Thomas H. Courtney

The physics of mechanical alloying: A first report

In this paper, we present a first attempt to define the basic geometry, mechanics, and physics of the process of mechanical alloying. The geometry of the collision events which lead to particle fragmentation and coalescence is modeled on the basis of Hertzian contacts between the grinding media which entrap a certain amount of material volume between the impacting surfaces. This geometry essentially defines the volume of material affected per collision, and from this information and characteristics of the specific mill and the material being processed, impact times, powder strain rates and strains, powder temperature increase, powder cooling times, and milling times can be approximated.

Shape instabilities of plate-like structures—I. Experimental observations in heavily cold worked in situ composites

Abstract The capillary shape instabilities associated with ribbon or finite plate dispersoids are described and documented with experimental evidence from three composite systems: (1) drawn castings of CuFe containing ribboned Fe fibers (14.3 vol.% Fe), (2) rolled liquid-phase sintered NiW alloys containing elliptic W plates (48 vol.% W), (3) rolled “hypoeutectic” NiW alloys containing W blades which occupy 17% of the eutectic microconstituents volume. The primary instabilities observed include cylinderization via edge recession, boundary splitting via the thermal grooving of internal boundaries, and edge spheroidization via the ovulation of ridges formed by edge recession. For a given plate-shaped dispersoid, the dominant instability is determined by cross sectional aspect ratio (width/thickness) and, when internal boundaries are present, the ratio of the internal boundarys energy to that of the phase interface.

Shape instabilities of plate-like structures—II. Analysis

Abstract In this paper, a companion to the previous one, a susceptibility analysis which delineates the primary instability mode of a terminated plate as it depends on plate width to thickness (aspect) ratio and the energy of internal boundaries of plates is presented. The analysis is based on a simple averaging of Ficks first law, and thus is based on geometrical, yet physically plausible, approximations. The analysis is carried out for both volume diffusion and surface diffusion control of the instability process. Direct cylinderization of plates is favored when the plate aspect ratio is small and the energy of internal boundaries that may be present is low. Boundary induced splitting of plates is favored when the boundary energy is high, whereas edge spheroidization is the dominant instability mode for plates with large aspect ratios containing low energy internal boundaries. The results of the analysis can be succintly represented in terms of plate instability diagrams which define the dominant instability mode in terms of plate aspect ratio and internal boundary energy. Lines of constant instability times can be superimposed on the diagrams, thereby increasing their utility.

Ductile two-phase alloys: prediction of strengthening at high strains

When alloys containing two ductile phases are heavily deformed, composite-like microstructures develop and strengths well in excess of either of the phases in single phase form may be exhibited as a result of microstructure/dislocation density effects. In this paper a previously-published model for such strengthening is reviewed, and its application in a predictive capacity discussed. Flow stressvs fabrication strain data for the two components in single phase form and for one two-phase alloy are necessary for this purpose. The model may then be applied to predict strength for any other two-phase alloy as a function of composition, fabrication strain, and interphase spacing. The approach is illustrated using existing data for several alloy systems. For Ag-Fe and Cu-Nb alloys (with very limited mutual solubility) strengths can be predicted within 15 to 20 pct of the experimental values over the entire range of strains and volume fractions for which data are available. In systems where the potential for precipitation hardening exists (e.g., Cu-Fe) thermal history is important. When such hardening becomes a significant factor, the model cannot be used in its present form due to uncertainty over how to “add” the strengthening from this effect. Such hardening may, however, be useful in further improving the properties of these materials.

Multiple shear band formation in metallic glasses in composites

Multiple shear banding is observed in metallic glasses during tensile deformation of laminated composites containing such glasses. The phenomenon is related to (1) the local stress concentration that develops as a result of the formation of the first shear band, (2) the distribution in stress required to initiate shear banding in tensile loading, and (3) the properties of the surrounding matrix. The tendency for localized and uniform multiple shear banding has been determined. This was done by utilizing a finite element method (FEM) to simulate the local stress state in the vicinity of the shear band first formed, and by determining the distribution in shear band initiation strengths. The experimental data were combined with the FEM analysis to “predict” locations of secondary shear band initiation. Localized secondary banding is predicted for large initial slip displacements, whereas uniform banding is expected when the initial slip displacement is small.

Reaction rates during mechanical alloying

Abstract This paper presents a simple kinetic model of the coalescence and fracturing events that occur during mechanical alloying (MA). The model is based on reaction kinetics based on times between powder particle collisions and particle specific probabilities of welding and fracture. The model is combined with experimental studies and previous models of the MA process to provide information relative to the welding and fracturing probabilities of the various particle species involved. We find that, during MA of CuNb alloys in an attritor, the probability of welding for copper particles is approximately one in 2000 for a ball-to-powder charge ratio of 50 to one. Decreasing the charge ratio decreases the probability of particle welding and lengthens the milling time necessary for alloying.

Fracture Behavior of Laminated Metal Metallic Glass Composites

The crack growth behavior of metallic glass in laminated metal-metallic glass composites was investigated and compared to the crack growth characteristics of monolithic metallic glass. The composite arrangement significantly increases the crack growth resistance of the glass. Growth in the monolithic glass is catastrophic, whereas in the composite, it is stable. The behavior is described in terms of crack growth resistance(R) curves and discussed in terms of extrinsic and intrinsic contributions to toughness. It is found that an extrinsic factor,i.e., matrix bridging, makes the major contribution to increased crack growth resistance and that a limiting crack opening displacement model interprets the experimental data quite well. Enhanced glass deformation in the crack tip region, manifested by multiple shear band formation, is responsible for the intrinsic toughening observed. Physical models are developed to estimate the level of intrinsic toughening due to this effect.

Some tensile properties of metal-metallic glass laminates

The tensile properties of brass (Cu-30% Zn)-nickel base metallic glass (MBF-35 Metglas) laminates have been investigated. Laminates were prepared by soldering these constituents together with a Pb−Sn alloy. The metallic glass exhibited an enhanced tensile ductility in the metal matrix environments, and such enhanced ductility depended on the metal matrix strength and elongation. Multiple shear bands have been observed in the metallic glass ribbon with enhanced tensile ductility. The failure modes of the laminates have been analysed based on stress-strain concentration concepts, following failure of the glass. The results were consistent with the experimental observations.

Two-dimensional finite difference analysis of shape instabilities in plates

A two-dimensional finite difference analysis is applied to surface diffusion-controlled instabilities of plates. Plates can evolve into “cylinders,” or if the plates have longitudinal internal boundaries, they may split into two segments. The evolution process of plates containing internal boundaries into equilibrium shapes depends on both the initial plate aspect ratio (plate width to thickness) and the ratio of the internal boundary energy to the plate-matrix interface energy. When the internal boundary energy is relatively low or the initial plate aspect ratio is relatively small, the transverse equilibrium cross-sectional area shape is composed of two circular segments, with an appropriate dihedral angle dictated by the ratio of the interface energy terms. As either the internal boundary energy or the initial aspect ratio increases, plate splitting, rather than cylinderization, becomes the dominant instability mode. The results of this work are compared to a recent theory of Courtney and Malzahn Kampe (CMK) on shape instability diagrams.[1] The complicated interactive effects between cylinderization and boundary splitting were not considered in the analytical CMK approach; thus, when they are minimal, the results of this finite difference calculation are in reasonable accord with the CMK results, as far as predicting instability times are concerned. However, when the interaction is significant, cylinderization and/or splitting times are markedly changed. The present accurate calculations allow refinement of the CMK plate instability diagrams.

Transverse kinking of BCC fibers in drawn FCC(matrix)-BCC(dispersoid) in situ composites

Abstract The transverse kinking of bcc ribboned fibers in drawn fcc(matrix)-bcc(dispersoid) systems has been attributed to the development of deformation bands within the bcc crystals during the initial stages of drawing and the subsequent plane strain deformation which ensues after attainment of stable 〈110〉 end orientations. Though compatibility constraints do cause some transverse curving, as in the grains of bcc aggregates, their contribution is less dominant when bcc crystals are embedded in a softer, more compliant fcc matrix.