Materials Science and Engineering, A 158 ( 1992 ) 195-202
195
Microstructural development in A1-SiC composites made by resistance sintering of mechanically alloyed powders S. J. Hong, P. W. Kao and C. P. Chang Institute of Materials Science and Engineering, National Sun Yat-Sen University, Kaohsiung (Taiwan) (Received April 13, 1992)
Abstract SiC particles were found to be distributed homogeneously in the aluminum matrix by the mechanical alloying (MA) process. It was observed that the aluminum matrix of the MA powders consists mainly of fine subgrains with a wide range of misorientations. In addition, a band structure consisting of lamellae of elongated subgrains was observed. The substructure of the aluminum matrix of MA powders indicates that the average temperature in the MA process is quite low, i.e. near room temperature. It was found that the fine substructure of MA powders can be maintained after resistance sintering. The high strength of the resistance-sintered A1-SiC composites may be attributed to the fine subgrain structure in the alumirlum matrix and the high dislocation densities which exist owing to the presence of a worked structure arising from the MA process, and are generated by the thermal mismatch between aluminum and SiC particulates.
I. Introduction
Discontinuously reinforced metal-matrix composites are now recognized as important structural materials. The reinforcement of lightweight alloys with whiskers, platelets, or particles of ceramics such as silicon carbide or alumina results in composites of high specific strength and stiffness, suitable for advanced engineering applications such as in the aerospace and automotive industries. In particular, silicon carbide reinforced aluminum matrix composites are especially attractive because they have good specific properties ]1] and can be shaped and machined utilizing conventional metal working processes [2]. The AI-SiC composites have been produced either by powder metallurgy (PM) or molten metal techniques. Generally speaking, the foundry route has the advantage in fabrication cost, but the PM route gives better mechanical properties. In the molten metal routes, such as stir casting, problems of particle aggregation and segregation limit the size and volume fraction of reinforcement which can be incorporated [3], and the reaction of SiC with molten aluminum to form detrimental A14C3 at the interface must also be taken into account [4]. The PM route offers the most flexibility in terms of alloy chemistry, and reinforcement type, size, and volume fraction. However, some difficulties are also encountered in PM processing for fabricating A1-SiC composites. One of the limitations is that owing to the surface oxide film of aluminum powder, 0921-5093/92/$5.00
the simering of AI-SiC composites is extremely difficult even at high temperature and high pressure. In addition, the conventional mechanical mixing used in the PM route is not suitable for dispersing the fine particles in an aluminum matrix uniformly because of the large size difference between the reinforcing SiC particles and the aluminum powders. In order to overcome these problems, a technique combining mechanical alloying (MA) and resistance sintering has been utilized to fabricate AI-SiC composites successfully [5, 6]. Mechanical alloying (MA) developed by Benjamin [7, 8] is normally carried out in high-energy ball mills such as the Szegvari type attritor. The mechanical alloying process involves repeated welding and fracturing of a mixture of powder particles to produce an extremely fine microstructure [7-10]. To date, this process has been exploited mainly for dispersing a second phase within a matrix, such as in oxide-dispersion-strengthened alloys. In addition to producing homogeneous composite powders, the MA process also produces electroconductive powders which can be processed subsequently by resistance sintering. In order to maintain a fine microstructure, a short processing time is desirable for the consolidation of advanced materials powders made by processes such as rapid solidification, mechanical alloying, etc. Furthermore, a short processing time and/or low temperature also show beneficial effects in the fabrication of A1-SiC composites by minimizing the interfacial reaction. For this reason, a resistance-sintering process is © 1992--Elsevier Sequoia. All rights reserved
S.J. Hong et al. / Microstructure orAl-SiC composites
196
used to consolidate the mechanically alloyed A1-SiC powders [5, 6]. In the resistance-sintering process, a low voltage and high amperage current is applied through the powder compact which is contained in an insulated cavity of a stainless steel die set, and compressed simultaneously. Since the powder compact is heated directly by the applied current, a high heating rate and consequently a very short sintering time, within 1 s, can be achieved. Since the sintering process is so fast, no controlled atmosphere or vacuum is needed. Because aluminum powders in an ambient environment will have an oxide film on the periphery of each particle, it is difficult to sinter aluminum powders by the conventional PM technique. In resistance sintering, however, this film can be advantageously utilized to obtain localized rapid heating [5]. The previous studies [5, 6] have shown that high strength A1-SiC composites reinforced with a wide range of size and volume fraction of SiC particles can be made by resistance sintering of mechanically alloyed powders. In the present work, detailed microstructural observations were performed on both as-MA powders and resistance-sintered specimens in order to gain better understanding of the composites made by this novel process.
2. Experimentalprocedures 2.1. Materials The aluminum powder used in this work is a commercial atomized powder of 98.5% purity which has irregular shape with particle size less than 160/~m. The oxide content (A1203) is about 0.5%-1%. The aluminum powders were supplied by the Eckart-Werke company in Germany. Four different SiC particulates of mean particle sizes ranging from 0.66 to 85 ktm, which correspond to the 50% value on the cumulative weight distributioa, were used. Among these, the SiC powders with mcaa particle size of 0.66/am are fl type, while the others g ¢ a type. The particle size distributions are listed in Table 1. 2.2. Mechanical alloying The equipment used in this study is a water-cooled attritor containing a rotating impeller. The SiC contents, which varied from 10 to 30 vol.%, were mixed
TABLE 1. Size distribution of SiC particles used in this work
Averagesize (~m) Coarsest size (/~m)
A
B
C
D
0.66 =2
3 7
15 26
85 125
with aluminum powder and then introduced into an attritor, a high energy grinding mill in which the steel ball and powder charges were held in a stationary vertical, water cooled tank and agitated by impellers radiating from a rotating central shaft to produce mechanically alloyed powders. For each batch, 10 g of powder mixture and five stainless steel balls (10 mm diameter) were charged into the attritor, which was operated at 3440 rev min- ~ for 40 min in a sealed air atmosphere.
2.3. Resistance sintering The machine for resistance sintering was modified from a conventional spot welder. The mechanically alloyed AI-SiC composite powders were cold compacted in a steel die set using a pressure of 375 MPa. The green compact was then resistance sintered in a stainless steel die set lined with alumina tube to insulate the preform from the steel die wall. The assembled die set was placed on the lower electrode platen of a resistance welder. The capacity of the welder is 65 kVA (a.c. 60 Hz), and the maximum force of its air cylinder is 9.3 x 10 3 N. In this study, the sintering current was kept constant at 4 kA and the sintering pressure was held at 200 MPa. The effect of sintering time has been evaluated in previous studies [5, 6]. Since the electric current was held constant at 4 kA and the voltage across the specimen was found to be nearly constant throughout the sintering process, the energy input could be related to the sintering time. Owing to such a fast sintering process, the specific energy input can be estimated as a first approximation from the applied current, voltage, sintering time, and specimen weight by neglecting the heat dissipation through the die set. It was reported [6] that irrespective of the SiC content in the specimen, the maximum sintered density under the given sintering conditions (4 kA and 200 MPa) may be obtained with the specific energy input of about 2 kJ g- ~. Therefore, a specific energy input of approximately 2 kJ g-1 was used in this work. For constant sintering current, the voltage across the specimen was found to increase with increasing SiC content [6]. For composites containing 30, 20 and 10 vol.% SiC, this energy input corresponds to 13, 20 and 30 a.c. cycles ( 13/60, 1/3 and 1/2 s) of sintering time, respectively. 2.4. Metallography The specimens were mechanically polished and then etched with Keller's solution, or with a solution containing 50 ml Poulton's reagent+25 ml HNO3 (cone.) + 12 g chromic acid + 40 ml H20. For metallographic observation, the specimens were examined using an optical microscope and a scanning electron microscope (Jeol JSM-35CX). Owing to the presence of the SiC particles in the aluminum matrix, ion milling
S. J. Hong et al.
/
Microstructure of AI-SiC composites
was used for the preparation of transmission electron microscopy (TEM) specimens. Dupuoy [11] conducted an in situ ion thinning experiment on iron and AI-Ag specimens in a 3 MV microscope. Dislocation arrangements and microstructures in A1-Ag and iron were not altered by ion thinning even though some point defects are introduced into the near surface regions of the sample by ion bombardment. Recently, the ion milling technique has been successfully used in the study of AI-SiC composites [12-16]. Therefore, ion milling was considered quite suitable for the purpose of this study. For TEM observation, the mechanically alloyed AI-SiC powders were cold compacted in a steel die set and then carefully cut into slices 0.6 mm thick. Similarly, slices measuring 0.6 mm in thickness were cut from the resistance-sintered specimens. Subsequently, the slices were mechanically thinned to about 100/~m thick. Final thinning was carded out using argon ion beam bombardment, operated at 6 kV and 50/zA with a sample inclination angle of 10 ° to the ion beam. The thinned samples were then examined in the transmission electron microscope (Jeo1200CX).
197
Fig. 1. Typicallayered structure in MA powders ( 10 vol.%, 3 pm SIC).
2.5. Mechanical test
The resistance-sintered specimens of cylindrical shape (6 mm in diameter and 7.5 mm long) were compression tested at ambient temperature in an Instron 1125 universal testing machine with 2 m m m i n -1 cross-head speed.
3. Results and discussion
Fig. 2. Distribution of SiC particles in the MA powders (30 vol.%, 3 gm SIC).
3.1. Mechanical alloying
In general, the M A powders were found to vary in shape and included rounded, irregular and nearly equiaxed morphologies. In addition, agglomeration of powders into aggregates was frequently observed. In most cases, the soft constituents (aluminum powders) tend to be welded (mechanically) to the harder constituents (SiC particulates) to form composite particles in the M A process. The composite particles that were repeatedly welded and fractured in the MA process have characteristic layered structures as shown in Fig. 1. In the MA process the SiC particles are incorporated into the aluminum matrix by the high energy attritor and are homogeneously distributed throughout the aluminum matrix as shown in Fig. 2. However, owing to the strong impact imposed in the M A process, it was found that the SiC particles of larger size were broken into smaller fragments. Some examples of fracture of SiC particles which resulted from the MA process are shown in Fig. 3. By using microscopic counting of the SiC diameters, a frequency distribution
Fig. 3. Fracture of SiC particles resultingfrom the MA process. of SiC particle size was generated. To compare with the original particle size data, the number distribution was converted into weight distribution by assuming that the particles are spherical. According to this metallo-
198
S.J. Hong et al. / Microstructure of Al-SiC composites
graphic analysis, SiC particulates with an original mean size of 85/~m were reduced to about 35/~m after the MA process, but particulates with original mean size less than 15 p m showed little or no change after the MA process. The SiC content of the composite powders after MA was examined using wet chemical analysis. MA powders for each composition were put into a solution of one part HNO 3 (conc.) and three parts HCI (conc.). Following the complete solution of aluminum, SiC particles were collected using filter paper and were then dried in a vacuum oven. After drying, the weight of SiC particles was determined. Initially, the validity of this technique was checked by using known mixtures of aluminum and SiC powders which were not mechanically alloyed. The results indicate that this method is quite reliable and the accuracy of the analysis is better than 0.6 vol.%. Consequently, the SiC contents of the composite powders for each composition after MA were examined and the results are given in Table 2. It is shown that, in general, there is little or no change in the SiC content after the M A process. In order to study further the microstructure in mechanically alloyed A1-SiC powders, TEM was used. Several common features were found to exist in MA powders. The majority of the aluminum matrix consisted of fine subgrains with a wide range of misorientations between neighboring subgrains, which was indicated by the ring pattern obtained by selected area diffraction. Typical substructures of as-MA powders are shown in Fig. 4. Humphreys [17] has shown that very large lattice rotations may occur at second-phase particles and this will require high dislocation densities. The probability that subgrain wall formation will develop is thus enhanced at these sites. The subgrain size was found to vary from place to place within the aluminum matrix. In general, the subgrains near SiC particles (Fig. 4(a)) are smaller than those in areas free of SiC particles (Fig. 4(b)). According to quantitative metallographic analysis, the mean diameter of subgrains was about 0.3-0.6/~m regardless of the SiC content or particle size in the MA powders. In addition to the typical microstructure mentioned above, which consists of equiaxed subgrains, a band
structure consisting of lamellae of elongated subgrains was found in the MA powders (Fig. 4(c)). The walls of these elongated subgrains are nearly parallel to a specific direction. Subgrain banding is a result of inhomogeneous deformation (inhomogeneous stress states). Dillamore et al. [18] suggested that local differences in the stress state produce varying strains within a crystal, causing a relative rotation between segments of the grain, and a banded structure is formed in the grain.
::
l~m
TABLE 2. The SiC content in MA powders Nominal composition (vol.%)
SiC content (vol.%) 0.66 am SiC
3 am SiC
35/~mSiC
5 10 20 30
4.9 10.8 21.3 29.6
11.6 18.9 30.9
10.3 20.9 32.3
Fig. 4. Typical TEM images showing the microstructure of asMA powders: (a) 10 vol.%, 35 pm SiC; (b) 10 vol.%, 3 #m SiC; (e) 10 vol.% , 35/~m SiC.
S. J. Hong et al.
/
Microstructure of Al-SiC composites
199
Since only five steel balls were used in the attritor, the powder particle aggregates are most probably trapped between a steel ball and the water cooled tank wail. The cold tank wall may provide a good heat sink to remove the heat generated in the impacted powders by plastic deformation. Therefore, the average temperature of the powders during MA is believed to be very close to room temperature. Since the collisions between steel balls or between ball and tank wall may take place over a range of impact angles, different deformation modes may be imposed on the trapped powders. Owing to the high velocity of the steel balls, the strain rate imposed on the trapped powders is quite high, and was estimated to be about 103-104 s-1 using the model proposed by Maurice and Courtney [19]. The small subgrains in M A powders could result from the dynamic recovery process occurring during the plastic deformation which is generated in the mechanical alloying process. Most of the subgrains containing a large number of dislocations (Fig. 4) indicate incomplete recovery, which also implies that the average temperature in M A could not be much higher than room temperature. However, subgrains almost free of dislocation, which sometimes contain dislocation arrays, were also observed as shown in Fig. 5. This indicates that as a result of the high strain-rate deformation in MA, the local temperature in certain areas of the powders might be high enough to cause dynamic polygonization. During the MA process, the oxide layer inherently present on the aluminum powder surface is fractured upon impact. Oxides are dispersed into the materials, and new oxides are regenerated on the fresh surface during the process. In this work, since only a limited amount of air existed in the attritor tank, the oxide content in the M A powders should be very close to that in the original aluminum powder. From selected area
diffraction, only very weak indications of the A1203 phase were found, which could not be positively identified as ct-Al203 or 6-A1203.
Fig. 5. TEM image showing subgrains nearly free of dislocation (10 vol.%, 3/am SIC).
Fig. 6. Localized liquid phase formation in resistance-sintered specimen (30 vol.%, 0.66/~m).
3.2. Resistance sintering
Owing to the presence of surface oxide film on the prior particle boundary, a relatively higher resistance is expected in the contact area between adjacent particles than in the bulk of the particle. During the resistancesintering process, the temperature in the contact area between adjacent particles will rise much more rapidly than in the particle interior. Consequently, a localized liquid phase will be rapidly formed in this region [5]. Figure 6 shows an optical micrograph of a resistancesintered specimen containing 30 vol.% SiC, in which the light domains correspond to the local melt regions. Upon cooling, SiC particles in the melt regions were expelled by the solidification front of the aluminum melt and SiC-poor regions were then formed. After chemical etching, the SiC-poor regions were revealed as light domains under the optical microscope. In general, a localized liquid phase was observed in all the composites studied, which were resistance sintered with a specific energy input of approximately 2 kJ g- ~. The microstructure of sintered specimens was also examined by TEM. In general, the aluminum matrix in the composites consists of fine subgrains with dispersions of fine particles, which might be A1203 particles and/or SiC debris formed in the M A process. A1203 particles were introduced into the composites primarily as a result of fracture of the oxide skin surrounding the individual powder particles. The large deformation involved in the MA process, the dispersion of fine particles, and the very short sintering time, all contribute to the formation of a fine subgrain structure in these composites. In addition, by noting the large difference in T E M image contrast between neigh-
200
S.J. Hong et al.
/
Microstructure of Al-SiC composites
boring subgrains, the variation of misorientation between neighboring subgrains was found to be quite large. Figure 7 shows the typical microstructure of sintered composites. It was also observed that the interface between aluminum and SiC is quite good, as shown in Fig. 7(a). In addition, no interracial phase was found at the interface between aluminum and SiC. This observation is not surprising considering the very short sintering time. In view of the inherent variation in subgrain size from place to place within the matrix, tens of micrographs of a given foil and 3-5 different foils were examined for each condition. Table 3 presents the average subgrain size of sintered composites. The subgrain size of resistance-sintered composites generally decreases with increasing SiC volume fraction and decreasing SiC particle size. There are a large number of dislocations within the subgrains, which may represent the remaining dislocations from the MA process as well as the thermally generated dislocations. The large difference between the coefficients of thermal expansion (CTEs) of aluminum (23.5x10 -6 K -1) and SiC (4.5x10 -6 K -1)
t
0.51.tm
results in sufficient stress to generate dislocations at the AI-SiC interface when the composite is cooled from elevated temperatures of annealing or processing [15, 16]. In an in situ investigation [15], the dislocation generation process during cooling from annealing temperature was observed using a high voltage electron microscope equipped with a double tilt heating stage. In general, the dislocation densities in the aluminum matrix are different from place to place, but the dislocation density does not apparently decrease as one moves from the AI-SiC interface into the aluminum matrix. According to the Taya and Moil model [20], the punching of dislocations generated by the CTE mismatch strain in a particulate metal matrix composite is sufficiently extensive to cover most of the matrix domain. Therefore, it is conceivable that the overlap of dislocations generated by the CTE mismatch strain lowered the variation in dislocation densities from the AI-SiC interface to the aluminum matrix. Dislocation cells within large grains (greater than 10/~m) were also found occasionally in the sintered specimens as shown in Fig. 8. The dislocation cell structure, which was not observed in the MA powders, must be formed during the resistance-sintering process. It is suggested that the cell structure was formed in the melt regions. In those regions, large grains form after the melting and solidification cycle, and then a high density of thermally generated dislocations occurs upon cooling. Subsequently, a cell structure is developed from the high dislocation densities. For regions with fine subgrain structure, the higher flow stress will impose higher resistance to the dislocation generation by thermal mismatch between aluminum and SiC, and hence the cell structure is less likely to form. However, areas with banded structure consisting of parallel rows of elongated subgrains were also observed, as shown in Fig. 9. The band structure, a result of large plastic deformation at low temperature, must have originated from the MA process. The fine subgrain structure which shows only slight coarsening when compared with the as-MA structure and the band structure indicate that apart from those local melting regions, the average bulk temperature is too low, or the time at elevated temperature is too short, to cause TABLE 3. The subgrain size of sintered composites with various composition Composition
Subgrain size (/zm)
(vol.%)
Fig. 7. TEM images showing the microstructure of resistancesintered composites: (a) 10 vol.%, 35/zm SiC; (b) 10 vol.%, 3/zm SiC.
10 20 30
0.66/~m SiC
3/~m SiC
35/~m SiC
0.7 ---
1.3 0.9 --
2.3 1.4 1.0
S. J. Hong et al.
/
201
Microstructure of Al-SiC composites
TABLE 4. Properties of resistance-sintered A1-SiC composites Composite AI-0vol.%SiC Al-10vol.%SiC, 0.66/~m Al-10vol.%SiC, 3/~m A1-10vol.%SiC, 35/~m A1-20vol.%SiC, 0.66/~m AI-20vol.%SiC, 3/tm AI-20vol.%SiC, 35/~m AI-30vol.%SiC, 0.66 ktm A1-30vol.%SiC, 3/~m A1-30vol.%SiC, 35 #m
try (MPa)
Ou
ef
(MPa)
(%)
118 309 191 183 420 293 218 524 423 400
153 448 390 381 545 457 414 655 553 507
> 25 13.7 21.8 20.0 8.5 15.0 15.5 5.0 6.2 6.6
p
0.98 0.97 0.97 0.98 0.96 0.97 0.97 0.94 0.96 0.96
truultimate compressive strength, p relative density.
(b) Fig. 8. TEM images showing examples of the dislocation cell structure in the sintered specimens: (a) 30 vol.%, 35 pm SiC; (b) 10 vol.%, 35 pm SiC.
monotonically increasing trend witfi increasing SiC content and decreasing particle size, while the failure strain shows the reverse trend. The data shown in Table 4 are the averages of at least three tests, and the standard deviations of the data are less than _+20 MPa for both yield stress and ultimate strength and + 2.6% for compressive failure strain. The density was measured based on Archimedes' principle, and the relative density was estimated using the values of 2.7 g cm-3 for aluminum and 3.21 g cm-3 for SiC. It has been proposed [12-14] that the increase in strength due to SiC addition to aluminum or aluminum alloys is the result of a change in the matrix strength, i.e. an increase in dislocation density and a reduction in subgrain size. Based on the microstructural observations, the high strength of the composites made by resistance-sintering of M A powders can be attributed to the fine subgrain structure, the high dislocation densities originating from the cold-work imposed by MA, and the dislocations generated by thermal mismatch between aluminum and SiC.
4. Conclusions
Fig. 9. TEM image showing an example of band structure in the resistance-sintered specimens. significant coarsening of the substructure in the resistance-sintering process. 3.3. Mechanical properties
The results of compressive properties of resistancesintered composites with various SiC contents are shown in Table 4. The compressive strength shows a
(1) The microscopic observations showed that the SiC particles were homogeneously distributed in the aluminum matrix by the M A process. The aluminum matrix of the M A powders consists mainly of fine subgrains with a wide range of misorientations. In addition, a band structure consisting of lamellae of elongated subgrains was observed. Most of the subgrains were found to contain a large number of dislocations. This indicates incomplete recovery, which also implies that the average temperature in the M A process should be quite close to room temperature. (2) The substructure of MA powders was essentially maintained after resistance-sintering, with only slight coarsening of the subgrains. This indicates that apart
202
S. J. Hong et al.
/
Microstructure orAl-SiC composites
from those local melting regions, the average bulk temperature is too low, or the time at elevated temperature is too short, to cause significant coarsening of the substructure in the resistance-sintering process. The subgrain size of resistance-sintered composites generally decreases with increasing SiC volume fraction and decreasing SiC particle size. (3) There are localized melt regions uniformly distributed in the resistance-sintered specimens. The observed dislocation cell structures within large grains are believed to be formed in these melt regions during cooling down after resistance-sintering. The interface between aluminum and SiC was found to be quite good, and no interracial phase was found. (4) The compressive strength shows a monotonically increasing trend with increasing SiC content and decreasing particle size, while the failure strain shows the reverse trend. The high strength of the composites made by resistance-sintering of MA powders may be attributed to the fine subgrain structure, the high dislocation densities originating from the cold-work imposed by MA, and the dislocations generated by thermal mismatch between aluminum and SiC.
Acknowledgment This research was kindly supported by the National Science Council of R.O.C. (NSC80-0405-E-110-08).
References 1 S. V0Nair, J. K. Tien and R. C. Bates, Int. Met. Rev., 30 (6) (1985) 275. 2 A. P. Divecha, S. G. Fishman and S. D. Karmarkar, J. Met., 33(9)(1981)12. 3 D. J. Lloyd, H. Lagace,A. McLeod and P. L. Morris, Mater. Sci. Eng., A107(1989) 73. 4 W. C. Moshier, J. S. Ahearn and D. C. Cooke, J. Mater. Sci., 22(1987) 1154. 5 S.J. Hong and P. W. Kao, Mater. Sci. Eng., A l l 9 (1989) 153. 6 S.J. Hong and P. W. Kao, Mater. Sci. Eng., A148 (1991 ) 189. 7 J.S. Benjaminand T. E. Volin,Metall. Trans., 5 (1974) 1929. 8 J. S. Benjamin,Sci. Am., 234 (5)(1976) 40. 9 P. S. Gilman and J. S. Benjamin, Ann. Rev. Mater. Sci., 13 (1983)279. 10 J. S. Benjamin and R. D. Schelleng, Metall. Trans. A, 12 (1981)1827. 11 G. Dupuoy, in P. R. Swann, C. J. Humphreys and M. J. Goringe (eds.), Proc. 3rd Int. Conf. on High Voltage Electron Microscopy, AcademicPress, London, 1974, p. 447. 12 R.J. Arsenault, L. Wangand C. R. Feng, Acta Metall. Mater., 39(1)(1991)47. 13 R.J. Arsenault, Mater. Sci. Eng., 64 (1984) 171. 14 R. J. Arsenault and R. M. Fisher, Scripta Metall., 17 (1983) 67. 15 M. Vogelsang, R. J. Arsenault'and R. M. Fisher, Metall. Trans. A, 17(1986) 379. 16 R.J. Arsenaultand N. Shi, Mater. Sci. Eng., 81 (1986) 175. 17 E J. Humphreys,Acta Metall., 25 (1977) 1323. 18 I. L. Dillamore, P. L. Morris, C. J. E. Smith and W. B. Hutchinson, Proc. R. Soc. London, Ser. A, 329 (1972) 405. 19 D. R. Maurice and T. H. Courtney, Metall. Trans. A, 21 (1990) 289. 20 M. Tayaand T. Moil, Acta Metall., 35 (1987) 155.