Collapse of interconnected open

The closing behavior of interconnected open pores has been investigated in W-Ni systems where the dominant sintering mechanism is grain boundary diffusion. The samples were prepared by conventional powder metallurgy technique with large W particles containing Ni contents of 0.03 to 0.1 wt pct. The microstructure analysis indicated that pore collapse predominantly occurs at the three grain junction midpoints and produces closed pores at the four grain corners. The observed critical porosity, below which all the pores exist in isolated form, was found to be about twice as great as the critical porosity predicted by morphological perturbation theory. From these results, it is concluded that the grain boundary diffusion flux across the pore surface, as well as the capillary force, plays an important role in the closing behavior of interconnected open pores.     

A theoretical study of grain growth in porous solids during sintering

The processes of grain boundary migration, pore drag and pore/boundary separation are described on the basis of the phenomenological equations for boundary migration and surface diffusion. Cylindrical pores on triple grain junctions are assumed to represent the open porosity during intermediate-stage sintering. It is found that cylindrical pores can hardly detach from migrating boundaries. Three-dimensional closed pores, however, which predominate during final stage sintering, can separate from migrating grain junctions. The separation process is modelled numerically and the conditions for separation are formulated. Analytical approximations for the pore mobility are shown to describe the numerical results well. They serve to establish effective mobilities of grain boundaries bearing pores in various configurations. Classical theories of grain coarsening are modified by using these effective mobilities. Mechanical constitutive models of sintering contain the grain size as an internal variable. The present analysis leads to an evolution equation for the average grain size, which depends on the volume fraction of the pores and on their configuration.     

Determination of pore mobility during sintering

The mobility of pores being dragged by grain boundaries has been modeled in terms of shape-independent microstructural parameters measurable by stereological means. The derived mobility is expressed with respect to the amount of porosity per unit area of grain boundary and the driving pressure for grain boundary and pore motion,i.e., as velocity per unit driving pressure. The resultant mobility for pore surface diffusion-controlled motion is found to be inversely proportional to the mean-pore intercept, regardless of pore shape and volume fraction. Solutions for lattice and vapor transport yield mobilities independent of pore size but inversely proportional to pore volume fraction. Computed pore mobilities, assuming surface diffusion-controlled motion, during final-stage sintering of copper and tungsten are shown to decrease with densification. In one case, mobility was found to increase during early densification, prior to the final stage. These results are explained with reference to the simultaneous changes occurring in grain boundary and pore surface areas during densification.     

Pore-boundary interactions and evolution equations for the porosity and the grain size during sintering

The retardation of grain boundary migration by a pore is analysed numerically and by an analytical approximation, which becomes exact in the limiting case of small velocities. At high velocities, the numerical solution describes separation of the pore from the boundary. Based on the analysis of a single migrating boundary facet dragging a pore, evolution equations for the grain size and the porosity are suggested for the final stage of sintering. It turns out that three-dimensional pores on two-grain junctions have an only moderate effect on the rate of grain coarsening: pores with a high mobility follow the migrating grain boundary easily, while those with a low mobility detach from the boundary. It is also shown that a two-dimensional pore does not detach and can therefore reduce the coarsening rate to very low values if the pore mobility is low. This strong dependence on the pore configuration suggests that other possible configurations need to be analysed, before final evolution equations can be formulated.     

Equilibrium pore surfaces,sintering stresses and constitutive equations for the intermediate and late stages of sintering—I. computation of equilibrium surfaces

The intermediate stage of sintering is characterized by equilibrium surfaces of the open pore space between the grains. These doubly curved surfaces are determined numerically for the three cubic arrangements of grains (simple cubic, b.c.c. and f.c.c). The numerical program constructs surfaces of constant mean curvature connected via the dihedral angle to grain boundaries having zero mean curvature. The pore morphologies resulting from the analysis are different from the conventional picture of interconnected pore channels along grain edges. According to the present results, open porosity rather consists of interconnected pillow-shaped gaps between next-nearest grain neighbors. The transition to closed porosity occurs when the connections between these gaps close, a process which leads to relatively large isolated pores on two-grain junctions between former next-nearest neighbors. The numerical results for the contact areas between grains and for the sintering stress are approximated by quadratic functions of the pore volume fraction and of the dihedral angle, and the best-fit coefficients are tabulated. The results are used in a companion paper in which constitutive equations for the mechanical behavior during sintering are derived.     

The effect of curvature on the grain boundary migration induced by diffusional coherency strain in mo-ni alloy

When a liquid phase sintered Mo-Ni alloy is heat-treated at 1400°C after replacing the liquid matrix with a Cu melt, the grain boundaries between some grains migrate, producing a Ni depleted Mo-Ni solid solution behind them. The phenomenon is same as those commonly referred to as DIGM with the Cu melt acting as the sink for Ni atoms. When Fe of 1% by weight is added to the Cu melt, the grain boundaries do not migrate, because the compressive coherency strain produced by Ni diffusion from the lattice is exactly compensated by the tensile strain due to the Fe diffusion into it. The diffusional coherency strain energy is thus shown to be the driving force for the grain boundary migration. Because Mo is insoluble in liquid Cu, the grain boundaries are pinned at the grooved ends. The grain boundary curvature thus increases during the migration, causing a migration reversal and consequently an oscillatory motion. The observed critical curvature for the migration reversal falls closely into the range predicted on the basis of the generation of misfit dislocations when the migration velocity decreases to a critical value because of the curvature. The reversal of the grain boundary migration resulting in an oscillatory motion is thus shown to be a natural consequence of the coherency strain hypothesis for the driving force if the inhibiting effect of the grain boundary curvature is taken into account.     

Effect of entrapped inert gas on pore filling during liquid phase sintering

The effect of an inert gas entrapped in isolated pores on liquid flow into them during liquid phase sintering has been studied. An analysis of the balance between the capillary pressure of the liquid menisci and the gas pressure shows that the entrapped gas delays the pore filling and produces bubbles. If the gas pressure exceeds a critical level, the pores remain intact and the critical point for their filling will never be reached. These predictions are confirmed by experimental observations on large spherical pores produced artificially in an Fe-Cu alloy. Argon gas is trapped in the pore by first sintering in Ar-H₂ mixture gas and then in H₂ after the isolated pores are formed. The entrapped inert gas of even low pressure is thus shown to cause a substantial porosity in liquid phase sintered specimens. Formerly a Doctoral Student at the Korea Advanced Institute of Science and Technology.     

Theoretical modeling of densification during activated solid-state sintering

Activated solid-state sintering relies on the addition of low concentrations of grain boundary segre-gating species to increase diffusion rates. In this article, enhanced diffusion through an activated layer at the grain boundaries has been modeled for the case of tungsten sintered with transition element additions. Both constant heating rates and isothermal sintering are considered. As in classical treatments, sintering is divided into three stages, but modifications are proposed based on recent observations and theories regarding packing coordination, pore morphology, pore location, grain growth, and pore-grain boundary separation. The intermediate and final stages of sintering are al-lowed to overlap based on the amount of closed porosity to account for both pore closure early in the process and the gradual increase in packing coordination with densification. Mean curvature theory is used to estimate pore curvature during the intermediate stage of sintering. In the final stage, pores are modeled on both the corners of a tetrakaidecahedron and on its square facets. The pore location has only a small effect on densification, while the grain boundary mobility is more of a factor. The model allows pore-grain boundary separation to match experimentally measured grain sizes. The model predictions are compared to dilatometer curves of pure tungsten and tungsten sintered with additions of Co, Fe, Ni, and Pd. For the Co- and Fe-activated samples, the model is modified to account for an increase in diffusional activation energy due to dissolution of the activator in tungsten. Formerly Director of Materials Development, P/M Lab, Department of Engineering Science and Mechanics, The Pennsylvania State University.     

矿石颗粒级配对堆浸体系三维孔隙结构的影响

为研究堆浸体系矿石粒径分布对孔隙结构的影响,对不同级配矿岩散体构成的浸柱开展显微CT扫描测试,得到浸柱内部结构图像。通过阈值分割算法对孔隙结构进行提取,建立浸柱三维孔隙模型,对浸柱体孔隙率和面孔隙率的空间分布特征进行研究。利用最大球算法构建浸柱孔隙网络模型,进而分析矿石粒径分布对孔喉半径、喉道长度、孔喉体积、形状因子和配位数等参数的影响规律。结果表明:矿石颗粒级配性越好,矿堆孔隙率越低;矿石粒径越均匀,矿堆不同区域孔隙率差异越小;矿石粒径分布对孔隙尺寸和连通性影响较为显著,对孔喉形状因子影响较小。随着细颗粒矿石的减少,大孔隙增多,孔喉半径、喉道长度和孔喉体积相应增大;随着矿石粒径均匀性的增加,堆浸体系中孤立孔隙所占比例减少,高配位数孔隙所占比例增大,即矿堆内的孔隙空间具有更好的连通性。      

On the removal of pores from castings by sintering

The causes, sizes, and distribution of porosity in castings have been reviewed and quantitatively evaluated for several important modes of alloy solidification. In general, gas exsolution is found to be the most probable cause of porosity in castings which solidify in either a cellular or dendritic fashion. On the other hand, solidification alone may cause porosity creation if the interdendritic liquid metal cannot feed the solidification shrinkage. This effect may be enhanced by gas exsolution. Removal of porosity by “sintering” after solidification requires that the grain size be of the order of, or smaller than, the pore spacing, and that the pores be small (>1 μ) for removal within reasonable times (tens of hours). When gas exsolution is the cause of pore creation, the gas must be diffused out of the sample to permit pore shrinkage. Small ingot sizes (>10 cm) and rapidly diffusible gases (H₂) are required for pore elimination within reasonable times (tens of hours). The application of low pressure (>20 atm) during sintering increases the rate, or the size (to >10 mμ) of the pores which can be eliminated within >20 hr. 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.     

Processing and damping behaviour of porous copper

Abstract

The well distributed open cellular porous copper was fabricated by present powder metallurgy technique based on space holder method, Depending on the volume fraction and size of the space holding particle, the porosity can be varied in the wide range of 30–85% and pore size from micron to millimetre in magnitude of order respectively. The damping behaviour and related relative dynamic modulus of the porous copper were investigated by a multifunction internal friction apparatus as a function of temperature from room temperature to 600°C. The results of investigation disclose that the porous copper can obtain a higher damping capacity than that of bulk one. In addition to this, an internal friction peak was found in the spectra of internal friction against temperature for the porous copper, it was proposed that the viscous sliding of the grain boundaries should be responsible for the appearance of the peak, and the dependence of the peak on porosity can be understood in terms of the anelastic relaxation mode of grain boundary.     

Geometry of grain boundaries

The first part of this paper deals with the problem of describing and measuring microstructure in exact terms. The Euclidean parameters: volume, area, length, and angle can be measured and expressed only in terms of the total of each in unit volume. Average properties, such as average grain diameter, are accessible only through the topological parameters, specifically number in unit volume, which can be measured only by serial sectioning. The parameters which have been used to represent the concept of grain size are analyzed and shown in most cases to represent a function of grain boundary area. In a second section of this paper the geometric problem of plastic slip through a grain boundary is analyzed. A method is proposed by which all of the components of the deformation, as well as the crystallographic directions, can be manipulated simultaneously through the use of a stereographic projection. The third section of this paper is concerned with the geometry of grain growth. The polycrystalline state is described as a grain boundary network, which must respond to the requirements of surface tension. The several topological changes in a network which can contribute to grain growth are described.     

Quantitative determination of topological and metric properties during sintering of copper

Quantitative paths of microstructural change, represented as a variation of topological and metric properties with pore volume fraction, were experimentally determined by applying quantitative microscopy to sequences of samples sintered without compaction from two size fractions of spherical copper powder, and one size fraction of dendritic copper powder. The two spherical size fractions followed paths of microstructural change during sintering that were identical except for a scale factor. The connectivity of the pore network first increased slightly, then decreased, reaching zero at a pore volume fraction (V _V ) of about 0.08. Isolated pores begin to appear atV _V = 0.20, and increased in number. The area of the pore-solid interface at first decreased slowly, then more rapidly and ultimately linearly with pore volume fraction, as has been reported in other systems. Total curvature of pore-solid interface decreased from the positive value characteristic of the loose powder stack to a negative value, passed through a minimum, and increased toward zero as full density is approached. The area of grain boundary initially increased slowly, as interparticle contacts grew; at aboutV _V = 0.15, grain growth set in, and the grain boundary area decreased, as the mean grain intercept rapidly increased with densification. The dendritic powder had a highly irregular surface shape, and consequently a loose stack structure containing more than 90 pct porosity. The path that it followed was qualitatively, but not quantitatively, similar to that observed for the spherical powders. These observations are discussed in terms of the unit geometric processes that dominate each of the three stages of loose stack sintering.     

Quantitative determination of topological and metric properties during sintering of copper

Quantitative paths of microstructural change, represented as a variation of topological and metric properties with pore volume fraction, were experimentally determined by applying quantitative microscopy to sequences of samples sintered without compaction from two size fractions of spherical copper powder, and one size fraction of dendritic copper powder. The two spherical size fractions followed paths of microstructural change during sintering that were identical except for a scale factor. The connectivity of the pore network first increased slightly, then decreased, reaching zero at a pore volume fraction (V _V ) of about 0.08. Isolated pores begin to appear atV _V = 0.20, and increased in number. The area of the pore-solid interface at first decreased slowly, then more rapidly and ultimately linearly with pore volume fraction, as has been reported in other systems. Total curvature of pore-solid interface decreased from the positive value characteristic of the loose powder stack to a negative value, passed through a minimum, and increased toward zero as full density is approached. The area of grain boundary initially increased slowly, as interparticle contacts grew; at aboutV _V = 0.15, grain growth set in, and the grain boundary area decreased, as the mean grain intercept rapidly increased with densification. The dendritic powder had a highly irregular surface shape, and consequently a loose stack structure containing more than 90 pct porosity. The path that it followed was qualitatively, but not quantitatively, similar to that observed for the spherical powders. These observations are discussed in terms of the unit geometric processes that dominate each of the three stages of loose stack sintering.     

Effects of Pore Nucleation,Growth and Solidification Mode on Pore Structure and Distribution of Lotus Type Porous Copper

Effects of pore nucleation, growth and solidification mode of matrix on pore structure and distribution of lotus-type porous Cu fabricated by Gasar process were investigated. The results showed that it was difficult to obtain an ordered pore structure when the matrix contained equiaxed grain. An ordered pore structure, with increased pore length and circularity, could be obtained when the matrix consisted of columnar grains. The pore distribution moved from the grain boundaries to the interior of grain with increasing gas pressure. It was further noticed that the average pore diameter decreased and the pore density increased due to decreased activation energy and increased rate of nucleus formation. Due to slight depressions at grain boundaries of the solid/liquid interface, the pore nucleation was favored at grain boundaries and thus the average pore diameter in grain boundaries was larger than that in grains.     

Influence of Crystallography on Ferrite Nucleation at Austenite Grain-Boundary Faces,Edges, and Corners in a Co-15Fe Alloy

The nucleation of ferrite precipitates at austenite grain faces, edges (triple lines), and corners (quadruple points) was studied in a Co-15Fe alloy in which the matrix phase was retained upon cooling to room temperature by serial sectioning coupled with electron backscatter diffraction analysis. Nearly half of the edges and corners were vacant at an undercooling of 60 K from the γ/(α + γ) boundary where the precipitation occurred significantly at grain faces. A significant proportion of precipitates had Kurdjumov–Sachs (K–S) and to a lesser extent Nishiyama–Wassermann (N–W) orientation relationships with more than one grain at all boundary sites. Vacant edges and corners were readily observed, of which the misorientations of matrix grain boundaries would permit a precipitate to have a specific orientation relationship with multiple grains. Small differences in the nucleation activation energy among the grain faces, edges, and corners may lend support to a view proposed from experiments of nucleation in Fe-C base alloys that ferrite nuclei are more or less surrounded by low-energy facets of α/γ phase boundary.     

The role of pore evolution during supersolidus liquid phase sintering of prealloyed brass powder

ABSTRACT

The aim of this research is to study the pore structure as well as to assess the liquid phase sintering behaviour of Cu-28Zn powder specimens at different green density levels and temperatures. For this purpose, samples were compacted to obtain six different green densities and then sintered at 870°C, 890°C and in part at 930°C for 30?min. The results revealed that the spherical pores which are formed inside the grains can be swept by grain boundaries due to grain growth and join to primary pores so that secondary intragranular pores are eliminated and intergranular pores enlarged at higher temperatures. Also, the pores move upwards to the top of sample due to buoyancy forces. The role of pore structure in distortion is more tangible at higher temperatures (930°C) so that O-shape and X-shape distortions were observed at high and low green density samples, respectively.     

纳米隔热材料的孔隙结构特征与气体热传输特性

为研究纳米隔热材料孔隙结构内部的气体热传输特性, 采用溶胶-凝胶工艺结合超临界干燥技术, 制备了一系列具有不同孔隙结构特征的样品, 通过热导率、氮气吸-脱附和真密度测试, 全面、准确获取了其孔隙结构信息, 并专门、系统研究了孔隙结构特征与气体热传输特性之间的关系.研究结果表明: 与气相贡献热导率相对应, 材料具有双尺度孔隙结构特征, 并且当大孔隙尺度不及小孔隙的10倍时, 可进一步等效为单尺度孔隙.考虑气固耦合传热的本征气相贡献热导率随孔隙尺度的增大而升高, 与气相热导率变化类似且成一定的比例关系, 孔隙尺度小于200 nm和大于500 nm时的比例系数分别为2.0和1.5, 200~500 nm时则为2.0~1.5.当大、小孔隙尺度的比值不超过10时, 或者这一比值为100~1000且大孔隙含量低于10%时, 气相贡献热导率随环境气压的降低依次呈现快速下降、缓慢下降和无变化三个阶段; 当这一比值超过3000时, 即使大孔隙含量很低(不超过10%), 气相贡献热导率也会依次呈现快速下降、缓慢下降、快速下降和无变化四个阶段.      

Quantification and Taxonomy of Pores in Thermal Spray Coatings by Image Analysis and Stereology Approach

Porosity is one of the most important microstructural features in thermal spray coatings and has been actively studied and measured by many methods. Image analysis techniques have become popular techniques in determining porosity in coatings because of simplicity, accessibility, and an ability to measure both open and closed porosities as well as pore characteristics such as size, shape, orientation, and spatial distribution. In the current study, an image analysis technique has been complemented by several stereology procedures to determine the porosity level and characteristics of pores within coatings. Stereology protocols such as Delesse, DeHoff, and Cruz-Orive analyses were used to derive the porosity level, pore size, and shape distributions, and the effectiveness of each stereology protocol was compared. Standoff distance (SOD) and annealing process did not alter the distribution trend of number of pores but influenced the distribution of pore volume fractions significantly. The bivariate size–shape distribution of the pores was used to predict the dominant pore type and fractions of pores that arose from different formation mechanisms. It was found that nearly spherical pores that originated from gas bubbles and entrapped gas pockets dominate at shorter SOD, while the different types of pores become more evenly distributed when the SOD was increased.     

Effects of fine porosity on the fatigue behavior of a powder metallurgy superalloy

Hot-isostatically-pressed powder-metallurgy Astroloy was obtained which contained 1.4 pct, fine porosity at the grain boundaries produced by argon entering the powder container during pressing. The pores averaged about 2μ,m diam and 20 μ m spacing. This material was tested at 650 °C in fatigue, creep-fatigue, tension, and stress-rupture and the results compared with previous data on sound Astroloy. The pores influenced fatigue crack initiation and produced a more intergranular mode of propagation. However, fatigue life was not drastically reduced. A large 25 μm pore in one specimen resulting from a hollow particle did reduce life by 60 pct, however. Fatigue behavior of the porous material showed typical correlation with tensile behavior. The plastic strain range-life relation was reduced proportionately with the reduction in tensile ductility, but the elastic strain range-life relation was little changed reflecting the small reduction in strength divided by modulus for the porous material.