sliding and pore formation. Displacement-controlled bend tests of chevron- notched specimens were performed to introduce stable crack growth. Above 800 °C ...
MaterialsScience and Engineering, A105/106 (1988) 343-351
343
The Mechanical Behaviour of Cemented Carbides at High Temperatures* H. G. SCHMIDt, D. MARl and W. BENOIT lnstitut de G#nieAtomique, t~colePolytechnique F#d~raleLausanne, Lausanne (Switzerland) C. BONJOUR
Stellram SA, Nyon (Switzerland) (Received November 9, 1987)
Abstract
Specimens of WC-11wt. %Co were tested under three-point bending conditions at temperatures ranging between 20 and 1000 °C to investigate the effect of chromium and ruthenium additions on the mechanical behaviour of cemented carbides. Below 800 °C, a linear elastic brittle behaviour is observed. Above 800 °C, creep exponents of about n = 2 and activation energies between 3 and 5 eV were measured. Pore formation and growth were observed during creep. These results agree well with models based on creep by grain boundary sliding and pore formation. Displacement-controlled bend tests of chevronnotched specimens were performed to introduce stable crack growth. Above 800 °C, creep crack growth occurs owing to pore formation and growth. The pore distribution around the crack tip has been observed using a scanning acoustic microscope. It is shown that the equivalent strain distribution around a creep crack according to the models of Riedel agrees well qualitatively with the experimentally determined pore density. The transition between the linear elastic and viscoplastic behaviour (i.e. creep) is accompanied by a Portevin-Le Chatelier type of effect. If creep occurs in a tool made from this material, the edge blunts and is no longer useful for cutting. A characteristic time tft is introduced describing the transition between the brittle and creep behaviour. It is shown that cemented carbides with a ruthenium addition have longer transition times than those without. There*Paper presented at the 3rd International Conference on the Science of Hard Materials, Nassau, The Bahamas, November 9-13, 1987. tPresent address: Drpartement Matrriaux, l~cole Polytechnic Frdrrale Lausanne, Lausanne, Switzerland, and Nordische Universit/it, Institut fiir Werkestofftechnik,Neumiinster, FRG. 0921-5093/88/$3.50
fore, cemented carbides with ruthenium are advantageous as cutting tool materials since they can be used for longer times at a high temperature. 1. Introduction Cemented carbides are ceramic-metal composites which combine the high hardness of ceramics with a fracture toughness comparable with that of metals at room temperature [1-7]. At high temperatures (above 600 °C), rapid softening takes place [8-11]. Up to 1000 °C, creep associated with grain boundary sliding and pore formation and growth has been found to be responsible for the softening of W C - 1 [wt.% Co [9, 10]. The cemented carbides are mostly used for cutting tools. If creep occurs, then the material blunts and will obviously lose its desirable properties as a cutting material. It has been shown that a transition time between the linear elastic brittle behaviour and the viscoplastic creep behaviour is able to characterize the time limit of a cutting tool in service at a high temperature [9, 10]. Empirical results obtained at Stellram SA have shown [25] that cemented carbide cutting tools with approximately the same weight percentages of cobalt but with a small amount of ruthenium give much longer lifetimes. This work is the continuation of our investigations [9, 10] of the high temperature fracture of WC-11wt.% Co specimens, and the changes in the mechanical behaviour of WC-11wt.% Co cemented carbides with additions of chromium and ruthenium are studied. 2. Materials and procedures The nominal specimen compositions were W C - 1 lwt.%Co, W C - 1 l w t . % C o - 1.5wt.%Cr and WC-1 lwt.%Co-l.65wt.%Ru. The average grain © Elsevier Sequoia/Printed in The Netherlands
344 TABLE 1 The average bending fracture stress osB and the Weibull parameter mweibulI
3. Measurement methods
where g is the strain rate, a is the applied stress, E is Young's modulus, A and B are constant factors, n is the creep exponent, AQ is the activation energy, k is the Boltzmann constant and T is the temperature. The high temperature fracture test is characterized by the crack resistance R and the transition time tft which has been introduced in our preliminary work [9, 10]. The reasons for using these parameters are as follows. (1) The concepts of linear elastic fracture mechanics (Kic, Weibull statistics, S - p - T diagram etc.) and elastic-plastic fracture mechanics (J integral, crack-opening displacement etc.) are not valid for describing the behaviour of elastic-viscoplastic materials [12-15]. Any arbitrary values of Kic and JIc c a n be measured. (2) In the case of linear elastic or elastic-plastic fracture the critical values K~ or/and J~ characterizing the material behaviour at a given temperature have one value. In the case of viscous materials, C* or the time tf to failure depends on the temperature and the applied stress [14-17]. This situation makes it more difficult to distinguish between different qualities of materials. Thus, we would like to have only one value which characterizes the behaviour of the viscous material at a given temperature. Therefore, we derived a transition time tft to failure from the time-to-failure concept [9, 10]. This transition time t~ is defined as the time when the stress-strain field around the propagating crack tip changes from a linear elastic or elastic-plastic stress-strain field to a viscoelastic or/and viscoplastic stress-strain field [9, 10]. Our method for measuring t~t is as follows. Chevron notched three-point bending specimens with the same geometry are tested with different constant displacement rates while a crack propagates from the initial crack length to fracture. The measured parameters are load P, displacement 6, displacement rate 6 and temperature T. The corresponding tf is given by
In this work, we shall characterize the creep behaviour by Norton's law:
tf
Composite
OBB (MPa)
mweibull
(wt.%) WC-11Co WC-11Co-I.5Cr WC-11Co-l.65Ru
2458 + 170 2497 + 475 3478 + 450
14 6 7
size of the powder of all specimens was 3.6/~m. The mean free path within the cobalt phase was about 1.1 /~m for all specimens. The fracture values in Table 1 were obtained at room temperature for three-point bending tests with specimens of dimensions 35 mm x 7 mm x 3.5 mm. The fracture tests were performed with a closed-loop testing machine (Instron 1361). The three-point system is surrounded by an induction furnace in a vacuum chamber [9, 10]. Three-point single-edge-notched bending specimens of the dimensions shown above, with a chevron notch were used to obtain stable crack growth. Precracking [2] to obtain straight crack fronts was not necessary since the measured quantities tft and/~ (see eqns. (2) and (3)) refer to the crack fronts of any geometry. Therefore, displacement-controlled tests were carried out without precracking where the displacement rates varied between 100 and 0.2/.tm s-~. The temperature was measured using a pyrometer and/or a Pt-Rh thermocouple. The higher bending fracture stress of the WC-11wt.%Co-l.65wt.%Ru at room temperature may be one indication that there is an improvement in materials behaviour. However, the Weibull parameter is very low. Indeed, some of the measured bending fracture stresses for WC-11wt.%Co-l.65wt.%Ru have been below the highest values for WC-11wt.%Co. Furthermore, the longer lifetimes at elevated temperatures is also not explained by the room temperature bending stress values.
0 E
= - + Bo"
B=A
exp - ~
( 1a)
(lb)
6ma x -- 60
6
(2)
where 6max is the maximum displacement at fracture and 60 is the displacement at crack initiation. If the behaviour of the crack tip field is linear elastic, then the maximum displacement (deformation) 6max is not dependent on tf. If the crack
345 700 60O 500 o
E
/
,,o 100~ lO~m/sec
i
I 33~m/sec . . . . 0
/
33~m/sec~t
l~m/se¢
400
/
200
"
1 t+ log [sec]
Itllll
/ I/',
300
I00 ,I ~
2
3
(Q)
0
Fig. 1. Maximum displacement 6.m x at different displace-
700
ment rates v s . time to failure as log(tf), to determine the transition time t, for WC-1 lwt.%Co tested at 870 °C. (After Schmid [10].)
600
n
0.I
t
i
i
i
0.2
0.3
0.4
0.5
PI,."//'
500 40O
tip field becomes viscoplastic, then the specimen deforms more and alma× increases. Therefore a plot of almaX VS. tf provides tf, (Fig. 1 ), where tft is given by the intersection of the constant -6ma ~ line at short lifetimes tf and the increasing 6ma~ due to creep at longer lifetimes [9, 10]. A transition displacement rate c~ can be defined according to eqn. (2), which is equivalent to the definition of tft. The transition displacement rate dt is the displacement rate which is sufficiently slow that viscoplastic effects take place and the linear elastic fracture behaviour changes to viscoplastic fracture behaviour. The tft or 6t value depends on the size and the geometry of the chosen specimens. The main goal of this work is to characterize the mechanical behaviour of specimens of the same geometry and the same microstructure but of different chemical compositions. Thus the proposed quantity tft satisfies this purpose. The fracture toughness when linear elastic brittle behaviour predominates has been characterized by measuring the average crack resistance /~ [9, 10]; this is developed from the work of fracture [ 16]:
300 2OO I00 o.,
o o
-J
o.+
700 I 6o0
It'"~.
500 ~-
iI''~ I ~[ X,.,.~.
300
I/
~'
"*-~# i~+,.
2°° I
--.~..
I O0 I (c)
O0 . . . .
0'.1 . . . .
0
(3)
Am
where A~ is the crack surface created and P is the load. 4. Results 4.1. Controlled crack propagation tests
The preliminary studies have shown that above 800 °C the nature of the load-displacement
'013 . . . .
OJ.4. . . .
0:5
600 5O0 4OO
300 200
, / ' ~ ' ~ " ' " ~ "~.,,,.~ /'
'~,,~
"",,,..,,,,,,...,
I00 (d)
f Pd6
012' '
7OO
o "0 . . . .
~, o ' . ' I'
0ma×
R=
o.+
Fig. 2. Load-displacement
' .... 0.2
~ . . . . . . . . . 0.4 0.5 Displ (mm)
curves
of
' 0.5
WC-I lwt.%Co-
1.65wt.%Ru tested at 940 °C with various displacement rates 6: (a) 50 ~m s i; (b) 10 /~m s t; (c) 3 /zm s i; (d) 1/zm s i. The arrows show unstable crack propagation.
curves for WC-1 lwt.%Co indicate elastic-viscoplastic behaviour (Fig. 2). Qualitatively, the same behaviour has been observed for the cemented carbides with chromium or ruthenium additions. Above 900 °C, instabilities occur in the load-dis-
346 TABLE 2
T (oc) 20 640 780 820 880 910 950
Crack resistance values k for brittle behaviour
R (J m- 2)for the following W C - l lwt. %Co
WC-11wt. %Co-l.5w~ %Cr
W C - l lwt. %Co-l.65wt. %Ru
400 ± 20
490 ± 80
600 ± 100 218 334 440
313 350 400
450 500
placement curves (Fig. 2). These instabilities appear just below the transition from the linear elastic behaviour (Fig. 2(a)) to the viscoplastic behaviour (Figs. 2(b) and 2(c)). If the displacement rate is slow, the instabilities disappear (Fig. 2(d)). The instabilities at increasing load can be compared by the Portevin-Le Chatelier effect [18]. If the load decreases owing to crack extension, instabilities of the crack propagation occur (Fig. 2(c)). It was occasionally not possible to introduce stable crack growth (Fig. 2(b)). The crack propagation was catastrophic. The crack resistance values obtained from the load-displacement curves for linear elastic behaviour (tf < tft) are shown in Table 2. 4.2. Creep tests The creep tests performed on specimens of WC-1 lwt.%Co with the same geometry as those used in fracture experiments indicate two distinct behaviours. Below 900 °C, a saturation creep strain is observed (Fig. 3(a)). At 900 °C for stresses higher than 100 MPa, and at 1000 °C for all stresses employed, we obtain "typical" creep curves (Fig. 3(b)) with a stationary state. The point of inflection of stress-strain curves was obtained in order to determine Norton's creep law parameters (eqn. ( 1 )) (Table 3). Constant-strain-rate tests were also performed. Instabilities of the Portevin-Le Chatelier type were observed for samples of WC-1 lwt.%Co at 900 and at 1000 °C. The stress-strain curves of hot-pressed pure WC and WC-1 lwt.%Co obtained under the same testing conditions indicate very different behaviours (Fig. 4). WC and WC-Co have very similar structures; in fact, voids in WC could be considered to be replaced by cobalt in WC-Co. The results obtained favour the idea that grain boundary sliding is predominant in WC-Co creep instead of the deformation of the WC grains. This is also confirmed by the
08' J _ 0 6
g ~_o~; 02 0
0
20
40
Time
(Q~
60
[h]
16
o•1.2 .c_ m L
./~
,,i
....
i ....
0
J ....
i ....
J ....
i ....
i ....
5000
(b)
K ....
, ....
i
10000
Time (s]
Fig. 3. (a) Strain-time curves for W C - 1 1 w t . % C o (a) at 800 °C under a constant stress of 110 MPa and (b) at 900 °C under constant stress of 300 MPa. TABLE 3
Norton's creeplaw parameters
T (°C)
n
B (s l mm2" N - " )
AQ (eV)
800 900
2.1 2
6.8 x lO-J4 9.6 x 10 -12
4.8
formation of cavities in the cobalt matrix during creep (Figs. 5 and 6). 4.3. Microscopy investigations When viscoplastic behaviour occurs (see Figs. 2 and 3), a bright zone around the crack tip in the
347
40O
300
200
(b)
lOO
,
o
.1
J
. . . .
i
.2
,3
. . . .
i
.4
. . . .
I
,~
.5
[°Io3 Fig, 4. Stress-strain curves for (a) pure WC and (b) W C - l l w t . % C o at 1000°C with a strain rate g of 1,6 × 1 0 - S s - L
F
4 0 pm 4
Fig. 6. Scanning acoustic micrographs of WC-11wt.%Co crept at 900 °C and a load of 200 MPa. The arrows show the pores.
contrasts of the small pores, an Ernst Leitz scanning acoustic microscope was chosen (Fig. 6). The black dots (particles) have much larger diffraction contrasts [9, 10] than the small pores do. This technique permits measurements of the density of the pores within large creep zones [9, 10]. 5. Discussion
5.1, The load-displacement experiments The load-displacement experiments show that three different types of mechanical behaviour exist (Fig. 2).
Fig. 5. Scanning electron micrographs of the surface of WC-1 lwt.%Co tested at 900 °C with 6 = 1 ,urn s-l: (a) the
arrows show the bright creep zone; (b) the arrows indicate the pores. scanning electron micrograph (in Fig. 5(a)) can be detected. Within this zone, creep pores are always observed along the W C - W C and W C - C o interfaces (Fig. 5(b)). In order to enhance the
5.1.1. Linear elastic behaviour with stable crack growth at high displacement rates (Fig. 2(a)) The shape of the load-displacement curve is that of a linear elastic brittle material with stable crack growth. This shape is limited by the transition displacement rate 6t. Linear elastic shapes were found at all temperatures for all materials tested. The crack resistance values (see Table 2) were obtained in order to check whether there exist strong deviations from the behaviour that has been investigated extensively by Fantozzi et
348
al. [8]. The minimum values of the crack resistance occur at about 600 °C, as reported in ref. 8. This fact confirms the assumption of the model [9, 10] that the crack resistance below 600 °C is effected by the ligament rupture mechanism [2, 5, 7, 9, 10]. The plastic deformation of the unbroken cobalt ligament behind the crack tip controls the crack propagation. Above 500 °C the cobalt becomes weak and the contribution of the ligaments to the crack resistance decreases. Up to 1000 °C, the crack resistance reaches the room temperature values. This increase may be effected by the deformation of the WC skeleton [19, 20]. However, the mechanical behaviour of the materials tested should be investigated in more detail between 500 and 800 °C.
The theories of cracks in elastic-non-linear viscous materials are almost all focused on the description of non-propagating cracks [14, 15, 21, 22]. Hui and Riedel [23] proposed a model for a propagating crack under uniaxial tension in a non-linear viscous material using Norton's material law (eqn. ( 1 )). One result of this model is that, below a certain minimum growth rate, no stable steady state crack growth is possible if the creep exponent is less than 3. In our creep experiments on WC-1 lwt.%Co, a creep exponent n of 2 was determined. No stable steady state growth should be possible below a certain minimum crack propagation rate. Effectively, unstable crack growth was only found in an intermediate range (Fig. 7).
5.1.2. Unstable elastic-viscoplastic behaviour with intermitted stable crack growth or instantaneous fracture below 6~ The instabilities at increasing load (the Portevin-Le Chatelier effect) occur above 900 °C and is observed in all three materials. Behaviour similar to the Portevin-Le Chatelier effect was always accompanied by steps of unstable crack propagation (Fig. 2(c), arrow) or instantaneous fracture (Fig. 2(b), arrow). The range of instabilities below the transition from linear elastic to viscoplastic increased with increasing temperature (Fig. 7). The instabilities were always found just below 6t. Sometimes instabilities in the crack propagation were found without the Portevin-Le Chatelier effect. Between 800 and 900 °C a transition from linear elastic to viscoplastic takes place without the instability effects. Perhaps these instabilities always exist but the range near the point of transition is too small and the steps in displacement rates are too large for them to be detected.
5.1.3. Stable steady state creep crack growth below 6 t This type of creep crack growth (Fig. 2(d)) occurs if a transition from linear elastic to viscoplastic exists. The micrograph in Fig. 5(a) shows a creep crack which propagated over 90% of the total possible crack extension ( a t o t = 3 mm) at 870 °C and a displacement rate 6 of 1 /~m s-1. The bright zone around the crack is the damage zone (i.e. the zone which remains plastically deformed and damaged by pores behind the creep zone). The thickness of this zone is nearly constant over 90% of the crack length a (= 2.7 mm). Therefore, a creep damage zone has propagated through the material with a nearly constant diameter, creating the creep crack. In order to study the formation of the creep crack in detail, a micrograph obtained by scanning acoustic microscopy of the region around the crack tip of a specimen tested at 900 °C and 1 /~m s-1 is shown in Fig. 8(a). The crack propagated over 2.7 mm and the displacement was halted. After 5 min the specimen was quenched. The white lines represent the contours of the zones of the same specimen which were obtained with backscattered electrons in a scanning electron microscope (see also Fig. 5(a)). The image enhancement of such micrographs has been reported in detail by Schmid and coworkers [9, 10]. This image shows the typical situation of crack growth by cavity formation and coalescence joining with the main crack, as has been postulated in the models of Riedel [14, 15] (Fig. 8(b)). The circle around the crack tip encloses the creep zone. Within the creep zone the pore density D has been measured [9, 10] parallel to the
3~
_2
0
800
900
1000
1100
T [°E.]
Fig. 7. Range of instabilities (the Portevin-Le Chatelier effect) as shown by the displacement rate as log 6 vs. temperature T.
349
lOOpm I-
(b)
-I
Fig. 8. (a) Enhanced scanning acoustic micrograph of the creep zone around the crack tip in WC- 1 lwt.%Co with the contours of a scanning electron micrograph of the same region according to Schmid and coworkers [9, 10] (T = 900 °C; 6 = 1 /am s t). The arrows show the pores. (b) Crack growth by cavity formation and coalescence joining with the main crack according to Riedel
[14[.
crack line at a distance of about 40 # m (Fig. 9(a)):
16000 o
D = --
S
12000
(4)
o
~
j~
where N~ is the number of pores (cavities) measured within the surface area S. The question arises of whether or not there exists a correlation between the pore density and the strain field. Therefore, we calculated the distribution of the equivalent strains g in arbitrary units according to Riedel [21] along the line indicated in Fig. 9(a):
iid
.n=2
E E 8000
~
o
°
~
4000
t3-
-300
~
....
~
}
300
(a) f
Disf.[
(5) where r is the distance to the crack tip. The theoretical equivalent strain distribution agrees well qualitatively with the experimentally determined pore density (Fig. 9(a)). The continuous increase in the pore density suggests a continuous nucleation of the grain boundary cavities, as suggested by Riedel [22]. Dyson [24] evaluated data on cavity densities and concluded that the number of cavities is related approximately to the creep strain. He proposed an empirical law for the description of the nucleation rate J*: ] * =-
(6)
where t~ is a constant. Our measurements confirm the empirical assumptions of Dyson [24] in that we can conclude that continuous nucleation and growth of
u 0~ u
Cr endwithout
-~
(b)
. . . . . . . . .
700
I
i
I
b
i
. . . . .
I
. . . . . . . . .
900
I
. . . . . . . . .
I
~
1100
T [°El
Fig. 9. (a) Density D of the creep pores (o) from the scanning acoustic micrograph (Fig. 8(a)) and the calculated equivalent strain field g ( ) according to Riedel [21] as a function of the position within the creep zone and the damage zone. The contours of the zones (black lines) were derived from a scanning electron micrograph from the same specimen shown by Schmid and coworkers [9, 10]. (b) Transition time to failure, as log(tft), w ' . temperature for WC11 wt.%Co, WC- 11 wt.%Co- 1.5wt.%Cr and WC- 11 wt.%Co1.65wt.%Ru.
350
grain boundary cavities caused the crack growth of the WC-Co hard metals tested. 5.2. The effect of ruthenium and chromium as additive INCO Europe developed ruthenium as a carbide additive for cutting tools that provide faster metal removal [25]. An extensive series of evaluation trials [25] on WC-Co hardmetals with the Ru additive (the X44 and non-ruthenium tips) has been carried out. The main result is "that ruthenium type inserts can continue cutting for 50%-100% longer than equivalent non-ruthenium tips, before critical amounts of wear are reached". Stellram described X44 as an "extraordinary grade of great tenacity and high resistance to heat". Successful experiences with other carbides and ruthenium have been performed by Jackson and Warren [26]. The aim of this study is to describe the observed qualitative experience by physical quantities in order to understand the limiting mechanisms. The understanding of these mechanisms should give rise to the production of better materials for cutting tools. A cutting tool is only useful if no creep deformation can take place. Creep deformation is, of course, a type of wear which limits the use of cutting tools. Therefore the transition time tft to failure describes the length of time during which creep deformation does not contribute to the wear. Thus, tft gives an estimate of the time at which "critical amounts of wear are reached". The transition times for WC-1 lwt.%Co and WC-1 lwt.%Co-l.5wt.%Cr are similar (Fig. 9(b)), but at a given temperature the WC- 11 wt.%Co- 1.65wt.%Ru remains linearly elastic three times longer. Within the scatter of the measurements, this fact agrees with the experience that "ruthenium-type inserts can continue 50%-100% longer than equivalent nonruthenium tips" [25]. In terms of materials science, we can conclude that the ruthenium addition makes the WC-Co hard metal more resistant to creep. Our microscopy investigations of the creep damage confirm the observations that creep is inhibited by the ruthenium additive. Creep pores were never observed in any specimens that were tested to shorter times than tfr At longer test times than tft, creep pore formation always takes place. The distribution of the creep pores (Fig. 9(a)) agrees well with the equivalent strain field distribution of elastic-viscoplastic materials (eqn.
(5)) according to Riedel [21]. This observation confirms our definition of tft (see Section 3). The slope of an Arrhenius plot of the transition time vs. 1/T gives the activation energy A Q for the controlling process [10]: tft = t 0
exp - ~
(7)
where to is a constant factor, k is the Boltzmann constant and T is the temperature. An activation energy AQ of 3.3 + 1 eV was determined for all three materials. Thus, we suggest that the same creep mechanism is responsible for the creep behaviour of all three materials. However, the ruthenium addition reduces the creep rate.
6. Conclusions
The behaviour of the three materials tested show the following similarities. ( 1 ) The microstructures of the three materials are the same. (2) We observed the same rupture mechanism up to 600 °C with about the same crack resistances. The WC grains build up a linear elastic skeleton. This skeleton provides the conditions for the ligament rupture mechanism. This mechanism is controlled by the plasticity of the cobalt phase. (3) If creep occurs, cavity formation and growth take place along the WC-WC and WC-Co grain boundaries within the cobalt phase. (4) The density of the pores is closely related to the creep strain field according to the theory of viscoplastic solids. (5) The creep crack growth is controlled by cavity formation joining the main crack. (6) The activation energies of the creep mechanism obtained by creep tests and by transition time measurements are the same for the three materials. (7) The development of large creep zones with large deformation can only take place if the skeleton is destroyed. (8) In bending tests the plastic deformability of the WC below 1000 °C is much less than the observed deformations. (9) Therefore only grain boundary sliding in WC-WC interfaces and/or decohesion can produce the large deformations observed. Grain
351
boundary sliding in several hard metals has been reported [3, 27]. In spite of all these similarities, the ruthenium addition significantly changes the high temperature behaviour. There is one possible reason for such a change. The ruthenium addition has reinforced the bonding of the WC-WC interfaces. The nature of the WC-WC interfaces in general and the type of interface which has been created by the ruthenium addition is in fact not yet well investigated. Probably the bonding of the WC-Co interfaces is also reinforced by the ruthenium addition. This could be the reason that the crack resistance of the material with the ruthenium addition is the highest of the three materials tested. Thus the nature and the mechanical behaviour of the interfaces in W C - C o composites should be investigated in the future. Acknowledgments We would like to thank Professor Ilschner for supporting the acquisition of the quantitative image analyser and our colleagues J. J. Ammann, Dr. Earthman, Dr. Eggeler, C. Mills, Professor H. O. K. Kirchner (Carnegie-Mellon University, Pittsburgh, PA, U.S.A.) and B. Senior for many hours of fruitful discussion and help with the experiments. This work was supported by Stellram, Nyon, Switzerland, and Commision pour l'Encouragement de la Recherche Scientifique Project 1304. Further support was given by Leitz Wetzlar, F.R.G. References 1 H. E. Exner, A. Walter and R. E Pabst, Mater. Sci. Eng., 16(19741231. 2 L. S. Sigl, H. E. Exner and H. E Fischmeister, in A. Almond, C. A. Brookes and R. Warren (eds.), Proc. 2nd Int. Conf on the Science of Hard Materials, Rhodes, September 23-28, 1984, in Inst. Phys. Conf. Ser., 75 (1986)631. 3 R. J. Gottschall, W. S. Williams and I. D. Ward, Philos. Mag. A, 41 (19801 1.
4 F. Osterstock, Phil. Thesis, Universitd de Caen, 1980. 5 H. G. Schmid, 18 Arbeitskreis Bruchvorgiinge, Deutscher Verband ffir MaterialpriJfung, Berlin, 1986, p. 71. 6 J. Hong and J. Gurland, in R. K. Viswandham, D. J. Rowcliffe and J. Gurland (eds.), Science of Hard Materials, Plenum, New York, 1980, p. 649. 7 V. D. Kristic and M. Komac, Philos. Mag. A, 51 (19851 192. 8 G. Fantozzi, H. Si Mohand and G. Orange, in A. Almond, C. A. Brookes and R. Warren (eds.), Proc. 2nd Int. Conf. on the Science of Hard Materials, Rhodes, September 23-28, 1984, in Inst. Phys. Conf. Ser., 75 (1986) 699. 9 H. G. Schmid, D. Marl, W. Benoit and C. Bonjour, in B. Wilshire and R. W. Evans (eds.), Proc. 3rd Int. Conf. on Creep and Fracture of Engineering Materials and Structares, Swansea, Vol. 3, Institute of Metals, London, 1987, p. 975. 10 H.G. Schmid, Mater. Forum, •0(3)(1987) 184. 11 B. Johannesson and R. Warren, in A. Almond, C. A. Brookes and R. Warren (eds.), Proc. 2nd lnt. Conf. on Science of Hard Materials', Rhodes, September 23-28, 1984, in Inst. Phys. Conf. Ser., 75(1986) 713. 12 A. Bornhauser, K. Kromp and R. F. Pabst, J. Mater. Sci., 20(1985) 2586. 13 J. R. Rice, P. C. Paris and G. Merkle, Progress in Flow Growth and Fracture Toughness Testing, ASTM Spec. Tech. Publ. 536, 1973, p. 241. 14 H. Riedel, Advanced Semin. on Fracture Mechanics, l~pra, 1981. 15 H. Riedel, Arbeitskreis Bruchvorgiinge, Deutscher Verband ffir Materialprfifung, Berlin, 1980, p. 165. 16 A. F. C. Cocks and M. E Ashby, Prog. Mater. Sci., 27 (1982) 189. 17 M. E Ashby and B. Tomkins, in K. J. Miller and R. F. Smith (eds.), Proc. 3rd Int. Conf. on the Mechanical Behaviour of Materials, Cambridge, C~lmbridgeshire, August 20-24, 1979, Vol. 1, Pergamon, Oxford, 1979, p. 47. 18 L. P. Kubin, K. Chihab and Y. Estrin, in D. Walgraef (ed.), Patterns, Defects and Microstructure in Nonequilibrium Systems, Nijhoff, Dordrecht, 1987, p. 22(/. 19 V. Jayaram, Acta Metall., 35 (1987) 1307. 20 R. Greenwood, M. H. Loretto and R. E. Smallman, Acta Metall., 30(1982) 1193. 21 H. Riedel, Z. Metallkd., 69(1978) 755. 22 H. Riedel, Z. Metallkd., 76(19851669. 23 C.Y. Hui, H. Riedel, Int. J. Fract., 17 ( 1981 ) 4(19. 24 B. F. Dyson, Met. Sci., 10(19761 349. 25 K. Brookes, Metalwork. Prod., 7(1979177. 26 J. S. Jackson and R. Warren, Powder Metall. Int., 17 (34) (1988) 255. 27 R. Arndt, Z. Metallkd., 63 ( 19721274.
