Homogenization by diffusion

The problem of removal of microsegregation by solid-state diffusional processes is reviewed. For most cases of practical interest, volume diffusion coefficients as measured in laboratory couples determine homogenization rates. If the initial distribution of solute is sufficiently regular and well-characterized, the decay of microsegregation can be predicted with good precision. Often, however, order-of-magnitude estimates are all that is required, and these may be made from less complete information. The interactions of diffusing solutes with crystalline defects and with other solutes, are of practical as well as academic interest: in particular, multi-component interactions can significantly influence the course of homogenization. This paper is based on an invited talk presented at a symposium on Homogenization of Alloys, sponsored by the IMD Heat Treatment Committee, and held on May 11, 1970, at the spring meeting of The Metallurgical Society of AIME, in Las Vegas, Nev.     

Mg-xGd-Zr合金均匀化过程研究

实验采用光学金相、扫描电镜和布氏硬度测试等方法,研究了Mg-xGd-Zr(x=1%、2%、3%)合金不同均匀化制度下的组织形貌变化,并对合金中方块相的形成进行了分析。结果表明,随着Gd含量的升高,合金中共晶组织增加晶粒尺寸减小,3种合金合适的热处理工艺,分别为793K×6h、793K×8h和793K×12h。在均匀化过程中随着时间的延长共晶组织发生分解,但方块相依旧存在,且其数量与合金中Gd含量呈正比,同时Gd含量从铸态的41.5%~56.2%升高至均匀化态的72.5%~88.5%。     

土工格室的渐近均匀化分析

在线弹性范围内,根据均匀化理论,结合有限元方法预测了土工格室加筋层等效弹性模量.通过将不同的方法计算出的弹件模量与复合地基试验资料对比,证实了采用均匀化理论分析土工格室的弹性模量是可行的.     

Homogenization of primary microsegregation

The homogenization kinetics of a segregated binary alloy have been studied using electron probe microanalysis after annealing for various times at several temperatures. The concentration and number of microsegregation nodes are quantitatively examined in detail and compared with the evolution of the whole solidification substructure revealed by X-ray images and metallography. The comparison leads to the conclusion that nodes are representative of all solidification substructure and can be taken as a characteristic. The combined study also shows that nodes dissolve in two stages, starting preferentially along cell walls and continuing later in a more uniform fashion. However, a single activation energy near that for bulk diffusion is obtained for the whole process, showing that the homogenization is a collective process and volume diffusion limited.     

Homogenization of Masonry Using Numerical Simulations

Homogenization is one of the most important steps in the numerical analysis of masonry structures where the continuum method is used. In the present study, equivalent elastic properties, strength envelope, and different failure patterns of masonry material are homogenized by numerically simulating responses of a representative volume element (RVE) under different stress conditions. The RVE is modeled with distinctive consideration of the material properties of mortar and brick. In the numerical simulation, various displacement boundaries are applied on the RVE surfaces to derive the stress-strain relation under different conditions. The equivalent overall material properties of the RVE are averaged by integrating the stresses and strains over the entire area. Failure of masonry is defined by three different modes, namely, tensile failure of mortar (Mode I), shear failure of mortar or combined shear failure of brick and mortar (Mode II), and compressive failure of brick (Mode III). The homogenized elastic properties and failure model can be used to analyze large-scale masonry structures.     

铝土矿均化方式的改进

为了提高铝土矿均化效果,稳定入磨矿石A／S,提出了“4,3,2,1”堆料法。生产实践表明,采用这种方法,铝土矿的均化效果较好。     

Elastoplastic Mesoscale Homogenization of Composite Materials

Mesoscale homogenization provides a computationally efficient way of capturing some degree of local variation in the behavior of a composite microstructure. In this work, techniques are explored in which the local two-phase microstructure is homogenized using the moving-window generalized method of cells (GMC) technique. Both elastic and plastic material behavior is investigated using GMC-generated anisotropic stress-strain curves. An optimization procedure is used to define Hill’s yield criterion parameters which best fit the GMC-generated data. Two perfectly plastic models are developed based on the GMC results; these are called the subcell initial yield model and the matrix average yield model. A technique is also developed which incorporates hardening behavior. Different windowing techniques are investigated: an overlapping windowing technique which requires more computational time, and a nonoverlapping technique which requires less computational time. It is found that the matrix average model using small nonoverlapping windows is the best technique in the cases studied, combining accuracy and computational efficiency.     

Homogenization of random concentration profiles by diffusion

A statistical analysis of the homogenization problem is given. The initial concentration profile is defined as a random function, nonperiodically oscillating around a constant value. The time evolution of the autocorrelation function that characterizes the concentration profile is investigated. Homogenization is shown to proceed less rapidly than for a sinusoidal concentration profile.     

高铌TiAl基合金热变形组织的均匀化

研究了热加工和热处理对大尺寸高铌TiAl基合金组织均匀化的影响.结果表明,两次包套锻造能够有效地破碎大尺寸高铌TiAl基合金铸态组织.锻造过程中,铸态组织发生较大程度的动态再结晶,合金锻后组织经过热处理未出现残留的粗大的片层组织.合金在凝固中由于偏析形成的高温β相通过热加工和随后的热处理得到了有效的消除,热处理后所获的双态组织均匀且细小.     

Higher-Order Homogenization of Initial∕Boundary-Value Problem

Higher-order homogenization of an initial∕boundary-value problem with oscillatory coefficients in one dimension is studied. Validity range and limitations of the theory are established. We show that the higher terms are necessary to account for wave dispersion but introduce secular terms that grow unbounded in time. Numerical procedures requiring superconvergent recovery of higher-order derivatives are described.     

GH907合金铸锭均匀化热处理

为了系统研究GH907合金铸锭枝晶间Laves相的固溶规律和铸锭中铌元素的扩散规律,以指导生产实践。以抚顺特钢生产的GH907合金508 mm铸锭为研究对象,利用光学显微镜、扫描电镜等手段,系统研究了GH907合金铸锭不同温度和时间下的均匀化情况。结果表明,GH907合金铸锭枝晶间Laves相的最佳扩散温度为1 160 ℃,扩散10 h以上Laves相可以完全消除;同时计算得知,GH907合金铸锭中铌元素在1 160 ℃下的表观扩散系数为D＝0.488 55×10-14 m2/s;理论计算表明,在1 160 ℃下处理56 h后,GH907合金中铌元素的残余偏析指数δi可以达到0.02。     

Homogenization of metal matrix composites by high-pressure torsion

This article deals with the homogenization of metal matrix composites (MMCs) with inhomogeneous particle distribution by severe plastic deformation. In this study, Al6061-10 pct SiC and Al6061-20 pct Al₂O₃ powder metallurgy (PM) MMCs with clustered particle distribution in the as-fabricated condition are subjected to high-pressure torsion (HPT) at room temperature. The evolution of the microstructure during HPT is investigated. It is shown that, in the two materials, two different types of particle clusters appear that behave differently during deformation. In MMCs with dense particle clusters, the process of declustering during HPT occurs through a mechanism of particle debonding from the surface of the clusters. On the contrary, in MMCs with diffuse particle clusters, the deformation of the clusters is mainly responsible for the homogenization; therefore, the strain necessary to obtain a homogeneous particle distribution can be predicted by the Tan and Zhang model (M.J. Tan and X. Zhang: Mater. Sci. Eng. A, 1998, vol. 244, pp. 80–85).     

Random Field Modeling of Elastic Properties Using Homogenization

This paper addresses the random field characterization of elastic properties. Consistent random field properties of a continuum are derived from a simple stochastic micromechanical model of the continuum. Existing displacement-based techniques to homogenize the discrete microstructure are discussed and a new force-based technique is introduced. The stochastic features of a micromechanically consistent continuum can be considerably different from those based on a straightforward randomization of deterministic constitutive laws. Examples indicate the relevance for structural reliability. The impact of uncertainties associated with selecting micromechanical models is assessed.     

Homogenization modeling for the mechanics of perfused myocardium

Altered coronary perfusion can change the apparent diastolic stiffness of ventricular myocardium--the 'garden hose' effect. Our recent findings showed that myocardial strains are reduced during ventricular filling, primarily along the directions transverse to the coronary microvessels. In this article, we review hypotheses and theoretical models regarding the role that regional wall stress plays in the mechanical interaction between myocardium and coronary circulation. Various mechanisms have been used to explain the effects of the tissue stress on coronary flow, as well as the effect of coronary dynamics on myocardial mechanics. Many models of coronary pressure-flow relations using lumped parameter circuit analogs. Poroelasticity and swelling theories have been used to model the mechanics of perfused muscle. Here, we describe a new mathematical model of the mechanics of perfused myocardium derived using homogenization theory. In this model, perfused myocardium is treated as a nonlinear anisotropic elastic solid embedded with cylindrical vessels of known distensibility. The solid compartment is incompressible but the vascular compartment may change volume according to a simple relation between vessel diameter and perfusion pressure. The work done by the perfusion pressure in changing vascular volume contributes to the macroscopic strain energy and hence affects the stress and stiffness of the composite. Conversely, the stress in the tissue affects microvessel diameter and volume, since tractions transverse to the vessel axis oppose the internal blood pressure. Finite element simulations of passive filling show good agreement of model with experimental results.     

2050铝锂合金铸锭双级均匀化工艺研究

研究了双级均匀化制度对2050铝锂合金组织的影响,并对均匀化效果进行了综合评价。确定该合金的双级均热制度为470℃/8h+505℃/24h,在工业化生产中已经得到了应用。     

Homogenization of compacted blends of nickel and tungsten powders

The diffusional homogenization of compacted blends of elemental Ni and W powders was studied using quantitative metallography and X-ray compositional line broadening. Homogenization treatments were carried out in the temperature range from 1156 to 1271°C (in the region of the Ni-W phase diagram where only the terminal solid solutions exist). The mean compositions of the compacts studied ranged from 0.06 to 0.14 atomic fraction tungsten (in the Ni-rich solid solution). Other variables studied included the size and shape of the W particles, compaction pressure, and the effect of applied load during the homogenization treatment. Experimental measurements of the solution of the unstable W-rich phase and the increase in W concentration in the Ni-rich matrix were compared to calculated values obtained from a concentric-sphere mathematical model which assumed volume interdiffusion (concentration-independent diffusion coefficients) and local equilibrium at the heterophase interface. The model provided a fairly good approximation of the homogenization kinetics and the effects of the major processing and powder parameters investigated. The primary sources of discrepancy between model predictions and experimental data appeared to result from modest surface diffusion contributions to homogenization and imperfect powder blending.     

Homogenization of compacted blends of nickel and tungsten powders

The diffusional homogenization of compacted blends of elemental Ni and W powders was studied using quantitative metallography and X-ray compositional line broadening. Homogenization treatments were carried out in the temperature range from 1156 to 1271°C (in the region of the Ni-W phase diagram where only the terminal solid solutions exist). The mean compositions of the compacts studied ranged from 0.06 to 0.14 atomic fraction tungsten (in the Ni-rich solid solution). Other variables studied included the size and shape of the W particles, compaction pressure, and the effect of applied load during the homogenization treatment. Experimental measurements of the solution of the unstable W-rich phase and the increase in W concentration in the Ni-rich matrix were compared to calculated values obtained from a concentric-sphere mathematical model which assumed volume interdiffusion (concentration-independent diffusion coefficients) and local equilibrium at the heterophase interface. The model provided a fairly good approximation of the homogenization kinetics and the effects of the major processing and powder parameters investigated. The primary sources of discrepancy between model predictions and experimental data appeared to result from modest surface diffusion contributions to homogenization and imperfect powder blending.     

Homogenization of compacted blends of Ni and Mo powders

The homogenization behavior of compacted blends of Ni and Mo powders was studied primarily as a function of temperature, mean compact composition, and Mo powder particle size. All compact compositions were in the Ni-rich terminal solid-solution range; temperatures were between 950 and 1200°C (in the region of the phase diagram where only the MoNi intermediate phase forms); average Mo particle sizes ranged from 8.4 μm to 48 μm. Homogenization was characterized in terms of the rate of decrease of the amounts of the Mo-rich terminal solid-solution phase and the MoNi intermediate phase. The experimental results were compared to predictions based upon the three-phase, concentric-sphere homogenization model. In general, agreement between experimental data and model predictions was fairly good for high-temperature treatments and for compact compositions which were not close to the solubility limit of Mo in Ni. Departures from the model are discussed in terms of surface diffusion contributions to homogenization and non-uniform mixing effects.