Modeling of mechanical alloying: Part II. Development of computational modeling programs

Computational modeling programs incorporating the physics of powder deformation, fragmentation, and coalescence occurring during mechanical alloying (MA) are developed. The programs utilize the equations developed in part I of this series; equations predicting the extent of powder deformation during an effective impact in MA and those specifying criteria for powder particle fragmentation and coalescence. Two programs have been developed for these purposes. One, MAPI, considers the behavior of a single species with the option of adding dispersoids. The other, MAP2, considers two ductile species being welded to form a third, composite species. Applications of the programs to previous experimental data, and for the purpose of identifying the effect of material and process variables on alloying behavior, are provided in the article following this one. 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     

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.     

Macrosegregation in a multicomponent low alloy steel

Macrosegregation theory is extended to predict the formation of channel-type segregation for multicomponent systems. Specifically, calculations are carried out for 0.7 pct C steel, by considering heat, mass and momentum transport in the mushy zone. In the model used for calculations the momentum transport equation and the energy equation were solved simultaneously. It is confirmed, by comparing calculated results with experimental results, that this model successfully predicts the occurrence of channel-type segregation. This analysis is also more rigorous than previous works on macrosegregation because previous analyses were done by solving for convection in the mushy zone with an “uncoupled” temperature field. Using the model, the effects of adjusting the compositions of silicon and molybdenum in steel were quantitatively evaluated in order to show how channel-type segregates can be avoided by adjusting alloy composition. A method of optimizing composition to minimize segregation is presented. It is recommended that this methodology be applied to alloy design so that ingots of alloys amenable to commercial practice can be obtained readily with a minimum amount of “trial-and-error” development work and expense. Formerly Research Affiliate, Department of Materials Science and Engineering, Massachusetts Institute of Technology AR, was Visiting Scientist, Department of Materials Science and Engineering, Massachusetts Institute of Technology     

Eutectoid decomposition in Ag-Ga

The kinetics and mechanisms of eutectoid decomposition in alloys near Ag-15.3 wt pct Ga (Ag-21.8 at. pct Ga) were investigated. Isothermal decomposition of the parent β phase exhibits C-shaped time-temperature-transformation (TTT) curves below the eutectoid temperature. Pearlite forms from the eutectoid temperature (380 °C) to at least 85 °C below this temperature. Two distinct types of pearlite form: a coarse lamellar structure at higher reaction temperatures and a fine lamellar structure with characteristically faceted boundaries. The fine pearlite forms in compctition with coarse pearlite below 315 °C, and the interlamellar spacings of the two pearlites differ by an order of magnitude. The constituents of coarse pearlite are the equilibrium α and β phases with fcc and hP9 crystal structures, respectively. Fine pearlite is composed of α and a metastable phase, β′', with a crystal structure identified as 9R (structure type hR3). Both types of pearlite undergo coarsening by a discontinuous, or cellular, reaction. Formerly Graduate Student, Materials Science and Engineering Department, Virginia Tech Formerly Undergraduate Student, Materials Science and Engineering Department, Virginia Tech, is This article is based on a presentation made during TMS/ASM Materials Week in the symposium entitled “Atomistic Mechanisms of Nucleation and Growth in Solids,” organized in honor of H.I. Aaronson’s 70th Anniversary and given October 3–5, 1994, in Rosemont, Illinois.     

Predicting the orientation-dependent stress-induced transformation and detwinning response of shape memory alloy single crystals

The present investigation examines three models that predict the orientation dependence of the stress-induced transformation strain in shape memory alloys (SMAs). The merits of each model are con-sidered in light of experimental results for three SMAs: NiTi, Cu-Ni-Al, and Ni-Al. Published experimental results fit model predictions well in most cases; the few exceptions can be accounted for by factors not included in the present models. As part of the comparison of model results with experimental observations, Ni-Al stress-strain curves generated by one of the models are found to closely match experimental stress-strain curves for the [001], [011], and [111] stress axis orientations. Finally, the predicted transformation stress anisotropy is analyzed in detail to examine the effect of detwinning of the stress-induced martensite. Formerly with the Department of Materials Science and Engineering, University of Virginia.     

Elevated-temperature stability of mechanically alloyed Cu-Nb powders

When two-phase mixtures of ductile metals are mechanically alloyed, they often assume a convoluted lamellar structure. Since these powders are consolidated at elevated temperatures, their structures (and, therefore, properties) are likely to be altered by consolidation processing. We have investigated microstructural changes that take place on heat-treating mechanically alloyed Cu −20 vol pct Nb alloys. The transition from a “platelike” to a spherical microstructure is described, and the kinetics of this process appear controlled by a type of boundary diffusion, even though the coarsening temperature was high in terms of the homologous temperature of Cu. Reasons for this behavior are suggested. Finally, during heat treatment (carried out in H), a Nb layer forms around the particles. The thickness of this layer (and the corresponding zone denuded of Nb within the particle) increases with continued elevated-temperature exposure, and at a rate consistent with the process being driven by curvature forces. Formerly Professor, Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA     

Nucleation kinetics of grain boundary allotriomorphs of proeutectoid ferrite in Fe-C-Mn-X2 alloys

The steady-state nucleation rates of ferrite allotriomorphs at the “faces” of austenite grain boundaries were measured in Fe-C-X₁-X₂ alloys, where X₁ was Mn and X₂ was successively Si, Ni, and Co, using techniques previously developed for counterpart studies on Fe-C and Fe-C-X alloys. The results were compared with the predictions of the classical nucleation theory, using the pillbox-shaped critical nucleus model. The volume free energy changes associated with nucleation in Fe-C-X₁-X₂ quaternary systems were evaluated from the central atoms model (CAM) for both para- and orthoequilibrium modes of transformation. The nucleation process was assumed to be controlled by volume and/or grain boundary diffusion of alloying elements. The so-called synergistic effects of alloying elements were considered in terms of the volume free energy change and interfacial energies on the basis of the results of the nucleation rate measurements. Formerly Graduate Student, Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh,PA Formerly R.F. Mehl Professor Emeritus at Carnegie Mellon University, is with GEO-Centers, Inc., Ft. Washington, MD,     

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.     

Crystallography of grain boundary α precipitates in a β titanium alloy

The crystallography of α(hcp) precipitates formed on the β(bcc) matrix grain boundaries has been studied with transmission electron microscopy (TEM) in a Ti-15V-3Cr-3Sn-3Al alloy. The α precipitates have a near-Burgers orientation relationship with respect to at least one of the adjacent β grains. Among the possible 12 variants in this orientation relationship, the variant that [11•20]_α is parallel to the 〈111〉_β closest to the grain boundary plane tends to be preferred by the α precipitates. Additionally, further variant selections are made so as to minimize the deviation of orientation relationship with respect to the “opposite“ β grain from the Burgers one. Such rules in variant selection often result in the formation of precipitates with a single variant at a planar grain boundary. Prior small deformation of β matrix changes the variant of α precipitates at the deformed portion of grain boundary. It is considered that the stress field of dislocations in the slip bands intersecting with the boundary strongly affects the variants of α precipitates. Discussion of these results is based upon a classical nucleation theory. Formerly Graduate Student, Department of Materials Science and Engineering, Kyoto University Formerly Graduate Student, Department of Materials Science and Engineering, Kyoto University This article is based on a presentation made during TMS/ASM Materials Week in the symposium entitled “Atomistic Mechanisms of Nucleation and Growth in Solids,“ organized in honor of H.I. Aaronson’s 70th Anniversary and given October 3–5, 1994, in Rosemont, Illinois.     

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.     

Crack detection by resonant frequency measurements

The resonant frequency of 304 stainless steel specimens with a center-drilled hole has been measured as a function of fatigue cycles during crack initiation and propagation. Simultaneous measurements of crack lengths by scanning electron microscopy yield the resonant frequencyvs crack length. The change of resonant frequency is equivalent to the change of an effective elastic modulus. Analytical results for a “spring” model to predict the change in effective modulus due to the presence of cracks have been compared with results derived from resonant tests. In the model, the load transfer across the plane of the crack is represented by a distribution of springs of stiffness that depends on the crack length. Good agreement is observed between theory and experiment for cracks up to 500-μm long. The model may be used to obtain the crack length from resonance measurements. Formerly with the Materials Science and Engineering Department, Northwestern University, Evanston, IL 60208,     

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.     

The effect of ternary trace additions on the nucleation and growth of γ′ precipitates in an Al-4.2 At. Pct Ag alloy

The role of trace elements on the nucleation and growth kinetics of γ′ precipitates in an aged Al-4.2 at. pct Ag alloy was determined. Comparing the characteristic properties of different trace elements on the precipitate dimensions and density after aging showed that a combination of high solute/vacancy binding energy and diffusivity was required to significantly affect the length, thickness, and density of γ′ precipitates. The elements which had the most pronounced effect were In and Sn, and the high solute/vacancy binding energy of In and Sn appears to be largely electronic in origin. The mechanism by which these trace elements affect the micro-structure is to reduce the number of quenched-in dislocation loops for heterogeneous nucleation of γ′ precipitates. The decreased number of nucleation sites leads to a prolonged matrix super-saturation, which causes an increase in the length, thickness, and ledge density of γ′ precipitates. Formerly with the Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University Formerly with the Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, Pittsburgh, PA     

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.     

Measurements of magnetic fields and electromagnetically driven melt flow in a physical model of a hall-héroult cell

A physical model (approximately one-tenth scale and operated at 1000 A) was constructed to simulate the electromagnetically driven flow occurring in Hall cells. The model contained Wood’s metal, in which magnetic fields and velocities were measured, as the single liquid. Data have been generated for (future) comparison with mathematical models of Hall cells. The model has also proved useful in examining the effects of cell changes and upsets long thought by operators to have an influence on cell performance. Effects of current maldistribution in the “collector bars,” “cold” anodes, “muck,” and alternative bus-bar arrangements have been observed. In many cases, these effects can be predicted qualitatively from an examination of the model’s magnetic field. S.K. Banerjee, having received his Ph.D. from the Department of Materials Science and Mineral Engineering at the University of California.     

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.     

Hydrogen-enhanced localization of plasticity in an austenitic stainless steel

Microscopic observations and the results of static strain aging, stress relaxation, and strain rate change tests on 310s stainless steel foils, with and without hydrogen, have been presented to complement the stress-strain curves in a previous article. The hydrogen-free specimens showed minute yield points during static strain aging, while the hydrogen-containing specimens demonstrated “preyield microstrain. ” Thermal activation analysis of the strain rate change and stress relaxation plots led to the conclusion that the activation area for dislocation motion is decreased by hydrogen. Microstructural examination with the scanning electron microscope (SEM) revealed extensive strain localization, while transmission electron microscopy (TEM) studies showed microtwinning and austenite faulting in hydrogenated specimens tested at room temperature. The relation of hydrogen-induced changes in plastic deformation to hydrogen embrittlement is discussed. Formerly Graduate Student, Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign.     

Computer simulation of the forging of fine grain IN-718 alloy

In recent years, there has been great emphasis on the use of computer-aided tools in process design. The key to the success of any computer modeling is the accurate knowledge of the mechanical and thermal properties of the various components of a manufacturing system. In order to develop a data base of forging properties of the nickel-base alloy IN-718, isothermal constant strain-rate compression tests were conducted on the annealed fine-grain material over the temperature range 871 °C to 1149 °C (1600 °F to 2100 °F) and strain-rate range 0. 001 to 10 s⁻¹. Empirical relationships among flow stress, strain rate, and temperature developed based on these tests, along with experimentally measured heat-transfer and friction coefficients, were used in the program ALPID to simulate nonisothermal forging of “double-cone” specimens. The simulation results were compared with actual forging in an industrial forge press. The good agreement between simulation and forging results indicates that when a complete data base of materials properties is available, computer modeling can be used effectively to study the forging process. Formerly Graduate Student, Mechanical and Materials Engineering Department, Wright Formerly Graduate Student, Mechanical and Materials Engineering Department, Wright