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Compressive deformation and fracture in WC materials
Materials Science and Engineering, A105/106 (1988) 299-303
299
Compressive Deformation and Fracture in WC Materials* DAVID J. ROWCLIFFEt
SRI International, Menlo Park, CA (U.S,A.) VICKRAM JAYARAM-~, MARY K. HIBBS§ and ROBERT SINCLAIR
Stanford University, Stanford, CA (U.S.A.) (Received December 8, 1987)
Abstract
Plastic flow and fracture have been studied in WC single crystals and in WC-Co materials. Deformation was introduced by several techniques which resulted in the development of high compressive stresses which encourage slip in WC. Optical and transmission electron microscopy studies show that plastic flow in the carbide phase always precedes fracture. A simple analysis shows that there are only four independent slip systems in WC. Consideration of the limitations for slip in WC lead to a mechanistic model for fracture initiation in WC-Co. 1. Introduction
Fracture processes in cemented WC-Co have been modelled extensively [1-6]. Many of these models are logically based on observations of fracture surfaces which give information on the fracture path. Most models emphasize the role of plastic deformation in the binder phase because much of the final fracture occurs through the binder phase or at carbide binder interfaces. However, Sarin and Johannesson [6] suggest that even small amounts of plastic flow in the carbide phase exert a significant influence on the deformation of WC-Co. Studies of single crystals [7-9] show clearly that WC can undergo plastic deformation relatively readily under certain stressing *Paper presented at the 3rd International Conference on the Science of Hard Materials, Nassau, The Bahamas, November 9-13, 1987. tPresent address: Royal Institute of Technology, Stockholm, Sweden. :~Present address: University of California, Santa Barbara, CA, U.S.A. §Present address: Honeywell Inc., Bloomington, MN, U.S.A. 0921-5093/88/$3.50
conditions. Although dislocation multiplication [10] has been reported in deformed WC-Co, there has been little attempt to relate singlecrystal plasticity to specific deformation and fracture processes in WC-Co. This paper addresses this issue. Information is drawn from an extensive study of deformation and fracture of WC materials [8, 9, 11-15] which includes work on indentation [8, 9, 11, 12], isostatic compression [13] and dynamic impact using hard spheres [15]. These different stressing methods have in common a large component of compression in the presence of constraining forces which tend to restrict the development of high tensile stresses. This combination encourages accommodation of stress by plastic flow rather than by tensile fracture and, under these conditions, plastic flow in the carbide phase always precedes fracture. Using these considerations, this paper suggests a mechanistic model for fracture initiation in WC-Co based on limited slip in the carbide phase.
2. Deformation of single crystal WC It is well established that the slip plane in WC is {10i0}. The slip direction [8, 12, 16, 17] is (1123} with slip occurring by the motion of identical (a/6)[1123] partials [8, 12, 17]. Figure 1 illustrates schematically the slip traces S and some crack patterns for indentations on the (0001) and {1050} planes. For indentations on the basal plane, cracks develop at intersecting slip bands on {l120}(A) and on {10i0}(B). T h e former are more common and an example is shown in Fig. 2. Almond [18] observed similar cracks at intersecting slip bands in WC-Co but did not analyse them. Cracks of this type have been analysed by transmission electron micros© Elsevier Sequoia/Printed in The Netherlands
300
C ii Fig. 1. Slip traces and crack patterns in WC.
Fig. 2. Crack on {1120} formed at intersecting slip bands on the {0001} surface of WC.
copy [10]. It has been suggested that the cracks form by a mechanism analogous to that proposed by Cottrell for the nucleation of cracks in b.c.c. metals. In the case of WC the proposed interactions are as follows. (1) For a crack on (1210) ~[2113] + 111123] = ~[i2i0] (2) For a crack on (10i0),
Fig. 3. Spherical indentation on the {1010} plane of WC: B, basal plane crack; S, slip steps; R, ring crack; RM, r a d i a l median crack.
cence of edge dislocations can be expected to open up wedge cracks of the type that are observed. A second mechanism for fracture related to plastic flow has also been found. The basal plane crack C shown schematically in Fig. 1 has been observed at both the Vickers and spherical indentations made on {1050} and on {1120} planes and an example is shown in Fig. 3. The origin of this crack lies in the anisotropic nature of plastic flow in WC. During indentation on (1010), slip occurs on the two inclined {1050} planes, making a [0001] trace on the plane of indentation. The in-plane stresses normal to [0001] are readily relieved by plastic flow but relief of stress is not possible parallel to [0001] and the large tensile stress causes fracture. Inspection of Fig. 1 confirms that, with {1010}(1123) slip, it is not possible to extend WC plastically along its c axis. Further, a formal strain tensor treatment [11] shows that there are only four independent slip systems in the {10 i 0 }(1123) family rather than t h e five required for a general shape change in polycrystalline WC. This result has important consequences for WC-Co materials, as discussed below.
A[2i i3] + l[1123] = ½11050]
3. Intergranular fracture in polycrystalline WC-Co
The reaction to form ~[i2i0] partials has been confirmed by Hibbs et al. [12] but the second reaction was not verified, owing to experimental difficulties. However, both dislocations are sessile and, under the action of an applied stress, coales-
The direct consequence of only four independent slip systems with the inability to extend WC in the c direction is that it is not possible to transmit slip across certain contiguous WC-WC boundaries. This leads directly to a mechanism to
301
initiate intergranular microfracture and the WC-WC boundary configurations which are particularly susceptible can be readily proposed from the slip geometry. The specific conditions are as follows. ( 1 ) If the c axes of neighboring grains are nonparallel, there is a strain discontinuity across the boundary, leading to tensile (opening) stresses. (2) The worst case (maximum tension) is when the c axes of neighboring grains are orthogonal and the c axis of one grain is normal to the boundary. A further general requirement for fracture to occur preferentially at such boundaries is that the stress must be sufficiently high to exceed the fracture stress locally. Whereas this latter requirement does not follow directly from the considerations of limited slip systems, it arises implicitly because of the expected local inhomogeneity of strain in different carbide grains. The two mechanisms which can initiate fracture in single crystals have been found to cause occasional transgranular carbide fracture in deformed WC-Co. However, intergranular fracture by the mechanism related to plastic incompatibility is much more common and the main cases are described in Section 4. 4. Analysis of grain boundaries in deformed WC -Co
More than 50 WC-Co grain boundaries in deformed WC-6wt.%Co and WC-10wt.%Co were analyzed by transmission electron microscopy. The details have been reported elsewhere [11, 13, 14] and only a few examples of the main
types of boundary are considered here. Figure 4 illustrates a "worst-case" example, i.e. a mutual orientation of contiguous grains in which the c axes are orthogonal and the c axis of one grain is normal to the plane of the boundary. An intergranular crack has been initiated at a two-grain junction because of the local incompatibility. 35 such boundaries were analyzed in highly deformed samples and each was cracked as predicted. Similarly, many uncracked boundaries in nearby regions were also examined and it was found that they generally lay in orientations favoring transfer of slip. Multigrain junctions are common in WC-Co and the need to accommodate strains in several neighboring grains increases the likelihood of finding orientations that cause a strain discontinuity. In Fig. 5, grains F and G are separated by a twist boundary about the c axis. According to the analysis presented here, this boundary should not crack, if this were a two-grain junction. However, the presence of the third grain, H, causes a strain discontinuity across the boundary with grain F and this discontinuity leads to the observed fracture. Several different situations arise at junctions where a cobalt binder phase is present. It was generally found that, in multigrain junctions containing a compatible WC-WC boundary and neighboring cobalt pockets, both the carbide grains and cobalt pockets could be highly strained without fracture. It is likely that yielding in adjacent cobalt grains partially relieves some of the discontinuity difficulties arising from the limited number of slip systems in WC. In addition, very large amounts of strain can be accom-
!i!ii
Fig. 4. A cracked grain boundary containing a basal plane. The electron beam direction is close to [ 1120].
Fig. 5. lntergranular crack along a twist boundary between grains F and G. The crack initiated at the boundary between G and H (black arrow).
302
Fig. 6. Slip steps in WC adjacent to a cobalt pocket.
modated locally in the cobalt as illustrated in Fig. 6. The large slip steps in the WC grain are equivalent to about 5% plastic strain. Thus, local strains in deformed WC-Co can be expected to be much higher than the average strain, which should have important consequences for fracture initiation. The presence of cobalt between WC grains and, where present, its effect on deformation and fracture has been the subject of much discussion. Our studies suggest that the presence of cobalt between WC grains does not ensure transfer of large strains if the WC grains are unfavorably oriented and the cobalt layer is relatively thin. A limited number of observations and an approximate calculation [14] suggest that cobalt layers 500 A or less thick are insufficient to prevent fracture. Figure 7 shows an example of intergranular cracking at an unfavorably oriented WC-WC boundary containing cobalt, whereas an adjacent cobalt-free WC-WC compatible boundary remains uncracked even though both grains are heavily deformed. 5. Discussions and conclusions
In this paper, we reviewed evidence which points to limitations in plastic compatibility between contiguous WC grains as the main cause of the initiation of intergranular microfracture at such boundaries. The frequency of observation of this effect suggests that it could be the primary mode of failure initiation in WC-Co deformed under conditions of confined compression. It must be emphasized that these observations relate specifically to fracture nucleation, whereas macroscopic crack propagation clearly also
Fig. 7. Cracked (horizontal) WC-WC boundary containing cobalt and uncracked (vertical) boundary between contiguous carbide grains. The white vertical arrow denotes the c axis.
involves fracture of cobalt ligaments. However, the major route to transfer strain is through cobalt pockets and the accommodation of large strains can be visualized as a percolation of slip through the cobalt along Co-WC-Co paths rather than over the more difficult route through the major WC constituent, in grades containing 6-10 wt.% Co. This view is consistent with the observation of local strain concentrations in the cobalt pockets and suggests the following possible sequence of events that lead to fracture in WC -Co. (1) The applied stress exceeds the constrained yield stress for the cobalt binder phase which simultaneously transforms martensitically to the h.c.p, phase. Dislocations pile up in the cobalt setting up elastic stresses in the carbide which exceed the applied stress. (2) As the applied stress is increased, the constrained yield stress of WC is exceeded in WC grains adjacent to deformed cobalt grains. (3) Slip spreads across WC grains in the vicinity of cobalt. (4) Slip transfers across favorably oriented WC-WC boundaries, but intergranular cracks form at other boundaries owing to plastic incompatibility. (5) Additional slip systems operate in certain WC grains and transgranular cracks form at intersecting slip bands or owing to anisotropy of slip. (6) Intergranular and transgranular cracks link up for macroscopic fracture. Although most slip is probably transfered through the cobalt pockets, we emphasize the
3(13
importance of WC-WC boundaries because this is the more difficult route which ultimately leads to failure in the low cobalt content grades. This view is consistent with the observation of Lea and Roebuck [19] who have shown that about 50% of the fracture propagates through WC-WC boundaries. As the cobalt content is increased, the difficulties due to only four independent slip systems may be overcome in microstructures ~zontaining sufficient WC-Co paths to circumvent incompatible WC-WC boundaries.
Acknowledgment This work was supported by the National Science Foundation.
References 1 L. Lindau, in D. M. R. Taplin (ed.), Fracture 1977, Proc. 4th Int. Conf. on Fracture, Waterloo, Ontario, June 19-24, 1977, Vol. 2A, Pergamon, Oxford, 1977, p. 215. 2 J. L. Chermant and E Osterstock, J. Mater. Sci., 11 (1939) 1976. 3 J. R. Pickens and J. Gurland, Mater. Sei. Eng., 33 (135) 1978.
4 M. Nakamura and J. Gurland, Metall. Trans. A, i1 (141) 1980. 5 R.K. Viswanadham, T. S. Sun, E. F. Drake and J. A. Peck, J. Mater. Sci., 16 ( 1981 ) 1029. 6 V.K. Sarin and T. Johannesson, Met. Sci., 9 (1975) 472. 7 T. Takahashi and E. J. Friese, Philos. Mag., 12 (1965) 1. 8 M. K. Hibbs and R. Sinclair, Acta Metall., 29 (1981) 1045. 9 D.J. Rowcliffe, in R. K. Viswandham, D. J. Rowcliffe and J. Gurland (eds.), Proc. 1st Int. Conf. on Science of Hard Materials, Plenum, New York, 1983, p. 155. 10 T. Johannesson and B. Lehtinen, t'hys. Status Solidi A, 16 (1973)615. 11 V. Jayaram, R. Sinclair and D. J. Rowcliffe, Acta Metall., 31 (1983)373. 12 M.K. Hibbs, R. Sinclair and D. J. Rowcliffe, Acta Metall., 32 (1984)941. 13 V. Jayaram, A. Kronenerg, S. H. Kirby, D. J. Rowcliffe and R. Sinclair, Scr. MetalL, 20 (1986) 701. 14 V. Jayaram, Acta Metall., 35 (1987) 1307. 15 D.J. Rowcliffe, C. D. Craig and T. Cooper, in J. E. Field and J. R Dear (eds.), Proc. 7th Int. Conf. on Erosion by Liquid and Solid Impact, Cambridge, 1987, Cavendish Laboratory, Cambridge, 1987, p. 59-1. 16 S.B. Luyckx, Acta MetalL, 18 (1970) 223. 17 S. Hagege, J. Vincens, G. Nouet and P. Delavignette, Phys. Status Solidi A, 61 (1980) 675. 18 E. A. Almond, in R. K. Viswanadham, D. J. Rowcliffe and J. Gurland (eds.), Proc. 1st lnt. Conf. on Science of.Hard Materials', Plenum, New York, 1983, p. 517. 19 C. Lea and B. Roebuck, Met. Sci., 15 ( 1981 ) 263.
299
Compressive Deformation and Fracture in WC Materials* DAVID J. ROWCLIFFEt
SRI International, Menlo Park, CA (U.S,A.) VICKRAM JAYARAM-~, MARY K. HIBBS§ and ROBERT SINCLAIR
Stanford University, Stanford, CA (U.S.A.) (Received December 8, 1987)
Abstract
Plastic flow and fracture have been studied in WC single crystals and in WC-Co materials. Deformation was introduced by several techniques which resulted in the development of high compressive stresses which encourage slip in WC. Optical and transmission electron microscopy studies show that plastic flow in the carbide phase always precedes fracture. A simple analysis shows that there are only four independent slip systems in WC. Consideration of the limitations for slip in WC lead to a mechanistic model for fracture initiation in WC-Co. 1. Introduction
Fracture processes in cemented WC-Co have been modelled extensively [1-6]. Many of these models are logically based on observations of fracture surfaces which give information on the fracture path. Most models emphasize the role of plastic deformation in the binder phase because much of the final fracture occurs through the binder phase or at carbide binder interfaces. However, Sarin and Johannesson [6] suggest that even small amounts of plastic flow in the carbide phase exert a significant influence on the deformation of WC-Co. Studies of single crystals [7-9] show clearly that WC can undergo plastic deformation relatively readily under certain stressing *Paper presented at the 3rd International Conference on the Science of Hard Materials, Nassau, The Bahamas, November 9-13, 1987. tPresent address: Royal Institute of Technology, Stockholm, Sweden. :~Present address: University of California, Santa Barbara, CA, U.S.A. §Present address: Honeywell Inc., Bloomington, MN, U.S.A. 0921-5093/88/$3.50
conditions. Although dislocation multiplication [10] has been reported in deformed WC-Co, there has been little attempt to relate singlecrystal plasticity to specific deformation and fracture processes in WC-Co. This paper addresses this issue. Information is drawn from an extensive study of deformation and fracture of WC materials [8, 9, 11-15] which includes work on indentation [8, 9, 11, 12], isostatic compression [13] and dynamic impact using hard spheres [15]. These different stressing methods have in common a large component of compression in the presence of constraining forces which tend to restrict the development of high tensile stresses. This combination encourages accommodation of stress by plastic flow rather than by tensile fracture and, under these conditions, plastic flow in the carbide phase always precedes fracture. Using these considerations, this paper suggests a mechanistic model for fracture initiation in WC-Co based on limited slip in the carbide phase.
2. Deformation of single crystal WC It is well established that the slip plane in WC is {10i0}. The slip direction [8, 12, 16, 17] is (1123} with slip occurring by the motion of identical (a/6)[1123] partials [8, 12, 17]. Figure 1 illustrates schematically the slip traces S and some crack patterns for indentations on the (0001) and {1050} planes. For indentations on the basal plane, cracks develop at intersecting slip bands on {l120}(A) and on {10i0}(B). T h e former are more common and an example is shown in Fig. 2. Almond [18] observed similar cracks at intersecting slip bands in WC-Co but did not analyse them. Cracks of this type have been analysed by transmission electron micros© Elsevier Sequoia/Printed in The Netherlands
300
C ii Fig. 1. Slip traces and crack patterns in WC.
Fig. 2. Crack on {1120} formed at intersecting slip bands on the {0001} surface of WC.
copy [10]. It has been suggested that the cracks form by a mechanism analogous to that proposed by Cottrell for the nucleation of cracks in b.c.c. metals. In the case of WC the proposed interactions are as follows. (1) For a crack on (1210) ~[2113] + 111123] = ~[i2i0] (2) For a crack on (10i0),
Fig. 3. Spherical indentation on the {1010} plane of WC: B, basal plane crack; S, slip steps; R, ring crack; RM, r a d i a l median crack.
cence of edge dislocations can be expected to open up wedge cracks of the type that are observed. A second mechanism for fracture related to plastic flow has also been found. The basal plane crack C shown schematically in Fig. 1 has been observed at both the Vickers and spherical indentations made on {1050} and on {1120} planes and an example is shown in Fig. 3. The origin of this crack lies in the anisotropic nature of plastic flow in WC. During indentation on (1010), slip occurs on the two inclined {1050} planes, making a [0001] trace on the plane of indentation. The in-plane stresses normal to [0001] are readily relieved by plastic flow but relief of stress is not possible parallel to [0001] and the large tensile stress causes fracture. Inspection of Fig. 1 confirms that, with {1010}(1123) slip, it is not possible to extend WC plastically along its c axis. Further, a formal strain tensor treatment [11] shows that there are only four independent slip systems in the {10 i 0 }(1123) family rather than t h e five required for a general shape change in polycrystalline WC. This result has important consequences for WC-Co materials, as discussed below.
A[2i i3] + l[1123] = ½11050]
3. Intergranular fracture in polycrystalline WC-Co
The reaction to form ~[i2i0] partials has been confirmed by Hibbs et al. [12] but the second reaction was not verified, owing to experimental difficulties. However, both dislocations are sessile and, under the action of an applied stress, coales-
The direct consequence of only four independent slip systems with the inability to extend WC in the c direction is that it is not possible to transmit slip across certain contiguous WC-WC boundaries. This leads directly to a mechanism to
301
initiate intergranular microfracture and the WC-WC boundary configurations which are particularly susceptible can be readily proposed from the slip geometry. The specific conditions are as follows. ( 1 ) If the c axes of neighboring grains are nonparallel, there is a strain discontinuity across the boundary, leading to tensile (opening) stresses. (2) The worst case (maximum tension) is when the c axes of neighboring grains are orthogonal and the c axis of one grain is normal to the boundary. A further general requirement for fracture to occur preferentially at such boundaries is that the stress must be sufficiently high to exceed the fracture stress locally. Whereas this latter requirement does not follow directly from the considerations of limited slip systems, it arises implicitly because of the expected local inhomogeneity of strain in different carbide grains. The two mechanisms which can initiate fracture in single crystals have been found to cause occasional transgranular carbide fracture in deformed WC-Co. However, intergranular fracture by the mechanism related to plastic incompatibility is much more common and the main cases are described in Section 4. 4. Analysis of grain boundaries in deformed WC -Co
More than 50 WC-Co grain boundaries in deformed WC-6wt.%Co and WC-10wt.%Co were analyzed by transmission electron microscopy. The details have been reported elsewhere [11, 13, 14] and only a few examples of the main
types of boundary are considered here. Figure 4 illustrates a "worst-case" example, i.e. a mutual orientation of contiguous grains in which the c axes are orthogonal and the c axis of one grain is normal to the plane of the boundary. An intergranular crack has been initiated at a two-grain junction because of the local incompatibility. 35 such boundaries were analyzed in highly deformed samples and each was cracked as predicted. Similarly, many uncracked boundaries in nearby regions were also examined and it was found that they generally lay in orientations favoring transfer of slip. Multigrain junctions are common in WC-Co and the need to accommodate strains in several neighboring grains increases the likelihood of finding orientations that cause a strain discontinuity. In Fig. 5, grains F and G are separated by a twist boundary about the c axis. According to the analysis presented here, this boundary should not crack, if this were a two-grain junction. However, the presence of the third grain, H, causes a strain discontinuity across the boundary with grain F and this discontinuity leads to the observed fracture. Several different situations arise at junctions where a cobalt binder phase is present. It was generally found that, in multigrain junctions containing a compatible WC-WC boundary and neighboring cobalt pockets, both the carbide grains and cobalt pockets could be highly strained without fracture. It is likely that yielding in adjacent cobalt grains partially relieves some of the discontinuity difficulties arising from the limited number of slip systems in WC. In addition, very large amounts of strain can be accom-
!i!ii
Fig. 4. A cracked grain boundary containing a basal plane. The electron beam direction is close to [ 1120].
Fig. 5. lntergranular crack along a twist boundary between grains F and G. The crack initiated at the boundary between G and H (black arrow).
302
Fig. 6. Slip steps in WC adjacent to a cobalt pocket.
modated locally in the cobalt as illustrated in Fig. 6. The large slip steps in the WC grain are equivalent to about 5% plastic strain. Thus, local strains in deformed WC-Co can be expected to be much higher than the average strain, which should have important consequences for fracture initiation. The presence of cobalt between WC grains and, where present, its effect on deformation and fracture has been the subject of much discussion. Our studies suggest that the presence of cobalt between WC grains does not ensure transfer of large strains if the WC grains are unfavorably oriented and the cobalt layer is relatively thin. A limited number of observations and an approximate calculation [14] suggest that cobalt layers 500 A or less thick are insufficient to prevent fracture. Figure 7 shows an example of intergranular cracking at an unfavorably oriented WC-WC boundary containing cobalt, whereas an adjacent cobalt-free WC-WC compatible boundary remains uncracked even though both grains are heavily deformed. 5. Discussions and conclusions
In this paper, we reviewed evidence which points to limitations in plastic compatibility between contiguous WC grains as the main cause of the initiation of intergranular microfracture at such boundaries. The frequency of observation of this effect suggests that it could be the primary mode of failure initiation in WC-Co deformed under conditions of confined compression. It must be emphasized that these observations relate specifically to fracture nucleation, whereas macroscopic crack propagation clearly also
Fig. 7. Cracked (horizontal) WC-WC boundary containing cobalt and uncracked (vertical) boundary between contiguous carbide grains. The white vertical arrow denotes the c axis.
involves fracture of cobalt ligaments. However, the major route to transfer strain is through cobalt pockets and the accommodation of large strains can be visualized as a percolation of slip through the cobalt along Co-WC-Co paths rather than over the more difficult route through the major WC constituent, in grades containing 6-10 wt.% Co. This view is consistent with the observation of local strain concentrations in the cobalt pockets and suggests the following possible sequence of events that lead to fracture in WC -Co. (1) The applied stress exceeds the constrained yield stress for the cobalt binder phase which simultaneously transforms martensitically to the h.c.p, phase. Dislocations pile up in the cobalt setting up elastic stresses in the carbide which exceed the applied stress. (2) As the applied stress is increased, the constrained yield stress of WC is exceeded in WC grains adjacent to deformed cobalt grains. (3) Slip spreads across WC grains in the vicinity of cobalt. (4) Slip transfers across favorably oriented WC-WC boundaries, but intergranular cracks form at other boundaries owing to plastic incompatibility. (5) Additional slip systems operate in certain WC grains and transgranular cracks form at intersecting slip bands or owing to anisotropy of slip. (6) Intergranular and transgranular cracks link up for macroscopic fracture. Although most slip is probably transfered through the cobalt pockets, we emphasize the
3(13
importance of WC-WC boundaries because this is the more difficult route which ultimately leads to failure in the low cobalt content grades. This view is consistent with the observation of Lea and Roebuck [19] who have shown that about 50% of the fracture propagates through WC-WC boundaries. As the cobalt content is increased, the difficulties due to only four independent slip systems may be overcome in microstructures ~zontaining sufficient WC-Co paths to circumvent incompatible WC-WC boundaries.
Acknowledgment This work was supported by the National Science Foundation.
References 1 L. Lindau, in D. M. R. Taplin (ed.), Fracture 1977, Proc. 4th Int. Conf. on Fracture, Waterloo, Ontario, June 19-24, 1977, Vol. 2A, Pergamon, Oxford, 1977, p. 215. 2 J. L. Chermant and E Osterstock, J. Mater. Sci., 11 (1939) 1976. 3 J. R. Pickens and J. Gurland, Mater. Sei. Eng., 33 (135) 1978.
4 M. Nakamura and J. Gurland, Metall. Trans. A, i1 (141) 1980. 5 R.K. Viswanadham, T. S. Sun, E. F. Drake and J. A. Peck, J. Mater. Sci., 16 ( 1981 ) 1029. 6 V.K. Sarin and T. Johannesson, Met. Sci., 9 (1975) 472. 7 T. Takahashi and E. J. Friese, Philos. Mag., 12 (1965) 1. 8 M. K. Hibbs and R. Sinclair, Acta Metall., 29 (1981) 1045. 9 D.J. Rowcliffe, in R. K. Viswandham, D. J. Rowcliffe and J. Gurland (eds.), Proc. 1st Int. Conf. on Science of Hard Materials, Plenum, New York, 1983, p. 155. 10 T. Johannesson and B. Lehtinen, t'hys. Status Solidi A, 16 (1973)615. 11 V. Jayaram, R. Sinclair and D. J. Rowcliffe, Acta Metall., 31 (1983)373. 12 M.K. Hibbs, R. Sinclair and D. J. Rowcliffe, Acta Metall., 32 (1984)941. 13 V. Jayaram, A. Kronenerg, S. H. Kirby, D. J. Rowcliffe and R. Sinclair, Scr. MetalL, 20 (1986) 701. 14 V. Jayaram, Acta Metall., 35 (1987) 1307. 15 D.J. Rowcliffe, C. D. Craig and T. Cooper, in J. E. Field and J. R Dear (eds.), Proc. 7th Int. Conf. on Erosion by Liquid and Solid Impact, Cambridge, 1987, Cavendish Laboratory, Cambridge, 1987, p. 59-1. 16 S.B. Luyckx, Acta MetalL, 18 (1970) 223. 17 S. Hagege, J. Vincens, G. Nouet and P. Delavignette, Phys. Status Solidi A, 61 (1980) 675. 18 E. A. Almond, in R. K. Viswanadham, D. J. Rowcliffe and J. Gurland (eds.), Proc. 1st lnt. Conf. on Science of.Hard Materials', Plenum, New York, 1983, p. 517. 19 C. Lea and B. Roebuck, Met. Sci., 15 ( 1981 ) 263.