Metal Composites

Metal Composites

7 Deformation-Processed Metal/Metal Composites W. A. SPITZIG, C. L. TRYBUS,* AND J. D. VERHOEVEN Metallurgy and Ceramics Division Ames Laboratory-USD...

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Deformation-Processed Metal/Metal Composites W. A. SPITZIG, C. L. TRYBUS,* AND J. D. VERHOEVEN Metallurgy and Ceramics Division Ames Laboratory-USDOE Iowa State University Ames, Iowa I. Introduction II. Synthesis of Metal Mixtures A. Casting Methods B. Powder Metallurgy (P/M) Methods III. Deformation Processing of Metal Mixtures A. Composite Evolution by Axisymmetric Deformation Processes 1. Microstructural Development 2. Mechanical Property Development 3. Electrical and Thermal Conductivity Development B. Composite Evolution by Plane-Strain Deformation Processes 1. Microstructural Development 2. Mechanical Property Development 3. Electrical and Thermal Conductivity Development IV. Comparison of Axisymmetric and Plane-Strain Deformation Processes for Composite Development A. Microstructural Development B. Mechanical Property Development V. Optimizing Properties of Deformation-Processed Metal/Metal Composites References

I.

151 152 152 155 156 156 156 160 163 165 165 170 171

....

172 172 173 176 178

Introduction

Deformation-processed metal/metal composites encompass a fascinating group of materials. The composite is formed during mechanical processing (i.e., swaging, wire drawing, or rolling) of a ductile two-phase billet. The two phases codeform, causing the minor phase to elongate and become fibrous in nature within the matrix. Because the composite naturally forms "on site," these materials have sometimes been called in situ composites. They will be referred to here as deformation-processed composites (DPC). Remarkably, these materials can be deformation-processed to very high strains [1,2]; up to 13.4 has been reported for Cu/Nb [3] without the need for intermediate anneals. Even relatively brittle metals like Cr [4] and W [5] have been * Presently at INEL, EG & G Idaho, Idaho Falls, Idaho.

151 Copyright © 1991 by Academic Press, Inc. Allrightsof reproduction in any form reserved. ISBN 0-12-341832-1

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reported to deform into filaments within a matrix. In addition, strengths in these materials exhibit exponential positive deviations from the composite rule-of-mixtures (ROM) prediction [2, 6, 7]. Deformation-processed Cu matrix composites combine very high strengths with good electrical and thermal conductivities. It is the combination of properties that these composites have which is perhaps their outstanding feature. In this chapter we describe the microstructural, mechanical, and conductivity development which occurs during axisymmetric and planestrain deformation processing of metal/metal composites. Since the properties of deformation-processed metal/metal composites depend on the starting material, we begin by discussing the synthesis of these metal mixtures.

II.

Synthesis of Metal Mixtures

The first step in the preparation of deformation-processed composites is the fabrication of a billet of a two-phase alloy. Because very large deformation strains are employed, the initial shape of the phases in the billet is not very important. Experiments have shown that codeformation of both minor and matrix phases will produce aligned filaments of the minor phase after adequate deformation, regardless of its initial shape (globular, spherical, dendritic, etc.). Consequently, the initial billet may be fabricated by either solidification or powder processing. The basic requirements of the processing are that (1) phases of the desired compositions be produced, (2) the minor phase be uniformly dispersed throughout the matrix phase, (3) the phase boundaries be free of oxide films or other contamination, and (4) both phases be adequately ductile and have relatively similar flow stresses so that codeformation occurs and large total deformation strains may be employed.

A.

Casting Methods

Two-phase billets may be produced by casting techniques if the phase equilibria of the alloy of interest possesses a two-phase equilibrium field of the two desired phases. The size of the minor phase will depend upon the solidification rate and the nature of the solid/liquid reaction. In general, if a eutectic reaction occurs, the minor phase will be from 0.1 to 0.5 μιη at usual casting rates. If a eutectic reaction does not occur, the solid/liquid interface will be dendritic, with the minor phase freezing as dendrites from

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the liquid, and at usual casting rates the dendrites will range in size from approximately 3 to 50 μιη in diameter. By far, the majority of studies of DPC have been done on noneutectic Cu-base alloys, and therefore casting techniques will only be discussed specifically for this class of alloys. The principles are, however, the same for eutectic forming alloys. The binary phase equilibria between Cu and all of the high-strength b.c.c. metals (including Fe and Co) are similar and the Cu/Nb phase diagram is presented as a prototype in Fig. 1 [8]. The maximum solid solubility of Nb in Cu and of Cu in Nb are both quite small. Hence, nearly pure Nb dendrites form upon solidification and are present in a nearly pure solid Cu matrix at room temperature (Fig. 2a). Well-formed dendrites of the refractory metal phase can be obtained at compositions of up to 30/40 vol.% of V, Nb, Ta, Cr, and Fe in Cu. Some problems exist for Mo and W, which will be discussed below. The three alloys Cu/V, Cu/Nb, and Cu/Ta have all been successfully prepared by consumable arc-melting techniques [9]. The process employs a Cu electrode having slots milled longitudinally and into which the refractory metal is inserted and pinned. Melting occurs directly into a vertical watercooled Cu cylinder under «0.7 atm argon. It has been shown [9] that Cu Atomic Percent Niobium

zwePo-

30

Cu

40

SO

60

Weight Percent Niobium

70

100

Nb

FIG. 1. Cu/Nb phase diagram. Reprinted with permission from the American Society for Metals, J. B. Massalski, in Binary Alloys Phase Diagrams 1, p. 938.

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alloys with the refractory metal at the electrode tip before it runs off into the liquid pool, indicating that the electrode tip temperature is close to the liquidus of the alloy being prepared. Castings up to 15 cm in diameter have been made with good homogeneity. The average refractory metal dendrite diameter runs around 6 to 8 μηι for alloys cast at around 10 g/s into Cu cylinders lined with 1-cm-thick graphite (plasma-spray-coated with yttriastabilized zirconia). When the graphite liner is removed, the dendrite size decreases to 3 to 4 μιη in the middle of the casting with the outer 5 mm having sizes reduced to the 1 to 2 μιη range. Attempts to produce Cu/Mo by consumable arc casting have not been

DEFORMATION-PROCESSED METAL/METAL COMPOSITES

755

successful, and presumably Cu/W would behave similarly. As discussed in [9] the problem arises with Cu/Mo because the liquidus at around 20 vol.% Mo in Cu is near 2500°C, above the boiling point of Cu. Problems associated with this high temperature appear to prevent alloying on the electrode surface and inhibit the process from producing the uniform compositions found with V, Nb, and Ta. Powder processing of Cu-refractory metal powders has an excellent potential for reducing the as-cast dendrite sizes. There is a process control problem here, however, because as the cooling rate is increased to refine the dendrite size, a critical rate is reached where a transition occurs from dendrites to spheroids, due to the kinetically induced monotectic reaction [9], The spheroid shape is not harmful, but the spheroid diameters are considerably larger than the dendrite diameters. Experiments on splat-cooled Cu/20vol.%Nb alloys have shown that dendrite diameters as small as 0.22 μηι are possible [70]. Hence, if the billet could be produced with powders containing around 0.5 μιη Nb dendrite diameters, a significant improvement could be achieved over the consumable electrode melting processes. The powder billets could be prepared by hot isostatic pressing (HIP) without coarsening the Nb dendrite diameters. But it might be a problem in hot extrusion of the HIPed billet if large reduction ratios were used because the extremely fine filaments which form during extrusion are susceptible to coarsening. Successful production of Cu-refractory metal powders possessing uniformly dispersed submicron Nb dendrite diameters has not yet been reported. Attempts to produce such powders by the rotating electrode process (REP) were unsuccessful [77]. Experiments using REP were done on a consumably arc-melted Cu/20vol.%Nb ingot containing 8-/mi-diameter dendrites. Even with this fine dispersion of the Nb, the dwell time of the liquid on the rotating electrode was too short, and/or the liquid temperature was too low to fully dissolve the Nb into the liquid solution prior to drop solidification. Other techniques starting from a fully molten bath, such as gas atomization or atomization from a rotating disk following slow liquid formation from a Cu/Nb electrode surface, may be successful, but great care will be needed to avoid oxygen contamination of the liquid. B.

Powder Metallurgy (P/M)

Methods

The number of metal/metal combinations that can be deformationprocessed into composites is extensively enlarged by using P/M methods to fabricate the starting material. However, powder handling and consolidation methods must be matched with powder characteristics to produce a fully dense billet free from nondeforming particles.

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Billet fabrication by P/M consists of basically two steps: (1) powder mixing, and (2) powder consolidation. Powder characteristics such as powder size, shape, density, and composition will control the processing and handling procedures to be employed. Consolidation methods which have been successfully used include hot extrusion of loose powder mixtures, cold isostatic pressing followed by sintering, or hot extrusion and hot isostatic pressing. Clearly, this list does not exhaust the processing possibilities, but all the above processes result in a fully or almost fully dense billet. Retained porosity may reduce the subsequent workability of the billet, causing it to break up during deformation processing. Pores at the interfaces can enlarge during working and prevent the composite microstructure from developing [5, 12]. Thus, it is essential that the P/M billets be relatively pore-free to enable composite production. Nondeforming particles in the P/M billet are the chief cause of composite formation failure. As previously mentioned, porous or weak interfaces are one source of the problem. Interstitial contamination can render susceptible metals hard, brittle, and nondeformable [75]. Crystallinity may be a factor because it appears that single-crystal particles deform easier than their multigrained counterparts [4]. Particle size and shape may also play a role. Large spherical particles of Nb failed to form a filamentary structure, while smaller irregular ones did [12]. P/M methods have been developed for the production of Cu/Nb composite wires used in superconductor applications. Both hot [75,14] and cold [75-20] extrusion of loose powders have been employed to form Cu/Nb composites which were reacted with Sn to produce Nb3Sn filaments in a Cu matrix. Recently, it has been shown that P/M processing of Cu and Nb powders can also be used to fabricate high-strength Cu/20vol.%Nb composites [72], P/M processing has also been used to fabricate DPC of Ni/W [5], Ag/Ni [27], and Cu/Fe [22]. Figure 2b shows the as-extruded billet of a Cu/20vol.%Nb powder mixture [72].

III. Deformation Processing of Metal Mixtures A. 1.

Composite Evolution by Axisymmetric Deformation Processes MICROSTRUCTURAL

DEVELOPMENT

The tensile strengths resulting from cold axisymmetric deformation processes, such as rod rolling, wire drawing, or swaging, depend on the crystal structures of the two metal phases, being greater for f.c.c./b.c.c. combinations (Cu/Fe [7, 6, 22-24], Cu/Cr [4, 6], Cu/Nb [7, 2, 72, 25], Cu/V [7], Cu/Ta [26],

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Ag/Fe [24-27] than for f.c.c./f.c.c. combinations (Ag/Ni [6, 21\ Ag/Cu [28]) [7, 6]. The greater strengthening resulting in the f.c.c./b.c.c. composites is attributed to the b.c.c. metal developing a ribbonlike cross section as a result of the <110> fiber texture that develops during cold axisymmetric deformation [24, 29]. This texture promotes plane-strain deformation rather than axisymmetric flow in the b.c.c. metal. Because the fee. matrix deforms in an axisymmetric manner during wire drawing or swaging, the b.c.c. ribbons are constrained and forced to fold or twist about the wire axis to maintain compatibility with the matrix, resulting in irregular cross-sectional shapes. In f.c.c./f.c.c. mixtures the second phase undergoes axisymmetric deformation just like the matrix, resulting in the cross-sectional shape remaining nearly circular during processing [28]. Figure 3 shows the three-dimensional characteristics of Nb filaments in a Cu/20%Nb composite rod-rolled and wire-drawn to a reduction of η = 5.3 (η = ln(^ 0 /^), where A0 and A are the initial and final cross-sectional areas). All compositions will be given in volume percentages. The results are the same when swaging is used as the deformation process. Because of the similarity in the structure produced by axisymmetric deformation processes and the greater strengthening in f.c.c./b.c.c. metal mixtures, the effects of axisymmetric deformation processing on refinement of structure and substructural development will be confined to rod-rolled and wire-drawn Cu/Nb and Cu/Ta metal mixtures.

FIG. 3. Cu/20%Nb wire drawn to η = 5.3. Reprinted with permission from Scripta Metall., Effect of deformation made on the strength of deformation processed Cu-20% Nb composites, 23, W. A. Spitzig, © 1989, Pergamon Press pic.

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Microstructural Refinement

With increasing degree of deformation processing the spacing and thickness of the b.c.c. filaments continuously decrease. This is shown in Fig. 4 for the spacing of Nb and Ta filaments in Cu/20%Nb and Cu/20%Ta composites, respectively. Results are shown for arc-cast Cu/20%Nb and Cu/20%Ta with different initial Nb and Ta dendrite sizes and for Cu/20%Nb processed from a mixture of Cu and Nb powders. Also included are spacings for a eutectic Ag/30%Cu composite [28]. Coarser initial dendrite or powder sizes carry through the deformation process, but at the larger draw ratios the spacings are below 1 μτη in all the composites. The thicknesses of the Nb and Ta also decrease in a similar fashion to the spacings with draw ratio and are one-fourth those for the spacings at a given draw ratio. b.

Substructural Development

Figure 5 shows examples of microstructures of transverse and longitudinal sections of the cast Cu/20%Nb composite with initial dendrite size t0 — 6.2 μτη drawn to η = 3.1, 5.3, 10.3, and 11.9. Figures 5a-c compare the Cu

DRAW RATICU77) FIG. 4. Effect of draw ratio on the spacing (I) of Nb and Ta filaments in Cu/20%Nb and Cu/20%Ta. Data for Cu filaments in Ag/30%Cu are also shown \_28~]. Reprinted with permission from Ac ta Metall. 36, Comparison of the strengths and microstructures of Cu-20% Ta and Cu-20% Nb in situ composites, W. A. Spitzig and P. D. Krotz, © 1988, Pergamon Press pic.

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FIG. 5. TEM images of (a-e) transverse and (f) longitudinal sections of Cu/20%Nb wire drawn to various draw ratios (η). (a) η = 3.1 ; (b) and (c) η = 5.3; (d) η = 10.3; (e) and (f) η = 11.9. Selected Nb filaments are arrowed in (d-f). Reprinted with permission from Ada Metall. 35, Characterization of the strength and microstructure of heavily cold worked Cu-Nb composites, W. A. Spitzig, A. R. Pelton, and F. C. Laabs, © 1987, Pergamon Press pic.

structures in the Cu/20%Nb composites in transverse sections at η = 3.1 (Fig. 5a) and 5.3 (Figs. 5b and c). At the lowest draw ratio investigated (η = 3.1), dislocations are observed forming cells within grains, although the cell walls are not very coarse. Further reduction to η = 5.3 (Fig. 5b) coarsens the cell walls and reduces the cell size to about 0.25 μηι. These cells have low interior dislocation densities similar to what is observed in pure Cu and in Cu/12%Nb [30]. In other regions of the drawn Cu/20%Nb composite,

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high-angle grain boundaries with an average diameter of about 0.44 μηι are observed in the Cu, as shown in Fig. 5c. The regions containing predominantly cell boundaries had a <100> orientation, wereas the grains had developed a strong <111> texture and the Nb filaments had a <110> parallel to the wire axis. TEM analyses of transverse sections of Cu/20%Nb deformed to η = 6.9 were similar to those observed in the wire deformed to η = 5.3 (Figs. 5b and c). Figure 5d shows the microstructure in a transverse section of Cu/20%Nb wire drawn to η = 10.3. Thin (~0.01 μχή) Nb filaments (arrowed) are dispersed among 0.22-/xm-diameter Cu grains. The distribution of the Nb filaments is nonuniform, as seen by their tendency to form clusters in the lower left-hand corner of Fig. 5d. The selected area diffraction pattern (SADP) from the region in Fig. 5d shows that Nb has a strong <110> texture and that Cu has a predominant < 111 > orientation. Transverse and longitudinal sections of Cu/20%Nb wires drawn to η = 11.9 are shown in Figs. 5e and f, respectively. In both sections it is difficult to distinguish the phases. However, some of the Nb filaments were located by systematic dark-field imaging and are arrowed in these figures. Both Cu and Nb have average minimum grain dimensions of about 0.037 μιη and appear to contain dislocation densities of up to 10 10 /cm 2 in some regions. The filaments are long compared with their widths, and the average grain size was estimated to be about 0.15 μτη. Diffraction patterns indicate that the Cu grains have both low- and high-angle misorientations and that the wire is highly textured: Nb has a <110> orientation, whereas Cu has both <111> and <100> textures. Table I summarizes the results from TEM analyses for the grain sizes and cell sizes of Cu in pure Cu and in Cu/20%Nb (i 0 = 6.2 μηι) deformationprocessed to various draw ratios. At draw ratios above 6.9, dislocation cells were not observed in the pure Cu or in the Cu in Cu/20%Nb.

2.

MECHANICAL PROPERTY DEVELOPMENT

The effect of draw ratio on the ultimate tensile stress of arccast Cu/20%Nb with different initial Nb dendrite sizes and for Cu/20%Nb processed from a Cu/Nb P/M extrusion is shown in Fig. 6. Strengths for a Ag/30%Cu composite are included in Fig. 6 [28]. Also included in this figure are the strengths for pure Cu and pure Nb at the different draw ratios. The strengths of the Cu/20%Nb composites with increasing deformation are exponential in nature and show no signs of leveling off, even at the higher draw ratios where both the pure Cu and the pure Nb exhibit such behavior. In f.c.c./f.c.c. metal mixtures strengthening is linear in nature, as shown for the Ag/30%Cu composite [7, 6, 28]. It appears that additional strengthening

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DEFORMATION-PROCESSED METAL/METAL COMPOSITES TABLE I AVERAGE GRAIN SIZES AND CELL SIZES OF CU IN PURE C U AND IN Cu/20%Nb DEFORMATION-PROCESSED BY WIRE DRAWING TO VARIOUS DRAW RATIOS [2].

Material

Draw ratio 3.1

5.3

6.9

10.3

11.9

Average grain size, μπι

Cu Cu/20%Nb

66 50

0.81

— 0.23

0.80 0.44

0.51 0.22

0.50 0.15

N.O.a N.O.a

N.O.a N.O.a

Average cell size, μηι Cu Cu/20%Nb 1



0.30 0.30

0.25 0.25

— 0.23

Not observed.

4

6

8

10

12

DRAW RATIO,!??)

FIG. 6. Effect of draw ratio on the ultimate tensile stress of Cu, Nb, and Cu/20%Nb with different initial Nb size (i0). Data for Ag/30%Cu are also shown [2#]. Reprinted with permission from Ac ta Metall. 35, Characterization of the strength and microstructure of heavily cold worked Cu-Nb composites, W. A. Spitzig, A. R. Pelton, and F. C. Laabs, © 1987, Pergamon Press pic.

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would occur in the Cu/20%Nb composites at larger draw ratios. However, the very small diameter of the resulting wires (< 0.16 mm) makes mechanical property evaluations difficult. Figure 7 shows that the properties of the b.c.c. metal can influence the strength properties of the composite. Using Ta instead of Nb for the b.c.c. metal increases the strengths of the composite about 20%. This appears to be a result of the larger shear modulus of Ta as compared with Nb [26]. The ultimate tensile stress is correlated to the filament spacing (1) in Fig. 8. The slope of the lines in Fig. 8 is 1/2, indicating that strengthening correlates with spacing, in accord with a Hall-Petch [31, 32] mechanism. Similar behavior is also observed in f.c.c./f.c.c. deformation-processed metal mixtures [23, 28, 33], as shown for Ag/30%Cu [28] in Fig. 8, and in directionally solidified eutectic alloys [34, 35]. Included in Fig. 8 are the Nb spacings for the P/M-processed Cu/20%Nb composite. These spacings show the same 2200 2000 1800 σ 1600

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co 1200 UJ _J CO

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800 600 ^ Γ 400 200

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Cu-20%Ta = ° to 3.5/xm t0=7.1/xm Cu--20% Nb • t0=3.8/xm ■ t(f 6.2/xm

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2

4

6

8

10

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DRAW RATIO FIG. 7. Effect of draw ratio and initial dendrite size (i0) on the ultimate tensile stress of Cu/20%Nb and Cu/20%Ta. Reprinted with permission from Ada Metall 36, Comparison of the strengths and microstructures of Cu-20%Ta and Cu-20%Nb in situ composites, W. A. Spitzig and P. D. Krotz, © 1988, Pergamon Press pic.

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163

5000 Lü -J CO

So

1000

If .

500

I-OL 5

Cu:20%Nb • tp = 3.8/i.i

= ίύ

■ \0 = 6.2JJL\ Δ t 0 = 17.5 LU

DCO

Ag-30%Cu A t0 = 0.35/xm


h-cr

100 0.01

0.05 0.1 0.5 1.0 5.0 10.0 50.0 FILAMENT SPACING (X), μπ\ FIG. 8. Ultimate tensile stress dependence on the spacing (I) of Nb and Ta filaments in Cu/20%Nb and Cu/20%Ta. Data for Cu filaments in Ag/30%Cu are also shown [25]. Reprinted with permission from Ada Metall 36, Comparison of the strengths and microstructures of Cu-20%Ta and Cu-20%Nb in situ composites, W. A. Spitzig and P. D. Krotz, © 1988, Pergamon Press pic.

trend as those for the arc-cast composites at the smaller spacings but deviate at the larger spacings. This is due to the smaller Cu grain size in the original powder metallurgy processed compacts as compared to the as-cast compacts. If that expected increment of strength is subtracted out, the data for the powder metallurgy Cu/20%Nb composite would be similar to that for the arc-cast composite at the larger spacing values. This grain size difference between the powder metallurgy and arc-cast alloys becomes insignificant with increasing deformation processing. The ultimate tensile stresses are plotted against (λ)~1/2 where λ is the filament spacing, for Cu/20%Nb, Cu/20%Ta, and Ag/30%Cu in Fig. 9. The smaller slope for Ag/30%Cu, as compared to Cu/20%Nb and Cu/20%Ta, reflects the weaker strengthening with deformation processing in f.c.c./f.c.c, as compared to f.c.c./b.c.c. metal/metal mixtures. 3.

ELECTRICAL AND THERMAL CONDUCTIVITY DEVELOPMENT

Only a very limited amount of data [36] are available on the thermal conductivity of deformation-processed alloys. Several studies [28, 37, 38] have been done, however, on electrical resistivity properties, and the thermal conductivity properties are expected to closely scale with electrical conductivity. Figure 10 shows the electrical resistivity p for Cu/20%Nb (i 0 = 3.8 μνή) wire drawn to various draw ratios (η) for which the tensile stress data are presented in Figs. 6 and 7. The electrical resistivity rises more slowly with η than the ultimate tensile stress at low η values, but more rapidly at large η values. The increase in resistivity with deformation strain arises from a combination of increased electron scattering at dislocations, Apd, and at Cu/Nb

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W.A. SPITZIG, CL. TRYBUS, AND J.D. VERHOEVEN 2200 2000 1800 o

1600

{A

1400

o_ 2 (S> LÜ

or

a to 2

UJ

1200 1000

h-



S

2 K -J 3

800 600 400 200

Cu:20%To oï0=3.5/xm Cu : 20%Nb • To = 3.8/i.m Ag-30%Cu A to = 0.35/i.m

0 (X^.um* FIG. 9. Ultimate tensile stress dependence on the spacing (I) of Nb and Ta filaments in Cu/20%Nb and Cu/20%Ta. Data for Cu filaments in Ag/30%Cu are also shown [25]. Reprinted with permission from Acta Metall. 36, Comparison of the strengths and microstructures of Cu-20%Ta and Cu-20%Nb in situ composites, W. A. Spitzig and P. D. Krotz, © 1988, Pergamon Press pic.

interfaces, Apt. It is possible to evaluate Apd + Apt by measuring resistivity recovery upon heating. A recent study [38] has shown that the recovery of Api due to Nb filament coarsening is much faster than assumed in earlier work [37] and that Apd is constant at around 0.1 μΩ-cm at η > 4, which results in a calculated dislocation density of about 10 1 7cm 2 . This is consistent with TEM studies which measured dislocation densities of about 5 x 10 10 /cm 2 at η > 4 and showed that the Cu matrix undergoes dynamic recovery and recrystallization during wire drawing (Fig. 5) [2, 30]. The variation of Apt with η is showp in Fig. 10, where it is seen that larger values are found at the larger draw ratios. At the largest values of η the larger amount of interfacial surface area of the Nb filaments gives rise to a large increase in resistivity, even larger than that arising from phonon scattering at 0°C (1.55 μΩ-cm).

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cs >> 3

H


< o

Q: Lü _J ÜJ J

0

2

4

6

8

I

I

10

L

12

DRAW RATIO,(77) FIG. 10. Effect of draw ratio on the electrical resistivity of Cu/20%Nb. Δρ, is increase in electrical resistivity resulting from Nb interfaces.

B. 1.

Composite Evolution by Plane-Strain Deformation Processes MICROSTRUCTURAL

DEVELOPMENT

The effect of plane-strain deformation processes on composite development in two metal-phase mixtures has not been studied in much detail. Previous work appears to be limited to Ag/Ni [21] and Cu/20%Nb [39] composites. For Ag/50%Ni, hardening remains nearly linear with increased deformation processing by rolling [21], while Cu/20%Nb exhibits exponential hardening whether deformation-processing by rolling [39] or by wire drawing [2]. In deformation-processed metal/metal composites, it appears that f.c.c./b.c.c. metal combinations produce greater strengthening than f.c.c./f.c.c. metal combinations, regardless of the mode of deformation processing. Figure 11 shows the three-dimensional nature of the Nb filaments after rolling to η = 4.3 (η = ln(/z0/A), where h0 and h are the initial and final thicknesses). The planes marked A, B, and C are referred to as the longitudinal, transverse, and through-thickness planes, respectively, of the rolled sheet. The filamentary nature of the Nb is apparent on the longitudinal and the transverse planes. Because the mode of deformation is plane strain, both

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FIG. 11. Cu/20%Nb rolled to η = 4.3 (ηβ = 5.0). Reprinted with permission from Scripta Metall, Effect of deformation made on the strength of deformation processed Cu-20%Nb composites, 23, W. A. Spitzig, © 1989, Pergamon Press pic.

Cu and Nb deform by plane strain, resulting in the Nb taking on an aligned planar morphology even on the transverse section. Therefore, the Nb morphology on transverse sections is considerably different after axisymmetric and plane-strain deformation processing. The refinement of structure and substructural development in metal/metal composites during deformation processing by cold rolling will of necessity be primarily confined to a Cu/20%Nb metal/metal composite [39]. This composite is from the same ingot as the arc-cast Cu/20%Nb, with an initial dendrite size of 6.2 μπι, characterized during axisymmetric deformation processing in Section IIIA. Therefore, results for this material processed by wire drawing will be included on some figures for comparison purposes. Discussion of differences resulting from the mode of deformation processing will be done in Section IV. When comparing material deformation-processed by rolling and wire drawing, it is desirable to make comparisons at equivalent η values. Therefore, it is appropriate to evaluate an effective η (ηβ) for the rolled material that is directly comparable to the η obtained for axisymmetric deformation [40]. Therefore, r\e for the rolled material is taken as 2/^/3η, and when results for the rolled and wire-drawn composites are compared r\e will be used for the sheet material. a.

Microstructural Refinement

Figure 12 shows the effect of increasing deformation processing by rolling on decreasing the average values of the thickness (t) and the spacing (1) of Nb. The spacing of Nb was 25 μηι in the cast ingot. It is apparent in Fig.

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FIG. 12. Effect of rolling reduction or draw ratio on the spacing (I) and thickness (t) of Nb filaments in Cu/20%Nb. Reprinted with permission from Scripta Metall, Effect of deformation made on the strength of deformation processed Cu-20%Nb composites, 23, W. A. Spitzig, © 1989, Pergamon Press pic.

12 that the thickness and spacings of Nb decrease much more rapidly with increasing deformation processing by rolling as compared to wire drawing. b.

Substructural Development

Figure 13 shows the microstructures on transverse sections of Cu/20%Nb rolled to various η values. At η = 3.6 some areas are predominantly elongated Cu grains (Fig. 13a), while others are chiefly small grains and cells with heavily dislocated walls (Fig. 13b). Dark-field imaging techniques were used to identify the Cu and Nb. At low deformations, most of the Nb is still very thick (~0.4 μηι) and difficult to thin uniformly with the Cu by ion thinning; thus Nb is not seen in all areas. In Fig. 13b the large equiaxed Cu grain along with smaller equiaxed cells is indicative of dynamic recovery and recrystallization processes. There are many matrix dislocations present, and typical areas were found to contain an average dislocation density of 4.0 x 10 10 /cm 2 . Diffraction information from small areas yields a Cu/Nb orientation of <110>Nb || <112>Cu || rolling direction (RD). Transverse sections at η = 3.6 do not show strong texturing, but two Cu rolling textures frequently observed were {110}<112> and {100}<001>. Longitudinal sections

168

W.A. SPITZIG, CL. TRYBUS, AND J.D. VERHOEVEN

FIG. 13. TEM images of (a-c, e, f) transverse and (d) longitudinal sections of Cu/20%Nb rolled to various reductions (η): (a) and (b) η = 3.6; (c) and (d) η = 6.0; (e) and (f) η = 6.9. Selected Nb filaments are arrowed in (c-f).

look very similar to transverse ones showing both elongated Cu grains with high-angle grain boundaries and heavily dislocated cellular boundaries. As the total rolling deformation increases, the Cu and Nb become more lamellar in nature. Figures 13c and 13d are transverse and longitudinal sections, respectively, of the Cu/Nb composite sheet rolled to η = 6.0. At this degree of deformation Nb has a large aspect ratio, being very long and thin. Adjacent Nb filaments are separated by single and multiple blocks of Cu. Cells are not common in the Cu, but small, equiaxed, strain-free grains are observed. The average dislocation density of the Cu is 5.0 x 10 10 /cm 2 . Another difference between the two sections is that small twins are observed only in the longitudinal sections. Comparison of the two SADPs denote

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169

textural differencees. In the transverse view (Fig. 13c) rational and irrational orientations were found, and no obvious Cu orientation trend was detected. On the other hand, the SADP of the longitudinal section (Fig. 13d) is very regular and similar to the longitudinal sections of the η = 3.6 material, <110>Nb||Cu. TEM observations of sheet rolled to η = 6.9 (Fig. 13e) show that the Cu between the Nb are predominantly single grains, and neither cells nor equiaxed Cu grains were commmonly observed. Twinned Cu was plentiful in the transverse sections at this deformation only, and an example of these Cu twins is presented in Fig. 13f. The measured average dislocation density for this material was 4.3 x 1010/cm2. Wide-aperture SADPs of this sample indicate the strong texturing of Cu and Nb. Microdiffraction of single Cu grains on the transverse section consistently exhibited <110>Cu||RD and <110>Nb||Cu. TEM analysis of Nb filaments extracted from sheet rolled to η = 6.0 and 6.9 [39] shows that at lower levels of deformation the dislocations are randomly arranged, but as the deformation intensifies the dislocations form into low-angle (2° to 5° misorientation) dislocation boundaries parallel to the <110>Nb. Rolling textures in the filaments were found to be {100}<110> and {113}<110>. Nb filaments extracted from wires show similar results; boundaries aligned along <110>Nb misoriented about a common <110> by 2° to 35° [30]. Table II summarizes the results from TEM analyses for the grain sizes, TABLE II AVERAGE GRAIN SIZES, CELL SIZES, AND DISLOCATION DENSITIES OF CU IN Cu/20%Nb DEFORMATION-PROCESSED BY ROLLING TO VARIOUS REDUCTIONS

Rolling Reduction 3.6

0

6.0

6.9

average grain size, μτη 50

0.15

0.072

0.052

Average cell size, μη\



0.068

N.O. a

0.059 10

2

Average dislocation density (10 /cm )



4.0 a

Not observed.

5.0

4.3

170

W A SPITZIG, CL. TRYBUS, AND J.D. VERHOEVEN

cell sizes, and dislocation densities of Cu in Cu/20%Nb deformation processed by rolling to various reductions. Dislocation cells were not observed at the largest reduction examined, and the dislocation density did not appear to change with increasing rolling reduction but remained about 4.5 x 10 10 /cm 2 . 2.

MECHANICAL PROPERTY DEVELOPMENT

The effect of rolling reduction on the ultimate tensile stress of Cu/20%Nb is shown in Fig. 14. Results for both longitudinal and transverse specimens (Fig. 11) are included in Fig. 14. The differences between the strengths of these specimens are small and within experimental scatter, except at the smallest η value, where the longitudinal specimens were consistently slightly stronger than the transverse specimens. It seems that the aspect ratios and overlap of the filaments in the transverse direction are sufficient to produce 1

1 \J \J

1

1

I

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—r~

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-

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. 700

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p



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FIG. 14. Effect of rolling reduction on the ultimate tensile stress of Cu/20%Nb. Reprinted with permission from Ac ta Metall. 37, Characterization of the strength and microstructural evolution of a heavily cold rolled Cu-20%Nb composite, C. L. Trybus and W. A. Spitzig, © 1989, Pergamon Press pic.

171

7 DEFORMATION-PROCESSED METAL/METAL COMPOSITES

optimum strengthening [41]. The strength of rolled Cu/20%Nb with increasing deformation is exponential in nature and similar to that for wire-drawn Cu/20%Nb (Fig. 6). As with the wire-drawn composite, it appears that additional strengthening would occur with further deformation processing by rolling, but the thinness of the sheet materials (< 0.064 mm) makes mechanical property evaluations difficult. Figure 15 shows the effect of deformation processing by rolling on the average values of Nb spacing (1). The data from Fig. 8 for the corresponding wire-drawn composite are included in Fig. 15 for comparison. For the large range of Nb spacings obtained in Cu/20%Nb deformation processing by rolling or wire drawing, it is apparent that there is a drastic difference in the relationship between strength and filament spacing for these two modes of deformation processing. Limited data based on the increase in hardness with increased deformation processsing by rolling for a Ag/50%Ni composite are also included in Fig. 15 [21]. These limited data support a similar dependence of strength onfilamentspacing in rolled Ag/50%Ni as observed in rolled Cu/20%Nb. 3.

ELECTRICAL AND THERMAL CONDUCTIVITY DEVELOPMENT

Experimental data on the variation of electrical and thermal conductivities under plane-strain deformation conditions are not yet available. As a first approximation, it is reasonable to assume that the variations will be similar to those found for axisymmetric deformation. There may be significant differences, however, because of the differences noted above in the transverse filament morphology. The plane-strain deformation partitions the Cu into predominantly planar regions, whereas the axisymmetric deformation parti5000

ez) z •-CL

1000 500

DV)

Cu-20%Nb(t 0 =6.2 o Rolled • Wire Drawn [ Ag-50%Ni(T 0 =36.5/xm) Rolled

100 0.01

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0.05 0.1 0.5 1.0 _ 5.0 10.0 FILAMENT SPACING (X),/i.m

50.0

FIG. 15. Ultimate tensile stress dependence on the spacing (1) of Nb filaments in rolled or wire-drawn Cu/20%Nb. Data for Ag/50%Ni are also shown [27]. Reprinted with permission from Acta Metall. 37, Characterization of the strength and microstructural evolution of a heavily cold rolled Cu-20%Nb composite, C. L. Trybus and W. A. Spitzig, © 1989, Pergamon Press pic.

172

W.A. SPITZIG, CL. TRYBUS, AND J.D. VERHOEVEN

tions it into cylindrically shaped regions. The theory of Dingle [42] predicts a different dependence of interface scattering, Aph upon filament size for planar versus cylindrical filaments and, hence, the plane strain deformation may produce a different dependence of Apt on η than found for axisymmetric strain.

IV. Comparison of Axisymmetric and Plane-Strain Deformation Processes for Composite Development A.

Microstructural Development

The microstructure of Cu/20%Nb deformation processed by wire drawing or rolling possesses a myriad of features, each of which contributes to the macroscopic properties. Throughout the deformation the microstructure is changing, and these changes are quantified in Tables I and II. As the deformation level increases, Cu grain and cell sizes decrease, as does the Nb thickness and spacing. The structural features change, too, from a mixture of cells and grains to an absence of cellular structures at high deformation. The strain-induced microstructural changes in both wire-drawn and rolled Cu/20%Nb composites (Figs. 5 and 13 and Tables I and II) are in line with low-temperature dynamic recovery and recrystallization processes [43, 44]. The observation of bimodal distributions of cells and equiaxed grains with low dislocation densities in pure Cu and in the Cu in Cu/20%Nb suggests that during dynamic recovery dislocation generation and annihilation are in near equilibrium. At a critical deformation (η ~ 7), strain-induced dynamic recrystallization competes with dynamic recovery. The mechanism of dynamic recrystallization appears to be the conversion of subgrain walls into high-angle misorientation boundaries. These recrystallized grains have about the same size as the dislocation cells. It is likely that certain grains would achieve the critical strain for recrystallization at different stages of the deformation process because of nonuniform stress distributions within the drawn wire or rolled sheet. Therefore, it is expected that a continuous process of deformation/recovery/recrystallization occurs with increasing mechanical working during the wire-drawing process. These observations are in good agreement with previous results on less heavily deformed Cu, where recovery was observed near η = 2 and recrystallization was almost complete at η = 3 [43]. Because of the deformation/recovery/recrystallization cycle, the estimated observed free dislocation densities in the rolled or wire-drawn composites

7 DEFORMATION-PROCESSED METAL/METAL COMPOSITES

173

do not change much during deformation processing and remain at about 5 x 1010/cm2. These estimates are in good agreement with recent resistivity measurements on heavily deformed Cu/20%Nb, which indicate dislocation densities of about lO^/cm2 independent of draw ratio [38]. Therefore, the dislocation densities in the Cu/20%Nb composites are significantly less than the 1013/cm2 estimated dislocation densities from earlier resistivity measurements [45]. B. Mechanical Property Development The effect of deformation processing by wire drawing and rolling on the ultimate tensile stresses of Cu/20%Nb (i0 = 6.2 μιη) is shown in Fig. 16. At effective strains up to 6.3, specimens of wire-drawn and rolled Cu/20%Nb are identical. At greater effective strains, the rolled composite appears to be slightly stronger than the wire-drawn composite. Both rolled and wire-drawn Cu/20%Nb exhibit exponential hardening behavior in contrast to the linear 1800

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600

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5 4001-

C u - 2 0 % Nb o ROLLED • WIRE DRAWN

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u

JL

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4 6 8 10 12 EFFECTIVE TRUE STRAIN,(77e)

FIG. 16. Effect of rolling reduction or wire draw ratio on the ultimate tensile stress of Cu/20%Nb. Reprinted with permission from Acta Metall. 37, Characterization of the strength and microstructural evolution of a heavily cold rolled Cu-20% Nb composite, C. L. Try bus and W. A. Spitzig, © 1989, Pergamon Press pic.

174

WA. SPITZIG, CL. TRYBUS, AND J.D. VERHOEVEN

hardening observed in rolled and wire-drawn f.c.c./f.c.c. metal composites [4, 21, 28]. From Fig. 16 it appears that strengthening in axisymmetric and plane-strain deformation-processed Cu/20%Nb correlates reasonably well with the amount of mechanical deformation. This similarity in magnitude of strengthening with amount of deformation processing by rolling or wire drawing occurs even though the filament spacings decrease more rapidly by rolling than by wire drawing. This is shown quite clearly in Fig. 17 and is a direct consequence of plane-strain versus axisymmetric deformation processes if the filament spacing decreases in proportion to the sheet thickness and the wire diameter, respectively. Also, shown in Fig. 17 are data for rolled Ag/50%Ni [21] and wire-drawn Ag/30%Cu [28], which appear to be in good agreement with the results for rolled and wire-drawn Cu/20%Nb, respectively. Therefore, the filament spacings and thicknesses in both f.c.c./b.c.c. and f.c.c./f.c.c. metal mixtures decrease in a similar fashion with increased deformation processing. 1.0

CO

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FIG. 17. Effect of rolling reduction or wire draw ratio on the spacing of Nb filaments in Cu/20%Nb. Data for Ni filaments in Ag/50%Ni [27] and Cu filaments in Ag/30%Cu [2
7

DEFORMATION-PROCESSED METAL/METAL COMPOSITES

175

The reason for the weaker dependence of strength on filament spacing as a result of plane-strain deformation processing, as compared to axisymmetric deformation processing, is not obvious. Dislocation structures appear similar after both modes of deformation (Figs. 5 and 13) [2, 30, 39]. In Cu/20%Nb composites this difference in strengthening with spacing for these two modes of deformation processing has been attributed to the different morphology of the Nb filaments on transverse planes (Figs. 3 and 11) [39]. In wire-drawn Cu/20%Nb the filaments become convoluted about the wire axis during deformation processing and thereby essentially form tubes of Nb parallel to the wire axis with Cu inside them. Therefore, the Nb becomes an effective barrier to dislocation motion in the Cu matrix. The tubular nature of the Nb filaments in wire-drawn Cu/20%Nb is shown in Fig. 18, where the fracture surface of a tensile specimen was etched to remove the Cu. In rolled Cu/20%Nb the filaments remain planar during deformation, and, therefore, they are not expected to be very effective barriers to dislocation motion in the Cu matrix because the dislocations can move relatively unimpeded in directions parallel to the filament surfaces. This suggests that it is the planar and highly aligned nature of the filaments in plane-strain deformation-processed metal/metal composites that makes them less effective as obstacles to plastic deformation. The apparent similarity in microstructural refinement with deformation processing in f.c.c./b.c.c. and f.c.c./f.c.c. metal composites (Fig. 17) makes it difficult to rationalize the exponential hardening behavior in the former and linear hardening in the latter composites. While the difference in filament

FIG. 18. SEM image of etched fracture surface of a tensile specimen of Cu/20%Nb wire drawn to a draw ratio of η = 8.9. Cu has been etched away, revealing the Nb filament morphology.

176

WA. SPITZIG, CL. TRYBUS, AND J.D. VERHOEVEN

morphologies on transverse planes in these composite systems could be used to rationalize the différent hardening behavior for axisymmetric deformationprocessed composites, the filament morphologies on transverse planes for plane-strain deformation-processed composites is very similar in these two composite systems [21, 39]. The primary difference between the f.c.c./b.c.c. and f.c.c./f.c.c. composites appears to be in the different hardening rate of b.c.c. and f.c.c. filaments with increasing deformation processing. Typical f.c.c. metals show a gradually decreasing hardening behavior at large strains [46], as shown for Cu in Fig. 6. Typical b.c.c. metals tend to show a linear hardening rate up to large strains, although previous work has been limited to deformation strains below η ~ 6 [46]. The strength of pure Nb tends to show linear hardening behavior to η ~ 6, but beyond this the hardening becomes exponential (Fig. 6). Likewise the strengthening in Cu/20%Nb can also be reasonably represented by linear hardening up to η ~ 7 (Fig. 6). Therefore, the exponential hardening in f.c.c./b.c.c. metal composites most likely is a consequence of the exponential hardening of a b.c.c. metal in contrast to saturation hardening in a f.c.c. metal at the large η values where exponential hardening becomes apparent (n > 7). At the present time the strengthening mechanisms operative in these deformation processed composites are not fully understood and this topic is discussed in Chapter 3 of Treatise on Materials Science and Technology, Volume 32 by T. H. Courtney.

V. Optimizing Properties of Deformation-Processed Metal/Metal Composites The results of the studies on deformation-processed metal/metal composites show that strengthening is primarily influenced by the amount of deformation processing (η). Characteristics of the metal filaments that further enhance strenghtening are a b.c.c, rather than an f.c.c, crystal structure, decreasing initial size, and increasing elastic modulus. The mode of deformation processing does not appear to have much of an effect on the strength at a similar degree of deformation. With the results obtained on wire-drawn Cu/20%Nb and Cu/20%Ta composites, it is possible to empirically correlate strengthening with draw ratio (η), initial dendrite spacing (λ0), and composite shear modulus (GCOM) [26]. This correlation is shown in Fig. 19. The equation of the line in Fig. 19 is
= 0.0013 + 0.02iao)-1/2exp(*y/5.3).

7

DEFORMATION-PROCESSED METAL/METAL COMPOSITES

0

J

I

1

I

I

2

177

I

(I 0 ) H / t expr7/5.3).^m J / 2

FIG. 19. Normalized ultimate tensile stress [( where GCOM is the shear modulus of the composite] dependence on the normalised spacing (λ/λθ9 where λ0 is the initial spacing) of Nb and Ta filaments in Cu/20%Nb and Cu/20%Ta. Reprinted with permission from Ada Metall. 36, Comparison of the strengths and microstructures of Cu-20%Ta and Cu-20%Nb in situ composites, W. A. Spitzig and P. D. Krotz, © 1988, Pergamon Press pic.

Analysis of this equation shows that strengthening increases most rapidly with increasing η, followed by decreasing λ0 and increasing GCOM· For example, increasing η from 5 to 10 increases strength about 150%. Decreasing (λ0) from 6 to 3 μιη increases strength about 40%, and increasing the filament elastic modulus to twice that of Cu increases strength about 20%. For many applications of the deformation-processed Cu alloys, it is desired to produce maximum strength plus electrical and/or thermal conductivity. While this has not been specifically discussed here, previous work [3] has shown that at low η values a significant increase occurs in strength with only a small rise in resistivity, while at large η values the resistivity rises faster than strength with increasing strain (compare Figs. 6 and 10) Hence, for many applications, optimum combinations of strength plus conductivity will probably be found at intermediate η values in the 7 to 9 range.

178

W.A. SPITZIG, CL. TRYBUS, AND J.D. VERHOEVEN

Acknowledgments The authors are grateful to F. A. Schmidt and J. Wheelock of the Materials Preparation Center of Ames Laboratory for arc casting of the Cu/20%Nb and Cu/20%Ta alloys. We also acknowledge P. D. Krotz and L. K. Reed for assistance in wire fabrication and mechanical testing, and H. H. Baker for metallographic specimen preparation. Appreciation is extended to A. R. Pelton of Raychem Corp., F. C. Laabs, L. S. Chumbley, and E. D. Gibson for valuable discussions and help in SEM and TEM analyses. This work was performed at Ames Laboratory, operated for the U.S. Department of Energy by Iowa State University under contract no. W-7405-ENG-82. This research was supported by the Office of Basic Energy Sciences, Division of Materials Sciences.

References /. J. Bevk, W. A Sunder, G. Dublon, and E. Cohen, in "In Situ Composites IV" (F. D. Lemkey, H. E. Cline, and M. McLean, eds.), p. 121, Elsevier, Amsterdam, 1982. 2. W. A. Spitzig, A. R. Pelton, and F. C. Laabs, Acta Metall 35, 2427 (1987). 3. J. D. Verhoeven, W. A. Spitzig, F. A. Schmidt, and C. L. Trybus, Mat. Man. Proc. Adv., 4, 197 (1989). 4. P. D. Funkenbusch, T. H. Courtney, and D. G. Kubisch, Scripta Metall. 18, 1099 (1984). 5. Y. Leng, T. H. Courtney, and J. C. Malzahn Kampe, Mat. Sei. Eng. 94, 209 (1987). 6. P. D. Funkenbusch and T. H. Courtney, Acta Metall. 33, 913 (1985). 7. J. Bevk, J. P. Harbison, and J. D. Bell, J. Appl. Phys. 49, 6031 (1978). 8. J. B. Massalski, in "Binary Alloys Phase Diagrams," American Society for Metals, Vol. 1, p. 938, Metals Park, Ohio, 1986. 9. J. D. Verhoeven, F. A. Schmidt, E. D. Gibson, and W. A. Spitzig, J. Met. 38(9), 20 (1986). 10. J. D. Verhoeven, W. A. Spitzig, F. A. Schmidt, P. D. Krotz, and E. D. Gibson, J. Mat. Sei. 24, 1015 (1989). 11. C. L. Trybus, J. D. Verhoeven, F. A. Schmidt, and W. A. Spitzig, J. Mat. Sei. Lett. 7, 532 (1988). 12. C. L. Trybus, W. A. Spitzig, J. D. Verhoeven, and F. A. Schmidt, in "Processing and Properties for Powder Metallurgy Composites" (P. Kumar, K. Vedula, and A. Ritter, eds.), The Metallurgical Society, AIME, Warrendale, PA, p. 97, 1988. 13. R. Borman, H. C. Freyhardt, and H. Bergmann, Appl. Phys. Lett. 35, 944 (1979). 14. L. Schultz and R. Bormann, J. App. Phys. 50, 418 (1979). 15. H. C. Freyhardt, R. Borman, and K. Mroviec, in "Filamentary A15 Superconductors" (M. Suenaga and A. Clark, eds.), p. 289, Plenum Press, New York, 1980. 16. S. Foner, in "Advances in Cryogenic Engineering Materials" (R. P. Reed and A. F. Clark, eds.), p. 41, Plenum Press, New York, 1982. 17. J. Otubo, S. Pourrahimi, H. Zhang, C. L. H. Thieme, and S. Foner, Appl. Phys. Lett. 42, 469 (1983). 18. R. Fliikiger, R. Akihama, S. Foner, E. J. McNiff, Jr., and B. B. Schwartz, Appl. Phys. Lett. 35, 810 (1979).

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19. S. Pourrahimi, J. Otubo, C. L. H. Thieme, H. Zhang, B. B. Schwartz, and S. Foner, in "ICEC-ICMC Conference Japan 1982" (K. Tachikaua and A. Clark, eds.), p. 3119, Butterworths, London, 1982. 20. R. Flükiger, S. Foner, E. J. McNiff, Jr., and B. B. Schwartz, Appl. Phys. Lett. 34, 763 (1979). 21. J. J. Petrovic and A. K. Vasudevan, Mat. Sei. Eng. 34, 39 (1978). 22. Y. S. Go and W. A. Spitzig, J. Mat. Sei., to be published. 23. P. D. Funkenbusch and T. H. Courtney, Scripta Metall. 15, 1349 (1981). 24. G. Wassermann, in "The Strength of Metals and Alloys," Vol. Ill, p. 1188, American Society for Metals, Metals Park, Ohio, 1970. 25. W. A. Spitzig and P. D. Krotz, Scripta Metall. 21, 1143 (1987). 26. W. A. Spitzig and P. D. Krotz, Acta Metall. 36, 1709 (1988). 27. H. P. Wahl and G. Wassermann, Z. Metall. 61, 326 (1970). 28. G. Frommeyer and G. Wassermann, Acta Metall. 23, 1353 (1975). 29. W. F. Hosford, Jr., Trans. Am. Inst. Min. Eng. 230, 12 (1964). 30. A. R. Pelton, F. C. Laabs, W. A. Spitzig, and C. C. Cheng, Ultramicroscopy 22,251 (1987). 31. E. O. Hall, Proc. R. Soc. London B64, 747 (1951). 32. N. J. Petch, J. Iron Steel Inst. 174, 25 (1953). 33. R. K. Everett, Scripta Metall. 22, 1227 (1988). 34. R. W. Armstrong, in "Yield, Flow and Fracture of Polycrystals" (T. N. Baker, ed.), p. 1, Applied Science, New York, 1983. 35. M. McLean, in "Directionally Solidified Materials for High Temperature Service," Chap. 6, Metals Society, London, 1983. 36. J. E. Ostenson, D. K. Finnemore, J. D. Verhoeven, E. D. Gibson, and H. R. Shanks, J. Appl. Phys. 55, 278 (1984). 37. K. R. Karasek and J. Bevk, J. Appl. Phys. 52, 1370 (1981). 38. J. D. Verhoeven, H. L. Downing, L. S. Chumbley, and E. D. Gibson, /. AppL Phys. 65, 1293 (1989). 39. C. L. Trybus and W. A. Spitzig, Acta Metall., 37, 1971 (1989). 40. W. Johnson and P. B. Mellor, in "Engineering Plasticity," Chap. 6, Van Nostrand Reinhold, New York, 1978. 41. M. A. Meyers and K. K. Chawla, "Mechanical Metallurgy Principles and Applications," Chap. 12, Prentice-Hall, Englewood Cliffs, NJ, 1984. 42. R. G. Dingle, Proc. R. Soc. London A202, 545 (1950). 43. J. H. Cairns, J. Clough, M. A. P. Dewey, and J. Nutting, /. Inst. Metals 90, 93 (1971). 44. H. J. McQueen, Metall. Trans. 8A, 807 (1977). 45. J. Bevk, Ann. Rev. Mat. Sei. 13, 319 (1983). 46. J. Gil Sevillano, P. van Houtte, and E. Aernoudt, Prog. Mat. Sei. 25, 69 (1981). 47. W. A. Spitzig, Scripta Metall. 23, 1177 (1989).