Simulation of solid deformation during solidification: Shearing and compression of polycrystalline structures

Deformation of the semi-solid mush during solidification is a common phenomenon in metal casting. At relatively high fractions of solid, grain boundaries play a key role in determining the mechanical behavior of solidifying structures, but little is known about the interplay between solidification and deformation. In the present study, a polycrystalline phase-field model is combined with a material point method stress analysis to numerically simulate the coupled solidification and elasto-viscoplastic deformation behavior of a pure substance in two dimensions. It is shown that shearing of a semi-solid structure occurs primarily in relatively narrow bands near or inside the grain boundaries or in the thin junctions between different dendrite arms. The deformations can cause the formation of low-angle tilt grain boundaries inside individual dendrite arms. In addition, grain boundaries form when different arms of a deformed single dendrite impinge. During compression of a high-solid fraction dendritic structure, the deformations are limited to a relatively thin layer along the compressing boundary. The compression causes consolidation of this layer into a fully solid structure that consists of numerous sub-grains. It is recommended that an improved model be developed for the variation of the mechanical properties inside grain boundaries.     

含Nb-Ti微合金钢连铸过程中TiN析出行为研究

针对控制含Nb微合金钢铸坯角裂缺陷的增Ti固N控制工艺,通过热力学计算和试验分析手段,详细研究了钢中TiN颗粒的形成条件。经过研究得到结论：Ti元素可以稳定Nb在钢中的固溶状态,所生成的TiN颗粒在2 μm左右,属于非金属夹杂物范畴。随着冷却速率的增加,钢中生成的TiN颗粒位置逐渐由原奥晶界转为晶内析出。基于Ohnaka微观偏析模型计算凝固TiN凝固析出行为,当固相率达到0.95以上凝固前沿的[Ti][N]浓度积高于平衡浓度积,开始析出TiN。根据凝固前沿溶质元素偏聚程度排序：Scheil＞Ohnaka＞B-F＞C-K＞V-B＞Level。在钢液中析出的Al2O3类的高熔点氧化物降低了TiN形核势垒,促进了TiN颗粒的析出行为。     

单晶过渡液相扩散焊接头单晶化机理

为了探明单晶高温合金TLP扩散焊接头单晶化机理,采用扫描电镜（SEM）、背散射电子（BES）和背散射衍射（EBSD）分析接头微观组织.结果表明,接头内形成贯穿型晶界和等轴晶粒是接头无法实现单晶化的主要原因.在实际焊接过程中,应严格控制试样加工、中间层添加、装配、焊接等工序.在等温凝固阶段,液相依附于固态单晶基体以平面晶的方式外延生长,直至液相消失,界面上形成具有一致晶体取向的一块单晶,随着保温时间的延长,固态均匀化过程充分进行,冷却后将形成单晶化的接头.     

Direct Numerical Simulation of Solid Deformation During Dendritic Solidification

Deformation of the semisolid mush during solidification is a common phenomenon in metal casting and can lead to defects such as hot tears, macrosegregation, and porosity. The morphology of the solidifying mush, including the shape of the dendrites and the distribution of grain boundaries, plays a key role in determining its mechanical behavior. In the current study, a polycrystalline phase-field model is combined with a material point method stress analysis to numerically simulate the fully coupled dendritic solidification and elasto-viscoplastic deformation behavior of a pure substance in two dimensions. It is shown that solid compressive and shear deformations result in variations in the crystallographic orientation angle within a single dendrite that, in turn, affect the subsequent solidification behavior. Shearing of a dendritic structure occurs primarily in relatively narrow bands near or inside the grain boundaries or the thin junctions between different dendrite arms. The deformations can cause the formation of low-angle tilt grain boundaries inside of individual dendrite arms. In addition, grain boundaries form when different arms of a deformed single dendrite impinge. During compression of a high-solid-fraction dendritic structure, the deformations are limited to a relatively thin layer along the compressing boundary. The compression causes consolidation of this layer into a fully solid structure that consists of numerous subgrains.     

690镍基合金焊接结晶裂纹形成机理分析

采用横向可调拘束试验方法研究了690镍基合金焊带堆焊金属的结晶裂纹形成机理.结果表明,690镍基合金焊接结晶裂纹的形成与晶界(及亚晶界)偏析密切相关,Nb元素在其中有着重要影响:富Ni,Nb低熔点共晶相在晶界(及亚晶界)的偏析,导致堆焊金属的实际结晶温度降低,晶界(及亚晶界)处塑性储备减小、形貌被改善,促使结晶过程中裂纹萌生并沿平直晶界(及亚晶界)扩展.另外,Mn元素可通过抑制Nb元素在晶界的偏析,削弱Nb的上述不利作用,增强690镍基合金抵抗结晶裂纹的能力.     

Mechanism of competitive growth during directional solidification of a nickel-base superalloy in a three-dimensional reference frame

The microstructure evolution of bicrystal samples during directional solidification was studied, both by simulation and experiment, to explore the mechanism of competitive growth. A new orientation relationship of bicrystal samples, the non-uniplanar case, is proposed, which expands the orientation relationship of bicrystal samples from two dimensions to three dimensions. The results show that, in the non-uniplanar case, the favorably oriented grain overgrows the unfavorably oriented grain by developing new dendrites in the lateral gap where the primary dendrites of the unfavorably oriented grain diverge from the mold wall. During this process, the grain boundary is found to move in two directions, one perpendicular to the grain boundary and the other parallel to the grain boundary. To characterize the state of dendrite growth, a three-dimensional reference frame is constructed. In this reference frame, the mechanism of competitive growth can be categorized as a converging case, a non-uniplanar case and a diverging case. Furthermore, the simulation results are in good agreement with the experimental findings.     

焊接熔池凝固过程组织演变模拟

以枝晶生长动力学和晶粒生长能量最小原理为基础,建立了宏观传热与微观传质、形核、生长相耦合的焊接熔池CAMC晶粒生长二维数学模型.模型以CA方法模拟晶粒生长主干,MC在内部辅助晶粒生长以体现枝晶分枝机制,同时考虑非均匀形核对熔池结晶的影响因素,模拟了焊接熔池组织形成过程.结果表明,CAMC模型能够定量地描述熔池晶粒数目、尺寸和形貌演变,可以较准确地反映焊接熔池微观组织结构和熔池凝固过程中晶粒择优生长、柱状晶向等轴晶转换等物理机制.     

On the twinning occurrence in bulk semiconductor crystal growth

Based on known theories of twinning in semiconductor crystal growth, a new model is proposed to study the occurrence of twins during the solidification of photovoltaic multicrystalline silicon ingots. It is expected that twins will appear on facets existing at the grain boundary–solid–liquid triple line. Necessary conditions for the existence of facets are derived and it is shown that twinning remains a function of the probability of nucleation of twinned nuclei. It is demonstrated that this probability is in qualitative agreement with the experimental observation for cases where the grain orientation is such that an angle of 132° occurs between a facet and a grain boundary. However, full validation of the model requires accurate values of interfacial energies at the melting point, which are currently lacking.     

凝固过程晶粒生长动力学及拓扑转变机制的相场研究

基于连续相场动力学模型,研究了凝固过程形核、长大及粗化阶段的组织形貌演化,动力学转变,以及粗化过程拓扑转变,分析了形核与长大过程的关系。研究结果表明,形核长大过程中,晶粒体积分数逐渐增大至平衡值,总表面积先增大后减小,体积自由能是形核的驱动力,表面能是形核的阻力。形核伴随着长大,两者是相互重叠相互竞争的两个过程。晶粒生长过程中,边数大于六的晶粒持续长大,而边数少于六的晶粒不断缩小。小晶粒消失机制有:临近切换机制;三边﹑四边及五边晶粒直接消失机制;四边交叉点分离并最终导致小晶粒消失机制;晶界直接消失机制。模拟结果与实验结果符合较好。     

Metallurgical modeling of microcrack repairment during welding nonferrous materials: non-equilibrium solidification behavior of weld pool (I)

Metallurgical modeling of synergistic microcrack self-repairmen during welding single crystal and polycrystalline superalloys of high-temperature aerospace materials has been properly established.The idea of improvement of nickel-based superalloys weldability through non-equilibrium solidification behavior of backfill to self-repair arterial crack network is usefully proposed.Crystallographic control strategy of crack self-repairmen of fusion zone interdendritic solidification cracking and heat-affected zone (HAZ) intergranular liquation cracking is technically achievable,indicating that optimal niobium alloying beneficially refines weld microstructure,stabilizes the primary solidification path,increases the solidification temperature and concomitantly decreases the weld pool geometry.High-carbon grain boundary is more thermal stable and less contributes to incipient intergranular liquid film than that of low-carbon grain boundary.The theoretical predictions of cracking susceptibility are indirectly verified in a rather satisfactory manner.Additionally,the metallurgical modeling enhances predicative capabilities and thereby is readily applicable for other alloy systems.     

Effect of bonding temperatures on the transient liquid phase bonding of a directionally solidified Ni-based superalloy,GTD-111

The bonding phenomenon and the mechanism involved in the transient liquid phase bonding (TLP Bonding) of directionally solidified Ni-based superalloy GTD-111 was investigated. At a bonding temperature of 1403 K, the liquid insert metal was eliminated by isothermal solidification, which was controlled by the diffusion of B and Si into the base metal. The solids in the bonded interlayer simultaneously grew epitaxially from the mating base metal inward from the insert metal. The number of grain boundaries formed at the bonded interlayer corresponded with those of the base metal. Liquefaction at the grain boundary and dendrite boundary occurred at a temperature of 1433 K. At a bonding temperature of 1453 K which is higher than the liquefaction temperature of the grain boundary, liquids of the insert metal were connected with liquated grain boundaries; this connection extended as far as the grain boundary, which was approximately 1.5 mm from the interface. The composition of this liquid was a mixture of the insert metal and phase that existed at the grain boundary. At extended holding times, liquid phases gradually decreased, and liquids with a continuous band shape develop into distinct islands. However, the liquid phases did not disappear after a holding period of 7.2 ks at 1453K. The extended isothermal solidification process at the bonding temperature, which is higher than the liquefaction temperature for the grain boundary, was controlled by the diffusion of Ti. This resulted in its preferential liquefaction compared to B or Si in the insert metal.     

Uncertainty quantification in modelling equiaxed alloy solidification

Numerical simulations can provide insight into physical phenomena during alloy solidification processes that cannot be observed experimentally. These model predictions depend on the material, process and numerical parameters which contain inherit uncertainties due to their origin in experimental measurements or model assumptions. As a step towards understanding the effect of uncertain inputs on solidification process modelling, uncertainty quantification and sensitivity analysis are performed on a transient model of transport phenomena during the solidification of grain refined Al-4.5 wt.% Cu in a rectangular cavity. The effect of microstructural model parameters, thermal boundary conditions and material property input uncertainties are examined for their effect on macrosegregation levels and solidification time. Predictions of the macrosegregation level are most sensitive to the dendrite arm spacing of the rigid mushy zone.     

Metallurgical modeling of microcrack repairment during welding nonferrous materials: non-equilibrium solidification behavior of weld pool (Ⅰ)

Metallurgical modeling of synergistic microcrack self-repairmen during welding single crystal and polycrystalline superalloys of high-temperature aerospace materials has been properly established. The idea of improvement of nickel-based superalloys weldability through non-equilibrium solidification behavior of backfill to self-repair arterial crack network is usefully proposed. Crystallographic control strategy of crack self-repairmen of fusion zone interdendritic solidification cracking and heat-affected zone( HAZ) intergranular liquation cracking is technically achievable,indicating that optimal niobium alloying beneficially refines weld microstructure,stabilizes the primary solidification path,increases the solidification temperature and concomitantly decreases the weld pool geometry. High-carbon grain boundary is more thermal stable and less contributes to incipient intergranular liquid film than that of low-carbon grain boundary. The theoretical predictions of cracking susceptibility are indirectly verified in a rather satisfactory manner. Additionally, the metallurgical modeling enhances predicative capabilities and thereby is readily applicable for other alloy systems.     

Zn对Mg-9Al合金凝固行为的影响

研究了Zn元素对Mg-9Akl合金的凝固行为，尤其是对热裂倾向性的影响。通过热分析手段考察合金的凝固特征。用热裂环法评价合金的热裂倾向性，引入了热裂倾向性（HSC）因子的概念。并通过金相观察、扫描电镜和电子探针对合金的凝固、热裂行为进行了研究。研究发现，在凝固过程中An,Al元素由于晶间偏析而在晶界富集。Zn元素的加入，增加了晶界低熔点相的量，并降低了其熔点，从而明显增加了合金的热裂倾向性。Mg-9Al-xZn合金的热凝产生于凝固后期，呈沿晶断裂。加入Zn元素对Mg-9Al合金的晶粒有细化作用。     

Ti-50.0Ni单晶形状记忆合金组织与记忆性能研究

在自制的定向凝固炉中,用带引晶器的石墨模壳制备出Ti-50.0at%Ni单晶.利用光学显微镜(OM)、扫描电镜(SEM)及其配置的能谱(EDS)仪研究合金的铸态组织,通过X射线衍射(XRD)和极图分析确定单晶晶粒取向,利用自制模具对合金的记忆性能进行评价.结果表明:试样横截面与纵截面均呈枝状晶分布特征,枝晶生长方向与定向凝固方向基本一致,未出现晶界,单晶横截面法向与[111]取向夹角为15°.由于消除了晶界对马氏体相变的不利影响,同时[111]取向是TiNi合金能获得较大可恢复应变的择优取向,与普通铸造的TiNi多晶相比,材料的形状记忆最大可恢复应变和记忆疲劳性能都得到一定提高.     

Predicting the columnar-to-equiaxed transition for a distribution of nucleation undercoolings

A deterministic mathematical model for steady-state unidirectional solidification is proposed to predict the columnar-to-equiaxed transition. In the model, which is an extension to the classic model proposed by Hunt [Hunt JD. Mater Sci Eng 1984;65:75], equiaxed grains nucleate according to either a normal or a log-normal distribution of nucleation undercoolings. Growth maps are constructed, indicating either columnar or equiaxed solidification as a function of the velocity of isotherms and temperature gradient. The fields of columnar and equiaxed growth change significantly with the spread of the nucleation undercooling distribution. Increasing the spread favors columnar solidification if the dimensionless velocity of the isotherms is larger than 1. For a velocity less than 1, however, equiaxed solidification is initially favored, but columnar solidification is enhanced for a larger increase in the spread. This behavior was confirmed by a stochastic model, which showed that an increase in the distribution spread could change the grain structure from completely columnar to 50% columnar grains.     

定向凝固高温合金晶界形貌的分形描述SCIEI

用分形分析的方法定量描述了定向凝固高温合金的树枝晶晶界形貌。结果表明，随着凝固速率的提高，晶界分形维数均增大。还讨论了凝固合金系统熵与晶界分形维数之间的关系。     

空心钢锭芯部换热条件的确定

在空心钢锭凝固过程中,芯子内套筒与冷却介质之间的换热条件对空心钢锭的凝固过程及质量有着重要的影响。该换热条件取决于冷却介质管路结构参数和冷却介质本身的特性。本文从气体动力学及传热学角度确定了空心钢锭芯部的换热条件。     

Microstructure and segregation of magnesium alloy solidified under magnetostatic field

Magnesium alloys are materials with predominant performance, but its formability is needed to be improved. Increasing the content of soluble inside grain, the formability will be improved. The results show that when magnetostatic field is applied to the process of solidification of magnesium alloy, the grain is refined, and the soluble content inside grain increases, on the contrary the content of soluble decreases at grain boundary. Compared with the common solidification, when the magnesium alloy ZK60 is solidified under magnetostatic field, the content of calcium and zinc decrease respectively from 15. 62%, 5. 6% to 14. 85%, 3.7% at grain boundary; the content of zinc increases from 0.68% to 0.91% inside grain. This will increase distortion inside matrix and more dislocation will supply slid deformation, as a result the formability will be improved.