Materials Science and Engineering, 59 (1983) 115-126
115
Cold Deformation of a Nickel-base Superalloy CLAIRE Y. BARLOW and BRIAN RALPH
Department of Metallurgy and Materials Science, University of Cambridge, Cambridge CB2 3QZ (Gt. Britain) (Received July 29, 1982; in revised form October 25, 1982)
SUMMARY
A n analysis o f the low deformation level (less than 5% strain) characteristics o f polycrystalline samples of an engineering alloy is presented. The material used was a wrought nickel-base superalloy, Nimonic 80A, the microstructure o f which had been modified in a controlled way to give a related series of phase distributions. This allowed the roles of the various microstructural constituents to be assessed. Selected mechanical property data were correlated with the d e f o r m a t i o n microstructures, as determined by transmission electron microscopy. The presence of carbide particles on the grain boundaries was f o u n d to affect both the observed deformation patterns and the work-hardening rate. However, although the majority o f the dislocation nucleation events occurred at the grain boundaries, the stress-strain characteristics were more sensitive to intragranular than to intergranular microstructures.
1. INTRODUCTION
The microstructures of nickel-base superalloys are primarily designed to confer creep resistance and high temperature stability. However, the ability of the alloys to withstand cold deformation is also of relevance, e.g. in relation to their fabrication and to some service applications. Microstructural studies of crept material have led to a reasonably good understanding of the relative roles of the constituent components of the microstructure in the creep deformation regime (e.g. in Nimonic 80A [1-3]). For cold deformation of superalloys the situation is less well understood. In particular, there has been little indication in the literature of the influence of the grain boundary region microstructure on 0025-5416/83/0000-0000/$03.00
mechanical properties and deformation substructures. The alloy selected for this study is Nimonic 80A, which is an early wrought nickel-base superalloy exhibiting most of the microstructural features of the later (more complex) alloys in the series (see for example refs. 4 and 5). The material as heat treated for service contains precipitated phases on intergranular and intragranular sites, and the matrix is solid solution strengthened. The grain boundaries are heavily decorated with carbide particles, Mz3C6 or M7C3, in the size range 0.1-1 pm, depending on the precipitation aging condition chosen. There are also some larger (1-5 pm) carbide (M7C3) and carbonitride (M(C, N)) particles dispersed through the material, which appear at both intergranular and intragranular sites. The matrix contains a fine dispersion (0.15 volume fraction of particles with diameter ranging in this study from 15 to 50 nm) of a coherent intermetaUic phase 7' (Ni3(A1, Ti)). The cold deformation characteristics of the nickel-base superalloys are generally considered to be dominated by the 7' distribution (see for example ref. 6). Several studies have been made which have served to characterize the effect of 7' on yield stress and workhardening parameters (see for example refs. 7-9). The magnitude of the matrix solidsolution-strengthening effect, which is influenced by the partitioning of elements between 7 and 7', is also documented (e.g. in ref. 6). The effect of grain boundary carbide particles on low temperature mechanical behaviour has been the subject of some controversy [10, 11], but opinion is generally that the influence of these particles is small. There is, however, evidence that the particles may be responsible for the formation of grain boundary cracks (which are revealed as cavities on annealing) during cold deformation © Elsevier Sequoia/Printed in The Netherlands
116 (e.g. as discussed in refs. 12-15). The intra-
granular M7C 3 or M(C, N) particles are difficult to eliminate, so their effect on properties has not been quantified. However, on account of their low volume fraction, rounded shape and uniform distribution in wrought alloys they are thought to have little direct influence on mechanical properties [3, 6]. The microstructural modifications performed in this study were directed towards elucidating the effect of the grain boundary carbide particles on cold deformation microstructures and mechanical properties and involved changing the distributions of both the 7' and the boundary carbide particles. It was not possible to do this entirely independently for each phase, as precipitation of both phases occurs in the same temperature range, b u t nevertheless consistent modifications were achieved to the intergranular and intragranular phase distributions. The study concentrated on the low strain characteristics of the material, where the deformation microstructural features were well defined and discrete. As deformation increased, the features became increasingly indistinct and obscured by dislocation debris, so microstructural observations were less satisfactory. No new features were introduced into the deformation structures when the strain levels were increased to about 20%, so the observations made will still have relevance to this deformation regime. 2. EXPERIMENTAL DETAILS Two slightly different alloys were used: the commercial alloy Nimonic 80A, and a reduced carbon version of the same material. The compositions are given in Table 1. The microstructures were produced by the routes shown in Table 2, and schematic microstructures are also given. The grain size of materials A, B and C was 25 pm, and that of material D was 35 #m.
Bar specimens of the material were deformed in uniaxial tension. Detailed microstructural work was performed on material A deformed to strains of between 0.8% and 2.5%. The deformed microstructures were examined principally by high voltage electron microscopy (HVEM), using an Associated Electrical Industries EM7 instrument operating at 1 MV. Conventional transmission electron microscopy (CTEM) was also employed, with a Japan Electron Optics Laboratories t y p e JEM 200A instrument operating at 200 kV. The advantages of HVEM have been outlined elsewhere [16], and CTEM was used where higher resolution was required. The material for electron microscopy was prepared from transverse sections of the bar specimens. These were electropolished to perforation using standard techniques.
3. MICROSTRUCTURAL OBSERVATIONS 3.1. General observations and intragranular deformation
The observations presented in this section are mostly of material A, deformed to strains of up to 2.5%. Deformed samples of all the alloy states A - D have been examined, but the deformation microstructures were qualitatively similar. As quantitative methods of characterizing the microstructures could not readily be used [16], the observations from material A alone may be used to illustrate the features of interest. The principal features of the deformed microstructure are seen in Fig. 1. The matrix contains linear dislocation arrays, slip bands, which are often manifest b y changes in contrast across the bands. The constituent dislocations are not resolved in this figure. The spatial distribution o f the bands is very inhomogeneous and varies b o t h between different grains and between different regions o f each grain. The latter effect is particularly marked in grain A, in which the
TABLE 1 Alloy composition Alloy
C (wt.%)
Cr (wt.%)
Ti (wt.%)
At (wt.%)
Other elements (wt.%)
Commercial N i m o n i c 8 0 A
0.06
19.5
2.5
1.3
~ 4.5; balance Ni
Low carbon alloy
0.006
19.5
2.6
1.5
~ 4.5; balance Ni
117 TABLE 2 The microstructures of the alloys used Description of microstruc ture
Structure
Commercial alloy: small boundary carbide particles; small ~"
A
Carbide-free grain boundaries; very fine 7'
B
Large boundary carbide particles; bimodal 7' distribution
C
Well-separated boundary carbide particles; bimodal 7' distribution
D
Schematic diagram of grain boundary region
Method of generation Schematic diagram of in tragranular region ~" distribution
lpm
0.1pm i, B
•
•
B
•
_-
:
Fig. 1. HVEM micrograph of material A (2% strain). Three slip systems (labelled 1-3) are indicated in grain A, and the number density of slip bands is increased close to the grain boundary. n u m b e r d e n s i t y o f slip b a n d s is seen t o increase t o w a r d s t h e grain b o u n d a r y . F u r t h e r , it m a y b e o b s e r v e d t h a t t h e r e are t h r e e slip s y s t e m s o p e r a t i n g close t o t h e grain b o u n d a r y in grain A ( r e p r e s e n t a t i v e b a n d s are labelled 1-3). The system designated 3 operates only in a localized r e g i o n close t o t h e grain triple j u n c t i o n (grain edge), a n d s y s t e m 2 also
•
.
•
o ...
°
".,
. "o
..
•
.
Two-stage heat treatment on commercial alloy: 2 h at 1050 °C, air cooled + 24 h at 700 °C, air cooled Recrystallization of two-stage heat-treated commercial alloy: 2 h at 1050 °C, air cooled + 16 h at 700 °C, air cooled, 10%e + 23 rain at 972 °C, air cooled Three-stage heat treatment on commercial alloy: 2 h at 1050 °C, air cooled + 24h at 850 °C, air cooled + 16 h at 700 °C, air cooled Reduced carbon alloy, modified three-stage heat treatment: 2 h at 1050 °C, air cooled + 2 h at 850 °C, air cooled + 16 h at 700 °C, air cooled
Fig. 2. HVEM micrograph of material A (0.8% strain). Two principal slip bands (labelled A and B) are seen, and there are also paired dislocations between the slip bands. The grain boundary is decorated with M23C6 carbide particles (in dark contrast).
d e c r e a s e s in p r o m i n e n c e a w a y f r o m this area. In general, t h e grain b o u n d a r i e s (and grain edges in p a r t i c u l a r ) w e r e a s s o c i a t e d w i t h regions o f m u l t i p l e slip, even w h e n t h e grain c e n t r e s d e f o r m e d b y single slip only. In t h i n n e r regions o f m a t e r i a l (as s h o w n , f o r e x a m p l e , in Fig. 2) t h e slip b a n d s c o u l d
118
be resolved as linear dislocation arrays or pile-ups. Two principal slip bands are visible in this region (labelled A and B), and both terminate at a grain boundary (however, see Section 3.4.1). The dislocation density is seen to be significantly higher in A than in B, and there is a marked change in matrix contrast across band A. In neither band are the dislocations paired, although the randomly distributed dislocations outside the slip bands are seen to be in pairs separated by no more than 10 nm. An explanation for this observation is suggested in Fig. 3, in which 7' particles are seen to have been completely sheared b y dislocations travelling on a set of parallel slip bands (indicated by arrows). The requirement for pairing derives from the superlattice structure of the 7' phase; this structure is such that a single perfect matrix dislocation passing through a ~/' particle leaves behind it an antiphase domain boundary, which is removed b y the passage of a second dislocation (see for example refs. 17 and 18). The presence of matrix dislocation pairs thus indicates that dislocations are cutting through rather than bowing round the particles. The dislocations seen in the matrix tended to be " w a v y " rather than straight, so that t h e y lay between 7' particles rather than within t h e m (e.g. Figs. 2 and 4) but there was no evidence of dislocation bowing (which would leave dislocation loops around the particles) even in the large ~/' samples. However, when the particles intersected by the slip bands are
Fig. 3. CTEM micrograph of material C (1% strain), showing the shearing of ~/' particles as a result of repeated dislocation passage along a set of slip bands (indicated by arrows).
Fig. 4. HVEM micrograph of material A (1% strain), showing the increased dislocation activity around an intragranular MTC3 particle. completely sheared, the requirement for pairing is lost. The dislocations in the slip bands in Fig. 3 would therefore be expected to appear as in Fig. 2, as arrays of single dislocations. The random dislocations have not been associated with sufficient deformation to shear the 7' particles completely and must still be paired.
3.2. Intragranular carbide particles Increased dislocation activity was normally found around intragranular carbide particles, as in Fig. 4. In this example, m u c h of the structure is localized, so that a random dislocation array is seen surrounding the particle. Slip bands extending across the grain were also initiated on occasion. Occasionally the carbide particles were found to be cracked, and the cracks were associated with very intense transgranular slip bands (see Fig. 8). 3.3. Slip band interactions at grain boundaries The regions of increased dislocation activity normally associated with grain boundaries have been mentioned with reference to Fig. 1. Such activity is accompanied b y matrix rotation [19], and the cumulative effect m a y be monitored by observing the arcing of diffraction spots, as in Fig. 5. It can be seen that arcing is much more pronounced when the selected diffracting region is close to the grain boundary than for material approximating to the grain centre. This example is from heavily deformed material, but the effect was still general at lower deformation levels.
119
Fig. 5. CTEM micrograph of material A (20% strain). The diffraction patterns from the grain boundary region 1 and the regions 2 and 3 approximating to grain interiors (the selected area aperture positions are indicated) are also shown.
Figure 6 shows grain boundaries with a single slip band from each grain impinging on the grain boundary. In Fig. 6(a) the bands are slightly displaced, while in Fig. 6(b) t h e y are apparently coincident. In b o t h examples the number density of slip bands was low, so the probability that two incoming bands intersect the b o u n d a r y in such close proximity is very small. It thus seems likely that at least one band in each example nucleated at the b o u n d a r y and that the two slip events are therefore not independent. This could be achieved if one incoming dislocation array causes the sympathetic nucleation of another array close to the intersection point or alternatively if t w o (necessarily dependent) nucleation events produce dislocations in opposite grains. Direct evidence for association between the slip bands is seen in Fig. 6(a) as an array
of extrinsic dislocations (indicated b y E) lying between the intersection points. Figure 7 shows a grain boundary with two intersection points, A and B, at which respectively three and four slip bands meet. There is some local misorientation contrast at b o t h A and B, b u t it is more pronounced at A. Figure 8 shows an intense slip band (nucleated at a cracked intragranular carbide particle) which is blocked b y a large grain boundary carbide particle (at C). The region in dark contrast close to the grain b o u n d a r y is indicative of matrix rotation. The original band has been halted before reaching the grain boundary, and a resultant secondary band nucleated normal to the original band. The changes in matrix contrast as a result of rotation at the heads of slip bands at grain boundaries can be used (in the absence of
120
Fig. 7. HVEM micrograph o f material A (2% strain), showing multiple slip band interaction at a grain boundary. Three bands (indicated b y arrows) intersect at point A and four (indicated by arrows) at point B.
Fig. 6. Interactions of single slip bands at grain boundaries: (a) CTEM micrograph of material B (1% strain) (two matrix dislocation pile-ups A and B are shown, with associated extrinsic boundary dislocations E; the segment S may have acted as a matrix dislocation source); (b) HVEM micrograph o f material A (0.8% strain) (the slip band (indicated by white arrowheads) is crossing a grain boundary in thicker material).
recovery) to indicate the variations in strain. The specimen was tilted in dark field using the methods o f Humphries [19], and a "cont o u r m a p " was plotted (Fig. 9). The slip band traces are also indicated. It may be seen that the rotation was particularly severe when slip bands intersected the boundary at large carbide particles.
3.4. Discussion o f microstructural observations 3.4.1. Intragranular deformation The slip band at A in Fig. 2 and those in Fig. 6(a) are imaged as dislocation pile-ups,
Fig. 8. HVEM micrograph of material A (2% strain), showing the blocking of an intense matrix slip band (in light contrast) at a boundary carbide particle C which leads to nucleation o f a secondary band at a low angle to the grain boundary.
and in each case the dislocation spacing is seen to decrease on approach to the grain boundary. They thus appear as examples of a dislocation array which has been halted at a barrier (see for example ref. 20), leading to a stress concentration at the grain bound° ary. However, it is proposed here that in materials with high glide stresses an indistinguishable dislocation array could be produced b y t h e operation o f a source on the grain boundary, sending dislocations o u t into the matrix. As discussed in Section 3.4.2 and in the literature (e.g. in ref. 15) it is indeed anticipated that most dislocations will
121
/
/i Ipm Fig. 9. C o n t o u r p l o t o f m i s o r i e n t a t i o n lobes at p o i n t s o f i m p i n g e m e n t o f slip b a n d s at a grain b o u n d a r y in m a t e r i a l A ( C T E M ; 2% s t r a i n ) : - - - , m i s o r i e n t a t i o n o f 1°; - - . --, m i s o r i e n t a t i o n o f 2°; . . . . . . , misorient a t i o n o f 3 °.
be nucleated at grain boundaries. An excess stress must be placed on the source to cause its operation, and this stress must also be sufficient to cause the nucleated dislocations to glide off. The stress on the leading dislocation in the array is supplied b y the following dislocations, and the leading dislocation will come to rest at a point such that this supplied stress is equal to the glide stress. As the dislocations also exert a back stress on the following dislocations, the stress supplied b y the source for the glide of the dislocations close to the source will be higher than the stress experienced b y the leading dislocation. This will be associated with smaller dislocation spacings near to the source than more distant from it, producing a situation spatially analogous with a dislocation pile-up. It is therefore not possible to discern from observations o f dislocation spacings alone whether a given slip band was nucleated at, or terminated b y interaction with, an obstacle. In some cases, other pointers may indicate the direction of movement o f the dislocations in an array. If, for example, the tendency to
dislocation pairing increases away from the obstacle, the indication is that the ~/' intersected b y the slip band has been completely cut close to the obstacle, b u t not at a distance. The a m o u n t of dislocation movement has thus been greatest close to the obstacle, implying that the slip band nucleated there. Reference to Fig. 6(a) allows the sense of the slip bands to be determined using this criterion. In band B the dislocations are paired close to t h e boundary, implying that the dislocations are incident on the b o u n d a r y and were not nucleated there. The dislocations in band A are not paired and hence probably nucleated at the boundary, using the dislocation segment S as a source. It is also frequently observed that bands terminate (normally with an increased dislocation spacing) in the matrix, in the absence of any obvious obstruction. In these cases the source may be found at the other end of the band.
3.4.2. Slip bands and grain boundaries The dual role of grain boundaries as sources of dislocations as well as obstacles to slip leads to rather complex deformation microstructures. The t w o activities are complementary, and it is often not possible to state categorically whether dislocation nucleation or absorption has occurred in a specific example. This, however, does not materially affect the interpretations given below. In the discussion of slip band interactions at grain boundaries, it is assumed that in each instance one slip band in the event was incident on the boundary, and the others were subsequently nucleated at or close to the intersection point. It thus follows that the secondary slip bands arose to a c c o m m o d a t e the strain introduced b y the initial band. Most of the following discussion is in terms of slip bands rather than in terms o f individual dislocations. This is because the dislocations constituting the slip bands were often not readily imaged. However, as demonstrated b y bands A and B in Fig. 2, slip bands may contain very different number densities of dislocations. The conclusions drawn from these studies must therefore be qualitative rather than quantitative. The plastic deformation of a polycrystalline aggregate leads to compatibility stresses between adjacent grains, and these will give rise to arrays of dislocations termed geo-
122
metrically necessary (as opposed to statistically stored [21]). It m a y thus be expected that stresses will be higher at grain boundaries than within the grains, and where three grains intersect at a grain edge the situation will be exacerbated. The presence of regions of increased slip band number density close to grain boundaries {as in Fig. 1) is thus in accordance with the expected compatibility stresses and may be used as evidence for dislocation nucleation in the vicinity of grain boundaries. Additional evidence for dislocation nucleation at boundaries derives from t h e multiple slip band interactions discussed. However, the dislocation debris near the boundaries leads to loss of resolution, so that it has not usually been possible to identify the exact position o f the source (with the possible exception of that in Fig. 6(a)). The indication in every case was that the sources lay on the grain boundaries rather than in the matrix close by, and this would be a logical conclusion for two reasons. First, the compatibility stresses would be expected to be greatest at the grain boundaries. Second, the boundaries contain a number of possible sites for sources, such as ledges or particles. No direct microstructural evidence has been found for the location of sources on grain boundary carbide particles, although intragranular carbides do act as dislocation sources. When a slip band is incident on a grain boundary, dislocations may be absorbed into the boundary. The interaction of matrix dislocations with grain boundaries is complex, is only partly understood and relates to the grain boundary structure (see for example refs. 22 and 23). A matrix dislocation running into a boundary is accommodated and forms one or more extrinsic dislocations [24]. These c o m p o n e n t dislocations will in general only be mobile under a combination of climb and glide, as the dislocation glide plane is not contained within the boundary plane. However, the diffusion distances required for climb in the boundary are very much shorter than those in the matrix, so dislocations are mobile at comparatively low temperatures. The indication of this study (both from the direct observation of Fig. 6(a) and from the analysis below) is indeed that there is dislocation mobility (giving grain boundary sliding) at r o o m temperature in these alloys,
i.e. at about 0.2TM (where TM is the melting point). Thus when a matrix dislocation pileup enters a grain boundary it can produce arrays of boundary dislocations. Unless these can be annihilated or incorporated into the boundary structure, a back stress will clearly build up, preventing the absorption of further matrix dislocations. The situation may be alleviated by the production of matrix dislocations, in either grain, as a secondary slip event. Models involving the movement of extrinsic dislocations to explain strain transference across grain boundaries in general cases have been proposed [22, 25]. However, the above analysis indicates that such an approach is also applicable in instances where only one grain shows dislocation activity. Where adjacent deforming grains have available slip systems which are nearly parallel, it is possible for a single secondary slip band to accommodate most of the strain introduced b y the primary incident band. This gives a slip band which is almost continuous across the boundary, as discussed in early studies of polished sections (e.g. the study reported in ref. 26). However, when a dislocation model is used, it is clear that any deviations must be allowed for by the introduction of extrinsic dislocations into the grain boundary, so that a Burgers vector analysis of the total dislocation interaction may be satisfied. It is proposed that the events in Fig. 6 illustrate such fully accommodated slip transfer interactions. These simple twoband interactions are expected to become less c o m m o n at higher strains, as there will be a build-up o f extrinsic dislocations in the boundary. This will hinder the accommodation of further dislocations, so an alternative reaction (e.g. the production of another matrix slip band) may eventually occur. Multiple slip band interactions are then readily explained on a similar basis. An incident slip band cannot be accommodated by shear on a single nucleated band, so more than one matrix band must be formed. A comparison of events A and B in Fig. 7 supports the argument: the matrix misorientation is greater where three bands rather than four intersect and, further, the dark lobe is more prominent in the grain where the second band is missing. It thus seems reasonable that event A is less fully a c c o m m o d a t e d by plastic strain than is event B.
123
Figures 8 and 9 indicate that strain accommodation is hindered b y the presence of carbide particles. The presence of more prominent misorientation lobes around the heads of slip bands intersecting b o u n d a r y carbide particles than those intersecting "clean" grain boundaries (Fig. 9) indicates that the strain is greater at carbide particles, so that the particles act as stress concentration points. Figure 8 is an example of the relief of such a stress, b y the nucleation of a secondary slip band near the carbide particle. Processes of this nature have been shown in this study to be c o m m o n at grain boundaries, and here the sources seem to lie actually on the grain boundaries. By contrast, in the example in Fig. 9 the source may lie in the matrix a short distance from the particle. The presence of carbide particles on grain boundaries has thus been shown to affect the deformation microstructure in the material and would be expected to influence the mechanical property data. The effect of the particles on the microstructure of deformation may be summarized as follows. (a) The particles constitute regions of boundary plane in which strain transfer between grains is not directly possible (unless particle shearing or cracking occurs). (b) The particles distort the boundary plane. It has been shown that such convolutions (whether or not they are associated with precipitation) may be expected to hinder the movement o f extrinsic dislocations, limiting the length of boundary in which extrinsic pile-ups may develop [27]. The situation may be exacerbated if, as has been postulated in other systems [28], the dislocation mobility in the interface between a refractory particle and the matrix is lower than that in the grain b o u n d a r y itself. The cumulative effect of these factors will be to make the a c c o m m o d a t i o n of matrix slip bands impinging on the grain boundary more difficult in the vicinity of grain boundary precipitates. This leads to stress concentrations around the precipitates, which will be greatest at the particle-grain boundary intersection. Stress relief is likely to occur b y the nucleation of further matrix slip bands from these regions. The production of slip bands from b o u n d a r y plane convolutions has been found in another nickel-base superalloy [29]. However, where (as in this study) the
convolutions are associated with refractory particles, there may still be residual stresses, which could be relieved b y cracking of the particle-grain b o u n d a r y interface. (c) Any differences in elastic modulus between the particle and matrix will lead to stress inhomogeneities around the particles. These may again be relieved b y slip band formation. The net result of these various effects on the mechanical properties of alloys containing grain boundary particles is therefore that they may be expected to be harder than equivalent particle-free alloys. 4. MECHANICAL PROPERTIES: RESULTS AND DISCUSSION
Two parameters were chosen to illustrate the effect of microstructural modification on mechanical properties: the "flow stress", or stress at which dislocation movement became general; the work-hardening rate at a series of strains. Both sets of values were obtained directly from the load-extension chart o u t p u t from the tests, and the flow stress values were estimated to be in the middle of the elasticplastic transition region. It should be noted that the work-hardening rate values are distorted b y the relaxation of the testing machine and so are lower than the true values expected. The data are presented in Table 3. Between three and seven tests were run for each parameter, and the uncertainties from this scatter are quoted. The slightly different grain size of material D has been ignored in the subsequent analysis; it would be expected to cause a small relative reduction in b o t h flow stress and work-hardening rate. 4.1. F l o w stress
The different microstructures gave a range of values of flow stress. The highest value was TABLE 3 Yield points and work-hardening rates at various strains Material Yield point (MPa)
0.5%e
2.5%e
5%e
A B C D
5.15-+0.08 3.12-+0.06 5.94+0.6 5.89-+0.7
3.28-+0.03 3.11-+0.08 2.82-+0.03 2.88+0.26
2.29+0.1 2.09-+0.03 2.92-+0.03 1.87-+0.03
820-+5 600-+5 760-+5 740+5
Work-hardening rates (MPa)
124 obtained from the microstructure designed for o p t i m u m high temperature properties, material A, and the lowest from material B, which is not precipitation hardened. The flow stress data are expected to reflect the ease o f formation or operation of dislocation sources. As discussed above, the sources lie primarily on the grain boundaries. The analysis is complicated by the presence of ordered regions in the matrix. These are in the form o f 7' particles (materials A, C and D) or less well-defined particles of short-range order (material B). Dislocations must travel through these regions in pairs, and it may thus be necessary to nucleate dislocations in pairs. Models for the formation of "superlattice" dislocation sources have been proposed (e.g. as in ref. 30), but these still require the prior operation of single dislocation sources. There are therefore several stages to be considered in the production of general slip, and these are (a) the nucleation of single dislocation sources and (b) the operation of single dislocation sources. There is then the possibility of two further processes: (c) the nucleation of superlattice dislocation sources and (d) the operation of superlattice dislocation sources. It is expected that the ease of stage (a) will vary with boundary structure. In the event that stage (a) is the factor controlling the yielding behaviour, materials with the same intragranular structure but with different intergranular structures should exhibit different yield values. Such a pair of materials is provided by C and D, with very different area fractions o f carbide particles on the grain boundaries. Whether or not the carbide particles are directly associated with dislocation nucleation, their presence on the grain boundary must affect dislocation nucleation, both by producing convolutions in the boundary plane and by limiting the length of clean boundary available for dislocation accommodation reactions (as discussed in Section 3.4.2). However, the flow stresses are comparable in C and D, indicating that source generation is not the controlling factor in yield behaviour. Stage (b) will be sensitive to the resistance of the material offered to the movement of single dislocations and will thus be dependent on the 7' dispersion. In the early stages o f deformation the stress will depend on the a m o u n t of new 7-~/' interface produced by
the passage of a single dislocation through the 7' particle arrays. This may be calculated and is found to be only 2% greater for the 7' dispersions in materials C and D than for that in material A. A value cannot be compared for material B, as the degree of short-range ordering is unknown. On the basis of this hardening factor [ 31] the differences between the materials should be slight. There is a second hardening factor, in that the 7' strain fields m a y contribute to the impedance to dislocation movement [ 32 ]. Where this factor is dominant, material A (with all the ~/' in a fine dispersion) will present more hindrance to dislocation movement than will C or D. Again material B cannot be compared, as the magnitudes of the strain fields around the regions of short-range order have not been measured. However, it is anticipated that the fields would be comparatively weak, in accordance with data on other precipitationhardening systems (e.g. the results given in refs. 7 and 33). The experimentally determined values correlate well with this analysis, so that the operation o f single dislocation sources m a y be postulated to decrease in difficulty from material A through materials C and D to material B. It may now be suggested that, even in the early stages o f deformation, there is no justification for superlattice dislocation sources in these materials. The need for such sources is determined by the extent of mobility of single dislocations in the material and is hence again related to the a m o u n t of antiphase domain boundary produced. As this is comparable in materials A, C and D, and yet the flow stresses are dissimilar, it appears that the formation of superlattice sources is not a controlling factor in yielding. Because this implies that a degree o f single dislocation movement is permissible, it seems unlikely that the requirement for superlattice sources is stringent.
4.2. Work-hardening rate At the 0.5% strain level, the work-hardening rate for material B is considerably lower than for the precipitation-hardened materials, and perhaps slightly greater for material with a large ~/' size (materials C and D) than for material with a small ~,' size. At higher strains the values are m u c h more similar. It is notable that, with the possible exception of materials
125
B and C, the work-hardening rate drops steadily with strain. In a single-phase polycrystal the workhardening rate will be sensitive to the ease of operation of dislocation sources and to dislocation interactions. Where sources are apparently not difficult to produce, as in the materials studied, dislocation interactions will probably provide most of the contribution to the work-hardening rate. In the materials studied, however, the dislocations are confined to well
(1) The yield stress and initial work-hardening rate are determined mainly b y the 7' distribution.
(2) Deformation is more intense and complex close to grain boundaries, and most dislocation nucleation occurs at the grain boundaries. (3) Dislocation a c c o m m o d a t i o n at grain boundaries is hindered b y the presence of boundary carbide particles, and the workhardening rate at higher strains is influenced b y this. (4) Strain transfer across grain boundaries b y the sympathetic nucleation of slip bands requires sections of carbide-free interface, and some grain boundary sliding will occur during room temperature deformation. (5) Dislocation nucleation and accommodation reaction are complementary and may be indistinguishable both microstructurally and analytically.
ACKNOWLEDGMENTS
The authors are grateful to Professor R. W. K. H o n e y c o m b e for the provision of laboratory facilities. Financial support from the National Physical Laboratory and the Science and Engineering Research Council is acknowledged, and from the Worshipful Company o f Goldsmiths for the provision of a Research Fellowship (C.Y.B.).
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