS-113 superalloy. The coupling to CALPHAD(CALculation of PHAse Diagram) thermodynamic database was realized via the TQ interface and the experimental diffusion coefficients were utilized in the simulation. Firstly, the classic unit cell with a single γ dendrite along 001 crystal orientation was employed for the phase-field simulation in order to reproduce the microstructure features.Then, such simple unit cell was extended into the cases with two other different crystal orientations, i.e., 011 and 111 . Thirdly, for 001 crystal orientations, the effect of γ dendritic orientations and unit cell sizes on microstructure and microsegregation was comprehensively studied, from which a new unit cell with multiple γdendrites was proposed. The phase-field simulation with the newly proposed unit cell was further performed in the TMS-113 superalloy, and the microstructure features including the competitive growth of γ dendrites,microsegregation of different solutes and distribution of γ′ grains, can be nicely reproduced.     

灰铸铁中初生奥氏体树枝晶二维金相切面与三维空间结构之间的关系

本文应用晶体几何学原理,对灰铸铁中初生奥氏体树枝晶进行了解剖研究,发现金相试样中复杂纷乱的枝晶二维切面是不同位向的树枝晶沿一定晶面切开的结果。利用树枝晶二维和三维空间结构之间的几何对应关系,可以比较方便、准确地对树枝晶的生长方式及形貌特征进行分析和计算。     

Microstructure and heat treatment for Ni3Al-based single crystal alloy with different crystal orientations

Ni₃Al-based single crystal alloy IC6SX with different crystal orientations were prepared by seed crystal method. The microstructure and heat treatment of the alloy were investigated. The results showed that the microstructure of the alloy was in dendrite structure, and the crystal orientation had significant effect on the dendrite morphology of this alloy. The precipitated phases of (MoNi)₆C and NiMo appeared in the microstructure of the three alloys with different crystal orientations during solidification process. Compared with other two alloys, the volume fractions of precipitated phases of both (MoNi)₆C and NiMo was the most in the alloy with [111] orientation and the least in the alloy with [001] orientation. The solidus and liquidus temperatures of the alloy IC6SX tested by differential scanning calorimetry (DSC) were 1356 °C and 1387 °C, respectively. Meanwhile, the effect of different solution temperatures on the microstructure of the alloy with different orientations was studied. The results showed that the precipitated phases of (MoNi)₆C and NiMo were eliminated with the solid solution treatment under the condition of 1300 °C/10 h. However, the incipient melting of the alloys occurred due to the dissolution of low melting point phases. As the temperature dropped to 1280 °C, the area of incipient melting in the alloy with different orientations decreased gradually. However, there was no incipient melting appearing in the three alloys with different orientations when the solution treatment temperature dropped to 1260 °C.     

Effects of Sr addition on the microstructures and mechanical properties of in-situ ZrB_2 nanoparticles reinforced AlSi9Cu3 composites

The effects of Sr addition on the microstructure and mechanical properties of in-situ ZrB_2 nanoparticles reinforced AlSi9Cu3 composites synthesized via direct melt reaction were systematically investigated. The addition of Sr could modify the morphology of eutectic silicon particles and refine the second dendrite arm spacing of α-Al dendrites.Alternatively, the ZrB_2 nanoparticles were also refined and distributed more homogenously, and nanoparticle agglomerations were reduced with the addition of Sr element. The results demonstrated that the addition of 0.06 wt% of Sr element can reach the optimal refinement of the second dendrite arm spacing of α-Al and the modification of eutectic Si. In this case, the ultimate tensile strength, yield strength and elongation reached 330 MPa, 226 MPa and 15.70%, respectively, which were remarkably enhancement in comparison with the base alloy.     

基于PF-LBM模型的自然对流影响枝晶生长模拟

基于二元合金枝晶生长的相场模型,建立耦合流场、温度场和溶质场等物理外场的多元合金相场模型,模拟了单晶粒和多晶粒在自然对流作用下的生长,观察了枝晶凝固过程中的枝晶形貌、流场以及溶质场的变化.研究发现:温度梯度和浓度梯度改变引起自然对流,使枝晶整体的对称性遭到破坏,上游枝晶尖端生长受到促进,生长速度大于下游,水平方向枝晶尖端生长速度介于上下游之间,二次枝晶臂生长速度、浓度与一次枝晶臂基本相同,能量起伏和结构起伏使枝晶受到的影响更加明显.此外,随着各向异性强度增加,枝晶尺寸变大,生长速度加快,主枝晶臂变细,内部凹陷变明显,尖端变尖锐,二次枝晶臂间距增大.当单晶粒各向异性强度为0.05时,出现明显的“颈缩”现象,多晶粒在各向异性强度为0.03时,出现明显“颈缩”现象.     

An investigation on supercooling directional solidification process of Cu-Ni single phase alloy

Supercooling directional solidification (SDS) is put fotward by combination of melt supercooling and conventional solidification by application of supercooling inheritance. On the self-designed SDS equipment, SDS of Cu-Ni alloy was achieved successfully The results are as follows f (i) The primary arm spacing is about 30 μm, the growth of secondary arms are strongly suppressed. The primary arm spacing is nearly the same as LMC method (GL=25 K/mm, V=500 pm/s), the primary stems are straight, fine and completed. with an inclination angle of about 5.8° (ii) A semi-quantitative T-T model is brought fotward to describe the dendrite growth rate V vs. undercooling AT The prediction of T-T model agrees well with experimental results. The formation of fine equiaxed dendrites, transition region and dendrite region can be explained successfully by △T-V-x relation of T-T model.     

Formation mechanisms and control method for stray grains at melt-back region of Ni-based single crystal seed

An experimental study together with numerical simulation was conducted to investigate the formation mechanisms and control methods for stray grains at melt-back of seed in this paper. The numerical simulation results showed that the convex solid/liquid (S/L) interface changed very slowly into a concave interface during the initial solidification stage and the undercooling was slightly affected by the S/L curvature change. The formation of stray grains below melt-back interface at seed perimeter could be suppressed with the decrease of clearance between the seed and mold. However when the clearance was further decreased to 0, an orientation deviation layer formed originated from the deformation of un-melted seed caused by different expend coefficient between the seed and mold. The nucleation of stray grains above the melt-back interface at the seed perimeter could be suppressed using the mold with small surface roughness. The isolated un-melted dendrite stem at semi-solid mushy of the seed with the large original primary dendrite spacing transfer to complex network structure, suppressing the formation of the stray grains, when the primary dendrite spacing of seed decreased or the seed underwent solution heat treatment. Then, the formation mechanisms of the stray grains at the melt-back region are discussed based on above results, and a method is proposed to suppress the formation of the stray grains for preparing single crystal components by re-used seed.     

Insight of the dendrite deformation in Ni-based superalloys for increased misorientation along convergent boundaries

The dendrite growth and the associated misorientation evolution on the platform base of a single crystal investment casting were investigated. It was found that the long secondary dendrite arm(LSDA) grew through the whole platform, and a convergent boundary of dendrite arms(CBDA) formed simultaneously between the corresponding branched arms and the extended secondary arms from the blade zone. The corresponding orientation measurement confirmed that the misorientation of dendrite arms between the two sides of the CBDA monotonically increased from 5.9° at one platform edge to 33.5° at the other platform edge. Additionally, the LSDA dendrite deformation was also identified by the accumulated misorientation within the LSDA dendrite core. Furthermore, it was deduced that the increased misorientation along the CBDA was caused by the LSDA dendrite deformation, and the reason of LSDA dendrite deformation was further discussed based on the associated strain distribution around the LSDA. Because of a 33.5° misorientation along the CBDA, it was indicated that the dendrite deformation might be the formation mechanism of high angle boundary.     

Inhibition of stray grains at melt-back region for re-using seed to prepare Ni-based single crystal superalloys

Assisted by the mold preinstalled an alumina tube into seed segment, the influence of the original primary dendrite spacing of seed on the formation of stray grains at melt-back region was investigated during Ni-based single crystal casting using seeding method. The results showed that the interface reaction between the seed and mold as well as the formation of stray grains at the surface of seed were avoid using an alumina tube with surface roughness of 0.35 μm as the mold inner wall. As the original primary dendrite spacing of the seed decreased to less than 201 μm, the morphology of un-melted solid phase in semi-solid zone changed from isolated dendrite stem to the complex network, resulting in the inhibition of the formation of stray grains inside of the seed. The seed with original primary dendrite spacing of 201 μm was also successfully re-used to fabricate single crystal casting.     

Mechanical properties of directionally solidified lead-antimony alloys

The Pb-17wt% Sb alloy was directionally solidified under two solidification conditions: with different temperature gradients (G=0.93–3.67 K/mm) at a constant growth rate (V=17.50 μm/s) and with different growth rates (V=8.3–497 μm/s) at a constant temperature gradient (G=3.67 K/mm) in a Bridgman furnace. Microstructure parameters, such as primary dendrite arm spacing (λ₁), secondary dendrite arm spacing (λ₂), and dendrite tip radius (R), were measured. The microhardness (Hv) and ultimate tensile strength (σ) of the directional solidification samples were also measured. The influences of solidification and microstructure parameters on Hv and σ were investigated. The results obtained in this work were compared with similar experimental researches in literatures. It is shown that the Hv and σ values increase with the increase of G and V, but decrease with the increase of λ₁, λ₂, and R.     

Effect of the withdrawal rate on the microstructure and thermal durability of a third-generation single crystal superalloy

Single crystal Ni-based superalloys are the typical structural materials for high-pressure turbine blades, and their microstructure is critical in determining their mechanical properties. The withdrawal rate is a key parameter affecting the microstructure during the single crystal growth process. In the present work the effect of the withdrawal rate on the microstructure of a third-generation single crystal superalloy containing 6.8 ?wt% Re has been investigated, and the creep resistance of the alloy determined. The results showed that increased withdrawal rate refined the dendritic structure, reduced dendritic arm spacing, promoted the growth of secondary tertiary dendrites and decreased solidification segregation with a reduced size of γ′ phase. The porosity density of the as-cast alloy first decreased and then increased with the withdrawal rate, while the minimum porosity densityoccurred when the alloy was under the solidification condition of withdrawal rate of 4.5 ?mm/min. The maximum creep rupture life of 326.4 ?h of the heat-treated alloys under the test condition of 1100 ?°C/140 ?MPa also appeared at the alloys under the withdrawal rates of 4.5 ?mm/min. It is believed that the minimum porosity density and reduced size of the γ′ phase may be the main reasons for the enhanced creep rupture life of the alloys with withdrawal rates of 4.5 ?mm/min. This investigation provides theoretical support and a practical basis for the development of third-generation single crystal superalloys.     

Effect of M-EMS on the solidification structure of a steel billet

Effects of mold electromagnetic stirring (M-EMS) on the solidification structure of 45# steel billet were investigated by examination of interdendritic corrosion. The results show that the primary and secondary dendrite arm spacings increase from the edge of the billet to the center and decrease obviously with increasing electromagnetic torque, which will be beneficial to refine the solidification structure and enlarge the equiaxed crystal zone. The ratio of equiaxed crystal increases by 15.9% with the electromagnetic torque increasing from 230 to 400 cN·cm. The increase of stirring intensity can improve the cooling rate and the impact of M-EMS on it reduces from the edge of the billet to the central area, where the cooling rates are similar at different torques. The closer to the central area, the less the influence of M-EMS on the cooling rate is. The ratio of the primary to secondary dendrite arm spacing is approximately 2.0, namely, λ₁≈2λ₂, and is constant irrespective of the stirring intensity and position of the billet. Original position analysis (OPA) results indicate that the center segregation of the billet is greatly improved, and the more uniform and compact solidification structure will be obtained with the increase of stirring intensity.     

Preparation and tensile properties of DD5 single crystal castings

The preparation procedure of DD5 single crystal castings was optimized. The microstructure characteristics of DD5 single crystal superalloy were investigated by microstructure observation and segregation behavior examination. The results show that the grain orientation is optimized by constraining the spiral crystallizer in [001] orientation and spatial scale. Also, the γ’ phase of inter-dendrites is larger and more irregular than that in dendrite arms. High temperature tensile tests of DD5 single crystal castings exhibit that the peak stress increases with increasing temperature, while the area reduction shows an opposite trend, when the temperature is below 800℃; meanwhile, when the temperature is between 800℃ and 1000℃, the fracture stress of the alloy is the same as the peak stress. The fracture mode changes from shear to ductile with increasing temperature from 600℃ and 1000℃.     

基于自适应有限元枝晶自由生长相场模型模拟

利用相场模型模拟了过冷熔体中单个完整等轴枝晶在凝固过程中的生长和形貌演化,采用自适应有限元方法求解相场模型的控制方程,研究了在计算域较大、界面层厚度较薄的情况下各向异性和过冷度等物理参数对枝晶形状和生长的影响.结果表明:过冷度越大,枝晶间竞争越激烈,生长速度越慢;各向异性系数越大,枝晶沿选定方向生长的趋势越强,生长速度越快,二次枝晶间距越小,侧向分枝越发达. 与有限差分方法(FDM)相比,采用自适应有限元法(AFM)在CPU计算时间和存储空间均降低了一个数量级,并且系统尺寸越大,自适应有限元法优势越明显,便于更大尺度多场耦合相场模型的数值模拟.通过比较均匀网格法和以往的晶体生长数值模拟实验,证明了自适应有限元法的准确性、高效性和鲁棒性.     

熔体温度处理细化亚共晶Al-Si合金组织

利用正交试验的方法对熔体温度处理细化亚共晶Al-Si合金的凝固组织进行了研究，结果表明，经过熔体温度处理后，凝固组织中一次枝晶尺寸明显减小，长的树枝晶变为短的树枝晶或等轴晶，并且枝晶数量明显增多；二次枝晶臂间距变化不明显，从原子团簇的角度分析认为，这是由于高，低温熔体混合后，低温熔体中大的原子团簇得到细化，从而导致混合熔体中形核质点增殖的结果，研究同时发现，高，低温熔体的混合方式对熔体温度处理效果有直接影响，熔体的均匀混合有利于增大熔体凝固过冷度，减小临界晶核半径，促进凝固组织的细化。     

Mechanical characterization and strain-rate sensitivity measurement of Ti- 7333 alloy based on nanoindentation and crystal plasticity modeling

The relationship between crystal orientations and meso-mechanical properties of β phase Ti-7333 titanium was investigated through the combination of nanoindentation experiments and simulation. The crystal plasticity finite element(CPFE) model for nanoindentation of single body-centered cubic crystal was established based on the experimental data. And the crystal plasticity constitutive law was implemented to simulate the nanoindentation process, obtaining satisfied results with an acceptable error. From the simulated pileup morphology patterns with different crystal orientations, it was found that the β phase experienced a symmetrical and orientation-related deformation process. Meanwhile, the strain-rate sensitivity(SRS) of β phase was investigated through nanoindentation tests based on continuous stiffness measurement(CSM) under different strain rates,varying between 0.2, 0.05 and 0.01 s~(-1). Two grains with different orientations exhibited similar SRS exponents,m, calculated from the experimental results.     

Effects of Mo addition on microstructure of a 4th generation Ni-based single crystal superalloy

The effects of Mo addition on the microstructure of a 4th generation Ni-based single crystal superalloy were investigated. Mo addition significantly promoted elements Mo, W and Re partition into γ phase and enhanced absolute lattice misfit at 1100 ?°C. The increase of Mo concentration from 2 ?wt% to 4 ?wt% also decreased the content of eutectic islands and the segregation ratios of other alloying elements in the as-cast state, especially Re and W. After heat treatments, the size of γ′ phase and width of γ channels decreased slightly with higher Mo content. More Mo additions slightly enhanced the segregation behavior of Re while reducing the segregation behavior of Mo. However, it revealed that the primary and secondary dendrite arm spacings were barely affected by Mo addition.     

Effect of M-EMS on the solidification structure of a steel billet

Effects of mold electromagnetic stirring (M-EMS) on the solidification structure of 45# steel billet were investigated by examination of interdendritic corrosion. The results show that the primary and secondary dendrite arm spacings increase from the edge of the billet to the center and decrease obviously with increasing electromagnetic torque, which will be beneficial to refine the solidification structure and enlarge the equiaxed crystal zone. The ratio of equiaxed crystal increases by 15.9% with the electromagnetic torque increasing from 230 to 400 cN·cm. The increase of stirring intensity can improve the cooling rate and the impact of M-EMS on it reduces from the edge of the billet to the central area, where the cooling rates are similar at different torques. The closer to the central area, the less the influence of M-EMS on the cooling rate is. The ratio of the primary to secondary dendrite arm spacing is approximately 2.0, namely, λ1≈2λ2, and is constant irrespective of the stirring intensity and position of the billet. Original position analysis (OPA) results indicate that the center segregation of the billet is greatly improved, and the more uniform and compact solidification structure will be obtained with the increase of stirring intensity.     

共轭双滑移取向铜单晶疲劳位错结构的SEM-ECC观察

利用扫描电镜电子通道衬度(SEM-ECC)技术观察和分析了[■ 2 3]和[■ 1 2]共轭双滑移取向铜单晶体的循环饱和位错结构.结果表明,驻留滑移带(PSBs)的位错结构随晶体取向的不同可呈现出不同的形态,如:[■ 1 2]晶体中的楼梯结构和[■ 2 3]晶体中的沿主滑移面排列的不规则或较规则胞结构.同时还观察到[■ 2 3]晶体中形变带的位错结构由一些不规则的墙和胞结构组成.对于晶体取向位于标准取向三角形[0 0 1]-[■ 1 1]边上的铜单晶体,其疲劳位错结构随晶体取向的不同发生有规律的变化,即:当晶体取向从[■ 1 2]分别向[■ 1 1]和[0 0 1]移动时,位错结构由PSB楼梯...     

Influence of withdrawal rate on the porosity in a third-generation Ni-based single crystal superalloy

The influence of withdrawal rate on the porosity in a third-generation Ni-based single crystal superalloy was investigated by a quantitative evaluation method. The results showed that the withdrawal rate obviously effected on the average area fraction, number and diameter of porosities except their radius ratios. In consideration of the microstructure observation for dendrite arms, an optimized withdrawal rate was obtained with a minimum porosity level as about 125 μm s~(-1). Simultaneously, a threshold value for the acceptance level of porosities might be set as about 0.1% in order to fulfill the requirements for Ni-based single crystal casting in laboratory scale. Finally, the formation reason of porosity was discussed and it was concluded that the feeding for the volume shrinkage of the last solidified eutectic liquids from the residual liquids and the isolating effect of the morphologies of dendrite arms might be two key factors in controlling the porosities level in Ni-based single crystal superalloy.