Controlled processing of heavy alloys containing 88 to 97 pct W resulted in high sintered densities and excellent bonding between the tungsten grains and ...
Microstructure Effects on Tensile Properties of Tungsten-Nickel-Iron Composites B.H. RABIN and R. M. GERMAN Controlled processing of heavy alloys containing 88 to 97 pct W resulted in high sintered densities and excellent bonding between the tungsten grains and matrix. For these alloys, deformation and fracture behavior were studied via slow strain rate tensile testing at room temperature. The flow stress increased and the fracture strain decreased with increasing tungsten content. The tradeoff between strength and ductility resulted in a maximum in the ultimate tensile strength at 93 pct W. Microstructure variations, notably grain size, explain sintering temperature and time effects on the properties. During tensile testing, cracks formed on the surface of the specimens at tungsten-tungsten grain boundaries. The crack density increased with plastic strain and tungsten content. The surface cracks, though initially blunted by the matrix, eventually increased in density until catastrophic failure occurred. An empirical failure criterion was developed relating fracture to a critical value of the surface crack tip separation distance. Application of the model explains the effects of microstructural variables on tensile properties.
I.
INTRODUCTION
TUNGSTENheavy alloys are W-Ni-Fe or W-Ni-Cu metalmetal composites produced by liquid phase sintering elemental powders. The alloys possess high density, strength, and ductility which makes them useful for several applications, including kinetic energy penetrators. The composite microstructure consists of nearly spherical grains of bodycentered cubic tungsten surrounded by a solidified facecentered cubic matrix phase containing Ni, Fe, and W. Although polycrystalline tungsten normally is brittle at room temperature, the matrix imparts ductility to the composite. Previous research into the mechanical properties of heavy alloys has identified several causes of ductility and toughness variations, including residual porosity, I~l intermetallic precipitation, IS-1~ hydrogen and impurity embrittlement, I'-~71 varying ductile to brittle transition temperature,18'~7'~81incomplete oxide reduction, I31 and tungsten precipitation in the matrix. I~9'2~ The processing routes needed to obtain high strength and ductility are now better understood. The first requirement for good properties is essentially full densification, achieved through control of the liquid phase sintering process. Subsequently, it is necessary to avoid the weakening of the tungsten-matrix interface by hydrogen embrittlement, impurity segregation, or intermetallic phase precipitation. The strength of the tungsten-matrix interface is controlled through appropriate heat treatments. A successful heat treatment involves heating in vacuum or inert gas followed by water quenching. 14'13'171 In past research, processing variations have dominated properties and precluded understanding the underlying microstructure/property relations. For example, Krock f~8~ concluded that the tensile properties of heavy alloys were independent of tungsten volume fraction and matrix mean free path. In contrast, Gurland and Parikh I2q found that yield
B. H. RABIN, formerly Graduate Research Assistant at Rensselaer Polytechnic Institute, is Senior Scientist, P/M Unit, Materials Group, EG & G Idaho, P.O. Box 1625, Idaho Falls, ID 83415. R.M. GERMAN is Professor, Materials Engineering Department, Rensselaer Polytechnic Institute, Troy, NY 12180-3590. Manuscript submitted June 1, 1987. METALLURGICAL TRANSACTIONS A
strength and deflection in bending depended on tungsten content. Votava I221 and Ekbom I23j reported that initial strain was localized mainly within the matrix and that at larger strains the deformation of individual tungsten grains resembled that of the composite. Likewise, O'Neil and Salyer ~241found that flow strength depended on tungsten content at low strains, but was independent of tungsten content over a few percent plastic strain. Fracture occurred uniformly through the tungsten grains and matrix, except at the highest tungsten levels when intergranular failure of the tungsten was observed. Churn and German I251found that crack propagation occurred by cleavage of tungsten grains ahead of the crack tip in bend tests. In contrast, several authors have reported crack initiation at tungsten-tungsten grain boundaries, t~'''22'231 These observations illustrate the disagreement among past observations. We believe such disagreement is largely the result of processing effects which have not been carefully controlled among studies. Thus, to date the only successful correlations between properties and microstructure have been through the tungsten contiguity. 1261Otherwise, there have been few quantitative microstructure/property relations proposed for the heavy alloys; the present study was undertaken with this goal in mind, using carefully processed alloys.
II.
EXPERIMENTAL
The characteristics of the tungsten, nickel, and iron powders used in this study are shown in Table I. Alloys were formed by mixing nickel and iron powders, in the ratio of 7 to 3 by weight, with tungsten powder. Standard flat tensile specimens were pressed using a double action floating die. Zinc stearate was used as a die wall lubricant, the compaction pressure was about 275 MPa, and the green densities were between 50 and 55 pct of theoretical. Liquid phase sintering was carried out using the processing cycle shown in Figure 1. For oxide reduction, the samples were held at 800 ~ for 1 hour in a dry hydrogen atmosphere (dewpoint = - 4 5 ~ The heating rate to the sintering temperature (above 1435 ~ was 10 K/min. VOLUME 19A, JUNE 1988-- 1523
Table I.
Vendor Designation Purity, pet Fisher subsieve size, /xm Mean particle size,/xm Surface area, mZ/g Apparent density, g / c m 3 Major impurities (ppm)
T 1600~Z_] I dry ~
III.
Powder Characteristics A. Microstructures
Tungsten
Nickel
Iron
GTE M-35 99.98 2.5 2.6 0.23 2.57 O (770) C (19) Na (15) K (11) Mo (8) S (
-~ >. 575 I 526 1
0.1
I
I
0.2
I
03
-1/2,I mean intercept length, --1/2, Lw t o m Fig. 8 - - T h e yield and ultimate tensile strengths of 95 pct W alloys sintered at 1480 ~ shown as a function of the inverse square root of the tungsten grain size.
15281VOLUME19A,JUNE1988
lO" Fig. 9-- Schematic diagramof the surfaceof a tungsten heavyalloy during a tensile test. Shown are the crack size 2X, the center-to-center crack separation distance A, and the crack tip separation distance 6.
METALLURGICAL TRANSACTIONS A
area, Vw is the volume fraction of tungsten, n,. is the number of two-dimensional contacts per grain, and A e is the projected grain area. An assumption made in this analysis is that the material between the failed contacts is homogeneous. The fracture path through the ligament is assumed to be independent of the details of the microstructure. Based on fracture surface analysis this assumption seems reasonable, except for the highest tungsten contents when intergranular failure was preferred. In addition to the microstructure variables which appear explicitly in Eq. [4], the value o f f increases with plastic deformation and also depends on the microstructure. The value of the 6c can be calculated for any alloy using Eqs. [3] and [4] if the microstructural characteristics are known along with the critical value o f f at fracture, f.. The quantities 2X and As were estimated in the following manner. For the range of tungsten contents and dihedral angles studied, the heavy alloy microstructure varied between two limiting cases. For low tungsten contents the microstructure consists of a skeleton of connected monosized spherical tungsten grains. For this case, the grain-grain contact size 2X is obtained from, X = R sin(~b/2)
[5]
where R is the grain radius and ~b is the dihedral angle. The projected area of a tungsten grain, A~, is given by,
Ag = ,n'R2 .
[6[
The values of 2X and Ag can be evaluated using experimental data for the mean intercept tungsten grain size through the relationship, t281 R = 3/4Lw.
[8]
Equations [5] and [6] can be evaluated by using the radius of a sphere based on equivalent volume. For heavy alloy microstructures which exhibit shape accommodation, the tungsten grain shape lies between the two extremes of a sphere and tetrakaidecahedron. Calculation of the contact size and projected grain area in such cases was made by assuming a linear variation in geometric properties with volume fraction between those for a sphere at Vw = 0.74 and a tetrakaidecahedron at Vw = 1.0. The equations developed above, along with the experimental results, allow the heavy alloy microstructures to be completely characterized for different volume fractions, dihedral angles, and grain sizes. As an example, consider the samples which were sintered at 1480 ~ The dihedral angle in this case was about 50 deg. The microstructural characteristics for alloys ranging from 88 to 97 pct W are listed in Table VI. A difficult problem is the determination of the critical fraction of failed contacts, f.. Intergranular cracks form when two conditions are fulfilled: 14~ (i) the tensile stress component normal to the boundary must exceed the boundary strength, and (ii) the shear stress component must not be relieved by activating slip in the adjacent grain. In the heavy METALLURGICAL TRANSACTIONS A
Alloy (Pct W)
Vw 88 0.74 90 0.78 93 0.85 95 0.89 97 0.94 Dihedral angle = 50 deg.
Lw (/~m)
nc
2X (/xm)
Ag (/xm2)
16 17 18 21 23
2.3 2.6 3.1 3.4 4.0
11 11 12 14 16
510 573 638 836 1070
alloys many of the tungsten-tungsten grain boundaries will have orientations that fulfill the second criterion. For these boundaries, the formation of the cracks would be governed by the local tensile stress component of the applied stress. At room temperature, polycrystalline tungsten is brittle and fails by intergranular fracture; the fracture stress provides a measure of the tungsten-tungsten grain boundary strength. The first grain boundaries to fail in the heavy alloys presumably also fail at the same grain boundary strength, but the presence of the matrix prevents catastrophic failure. As the stress is further increased, more tungsten grain boundary failures occur, with grain boundaries oriented perpendicular to the tensile axis failing first. At higher stresses the resolved tensile stress on boundaries oriented away from the normal to the tensile axis reach the critical value for boundary failure. Microstructural observations (Figure 3) confirmed this behavior; hence we let the fraction of failed contacts be governed by,
f = c2(o'w- O'ww)
[7]
The other microstructural extreme corresponds to single phase tungsten (i.e., Vw -- 1.0). The assumed polycrystalline grain shape is a tetrakaidecahedron where the mean intercept length is related to the edge length a a s , ~28] a = 0.592Lw 9
Table VI. Microstructural Characteristics Used in the Calculations for Alloys Sintered at 1480 ~ for 30 Minutes
[9]
where ~vr is the stress within the tungsten phase, Crww is the strength of the tungsten-tungsten grain boundaries, and c2 is a constant which depends on such factors as geometry, distribution of grain boundary strengths, and probability that condition (ii) is fulfilled (i.e., local stress state). Assume that the strain is distributed uniformly throughout the microstructure for plastic strains over a few percent. This assumption oversimplifies the problem, although slip line observations and calculations t4~l indicate that it is not unreasonable, especially for large plastic strains. 122'23'241 Then the stresses are additive, cr = ~rw + crM
[10]
where ~w and ~rM represent the true stresses within the tungsten and matrix phases, respectively. This equation can be rewritten to include volume fraction, or =
Vwo-~
+ (1 -
Vw)o-~,
[11]
where the stresses now represent the in situ flow stresses of the phases. This is the common form of the empirical rule of mixtures for the case of parallel loading. Rearranging Eq. [ 11] and substituting into Eq. [9] gives, f = c2[~r - {(1 - Vw)a~t - O'ww}].
[12]
Equation [12] shows that the fraction of failed contacts increases with the flow stress of the alloy, volume fraction of tungsten, decreasing matrix strength, and decreasing tungsten grain boundary strength. The tungsten grain boundary VOLUME 19A, JUNE 1 9 8 8 - - 1529
strength depends on such factors as impurity content and heat treatment. [13,17,42]Because of the difficulty in estimating the quantities in Eq. [12], this relationship has been simplified to the form, f = c2o"-
[13]
c 3 .
The experimental surface crack density was converted into the fraction of failed contacts and is shown as a function of true stress in Figure 10 for 88 and 95 pct W alloys. The fraction of failed contacts increased linearly with true stress and the intercept was dependent on tungsten content, as predicted by Eqs. [12] and [13]. The curve for the 90 pct W alloy (not shown) was between the 88 pct W and 95 pct W curves. The experimental value o f c2 in Eq. [12] was 1.95 x 10 -4 and was independent of tungsten content. Equation [13] allows the critical fraction o f failed contacts fc to be determined from fracture data. The fracture stresses, along with the data in Figure 10, were used to calculate the values off~ for the alloys sintered at 1480 ~ for 30 minutes. The values o f f , , along with the microstructural variables listed in Table VI, allow 6c to be calculated using Eqs. [3] and [4]. The results of these calculations are summarized in Table VII. The critical crack separation distance is a material parameter related to the resistance to tensile instability at the crack tip. As such, the value of 6~ depends on volume fraction and grain size. This is demonstrated in Table VII which shows the quantity 6c Vw/Lw. For these alloys this quantity was approximately constant. Thus, 6c was proportional to the tungsten grain size and inversely proportional to tungsten content. Intuitively, 6~ should scale with grain size because the fracture mechanism is indepen-
0.16
I
I
d 2
g 0.12 t~
/ 9 88W 9
. /
95W
0.08 "6 c o
0.04
"5
0 0.7
j 1.0 1,3 true stress, cr(GPo)
dent of the size of microstructural features, apart from the influence of grain size on stress-strain behavior. Similarly, as the tungsten content is raised the number of tungstentungsten contacts per grain increases and the work hardening exponent increases; thus, the resistance to tensile instability goes up and the critical value of ~ is reduced. Based on the current results, the failure criterion can be expressed as, 8cVw
1.9.
[14]
Equation [ 14] can be used to predict the properties for any set of microstructural variables and flow characteristics. For example, consider the alloys sintered at 1480 ~ for 30 minutes. The experimental true fracture strains and those calculated using the empirical failure criterion are shown in Figure 11 as a function of the volume fraction. The solid line in Figure 11 was drawn by connecting the points representing the calculated fracture strains for each alloy. The model reproduces the volume fraction dependence of fracture strain. This model predicts an increase in ductility and a decrease in strength as the tungsten grain size becomes larger or the volume fraction of tungsten decreases. Such behavior is substantiated by the data given in Tables II and VI, and Figure 6 and 8. Most engineering alloys exhibit lower strengths and higher ductilities when grain size is increased. However, there was little ductility improvement with grain growth resulting from long sintering times (Table III). One possible explanation is that the ductile-to-brittle transition temperature (DBTT) lies close to room temperature for these alloys. [8'j5'17'18]An increase in grain size can raise the DBTT and lower the ductility at room temperature. Bourguignon and German 1431 have reported ductility improvements by increasing the sintering temperature from 1465 ~ to 1580 ~ The tungsten grain size increased by a factor of two with a simultaneous change in dihedral angle and volume fraction of tungsten. In the current study a similar decrease in strength and increase in ductility were observed for a 93 pct W alloy as the sintering temperature was raised from 1460 to 1500 ~ The microstructural data for these alloys were used to calculate the influence of sintering temperature on ductility, giving a predicted frac-
1.6
Fig. 10--The fraction of failed tungsten-tungsten grain boundaries,f, on the surfaces of heavy alloyscontaining 88 and 95 pct W sintered at 1480 ~ for 30 min, shown as a function of true tensile stress.
-
tw
0.5
i
I
1480"C, 30min E ~
k
t~ ~ 0.3 =
9 measured
\
calculated
%
Table VII. Calculated Critical Crack Tip Separation Distances for Alloys Sintered at 1480 ~ for 30 Minutes
Alloy (Pct W) 88 90 93 95 97
True Fracture Strain 0.39 0.31 0.23 0.19 0.12
-+ 0.02 _+ 0.01 _+ 0.03 --- 0.02 _+ 0.02
1530--VOLUME 19A, JUNE 1988
f.
t% (/zm)
0.111 0.104 0.093 0.088 0.069
41 41 39 42 49
6cVw/-s 2.0 1.9 1.8 1.8 2.0 avg. = 1.9
0.1 i O.7 0.8 O.9 volume fraction tungsten, Vw Fig. 11- - Measured and calculated true fracture strains shown as a function of tungsten grain volume fraction for 88 to 97 pct W alloys sintered at 1480 ~ for 30 min. Calculations were made using the microstructural characteristics listed in Table VI and the failure criterion given by Eq. [14]. METALLURGICALTRANSACTIONS A
ture strain increase from 0.17 to 0.23 as the sintering temperature went from 1460 to 1500 ~ These predictions agree with the results shown in Table IV. It has been suggested E26jthat heavy alloy properties could be adjusted through changes in the dihedral angle. As an upper estimate of the dihedral angle influence on ductility, the changes in nc predicted by German's model ml can be included in the calculations. Additionally, the effect of the dihedral angle change on tungsten grain contact size is given by Eq. [5]. For a 95 pct W alloy, assuming the other microstructural variables are not influenced, a 10 deg reduction in dihedral angle will increase the ductility from 0.17 to 0.19. This small change would be difficult to observe experimentally. A dihedral angle reduction of at least 15 deg would be required to induce a significant ductility increase. Although in practice it is difficult to control independently the microstructural variables, the empirical fracture criterion is useful for predicting individual effects. The mechanism of tensile failure described in this paper has not been previously reported. Nevertheless, the failure criterion may not be unique to the heavy alloys and may be applicable to other ductile composites with similar microstructures, such as copper infiltrated steels or Mo-Ag alloys. The empirical model provides guidelines for determining how microstructure should be controlled through the liquid phase sintering process.
lurgy Laboratories at Rensselaer Polytechnic Institute. Many workers have made contributions to the continuing tungsten heavy alloy program at RPI; they are in part responsible for the further understanding achieved in this study. Special thanks go to Dr. Animesh Bose for his assistance with the experimental work and Jenny Redfern for help with the manuscript.
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3. 4. 5. 6. 7. 8. 9.
10.
V.
CONCLUSIONS
Selected processing was used to produce tungsten heavy alloys with near theoretical densities and excellent bonding between the tungsten grains and matrix. With this processing, variations in tungsten content, sintering temperature, and sintering time were used to alter the microstructure and properties. Alloys with tungsten contents below 93 pct W exhibit a maximum load during tensile testing, whereas the higher tungsten content alloys fracture prior to necking. The tradeoff between composite strengthening and decreased fracture strain with increased tungsten content resulted in a maximum in the ultimate tensile strength near 93 pct W. The fracture surface of the 93 pct W alloy exhibited a maximum proportion of tungsten cleavage. An increased proportion of intergranular fracture occurred at higher tungsten levels. An increase in grain size in a 95 pct W alloy resulted in lower strength without a significant influence on ductility. In contrast, an increase in sintering temperature in a 93 pct W alloy resulted in both lower strength and higher ductility. Crack initiation occurred on the sample surfaces at the tungsten-tungsten grain boundaries. The crack density increased with plastic deformation until catastrophic crack propagation occurre d . The formation of the grain boundary cracks depends on the microstructural variables and tensile stress. Fracture was correlated with a critical value of the surface crack tip separation distance, a material parameter related to the resistance of the alloy to undergo tensile instability at the crack tip. An empirical failure criterion based on a geometric model was developed to explain the influence of microstructural variables on tensile properties.
11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.
ACKNOWLEDGMENTS This research was sponsored by the United States Army Research Office and was performed in the Powder MetalMETALLURGICAL TRANSACTIONS A
29.
Developments in Powder Metallurgy, H.H. Hausner, H.W. Antes, and G. D. Smith, eds., Metal Powder Industries Federation, Princeton, NJ, 1981, vol. 14, pp. 189-203. H. Danninger, W. Pisan, G. Jangg, and B. Lux: Z. Metallkde., 1983, vol. 74, pp. 151-55. R.M. German and K. S. Chum: Metall. Trans. A, 1984, vol. 15A, pp. 747-54. E.C. Green, D.J. Jones, and W.R. Pitkin: Symposium on Powder Metallurgy, Special Report no. 58, Iron and Steel Institute, London, U.K., 1956, pp. 253-56. H. Takeuchi: NipponKinzoku Gakkaishi, 1967, vol. 31, pp. 1064-69. D.V. Edmonds and P.N. Jones: Metall. Trans. A, 1979, vol. 10A, pp. 289-95. L.G. Bazhenova, A. D. Vasilov, R. V. Minakova, and V. I. Trefilov: Soviet Powder Met. Metal Ceram., 1980, vol. 19, pp. 34-38. R.V. Minakova, A.N. Pflyankevich, O.K. Teodorovich, and I.N. Frantsevich: Soviet Powder Met. Metal Ceram., 1968, vol. 7, pp. 396-99. B.C. Muddle: Metall. Trans. A, 1984, vol. 15A, pp. 1089-98. L. Ekbom: Scand. J. Metall., 1976, vol. 5, pp. 179-84. H.K. Yoon, S.H. Lee, S-J. Kang, and D.N. Yoon: J. Mater. Sci., 1983, vol. 18, pp. 1374-80. M.R. Eisenmann and R.M. German: Inter. J. Refract. Hard Met., 1984, vol. 3, pp. 86-91. F.E. Sczerzenie and H.C. Rogers: Hydrogen in Metals, I.M. Bernstein and A.W. Thompson, eds., ASM, Metals Park, OH, 1974, pp. 645-55. R.M. German and J. E. Hanafee: Processing of Metal and Ceramic Powders, R. M. German and K. W. Lay, eds., The Metallurgical Society, Warrendale, PA, 1982, pp. 267-82. B . C . Muddle and D.V. Edmonds: Metal Sci., 1983, vol. 17, pp. 209-17. R . M . German, J.E. Hanafee, and S.L. DiGiallonardo: Metall. Trans. A, 1984, vol. 15A, pp. 121-28. R. H. Krock: Metalsfor the Space Age, E Benesovksy, ed., Metallwerk Plansee, Reutte, Austria, 1965, pp. 265-75. R . V . Minakova, N . A . Storchak, P.A. Verkhovodov, L . G . Bazhenova, and V.L. Poltoratskaya: Soviet Powder Met. Metal Ceram., 1980, vol. 19, pp. 842-46. R.V. Minakova, A.N. Palyankevich, O. K. Teodorovich, and I.N. Frantsevich: Soviet Powder Met. Metal Ceram., 1968, vol. 7, pp. 473-77. J. Gurland and N.M. Parikh: Fracture: An Advanced Treatise, H. Liebowitz, ed., Academic Press, New York, NY, 1972, vol. VII, pp. 841-78. E.J. Votava: Planseeber. Pulvermetall., 1973, vol. 21, pp. 79-87. L. Ekbom: Modern Developments in Powder Metallurgy, H.H. Hausner, H.W. Antes, and G.D. Smith, eds., Metal Powder Industries Federation, Princeton, NJ, 1981, vol. 14, pp. 177-88. J.W. O'Neil and P. W. Salyer: AFOSR 66-1670, ASRC 132-2 USAF, Massachusetts Institute of Technology, Cambridge, MA, 1965. K.S. Chum and R.M. German: Metall. Trans. A, 1984, vol. 15A, pp. 331-38. R.M. German, L. L. Bourguignon, and B. H. Rabin: J. Metals, 1985, vol. 37 (8), pp. 36-39. A. Bose, B.H. Rabin, S. Farooq, and R.M. German: Horizons of Powder Metallurgy, Part H, W.A. Kaysser and W.J. Huppmann, eds., Verlag Schmid, Freiburg, W. Germany, 1986, pp. 1123-26. E.E. Underwood: Quantitative Stereology, Addison-Wesley, Reading, MA, 1970. B.H. Rabin, A. Bose, and R. M. German: Microstructural Science, M. E. Blum, P. M. French, R. M. Middleton, and G. F. Vander Voort, eds., Elsevier, New York, NY, 1986, vol. 15, pp. 285-99. VOLUME 19A, JUNE 1988-- 1531
30. R . M . German: Metall. Trans. A, 1985, vol. 16A, pp. 1247-52. 31. R . M . German: Liquid Phase Sintering, Plenum Press, New York, NY, 1985. 32. R . M . German: Metall. Trans. A, 1987, vol. 18A, pp. 909-14. 33. T. Kang and D . N . Yoon: Metall. Trans. A, 1978, vol. 9A, pp. 433-38. 34. R.H. Krock: J. Mater., 1966, vol. 1, pp. 278-92. 35. E.G. Zukas: Metall. Trans. B, 1976, vol. 7B, pp. 49-54. 36. I.L. Mogford: Metall. Rev., 1967, vol. 12, pp. 49-67. 37. A . R . Rosenfield: Metall. Rev., 1968, vol. 13, pp. 29-40. 38. F . A . McClintock: Ductility, A S M , Metals Park, OH, 1968, pp. 255-77.
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39. J.R. Rice and M . A . Johnson: Inelastic Behavior of Solids, M.F. Kanninen, W . E Adler, A.R. Rosenfield, and R.I. Jaffee, eds., McGraw-Hill, New York, NY, 1970, pp. 641-72. 40. D. McLean: The Mechanics and Physics of Fracture, Proceedings of the Joint Meeting of the Metals Society and Institute of Physics at Cambridge, The Metals Society, London, U . K , 1975, pp. 179-91. 41. H. Fischmeister and B. Karlsson: Z. Metallkde., 1977, vol. 68, pp. 311-27. 42. A. Joshi and D. E Stein: Metall. Trans., 1970, vol. 1, pp. 2543-46. 43. L . L . Bourguignon and R. M. German: Inter. J. Powder Met., 1988, vol. 23, in press.
METALLURGICAL TRANSACTIONS A
