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Consolidation behavior of a particle reinforced metal matrix composite during HIPing
MaterialsRucucb Bullctia, Vol. 31, No. 10, p. 1277~1285.1996 Copyi@ 0 1996 Elsevicr Scicacc Ltd Printedin the USA. All ri8lm mcrval 0025-5408/M $15.00 +.OO
PI1 8002~5408(96)00111-O
CONSOLIDATION BEHAVIOR OF A PARTICLE REINFORCED METAL MATRIX COMPOSITE DURING HIPing
E. Pagounis’*, M. Talvitie’ and V.K. Lindroos’ ‘Laboratory of Physical Metallurgy and Materials Science, Helsinki University of Technology, 02 150 Espoo, Finland 2Rauma Materials Technology Oy, 33 101 Tamper-e, Finland (Referred) (Received March 26,1996; Accepted April 12,1996)
ABSTRACT Hot Isostatic Pressing (HIP) is a well known technique for the production of metal matrix composites. However, little attention has been given to the factors which influence the densification of these materials in actual processing conditions. In the present work the densification process was studied in an iron-based composite reinforced with fine TiC particles. The results revealed that the presence of a high amount of rigid-rigid contacts and the formation of ceramic particle networks within the composite powder mixture increase the pressure required for densification. The fine matrix particles were found to contribute more effectively to the densitication of the composite than the coarse particles do. KEYWORDS: A. composites, C. high pressure, D. microstructure INTRODUCTION Hot Isostatic Pressing is a materials processing technique in which high isostatic pressure is applied to consolidate a powder part or compact at elevated temperatures. This process usually results in a fully dense body, although partially dense bodies can also be intentionally produced. Undoubtedly, the main application area of HIP is in powder metallurgy (PM), although in other areas, such as diffusion bonding and densification of high performance castings, advantages over conventional techniques are offered, too. In the
*To whom correspondence should be addressed. 1277
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P/M processes the aim of the HIPing is to remove the pores originating during the packing of powder particles, and, hence, to produce a body with optimum density. Plastic flow, shear and creep processes, and diffusion may have the key roles on the densitication mechanism during HIPing. Although densification of monolithic materials has been studied extensively (l-3) in composites little work has been done on the deformation processing. This is quite surprising, considering that HIP is an attractive and widely used production route for composite materials (4). Experimental studies confirm that the presence of relatively undeformable particles greatly reduces the densification rate. Lange et al. (5) have reported that creep plays a minimal role in composite densification when hard inclusions were introduced in a much softer matrix. Accordingly, yielding and diffusion alloying are assumed to be the dominant mechanisms during the densification of composite mixtures. On the contrary, Suryanarayanan et al. (6) have demonstrated through metallographic observations that power law creep dominates densification in MoSiz-Nb and MoSiz-SiC composites. Finally, Kaysser et al. (7) have shown in a W-Ni composite hard material, that during the final stage of HIPing, densification by power low creep is small compared to pore shrinkage and the subsequent elimination of pores by vacancy transport along the grain boundaries. Similar phenomena have been described by Derby and Qin (8) for diffusion bonding. An important conclusion involved with the HIPing of composite materials is that densitication can be retarded by the presence of contacts between undeformable reinforcing particles which support a significant portion of the applied pressure. In addition, partitioning of deformation between soft matrix and hard inclusion powder will result in the increased deformation of the softer material. Hence, the need for the softer particle to absorb the deformation at hard-soft particle contacts has a dominant effect. The softer particles are not only more heavily deformed within the composite mixture than the hard particles, but they are even more heavily deformed in the composite than in the monolithic powder (9). Turner and Ashby (10) have studied the influence of the hard reinforcements (inclusions) on densification. Their results indicate that random mixing, high volume fraction, small relative size, and high aspect ratios of the reinforcing phase inhibit densification. The aim of the present work is to study the factors which affect densification of a composite powder mixture, consisting of commercially produced metal and ceramic powders, in actual processing conditions. This will help to understand the restricting influence of the reinforcements on densitication, in order to optimize the processing parameters.
EXPERIMENTAL
PROCEDURE
The starting matrix material used was high-Cr white iron in powder form (APM 2311, Powdermet Sweden AB). The composition of the white iron was (in wt%) 26Cr-2C-Fe (bal) and the particle size distribution (urn): 60% <75 and 40% 75-150. The reinforcement was dense sintered TIC (H.C. Starck) with particle size (pm) 5.6-22.5. Iron-based composites are interesting candidate materials for the chemical and process industry (11-13). The unreinforced alloy and the composites were produced according to a typical HIP procedure. Three compositions with 10, 20, and 30 ~01% of inclusions were prepared by mixing. The mixing of the metal and ceramic powders was done in a conventional Turbula mixer, first dry and then with 4 wt% ethanol to prevent segregation of the lower density ceramic particles. After mixing the powders were filled in capsules made of mild steel and dried for 18 hours. The capsules were sealed, evacuated, cleaned with sand blasting, and
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then inserted into the HIP equipment. The HIP parameters were the conventional ones for iron alloys, i.e., 1180 “C temperature and 100 MPa pressure for 3 hours. Immersion density measurements were done according to the Archimides principle method. In this technique the final density of the materials was determined by measuring the difference in a specimen weight in air and when suspended in distilled water at room temperature. The final relative density of the composites was then determined from the ratio of the measured density to the theoretical density of the composite as it is calculated from the rule of mixtures. The initial (packing) relative density was evaluated by calculating the actual volume of the powder mixture (M&F, + MTic/pTic)in capsules with a known volume. The density of the materials were taken as : pFe_dloy=7.7 g/Cm3 and p~~=493 g/id. RESULTS
Figure 1 shows typical microstructures of the composites containing 10, 20, and 30 ~01% TiC after HIPing. In the composite reinforced with 10 vol%, the TiC particles were relatively uniformly distributed and no prior particle boundaries (PPBs) were observed. In the composites containing higher amounts of reinforcements, the TiC particles surrounded
(a>
FIG. 1 Micrographs showing the composites containing various amounts of reinforcements after HIPing. (a) 10 ~01% Tic, (b) 20 ~01% Tic, (c) 30 ~01% Tic.
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ec 0.98 e t 0.97 > 'is 2 0.96 d 0.95
I
0
10
20
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0.67= .$ 0.66g 2 0.65'Z s 0.64; 'c; 0.63; o! 0.62 30
Volume percent TIC (%) FIG. 2
Initial and final relative density of the composite vs. TiC volume fraction. the coarser matrix particles and local agglomeration took place at the junctions between three or four matrix particles. Microstructural observations revealed that densification occurred mainly because of deformation of the smaller matrix particles, while the coarser remained almost unchanged. This was more visible for composites reinforced with 20 and 30 ~01% Tic, where the PPBs of the coarser matrix powders were almost unaltered. The initial and final relative density of the composite as a function of the reinforcement volume percent is presented in Figure 2. The increase in the initial relative density of the composite with the reinforcement content is consistent with theories (14,15) and experiments of particle packing in bimodal powder mixtures. The finer TiC particles were able to fill the areas associated with voids generated from the packing of the Fe-alloy powder (e.g., at the junctions between three or four matrix particles). The final relative density of the composite was decreasing with the increasing amount of added TiC particles, while the unreinforced alloy was fully densified after HIPing. The metallographic examination showed porosity in the composites in areas of local TiC clusters, as for example at the junctions between three or four coarse matrix particles (e.g., Fig. I (c)). The high concentration of TiC particles in these areas resulted in an increased number of rigid-rigid contacts and prevented the matrix from ‘squeezing in’ between the TiC particles to fully dens@ the composite. Porosity was also found at matrix PPBs, particularly in the composite reinforced with 30 ~01% fine TiC as shown in Figure 3. This figure also shows the porosity in local reinforcement clusters at the junctions between coarser matrix particles. It should be noticed here that the dark areas in Figures 1(c) and 3 were produced by spalling of nondensified TiC particles during polishing and, hence, they do not show the actual porosity, which is lower than that presented in the micrographs. DISCUSSION The main conclusion about the consolidation behavior of the composite materials during HIPing was that the presence of the reinforcements hindered densification. This feature was more distinct in the composites reinforced with higher amounts of TiC particles. Microstructural observations of the consolidated composites revealed that two phenomena
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FIG. 3 Porosity at prior particle boundaries (PPBs). restricted densification: (a) the presence of contacts between the rigid TiC particles, and (b) the continuous particle networks which spanned, mainly, the composites containing 20 and 30 ~01% Tic. Although the information concerning the densification mechanism in HIPed composite materials is very limited, some data concerning densification of modeled composite systems (5,9,10) have demonstrated that the presence of contacts between hard, undeformable inclusions hinder densitication, resulting in an increased porosity at the contact areas. This happens, fust, because no deformation occurs at the contact points (ceramic materials are undeformable) and, second, because in those areas the matrix particles need an additional deformation in order to fill the empty space. Accordingly, the relative number of each contact type nij, where the subscripts i and j refer to the type of particles forming each contact, has a key role during densification of composite powders. According to the gapless packing model (16) modified for a bimodal powder system these numbers are n n II =I n, +n*R ( 1
I
2n,nlR “12= (n,+nlR)2
‘22 = ,:;*R t
’
(‘)
1
where the subscript 1 refers to a matrix particle and 2 to a ceramic particle, ni is the number fraction of particle i, and R = rz/rl is the particle’s radius ratio. At the l-l contacts the densitication mechanisms follow those of the monolithic powder (l-3). Densification at the 1-2 contacts depends mainly on the plastic behavior of the matrix at the particular pressure and temperature condition and, to a first approximation the contact force-displacement (particle center-to-center displacement) relationship for a plastic-rigid contact (l-2) is the same as for a plastic-plastic (l- 1) contact. No deformation occurs at the 2-2 contacts and, therefore, the number nu should be as low as possible. Touching ceramic particles are associated with void formation, particularly at their three- or four-particle junctions. In addition, the 2-2 contacts support a portion of the applied pressure and, thus, partially shield the surrounding matrix from the full applied stress. This makes it necessary
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to apply a higher pressure in order to dens@ a composite powder mixture containing a high amount of rigid-rigid contacts. The results presented in Figure 2 showed that the final relative density of the composite decreased with the increasing reinforcement volume percent. This indicates that the deformed matrix particles could not completely fill the void space between hard, touching ceramic particles. The relative density pmof the matrix phase in the composite as a function of the composite relative density pc is given by
(I-fp 1
P,,*= c
(2)
‘-fP‘
where f is the reinforcement volume fraction. This equation allows prediction of the relative density of the matrix in the composite at any stage during the densification process. The initial (packing) and final relative density of the iron alloy matrix in the composite reinforced with various amounts of TiC particles were calculated and the results are presented in Table 1. As it can be seen, the initial relative density pm,of the matrix decreases with the increasing TIC ~01%. Accordingly, an additional deformation of the matrix would be required in order to completely fill the voids associated with touching TIC particles. The magnitude of the additional deformation is directly related to the difference in the initial relative density of the matrix powder with and without reinforcements. This difference has been referred to (5) as the ‘excluded volume’ and is associated with the packing of different sized particles. Therefore, the excluded volume contributes to increasing the pressure required to achieve a prescribed matrix density. Table 1 shows that the differences between the final relative density of the matrix in the composites and of the matrix alone (0 ~01% TIC) are smaller than between the initial relative densities. This means that the iron alloy matrix deformed quite well during the HIPing process and only some clusters of reinforcements restricted a complete matrix densification. However, a greater deformation would be required in order to fill all the ‘channels’ and interstices between touching TIC particles, and the applied pressure was not enough to achieve it, particularly for the composite containing 30 ~01% Tic. In the composites reinforced with higher amounts (>lO ~01%) of TIC particles, densification was also hindered by the presence of continuous networks of reinforcing particles. Lange (17) has reported that if the ratio pdp, is expressed by a linear function of the reinforcement volume fraction ‘f, then the ceramic reinforcements do not significantly affect the consolidation of the matrix powder. If, however, the expression is not linear, the ceramic reinforcements can be considered to hinder the consolidation of the matrix powder by TABLE I Relative Density of the Composites (c) and of the Composites’ Matrix (m)*
0
*
10 20 30
0.643 0.65 1 0.658 0.662 ~_____.___
0.643 0.627 0.606 0.578
I 0.992 0.987 0.965
I 0.991 0.983 0.950
Subscript i refers to the initial (packing) and subscript i‘to the final relative density.
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forming continuous or discontinuous touching networks. The site occupancy percolation theory reveals that at least one continuous network will form at f = 16% (18), whereas Lange et al. (5) have found that >95% of the inclusions will be part of the continuous network when f > 20%. In the case of the materials examined in the present study, there were not enough values to express the ratio pdp, as a function of ‘f, but microstructural observations confirmed the presence of continuous TiC networks inside the composites containing 20 and 30 ~01% Tic. These networks support a substantial portion of the applied pressure, particularly at the higher reinforcement volume fractions. The deformable phase is then subjected to only a portion of the applied pressure and, therefore, the reinforcement networks further increase the pressure required to obtain a given density. The insufficient pressure used during consolidation of the 30 ~01% TiC composite resulted in the porosity observed at prior matrix particle boundaries (Fig. 3). The above observations indicate that the pressure used to consolidate the composites was not enough to obtain fully densified bodies, because the deformation of the composites’ matrix was not sufficient to completely fill the channels and interstices between touching ceramic particles. It could be argued that additional deformation requires a greater applied stress per unit volume of matrix material in order to minimize the constraining influence of the undeformable ceramic particles. The virtual work equation for a powder compact containing plastic and rigid particles, subjected to an externally applied pressure P, predicts
PdV =
f,NeF,j~S, Nti = 6DNIMnij ij4
where P is the externally applied pressure, dV is the volume change because of densification, Fij are the normal contact forces on the ij contacts, drip are the incremental contact displacements between particle centers, Nij are the numbers of ij contacts, D is the density of the composite (expressed as % of theoretical), and N, is the total number of particles in the powder. In this expression, shear displacements where plastic particles slide over rigid particles have been neglected because their contribution in densification seems to be small. The evaluation of the pressure needed to attain a given density D of a composite powder can then be made, following the approach suggested by Turner and Ashby (10): P=18YDYD(:(Di:-D?)(s)
(4)
+n2,R, v=n,+n2R3,
AR=n 1,+n 22ARII’
AR2
+
(for rl 2 r2).
where Y is the yield strength of the monolithic powder, AW is a relative (to the monolithic powder) work term, Ro is a relative particle radius term, v is a relative volume term, AR and ARlz are relative contact displacement terms, D is the instantaneous density, Do is the packing density, and oil and o12 are the applied stress at the contact points. The second parenthesis in equation (4) represents the additional pressure needed to achieve a given density D for a composite powder relative to the pressure needed to achieve the same density in a monolithic powder with the same packing density Do. Consequently, it is
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FIG. 4 Clusters of TIC particles within agglomerated fine matrix particles. therefore obvious that the applied pressure required to deform the matrix in the composite system is generally larger than that corresponding to the matrix powder without the ceramic reinforcements. Microstructural observations revealed that during consolidation, the fine matrix particles were deformed more heavily than the coarse particles and, therefore, they contributed more effectively on the densification of the composite. Similar observations have been reported also in monolithic Ni-based superalloys (7). Theoretical and experimental observations of Nair and Tien (19) and of Li and Funkenbusch (20) in bimodal monolithic powder mixtures have shown that smaller particles deform considerably more than large particles do because of their different geometric compatibility during powder consolidation in HIP. The higher deformability of the fine matrix particles also in the composite mixtures of the present study indicates their positive influence during consolidation. This aspect works, however, only if the fine matrix particles are uniformly distributed within the coarse particles; agglomeration of fine matrix particles may result in clusters of reinforcing particles within the agglomerates, as shown in Figure 4. CONCLUSIONS Based on the present study the following conclusions can be drawn: .
The presence of contacts between the hard, undeformable ceramic particles restricts complete densification of the composite. In the composites containing a higher amount of reinforcements, continuous and discontinuous TIC networks hinder further densification. The above factors increase the required applied pressure for consolidating the composites.
l
As in the case of monolithic bimodal sized powders, in composite mixtures the smaller matrix particles contribute more effectively to the densification process.
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ACKNOWLEDGMENTS
The authors are grateful to The Technology Development Centre of Finland (TEKES) for financial support. REFERENCES 1. E. Arzt, M.F. Ashby and K.E. Easterling, Metall. Trans. 14A, 211 (1983). 2. A.S. Helle, K.E. Easterling and M.F. Ashby, Acta Metall. 33,2163 (1985). 3. W. Kaysser, in Hot Isostatic Pressing: Theory and Applications, ed. R.J. Schaefer and M. Linzer, p. 1, ASM International, Ohio (1990). 4. R. R. Mehrabian, Mater. Res. Sym. Proc. 120,3 (1988). 5. F.F. Lange, L. Ateraas, F. Zok and J.R. Porter, Acta Metall. Mater. 39, 209 (1991). 6. R. Suryanarayanan, S.M.L. Sastry and K.L. Jerina, Acta Metall. Mater. 42,374l (1994). 7. W. Kaysser, M. Aslan, E. Arzt, M. Mitkov and G. Petzow, Powd. Metall. 31,63 (1988). 8. B. Derby and C.-D. Qin, Acta Metall. Mater. 40 Suppl., S53 (1992). 9. E.K.H. Li and P.D. Funkenbusch, Metall. Trans. 24A, 1345 (1993). 10. C.D. Turner and M.F. Ashby, in Hot Isostatic Pressing ‘93, ed. L. Delaey and H. Tas, p. 3, Elsevier, Antwerp (1994). 11. M.J. Talvitie and V.K. Lindroos, Proc. of Powder Metallurgy ‘94, World Congr., p. 1465, Paris (1994). 12. E. Haimi, M. Talvitie, E.O. Ristolainen, J. Kivilahti and V.K. Lindroos, Scripta Metall. Mater. 30, 1333 (1994). 13. E. Pagounis, E. Haimi, J. Pietikainen, M. Talvitie, S. Vahvaselka and V.K. Lindroos, Scripta Materialia 34, 407 ( 1996). 14. N. Epstein and M.J. Young, Nature 196,885 (1962). 15. S. Yerazunis, S.W. Cornell and B. Wintner, Nature 207, 835 (1965). 16. J.A. Dodds, J. Colloid and Interface Science 77, 3 17 (1980). 17. F.F. Lange, J. Mater. Res. 2,59 (1987). 18. R. Zallen, Physics of Amorphous Solidr, Chap.4, Wiley, New York (1983). 19. S.V. Nair and J.K. Tien, Metall. Trans. 18A, 97 (1987). 20. E.K.H. Li, P.D. Funkenbusch, Acta Metall. 37, 1645 (1989).
PI1 8002~5408(96)00111-O
CONSOLIDATION BEHAVIOR OF A PARTICLE REINFORCED METAL MATRIX COMPOSITE DURING HIPing
E. Pagounis’*, M. Talvitie’ and V.K. Lindroos’ ‘Laboratory of Physical Metallurgy and Materials Science, Helsinki University of Technology, 02 150 Espoo, Finland 2Rauma Materials Technology Oy, 33 101 Tamper-e, Finland (Referred) (Received March 26,1996; Accepted April 12,1996)
ABSTRACT Hot Isostatic Pressing (HIP) is a well known technique for the production of metal matrix composites. However, little attention has been given to the factors which influence the densification of these materials in actual processing conditions. In the present work the densification process was studied in an iron-based composite reinforced with fine TiC particles. The results revealed that the presence of a high amount of rigid-rigid contacts and the formation of ceramic particle networks within the composite powder mixture increase the pressure required for densification. The fine matrix particles were found to contribute more effectively to the densitication of the composite than the coarse particles do. KEYWORDS: A. composites, C. high pressure, D. microstructure INTRODUCTION Hot Isostatic Pressing is a materials processing technique in which high isostatic pressure is applied to consolidate a powder part or compact at elevated temperatures. This process usually results in a fully dense body, although partially dense bodies can also be intentionally produced. Undoubtedly, the main application area of HIP is in powder metallurgy (PM), although in other areas, such as diffusion bonding and densification of high performance castings, advantages over conventional techniques are offered, too. In the
*To whom correspondence should be addressed. 1277
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P/M processes the aim of the HIPing is to remove the pores originating during the packing of powder particles, and, hence, to produce a body with optimum density. Plastic flow, shear and creep processes, and diffusion may have the key roles on the densitication mechanism during HIPing. Although densification of monolithic materials has been studied extensively (l-3) in composites little work has been done on the deformation processing. This is quite surprising, considering that HIP is an attractive and widely used production route for composite materials (4). Experimental studies confirm that the presence of relatively undeformable particles greatly reduces the densification rate. Lange et al. (5) have reported that creep plays a minimal role in composite densification when hard inclusions were introduced in a much softer matrix. Accordingly, yielding and diffusion alloying are assumed to be the dominant mechanisms during the densification of composite mixtures. On the contrary, Suryanarayanan et al. (6) have demonstrated through metallographic observations that power law creep dominates densification in MoSiz-Nb and MoSiz-SiC composites. Finally, Kaysser et al. (7) have shown in a W-Ni composite hard material, that during the final stage of HIPing, densification by power low creep is small compared to pore shrinkage and the subsequent elimination of pores by vacancy transport along the grain boundaries. Similar phenomena have been described by Derby and Qin (8) for diffusion bonding. An important conclusion involved with the HIPing of composite materials is that densitication can be retarded by the presence of contacts between undeformable reinforcing particles which support a significant portion of the applied pressure. In addition, partitioning of deformation between soft matrix and hard inclusion powder will result in the increased deformation of the softer material. Hence, the need for the softer particle to absorb the deformation at hard-soft particle contacts has a dominant effect. The softer particles are not only more heavily deformed within the composite mixture than the hard particles, but they are even more heavily deformed in the composite than in the monolithic powder (9). Turner and Ashby (10) have studied the influence of the hard reinforcements (inclusions) on densification. Their results indicate that random mixing, high volume fraction, small relative size, and high aspect ratios of the reinforcing phase inhibit densification. The aim of the present work is to study the factors which affect densification of a composite powder mixture, consisting of commercially produced metal and ceramic powders, in actual processing conditions. This will help to understand the restricting influence of the reinforcements on densitication, in order to optimize the processing parameters.
EXPERIMENTAL
PROCEDURE
The starting matrix material used was high-Cr white iron in powder form (APM 2311, Powdermet Sweden AB). The composition of the white iron was (in wt%) 26Cr-2C-Fe (bal) and the particle size distribution (urn): 60% <75 and 40% 75-150. The reinforcement was dense sintered TIC (H.C. Starck) with particle size (pm) 5.6-22.5. Iron-based composites are interesting candidate materials for the chemical and process industry (11-13). The unreinforced alloy and the composites were produced according to a typical HIP procedure. Three compositions with 10, 20, and 30 ~01% of inclusions were prepared by mixing. The mixing of the metal and ceramic powders was done in a conventional Turbula mixer, first dry and then with 4 wt% ethanol to prevent segregation of the lower density ceramic particles. After mixing the powders were filled in capsules made of mild steel and dried for 18 hours. The capsules were sealed, evacuated, cleaned with sand blasting, and
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then inserted into the HIP equipment. The HIP parameters were the conventional ones for iron alloys, i.e., 1180 “C temperature and 100 MPa pressure for 3 hours. Immersion density measurements were done according to the Archimides principle method. In this technique the final density of the materials was determined by measuring the difference in a specimen weight in air and when suspended in distilled water at room temperature. The final relative density of the composites was then determined from the ratio of the measured density to the theoretical density of the composite as it is calculated from the rule of mixtures. The initial (packing) relative density was evaluated by calculating the actual volume of the powder mixture (M&F, + MTic/pTic)in capsules with a known volume. The density of the materials were taken as : pFe_dloy=7.7 g/Cm3 and p~~=493 g/id. RESULTS
Figure 1 shows typical microstructures of the composites containing 10, 20, and 30 ~01% TiC after HIPing. In the composite reinforced with 10 vol%, the TiC particles were relatively uniformly distributed and no prior particle boundaries (PPBs) were observed. In the composites containing higher amounts of reinforcements, the TiC particles surrounded
(a>
FIG. 1 Micrographs showing the composites containing various amounts of reinforcements after HIPing. (a) 10 ~01% Tic, (b) 20 ~01% Tic, (c) 30 ~01% Tic.
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ec 0.98 e t 0.97 > 'is 2 0.96 d 0.95
I
0
10
20
Vol. 31, No. 10
0.67= .$ 0.66g 2 0.65'Z s 0.64; 'c; 0.63; o! 0.62 30
Volume percent TIC (%) FIG. 2
Initial and final relative density of the composite vs. TiC volume fraction. the coarser matrix particles and local agglomeration took place at the junctions between three or four matrix particles. Microstructural observations revealed that densification occurred mainly because of deformation of the smaller matrix particles, while the coarser remained almost unchanged. This was more visible for composites reinforced with 20 and 30 ~01% Tic, where the PPBs of the coarser matrix powders were almost unaltered. The initial and final relative density of the composite as a function of the reinforcement volume percent is presented in Figure 2. The increase in the initial relative density of the composite with the reinforcement content is consistent with theories (14,15) and experiments of particle packing in bimodal powder mixtures. The finer TiC particles were able to fill the areas associated with voids generated from the packing of the Fe-alloy powder (e.g., at the junctions between three or four matrix particles). The final relative density of the composite was decreasing with the increasing amount of added TiC particles, while the unreinforced alloy was fully densified after HIPing. The metallographic examination showed porosity in the composites in areas of local TiC clusters, as for example at the junctions between three or four coarse matrix particles (e.g., Fig. I (c)). The high concentration of TiC particles in these areas resulted in an increased number of rigid-rigid contacts and prevented the matrix from ‘squeezing in’ between the TiC particles to fully dens@ the composite. Porosity was also found at matrix PPBs, particularly in the composite reinforced with 30 ~01% fine TiC as shown in Figure 3. This figure also shows the porosity in local reinforcement clusters at the junctions between coarser matrix particles. It should be noticed here that the dark areas in Figures 1(c) and 3 were produced by spalling of nondensified TiC particles during polishing and, hence, they do not show the actual porosity, which is lower than that presented in the micrographs. DISCUSSION The main conclusion about the consolidation behavior of the composite materials during HIPing was that the presence of the reinforcements hindered densification. This feature was more distinct in the composites reinforced with higher amounts of TiC particles. Microstructural observations of the consolidated composites revealed that two phenomena
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FIG. 3 Porosity at prior particle boundaries (PPBs). restricted densification: (a) the presence of contacts between the rigid TiC particles, and (b) the continuous particle networks which spanned, mainly, the composites containing 20 and 30 ~01% Tic. Although the information concerning the densification mechanism in HIPed composite materials is very limited, some data concerning densification of modeled composite systems (5,9,10) have demonstrated that the presence of contacts between hard, undeformable inclusions hinder densitication, resulting in an increased porosity at the contact areas. This happens, fust, because no deformation occurs at the contact points (ceramic materials are undeformable) and, second, because in those areas the matrix particles need an additional deformation in order to fill the empty space. Accordingly, the relative number of each contact type nij, where the subscripts i and j refer to the type of particles forming each contact, has a key role during densification of composite powders. According to the gapless packing model (16) modified for a bimodal powder system these numbers are n n II =I n, +n*R ( 1
I
2n,nlR “12= (n,+nlR)2
‘22 = ,:;*R t
’
(‘)
1
where the subscript 1 refers to a matrix particle and 2 to a ceramic particle, ni is the number fraction of particle i, and R = rz/rl is the particle’s radius ratio. At the l-l contacts the densitication mechanisms follow those of the monolithic powder (l-3). Densification at the 1-2 contacts depends mainly on the plastic behavior of the matrix at the particular pressure and temperature condition and, to a first approximation the contact force-displacement (particle center-to-center displacement) relationship for a plastic-rigid contact (l-2) is the same as for a plastic-plastic (l- 1) contact. No deformation occurs at the 2-2 contacts and, therefore, the number nu should be as low as possible. Touching ceramic particles are associated with void formation, particularly at their three- or four-particle junctions. In addition, the 2-2 contacts support a portion of the applied pressure and, thus, partially shield the surrounding matrix from the full applied stress. This makes it necessary
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to apply a higher pressure in order to dens@ a composite powder mixture containing a high amount of rigid-rigid contacts. The results presented in Figure 2 showed that the final relative density of the composite decreased with the increasing reinforcement volume percent. This indicates that the deformed matrix particles could not completely fill the void space between hard, touching ceramic particles. The relative density pmof the matrix phase in the composite as a function of the composite relative density pc is given by
(I-fp 1
P,,*= c
(2)
‘-fP‘
where f is the reinforcement volume fraction. This equation allows prediction of the relative density of the matrix in the composite at any stage during the densification process. The initial (packing) and final relative density of the iron alloy matrix in the composite reinforced with various amounts of TiC particles were calculated and the results are presented in Table 1. As it can be seen, the initial relative density pm,of the matrix decreases with the increasing TIC ~01%. Accordingly, an additional deformation of the matrix would be required in order to completely fill the voids associated with touching TIC particles. The magnitude of the additional deformation is directly related to the difference in the initial relative density of the matrix powder with and without reinforcements. This difference has been referred to (5) as the ‘excluded volume’ and is associated with the packing of different sized particles. Therefore, the excluded volume contributes to increasing the pressure required to achieve a prescribed matrix density. Table 1 shows that the differences between the final relative density of the matrix in the composites and of the matrix alone (0 ~01% TIC) are smaller than between the initial relative densities. This means that the iron alloy matrix deformed quite well during the HIPing process and only some clusters of reinforcements restricted a complete matrix densification. However, a greater deformation would be required in order to fill all the ‘channels’ and interstices between touching TIC particles, and the applied pressure was not enough to achieve it, particularly for the composite containing 30 ~01% Tic. In the composites reinforced with higher amounts (>lO ~01%) of TIC particles, densification was also hindered by the presence of continuous networks of reinforcing particles. Lange (17) has reported that if the ratio pdp, is expressed by a linear function of the reinforcement volume fraction ‘f, then the ceramic reinforcements do not significantly affect the consolidation of the matrix powder. If, however, the expression is not linear, the ceramic reinforcements can be considered to hinder the consolidation of the matrix powder by TABLE I Relative Density of the Composites (c) and of the Composites’ Matrix (m)*
0
*
10 20 30
0.643 0.65 1 0.658 0.662 ~_____.___
0.643 0.627 0.606 0.578
I 0.992 0.987 0.965
I 0.991 0.983 0.950
Subscript i refers to the initial (packing) and subscript i‘to the final relative density.
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forming continuous or discontinuous touching networks. The site occupancy percolation theory reveals that at least one continuous network will form at f = 16% (18), whereas Lange et al. (5) have found that >95% of the inclusions will be part of the continuous network when f > 20%. In the case of the materials examined in the present study, there were not enough values to express the ratio pdp, as a function of ‘f, but microstructural observations confirmed the presence of continuous TiC networks inside the composites containing 20 and 30 ~01% Tic. These networks support a substantial portion of the applied pressure, particularly at the higher reinforcement volume fractions. The deformable phase is then subjected to only a portion of the applied pressure and, therefore, the reinforcement networks further increase the pressure required to obtain a given density. The insufficient pressure used during consolidation of the 30 ~01% TiC composite resulted in the porosity observed at prior matrix particle boundaries (Fig. 3). The above observations indicate that the pressure used to consolidate the composites was not enough to obtain fully densified bodies, because the deformation of the composites’ matrix was not sufficient to completely fill the channels and interstices between touching ceramic particles. It could be argued that additional deformation requires a greater applied stress per unit volume of matrix material in order to minimize the constraining influence of the undeformable ceramic particles. The virtual work equation for a powder compact containing plastic and rigid particles, subjected to an externally applied pressure P, predicts
PdV =
f,NeF,j~S, Nti = 6DNIMnij ij4
where P is the externally applied pressure, dV is the volume change because of densification, Fij are the normal contact forces on the ij contacts, drip are the incremental contact displacements between particle centers, Nij are the numbers of ij contacts, D is the density of the composite (expressed as % of theoretical), and N, is the total number of particles in the powder. In this expression, shear displacements where plastic particles slide over rigid particles have been neglected because their contribution in densification seems to be small. The evaluation of the pressure needed to attain a given density D of a composite powder can then be made, following the approach suggested by Turner and Ashby (10): P=18YDYD(:(Di:-D?)(s)
(4)
+n2,R, v=n,+n2R3,
AR=n 1,+n 22ARII’
AR2
+
(for rl 2 r2).
where Y is the yield strength of the monolithic powder, AW is a relative (to the monolithic powder) work term, Ro is a relative particle radius term, v is a relative volume term, AR and ARlz are relative contact displacement terms, D is the instantaneous density, Do is the packing density, and oil and o12 are the applied stress at the contact points. The second parenthesis in equation (4) represents the additional pressure needed to achieve a given density D for a composite powder relative to the pressure needed to achieve the same density in a monolithic powder with the same packing density Do. Consequently, it is
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FIG. 4 Clusters of TIC particles within agglomerated fine matrix particles. therefore obvious that the applied pressure required to deform the matrix in the composite system is generally larger than that corresponding to the matrix powder without the ceramic reinforcements. Microstructural observations revealed that during consolidation, the fine matrix particles were deformed more heavily than the coarse particles and, therefore, they contributed more effectively on the densification of the composite. Similar observations have been reported also in monolithic Ni-based superalloys (7). Theoretical and experimental observations of Nair and Tien (19) and of Li and Funkenbusch (20) in bimodal monolithic powder mixtures have shown that smaller particles deform considerably more than large particles do because of their different geometric compatibility during powder consolidation in HIP. The higher deformability of the fine matrix particles also in the composite mixtures of the present study indicates their positive influence during consolidation. This aspect works, however, only if the fine matrix particles are uniformly distributed within the coarse particles; agglomeration of fine matrix particles may result in clusters of reinforcing particles within the agglomerates, as shown in Figure 4. CONCLUSIONS Based on the present study the following conclusions can be drawn: .
The presence of contacts between the hard, undeformable ceramic particles restricts complete densification of the composite. In the composites containing a higher amount of reinforcements, continuous and discontinuous TIC networks hinder further densification. The above factors increase the required applied pressure for consolidating the composites.
l
As in the case of monolithic bimodal sized powders, in composite mixtures the smaller matrix particles contribute more effectively to the densification process.
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ACKNOWLEDGMENTS
The authors are grateful to The Technology Development Centre of Finland (TEKES) for financial support. REFERENCES 1. E. Arzt, M.F. Ashby and K.E. Easterling, Metall. Trans. 14A, 211 (1983). 2. A.S. Helle, K.E. Easterling and M.F. Ashby, Acta Metall. 33,2163 (1985). 3. W. Kaysser, in Hot Isostatic Pressing: Theory and Applications, ed. R.J. Schaefer and M. Linzer, p. 1, ASM International, Ohio (1990). 4. R. R. Mehrabian, Mater. Res. Sym. Proc. 120,3 (1988). 5. F.F. Lange, L. Ateraas, F. Zok and J.R. Porter, Acta Metall. Mater. 39, 209 (1991). 6. R. Suryanarayanan, S.M.L. Sastry and K.L. Jerina, Acta Metall. Mater. 42,374l (1994). 7. W. Kaysser, M. Aslan, E. Arzt, M. Mitkov and G. Petzow, Powd. Metall. 31,63 (1988). 8. B. Derby and C.-D. Qin, Acta Metall. Mater. 40 Suppl., S53 (1992). 9. E.K.H. Li and P.D. Funkenbusch, Metall. Trans. 24A, 1345 (1993). 10. C.D. Turner and M.F. Ashby, in Hot Isostatic Pressing ‘93, ed. L. Delaey and H. Tas, p. 3, Elsevier, Antwerp (1994). 11. M.J. Talvitie and V.K. Lindroos, Proc. of Powder Metallurgy ‘94, World Congr., p. 1465, Paris (1994). 12. E. Haimi, M. Talvitie, E.O. Ristolainen, J. Kivilahti and V.K. Lindroos, Scripta Metall. Mater. 30, 1333 (1994). 13. E. Pagounis, E. Haimi, J. Pietikainen, M. Talvitie, S. Vahvaselka and V.K. Lindroos, Scripta Materialia 34, 407 ( 1996). 14. N. Epstein and M.J. Young, Nature 196,885 (1962). 15. S. Yerazunis, S.W. Cornell and B. Wintner, Nature 207, 835 (1965). 16. J.A. Dodds, J. Colloid and Interface Science 77, 3 17 (1980). 17. F.F. Lange, J. Mater. Res. 2,59 (1987). 18. R. Zallen, Physics of Amorphous Solidr, Chap.4, Wiley, New York (1983). 19. S.V. Nair and J.K. Tien, Metall. Trans. 18A, 97 (1987). 20. E.K.H. Li, P.D. Funkenbusch, Acta Metall. 37, 1645 (1989).