Modeling of mechanical alloying: Part III. Applications of computational programs

The computational modeling programs described in part II of this series are used in two ways. One is to compare program predictions to previous experimental data, thereby testing to some extent the utility of the programs. At this stage of their development, program “predictions” with respect to processing time, microstructural scale, and similar parameters are accurate to within a factor of 2 or so. Even so, the predictions offer support of the model developed in part I of this series and provide a vehicle for both model and process refinements. In addition to “testing” the model and the program in these manners, the effect of uncertainty in input material properties on program predictions is explored. Formerly Graduate Student, Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22903 Formerly Professor, Department of Materials Science and Engineering, University of Virginia     

Modeling of particle size evolution during mechanical milling

The process of mechanical alloying (MA) involves the repeated deformation, welding, and fracture of powder materials during grinding in high-energy mills. During MA, the size and size distribution of the particles change as a result of the particles’ different fracture and welding rates. The evolution of particle volume distributions during such a combined “fission-fusion” process can be describedvia a differential-integral equation. While analytical solutions are known for systems in which only fusion takes place, there is apparently no such solution for the fission-fusion problem. In this article, we describe a discretized form of the fission-fusion equation and apply it to modeling of particle size distributions during milling of elemental powders using previously determined fracture and welding rates appropriate to the global system of particles. Predicted particle size distributions mimic well those determined experimentally. Formerly Graduate Student, Department of Formerly Graduate Student, Department of Formerly Graduate Student, Department of Formerly Professor, Department of Materials Formerly Professor, Department of Materials     

Milling dynamics: Part I. Attritor dynamics: Results of a cinematographic study

The motions of grinding media and powder in an attritor canister were studied by means of filming the agitated charge and frame-by-frame scrutiny of the footage. In conjunction with auxiliary experiments, this permitted semiquantitative analysis of the milling action. In particular, the mill can be divided into several regions characterized by different balances between direct impacts and rolling/sliding of the grinding media. Simple calculations suggest that impacts are more capable of effecting mechanical alloying (MA) than are rolling or sliding events in an attritor. Powder circulation within an operating mill was also investigated. Based on the results and the accompanying analysis, concepts for improved attritor design are presented. D. Maurice is formerly a Graduate Student, Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22903     

An investigation of Fe-Ni order in a steel

Formerly with the Department of Materials Science and Engineering, McCormick School of Engineering and Applied Science, Northwestern University.     

An investigation of the generality of incomplete transformation to bainite in Fe-C-X alloys

The overall kinetics of the isothermal transformation of austenite to bainite and to pearlite in high-purity Fe-C-3 at. pct X alloys (X = Mn, Si, Ni, or Cu) containing 0.1 wt pct C and 0.4 wt pct C were investigated with quantitative metallography and transmission electron microscopy (TEM) to ascertain the presence or absence of the incomplete reaction phenomenon. The incomplete transformation of austenite to bainite was not observed in the Fe-C-Si, Fe-C-Ni, Fe-C-Cu, or Fe-0.4C-Mn alloys. It was found, however, in the Fe-0.1C-Mn alloy. Transmission electron microscopy results indicate that sympathetic nucleation of ferrite without carbide precipitation is a necessary but not a sufficient condition for the development of the incomplete reaction phenomenon. Transformation resumes following stasis in the low-carbon Fe-C-Mn alloy with the formation of a nodular bainite. The results support the view that the incomplete transformation of austenite to bainite is a characteristic of specific alloying elements and is not an inherent trait of the bainite reaction. Formerly Graduate Student, Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University. Formerly Visiting Professor, Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University. Formerly Undergraduate Student, Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University. This paper is based on a presentation made in the symposium “International Conference on Bainite” presented at the 1988 World Materials Congress in Chicago, IL, on September 26 and 27, 1988, under the auspices of the ASM INTERNATIONAL Phase Transformations Committee and the TMS Ferrous Metallurgy Committee.     

On the characteristics of the threshold stress for superplastic flow in Zn-22 Pct Al

Formerly Graduate Research Assistant, Department of Chemical and Biochemical Engineering, Materials Science and Engineering, University California-Irvine.     

Constrained cavity growth models of longitudinal creep deformation of oxide dispersion strengthened alloys

Two models of constrained cavity growth are developed to describe the long-term longitudinal creep behavior of nickel based oxide dispersion strengthened (ODS) alloys. For both models the rupture time is taken as the time for a transverse grain boundary to cavitate fully. A diffusive cavity growth law is assumed to govern cavitation. The applicability of the respective models is determined by the particular grain morphology achieved by thermal-mechanical processing. The first model assumes that longitudinal grain boundaries are unable to slide; hence displacements due to cavitation must be matched by displacements due to dislocation creep in adjoining grains. This model predicts a low stress exponent at the transition from single crystal to cavitation creep behavior, and higher stress exponents at stresses below this transition. Good agreement is found between the model predictions and creep data for MA 754 at 1000 and 1093 °C. A second model considers a grain morphology wherein longitudinal grain boundaries are able to slide by means of deformation of pockets of fine grains. Cavitation of transverse grain boundaries is thus controlled by grain boundary sliding. This model predicts a stress exponent of 1 at low stresses, and serves as an upper bound for the creep rate when a duplex grain morphology is present. Model predictions are in good agreement with creep data for a heat of MA 754 with a duplex grain morphology. Formerly Graduate Research Assistant in the Department of Materials Science and Engineering at Stanford University     

Effect of hydrostatic pressure

Formerly Graduate Student, Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University     

Densities of liquid Fe-Ni and Fe-Cr alloys

Formerly Graduate Student, Department of Materials Science and Engineering, Carnegie Mellon University.     

Thermodynamics of nitrogen in Ca-CaF2 slags

Formerly with the Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University.     

Measurements of the electrical conductivity of Wood's alloy and other low melting point alloys

Formerly Graduate Student Research Assistant, Department of Materials Science and Mineral Engineering, University of California.     

The kinetics of ferrite nucleation at austenite grain edges in Fe-C and Fe-C-X alloys

Nucleation kinetics of proeutectoid ferrite allotriomorphs at the edges of austenite grains in Fe-C and Fe-C-X alloys, where X is successively Mn, Ni, Co, and Si, have been measured using a modification of the techniques previously developed to study nucleation at grain faces. Analysis of these data with classical heterogeneous nucleation theory has shown that ferrite nuclei formed at grain edges have low energy interphase boundaries. An equivalent conclusion was reached during our previous studies of ferrite nucleation at austenite grain faces. The influence of alloying elements on nucleation rates was also found to follow a pattern similar to that demonstrated for grain face nucleation. Formerly Graduate Student with the Department of Metallurgical Engineering and Materials Science, Carnegie-Mellon University,     

Microstructures and superplastic behavior of eutectic Fe-C and Ni-Cr white cast irons produced by rapid solidification

Superplastic behavior of two commercial grade white cast irons, eutectic Fe-C and Ni-Cr white cast irons, was investigated at intermediate temperatures (650 to 750 °C). For this purpose, rapidly solidified powders of the cast irons were fully consolidated by compaction and rolling at about 650 °C. The volume fractions of cementite in the eutectic cast iron and in the Ni-Cr cast iron were 64 pct and 51 pct, respectively, and both cast irons consisted of fine equiaxed grains of cementite (1 to 2 μm) and ferrite (0.5 to 2 μm). The cast iron compacts exhibited high strain-rate sensitivity (strain-rate-sensitivity exponent of 0.35 to 0.46) and high tensile ductility (total elongation of 150 pct to 210 pct) at strain rates of 10^-4 to 10^-3 s^-1 and at 650 °C to 750 °C. Microstructure evaluations were made by TEM, SEM, and optical microscopy methods. The equiaxed grains in the as-compacted samples remained unchanged even after large tensile deformation. It is concluded that grain boundary sliding (e.g., along cementite grain boundaries in the case of the eutectic cast iron) is the principal mode of plastic deformation in both cast irons during superplastic testing conditions. Formerly with the Department of Materials Science and Engineering, Stanford University Formerly Visiting Scholar, Department of Materials Science and Engineering, Stanford University     

The kinetics of composite particle formation during mechanical alloying

The kinetics of composite particle formation during attritor milling of insoluble binary elemental powders have been examined. The effects of processing conditions(i.e., mill power, temperature, and charge ratio) on these kinetics were studied. Particle size distributions and fractions of elemental and composite particles were determined as functions of milling time and processing conditions. This allowed the deduction of phenomenological rate constants describing the propensity for fracture and welding during processing. For the mill-operating conditions investigated, the number of particles in the mill generally decreased with milling time, indicating a greater tendency for particle welding than fracture. Moreover, a bimodal size distribution is often obtained as a result of preferential welding. Copper and chromium “alloy” primarily by encapsulation of Cr particles within Cu. This form of alloying also occurs in Cu-Nb alloys processed at low mill power and/or for short milling times. For other conditions, however, Cu-Nb alloys develop a lamellar morphology characteristic of mechanically alloyed two-phase ductile metals. Increasing mill power or charge (ball-to-powder weight) ratio (CR) increases the rate of composite particle formation. B.J.M. AIKIN, formerly Graduate Student, Materials Science and Engineering Department, University of Virginia, Charlottesville, VA. T.H. COURTNEY, formerly Professor, Materials Science and Engineering Department, University of Virginia.     

The structure and properties of aluminum alloys produced by mechanical alloying: Powder processing and resultant powder structures

Mechanical alloying of two aluminum alloy powders to form composite A1-A1₂O₃ powders has been studied. Changes in powder microstructure with processing are reported and interpreted. Mechanical alloying proceeds by the continual cold welding and fracturing of the constituent powder particles when subjected to the large compressive forces of a high speed mill. A suitable organic surfactant must be added so that a balance between cold welding and fracturing is obtained. The organic surfactant is embedded and finely distributed in the powder particles during mechanical alloying and is converted to discrete A1₄C₃ particles after hot pressing. The establishment of steady state processing conditions, characterized by equiaxed powder particles, a constant particle size distribution and a saturation hardness, is found to depend on the size distribution of the initial powders. The oxide particles formed and distributed during mechanical alloying are equiaxed, small (30 nm) and homogeneously distributed with a volumetric center to center distance of about 60 nm. Formerly Graduate Research Assistant in the Department of Materials Science and Engineering at Stanford.     

The formation of austenite in a low-alloy steel

Austenite formation from different microstructural conditions has been studied in an Fe-lV-0.2C steel. The starting microstructures of ferrite, bainite, and martensite, and the morphology of austenite formation have been examined in detail by light microscopy and transmission electron microscopy. Retained austenite in quenched martensitic areas has been used to establish the crystallographic relationships during austenite nucleation, and to indicate the behavior of the initial vanadium carbide dispersion present in the ferrite starting microstructure. Limited measurements were also made of the kinetics of austenitization. Formerly Research Student, Department of Metallurgy and Materials Science, University of Cambridge. Formerly of Royal Society, Warren Research Fellow, Department of Metallurgy and Materials Science, University of Cambridge.     

Influence of Interfacial Structure upon Carbide Precipitation at Austenite : Ferrite Boundaries in an Fe-C-Mo Alloy

During conventional isothermal transformation of an Fe-0.11 pct C-1.95 pct Mo alloy, eutectoid decomposition occurs by the interphase boundary carbide precipitation and the fibrous carbide mechanisms at 770° to 825 °C. When proeutectoid ferrite is formed and then recrystallized within the α + γ region, and subsequently further transformed at 770° to 825 °C, however, both of these eutectoid decomposition mechanisms are rendered inoperative. Carbide precipitation occurs instead entirely as isolated particles. This result supports the deduction that carbide precipitation at austenite : ferrite boundaries can occur only when these boundaries are locally immobilized by a partially coherent interfacial structure. A general approach to explaining the development of planar and curved interphase boundary precipitation, fibrous structure, and pearlite is developed in terms of two crystallographic factors. Formerly Research Associate in the Department of Metallurgical Engineering, Michigan Technological University, Houghton, MI 49931 and the Department of Metallurgical Engineering and Materials Science, Carnegie-Mellon University, Pittsburgh, PA 15213 Formerly Graduate Student, Michigan Technological University, and Visiting Graduate Student, Camegie-Mellon University Formerly Professor at Michigan Technological University     

The normalized coffin- manson plot in terms of a new damage function based on grain boundary cavitation under creep- fatigue condition

A new damage function based on a model for the creep-fatigue life prediction in terms of nucleation and growth of grain boundary cavities is proposed. This damage function is a combination of the terms related to the cavitational damage in the life prediction equation and is generally applicable to the materials in which failure is controlled by the grain boundary cavitational damage. The creep-fatigue data from the present and other investigations are used to check the validity of the proposed function, and it is shown that they satisfy the reliability of damage function. Additionally, using this damage function, one may realize that all the Coffin-Manson plots at the various levels of tensile hold time and temperature under strain-controlled creep-fatigue tests can be normalized to make the master curve. Formerly Graduate Student, Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology Formerly Graduate Student, Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology Formerly Graduate Student, Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology     

Shape recovery and phase

The deformation behavior and morphology of martensite in Ni-AI alloys have been studied by means of compression tests, optical microscopy, and transmission electron microscopy. Mar- tensite deformation modes were investigated by examining microstructure changes upon compression. The shape memory effect is quantified by studying the incremental strain by compression testing below theM _ftemperature and measuring the shape recovery in a high- temperature dilatometer. The martensite features internal twins, and the twin plane is determined as {11l}_fct. The magnitude of the lattice invariant shear (by twinning) is determined by measuring the relative thickness of twin pairs and is 0.128. Formerly with the Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign     

Interface structure in infiltrated composites of aluminum reinforced with alumina-silica fiber preforms

Formerly Graduate Student, Department of Materials Science and Engineering, Massachusetts Institute of Technology