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PROPRIÉTÉS MÉCANIQUES DES JOINTS DE GRAINS.MECHANICAL PROPERTIES OF GRAIN
BOUNDARIES
D. Mc Lean
To cite this version:
D. Mc Lean. PROPRIÉTÉS MÉCANIQUES DES JOINTS DE GRAINS.MECHANICAL PROPER- TIES OF GRAIN BOUNDARIES. Journal de Physique Colloques, 1975, 36 (C4), pp.C4-273-C4-280.
�10.1051/jphyscol:1975426�. �jpa-00216332�
PROPRIETES MECANIQUES DES JOINTS DE GRAINS.
MECHANICAL PROPERTIES OF GRAIN BOUNDARIES
D. Mc LEAN
National Physical Laboratory, Teddington, UK-
RCsumC. - Beaucoup des preuves expCrimentales indiquent que plusieurs des mCtaux trbs usitCs n'ont qu'une petite marge de sCcuritC en ce qui concerne la fragilitC intergranulaire.
L'abaissement de la cohCsion intergranulaire normale par
-
113 me est souvent dangereux. On explique la thCorie de cet Ctat plut6t critique, et on indique la mCthode d'kvaluer I'ordre de puretC dont il faut pour Cviter une telle accumulation des atomes Ctrangers aux joints des grains qu'il en rCsulte la fragilitk. En outre, on discute bribvement le glissement aux joints et la dkformation plastique des polycristaux.Abstract. - Much experimental evidence shows that many common metals have only a small margin of safety against brittle behaviour by intergranular fracture. A reduction of the normal intergranular cohesion by approximately one third is often dangerous. This fairly critical situation is explained, and the method is'given of estimating the degree of purity which will prevent the accumulation of foreign elements at grain boundaries that can cause the brittleness.
Sliding at grain boundaries and plastic deformation of polycrystals are also briefly discussed.
1 . Introduction. - There are five ways in which grain boundaries influence the mechanical proper- ties of metals : A They are obstacles t o slip, and thus enhance resistance t o deformation and may weaken resistance t o fracture. B They may be surfaces of weak cohesion. C At elevated tempera- ture they are surfaces of intense shear, a feature which affects creep properties and slightly increa- ses internal damping. D They are channels for fast diffusion and E Act a s sources and sinks f o r vacancies. Both the properties D and E are significant f o r mechanical behaviour a t high tempe- rature, but except for pure metals the experimental information available is meagre and they are not discussed here. This paper therefore discusses A , B and C.
2. Deformation (A).
-
Perhaps the one point concerned with deformation per s e that is worth remarking on, because although it is an unfashiona- ble topic it is a fundamental one, is the difference between the engineers' criterion for flow and the physical metallurgists' criterion. While in pure tension applied t o a polycrystal both groups use the applied tensile stress a s the criterion, in multi-axial stress a more general criterion is needed. Physical metallurgists know that, in principle, the Taylor shear stress T~ is the nearly correct criterion (or indeed a more stringent condition [I]), but engi- neers customarily employ the von Mises stress, also known a s the octahedral shear stress T,,,, and d o not appear t o err badly. What then is the relation between TT and T,,, ?There are some stress systems for which TT as well a s T,,~ has been calculated and the relative
values for a fcc metal are, taking the maximum principal stress a s unity :
pure tension, tension, pure shear plane stress plane strain
T,~, is thus always appreciably larger than T ~ , but the ratio TT/TOct does not vary much.
Both facts are understandable. TO,, is essentially the rms of the three maximum shear stresses irrespective of the planes and directions in which they occur. T~ on the other hand, is the shear stress on certain defined planes, namely the slip planes, in certain defined directions, namely the slip direc- tions, and can therefore scarcely b e a s large a s 70,~.
TO,, is also the shear stress acting on the planes
which are octahedral with respect t o the principal stress axes ; acting on three of these planes, it produces a certain change of shape of the metal specimen. TT is the stress which, acting on five crystal slip systems (or eight [l]), produces the same change of shape. The definitions are s o
similar that the small change in the ratio ~ ~is / 7 ~ ~ ~
not surprising.
Plastic anisotropy is ignored in the concept of T,,,
and neglected in calculations of TT. Since practical metals often have a considerable degree of plastic anisotropy, the error in using either TT o r T,,~ can therefore be appreciable and is probably a t least as large a s the error made when they are assumed t o be proportional t o each other.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1975426
C4-274 D. Mc LEAN
3. Initiation of grain boundary decohesion (A and B).
-
Intergranular embrittlement has been reco- gnised since the polycrystal structure of practical metals began to be appreciated, and has probably been a recurrent trouble, not understood, since metals were first used. A few examples are worth giving : An early recognition was made in 1886 by Bessemer [2], describing severe intergranular embrittlement in iron. For a long time it has been known that bismuth causes intergranular embrittle- ment in gold and copper and drastically impairs the ductility and breaking strength, e. g. from 50 9% to 8 % and from 1 200 to 120 N/mm2 respectively in the case of copper3. Molybdenum is s o badly embrittled along the grain boundaries by oxygen that in poorly deoxidised cast molybdenum the individual crystals can be separated from each other, although each separate crystal is then found to be fully ductile [4]. Perhaps the most extreme example of intergranular embrittlement is that of iron by nitrogen, for which a tensile strength as low a s 5 N/mm2 has been reported 151. It appears that intergranular embrittlement may occur in any metal, and the breaking strength can be reduced to between 1/100 and 1/10 of the normal level with a corresponding reduction in ductility.In the past, the obvious explanation has seemed t o be that the impurities which in general are necessary for embrittlement segregate t o grain boundaries and reduce the cohesion there t o a very low level indeed. The experimental evidence which has now been accumulated shows, however, that impurities cause only a modest reduction in cohe- sion
-
perhaps never below one-
half the normal.It appears that there is a critical level of cohesion above which the strength and ductility are normal and below which both are seriously affected, and that most metals in the normal state are only marginally above the critical level.
The direct part of the accumulated evidence just referred to is provided by quantitative studies of interface energy and interface chemical compo- sition [6]. From such studies, by making the reasonably well founded assumption that interface energy is proportional t o cohesive strength, the ratio R = grain boundary cohesion i transcrystal- line cohesion can be determined, 'the transcrystal- line cohesion being taken as the normal good cohesion unimpaired by impurity. For three badly ernbrittled alloys R is : Fe-P 0.57, Fe-Sn 0.62, Cu-Sb 0.56, compared with about 0.85 in the pure Fe3. Again, among ionic compounds R in the pure state is inherently lower than in pure metals. Three ionic compounds are known normally t o break along grain boundaries and have R values of approximately 0.5 : NaCl 0.53, KC1 0.48, LiF 0.41.
Others with larger R values d o not normally break along grain boundaries : A1203 0.75, Z r 0 2 0.78 [7].
This quantitative data consistently points t o
R = 0.5 a s being associated with grain boundary fracture. Since for a metal without harmful impuri- ties R = 0.85, the data therefore demonstrates that a modest reduction in grain boundary cohesion has damaging consequences.
There is also much qualitative- experience which can be seen to fit the concept that metals normally possess only a small margin of safety against intergranular embrittlement. Perhaps the clearest piece of qualitative evidence is in Guttmann's work on temper brittleness of steel [8] in which it is shown that minor changes in the heat treatment condition, e. g. which apparently produce nothing more than a small alteration in the morphology of the grain boundary carbides, can shift fracture from a transgranular to an intergranular path. It might also be pointed out that the recent discovery of numerous intergranular decohesions in the alloy Nimonic 80 A as an accompaniment of plastic deformation [9], which is referred t o again below, suggests that intergranular decohesion during plas- tic deformation is commoner than hitherto sus- pected since in this case it is not easily detected (and as the strength and ductility are normally good the discovery further indicates that macro-cracking does not necessarily follow from decohesion).
A n explanation of grain boundary ernbrittlement which incorporates the critical feature starts from item A of the Introduction, i. e. the fact that grain boundaries halt slip bands. Provided that the slip is concentrated into thin bands, i. e . that it is planar, large stress concentrations are set up along the grain boundary in the line of impingement. Known calculations then indicate that the magnified tensile stress rc near the line of impingement will usually be larger than the fracture stress proper, up, of the metal [lo] ; if in consequence a crack forms the local stress concentration is relieved. However, the local stress concentration can also be relieved by slip. The condition for relief slip t o take place is that the magnified, local shear stress T C exceeds the shear strength proper, T,,, of the metal. Again, with planar slip the magnified stress is s o large that this is likely to be the case. With a given stress 7, on the slip plane of figure 1, the ratio r = uJrc is calcula- ble ; it depends on the angle 8 at which the slip band meets the grain boundary and it can be increased when two slip bands meet at P in figure 1. Whether a crack forms, possibly leading to fracture, or whether relief slip occurs, permitting further deformation and delaying fracture, is then determined by whether
If the first inequality applies, a crack relieves the local magnified stress ; if the second applies, slip achieves the same purpose. Two calculations relat- ing to expression ( 1 ) have been made [3, 1 I], and
MECHANICAL PROPERTIES O F GRAIN BOUNDARIES C4-275
Grain boundary
/ \
. p,.'
/ \
/ '\
FIG. I . - When a sharp slip band strikes a grain bound;try large stresses are set up around the point of impingement. Here, the local concentrated stresses of interest near P are the tensile stress uc normal t o the boundary and the shear stress 7, along PQ (parallel to the impinging slip band). Calculation shows that u, and 7, diminish with distance from P at equal rates. In the applied stress, the tensile component normal to the grain boundary is ua and the shear component parallel to the slip band
I S r*.
give for pure copper r = 0.4 u,/T, and r = u p / r p .
Both calculations are approximate but follow somewhat different principles. Consequently these results can be taken to indicate that pure copper should be a ductile metal, a s it is, but that a modest reduction in up (item B of the introduction) converts it into a brittle metal, as it does.
Inequality 1 thus expresses the critical feature.
Inequality 1 is depicted graphically in figure 2.
FIG. 2. - The local concentrated stresses u, and rc of figure 1 plotted against each other. They increase along OC a s the applied stress T, is increased. The slope of OC is affected by the angle 0 (Fig. 1) the slip band and may be increased if two slip bands impinge together. The crosses (x) denote the metal's tensile and shear resistances r p and 7,. Should a crack be formed where the slip band impinges, a similar type of diagram represents the relations between the local concentrated stresses a t the crack edge and the metal's resistances. When improved purity raises the metal's representative point from Mz t o M I the
effective resistance to fracture is enhanced.
As the applied shear stress r , increases, the magnified stresses near the end of the slip band increase along OC. If the metal's strength proper- ties cr, and 7, are represented by M I , OC reaches T ,
before it reaches v,, and relief is by shear, but if the metal's properties are represented by M2 OC reaches cp before it reaches T,, and relief is by cracking.
Several factors influence t h e likelihood of cracking. The angle 0 in figure 1 is one factor ; if 0 is small OC in figure 2 is nearly horizontal and cracking is improbable. Maximum steepness of OC for a single slip band occurs when 0 = 70.5, as Stroh originally showed. With two slip bands meeting a t P in figure 1 OC can be steeper than for any orientation of a single slip band [ l l ] ; other things being equal, this is the situation most likely to cause cracking. The relative grain orientation is another factor in that, if the two grains have similar orientations, slip crosses the grain boundary with- out setting up large stress concentrations there.
This situation is referred to again in connection with figure 3 below. The metal's properties are also important. If the metal is one in which the slip is homogeneous instead of planar the stresses a, and
r c are much reduced and are represented in figure 2 by OC' instead of OC ; with perfectly homogeneous slip uc = applied tensile stress a, and is far too small to produce a crack. Clearly, a reduction in grain boundary cohesion by impurities, or because of the nature of the atomic binding forces as in some ionic crystals, can make the critical difference between ductility and brittleness by shifting the metal's representative point from M I to M2 in figure 2 and is the most widely appreciated cause of grain boundary embrittlement. However an increase in r p can have the same effect by moving the metal's representative point from M I to M3. The way in which this can happen deserves a brief discussion. The most effective relief by shear requires slip along the continuation of the impinging slip plane into the next grain, i. e. along PQ in
Breaking strength Vrnrn2
Misorientation, degrees
FIG. 3. - Influence of grain boundary misorientation on load for grain boundary fracture. The misorientation is a tilt about [100], so that data between 45" and 90" is equivalent to data between 45" and 0" and is therefore plotted in this range [l4].
figure 1, where the plane indicated by PQ is also parallel t o the slip plane AP in the direction perpendicular to the <lane of the paper. PQ will not usually be a normal slip plane. Further, recent workers [3, 12, 131 have supposed that shqar relief requires the nucleation of fresh dislocations, which accordingly along PQ have unusual Burgers vectors and glide on unusual slip planes, the Burgers vectors and slip plane being determined by the orientation of the adjoining grain. The nucleation stress for a dislocation depends on its Burgers vector and slip plane ; in a typical fcc crystal a range of 3 to 4 between the upper and lower values is t o be expected [ l l ] . Thus, at some grain boundaries, the adjoining grain is so oriented that T ,
is relatively small, and at other grain boundaries T, is relatively large. If a t these latter the representa- tive point in figure 2 lies to the right of OC, e. g. at M3, then these grain boundaries will crack. The upshot of these various factors is that in some metals no grain boundaries will be cracked by slip, in some a proportion will be so cracked, and probably only in a few a t most can all grain boundaries be cracked by slip.
In connection with the influence of relative grain orientation interesting results have been reported by Koblyanski and Goux [14]. These workers made molybdenum bi-crystals with tilt misorientation,,the grain boundary running transversely, and produced intergranular fracture by applying a bending stress with a wedge pressed against the grain boundary, there being a support at each specimen end. The misorientation was a tilt ~ about [loo] and the breaking stress was calculated assuming the bi- crystal to behave elastically up t o the point of fracture. Figure 3 shows how t h e breaking stress so, calculated varied with the tilt angle ; it is large near the single crystal position and very much smaller otherwise. One interpretation of these results is that at large misorientation the grain boundary cohesion is poor, which is analogous t o the explanation of impurity embrittlement mentioned at the beginning of this section. An alternative explanation is that at small misorientation slip passes through the grain boundary fairly easily, i. e. the grain boundary is not an' effective obstacle to slip, so that there is little stress magnification a t the boundary and at modest stresses OC' in figure 2 rather than OC represents the local situation there. A large applied stress is then necessary for fracture. At large misorientations OC in figure 2 represents the situa- tion at the grain boundary ; the metal's representa- tive point is evidently below this, e. g. at M2, and fracture occurs easily.
4. Extension of a grain Joundary decohesion. (B).
-
Once a small decohesion has formed it is acted on by the applied tensile stress a, a s well a s by the applied shear stress 7,. The response to these forces may be either extension of the crack orblunting by slip. As the rough calculations which can be made cannot decide accurately between these possibilities, and as experiment indicates that one or the other occurs according t o circumstances, it is reasonable to suppose that figure 2 again represents the situation with uc and 7~ now being .the magnified stresses at the edge of the decohe- sion. However, the general experience that local grain boundary decohesions eventually d o spread when the applied stresses are large enough suggests that work hardening causes T, to increase so that, even if M is originally t o the left of OC, it later crosses OC and transfers to the right. There are thus four somewhat different groups of metals : 1. The metal's representative point M is above the line OC for hitiation and also for extension, and there is consequently good ductility. 2. M is below OC for initiation but above OC for cracking. Then local decohesions occur but d o not spread immedia- tkly. If they d o not spread before some other fracture process breaks the sample, e. g. provoked else-where than at grain boundaries by inclusions, the local grain boundary decohesions do not impair the ductility. 3. Similar relations exist between M and OC, but now the decohesions d o spread before fracture is provoked elsewhere. The local decohe- sions then d o impair the ductility. 4. M is below OC both for initiation and for extension, resulting in very brittle behaviour.
There are known examples of all four groups.
Group 1 consists of all those polycrystalline metals in which neither local grain boundary decohesion nor grain boundary fracture occurs. An example of group 2 is the alloy Nimonic 80 A, in which numerous local decohesions have been detected 193 but, as this metal does not break along grain boundaries at room temperature, the ductility is unaffected. The discovery of many grain boundary decohesions in this alloy is new and surprising, and perhaps suggests that group 1 is smaller than has been thought. Group 3 is represented by copper bismuth alloys. Copper itself presumably belongs to group 1, as fracture is transgranular
-
e . g., in a tensile test ductility is high at about 50 % elon- gation and the fracture stress 'is approximately 1200 N/mm2-
but when alloyed with 0.02 % Bi the fracture is intergranular, tensile elongation is 8 % and the fracture stress 120 N/mm2. An example in group 4, in which ductility is non-existent, is provided by some Ti-A1 alloys in which planar slip occurs and the ductility is zero [15].It is known that the applied stress system can affect this grouping. That it should do so is reasonable, at least among the groups 2-4 in which grain boundary decohesion occurs. For compare the situation of grains under pure tension, e. g. in a straight test-bar under pure tension, and of grains where the applied stress system has a large hydrostatic component, e. g. near a notch in a bar
MECHANICAL PROPERTIES OF GRAIN BOUNDARIES C4-277
under stress. When in both places the shear stress
T~ (Fig. I) has reached the level that causes a decohesion, near the notch the tensile component ua (Fig. 1) is larger than in the grains under pure tension, and evidently the line OC (Fig. 2) for the stresses near the notch is more likely to lie to the left of the representative point M than for the stresses in a straight bar. Consequently, the higher the ratio of tensile t o shear stress in the applied stress system, the more brittle the behaviour, the more likely a given metal is to display group 4 behaviour rather than group 3, or group 3 rather than group 2.
The,existence of tough-brittle transition tempera- tures in bcc metals shows that strong lattice friction raises 7, significantly, probably because the speed of events is very great, both at P in figure 1 as a planar slip band drives on to the boundary and at the edge of a just-formed crack as it takes up the local magnified stress, and the slip resistance from lattice friction is presumably increased enough by high speed to augment the nucleation stress signifi- cantly. Then the points M are displaced to the right in both meanings of figure 2, i. e. the meaning in which figure 2 is concerned with initiation of a decohesion and the meaning in which it is con- cerned with extension of a decohesion, and brittle behaviour is more probable.
5. Value of metal purity. - Because a metal's intergranular cohesion a, is reduced by many impurities a s previous papers in this conference have shown, improvements in ductility and toughness can be made by purification. The bene- fits are realised in room temperature plasticity, fatigue, and creep performance a s these summaries of results obtained in British and French laborato- ries will show. The figures in brackets are referred to later :
l o The tough-brittle transition temperature of iron is sensitive to oxygen and nitrogen content [16, 171 and t o sulphur content [l7], selenium and tellurium content [I 7, 181, increasing with increas- ing content of these elements.
2" The fracture toughness (i. e. the quantity usually designated Kl,) of Ni-Cr-Mo alloy steel is improved when made with pure base metal as these data for Kl, indicate [19] :
- commercial purity (basic iron = 99.7 %) 1 330 N/mm3I2 (Sf = .05),
- special p u r i t y ( b a s i c iron = 99.98 %) 2 560 N/mm312
(2f
= .009).3" Fatigue tests in air on similar steels have shown that crack growth rate per cycle is substan- tially less in steels with the smaller impurity content ; the reduction in growth rate is typically 3-4 x [20]. (Sf = .06 for the commercial purity, and
009 for the special purity.)
4" Creep tests on Cr-Mo-V alloy steel comparing similar basic purities (Sf = .019 in the commercial purity and .008 in the special purity) have shown large gains in rupture life-time in the special purity grade, examples being from 600 to 30 000 h in a steel containing 1 % Cr, 1 % Mo and 114 % V and 2 000 t o 12 000 h in a steel containing 112 % Cr, 112 % Mo and 114 % V ; with other stresses the improvement was sometimes greater and sometimes less 1211. In some experiments on copper bi- crystals, grain boundary sliding was invariably accompanied by the production of grain boundary cavities when oxide particles were present in the grain boundary, but never when they were absent [22].
In these comparisons the grain boundary cohe- sion was crucial since the more brittle behaviour was always associated with an increase in the proportion of intergranular fracture. As removal of the impurities in question is known to result in a quite modest increase in up these results demons- trate again the critical nature of the distinction between ductile and brittle behaviour. The practical gain is of course very important since by attention to impurity content higher performance metals have been produced that are valuable for onerous applications, and some are now undergoing field trials.
A simple method of approximately estimating the degree of purity necessary to avoid intergranular embrittlement uses the studies of grain boundary segregation described earlier in this conference.
These studies show that the least soluble elements segregate most strongly to grain boundaries, and they are also those which in general are most likely to cause intergranular embrittlement. For such elements, it has been found [23, 71 that intergranu- lar embrittlement becomes noticeable when the fraction f = actual concentration + solid solubility attains the value
-
0.1 if the solid solubility is taken at the temperature at which segregation was allowed t o occur. Sometimes this solubility is not well known. If, instead, the maximum solubility at any temperature is used for the solid solubility for the reason that it is usually known a guide is obtained which is obviously more approximate ; it is that f<
.O1 should ensure freedom from inter- granular brittleness. In some of the examples 1-4 above the sumZf
for the probable harmful elements has been determined and is-noted in brackets, using for the solid solubility (in the alpha phase in the case of iron) the highest value a t any temperature since the solubility at the temperature of segrega- tion is not available in all cases. It will be seen from the bracketed figures thatZf
< .O1 ensures free- dom from intergranular embrittlement. Although the procedure is simple it has some scientific plausibility, since on the one hand the studies of grain boundary segregation have shown that f isC4-278 D. M c LEAN
quite a good universal measure of grain boundary impurity concentration and therefore of grain boundary cohesion, and on the other hand the argument in this paper indicates that grain boundary fractures may be expected below some fairly critical level of cohesion which is not very much smaller than that in a pure polycrystal. Consequen- tly the approximate confirmation of the two earlier results by the new ones is not unexpected, and suggests that the procedure is worth applying in any case where an approximate knowledge of the safe upper bounds t o impurity levels is helpful.
6. Grain boundary sliding (C).
-
The grain boundary sliding which takes place during creep is important because it is often thought to play a significant part in causing creep rupture. In engi- neering creep, if rupture does occur it is at points where there is strain amplification, e. g. around a rivet hole in Concorde or at joints in the pipework of a power station ; the plastic deformation of a few per cent at such points of strain amplification is associated with sliding distances of the order of 1-10 pm, while the stress is typically of order .lod to G (= shear modulus). It is interesting and in some respects instructive t o compare this sliding with that occurring under other conditions.A comparison with the sliding in fine scale creep is illustrated in figure 4. Using the torsion pendu- lum, creep is measured at stresses of = lop5 G (actually varying between zero and = G from the centre to outside of the wire specimen) and the grain boundary sliding distance is calculated assum- ing it to be the only source of plastic deformation.
The line marked torsion creep in figure 4 represents the sliding rate in aluminium polycrystal wire so calculated for the first to pm of sliding at the wire surface at 0.5 T, (absolute melting tempe- rature). There is actually only one experimental point but for clarity in the diagram a short line of slope corresponding to sliding rate stress2 is drawn through it. These rates are very much faster than those measured during the first 1-2 pm of sliding in tension creep of an aluminium polycrystal at 0.5 T,,, represented by 3 experimental points in figure 4, and this seems reasonable, partly because slide hardening occurs on each grain boundary individually and partly because the grain boundaries differ over a wide range in their speed of sliding according to these torsion pendulum experiments and the earliest strain is mainly caused by the fastest.
A second comparison can be made with the sliding that occurs in the grain boundary damping peaks which are detected with the torsion pendulum apparatus. The stress is again = G at the wire surface, and the sliding rate calculated is an average value over the full amplitude which occurs of
= l W 3 pm at the wire surface. The line marked
Stress
~ / m r n ~
Torsion darnplnq
(26)
/
Stress
N'rnrn210
1
FIG. 4 and 5. - Sliding data f o r aluminium and copper at 0.5 T,. Extrapolations from other temperatures have t o be made for both the torsion damping results (Al 280 t o 200 OC, Cu 240 t o 415 OC) and f o r t h e Al bi-crystal data (380 t o 200 " C ) , and were made using the experimental activation energies of 140 000 Jlmol
for Al and of 147 000 Jlmol f o r Cu.
torsion damping in figure 4 represents such a result for aluminium polycrystal wire, and extrapolates to somewhat faster values than the tension creep line, suggesting that in this metal sliding rate diminishes a moderate amount over the distance to 1 pm.
However, in the similar comparison in figure 5 for copper a t 0.5 T, the sliding rate at p m (torsion damping line) is still very much faster than that at
.= 1 pm (tension creep line). Since a grain boundary damping peak occurs at the temperature where grain boundary sliding first occurs fairly freely in the usual experimental time of = 1 s, if it is safe to generalise from these two results the conclusion would be that such damping peaks span a wide range of T, in different metals (as they do), the
MECHANICAL PROPERTIES OF GRAIN BOUNDARIES C4-279
temperature being lower the longer the initial fast rate of sliding is maintained. Solutes segregated to the grain boundaries and precipitates in the grain boundaries are presumably important factors in this.
A third comparison is with sliding measured in bi-crystals, usually at a stress of
-
G a s intorsion pendulum experiments but over a sliding displacement of 1-1 00 ym. The bi-crystal results represented in figures 4 and 5 by solid lines, when allowance i s made for stress, indicate sliding rates intermediate between the initial fast rate and the later slower rate just referred to. In a polycrystal, therefore, there is substantially greater retardation with distance of sliding than in a bi-crystal. At 0.5 T, the typical grain boundary is evidently an easily shearing interface, and in a polycrystal its sliding rate must accommodate itself to that of the grain interior. There is much other evidence to this effect.
Bi-crystals with a misorientation chosen so that there is very good matching in the grain boundary exhibit remarkably slow sliding at the low stresses used in these experiments. In Lagarde and Biscon- di's work [28] on copper the misorientation was controlled within 15 minutes of arc, and a plot of the sliding rate against misorientation shows deep cusps at critical misorientations at which the sliding rate is very slow. With symmetrical grain bounda- ries tilted about [loo] a particularly deep cusp occurs near 53O, which is the (012) twin (not a naturally occurring twin like the (1 11) fcc twin ; the proportion of coincident lattice positions, usually denoted 1/X, is 115 compared with 113 for the natural twin [30] and the calculated grain boundary energy is
-
0.9 times energy of non-critical grain boundaries [31] while that of the natural twin is-
O), and the dashed line in figure 5 shows that the sliding rate was-
lo7 x slower than for a non- critical misorientation. The disparity diminishes as the temperature is increased but remains signifi- cant. There is no experimental information t o show how it is influenced by stress. The feature which distinguishes a near-twin from an exact twin boundary, or a low angle boundary from a single crystal (where there is also a minimum sliding rate), is the presence of dislocations in the boundary plane. Perhaps, therefore, dislocations in the boun- dary plane improve the mobility. There is a parallel here with the behaviour of the grains themselves, since grain deformability improves with dislocationdensity up t o the level where the force of mutual elastic interaction becomes significant in compari- son with the applied stress.
Although grain boundaries seize up when cold., they are surfaces over which dislocations move easily at elevated temperature, presumably because diffusion is necessary and a t elevated temperature grain boundaries are channels of .rapid diffusion.
Indeed, at elevated temperature they shear more readily than the slip planes both at low and high stress. Thus, at very low stresses approaching G experiment shows that grain boundary sliding still occurs although grain interior deforma- tion is undetectable [28, 321. At high stresses in the range 1 0-2-104 G grain boundary sliding typically accounts for 1110- 112 of the total strain in polycrystals even though, according to evidence like that in figures 4 and 5, the sliding rate has been reduced by a factor of 103-104 from the bi-crystal value owing to restrictions imposed by grain interior resistances in polycrystals. However, whe- ther this property of easy shear is a property of the grain boundary interface per se, or arises because the interface normally contains many dislocations each of which contributes to the sliding, seems unsettled. In particular, consider the different behaviour of a twin boundary and a grain boundary in a fcc polycrystal undergoing creep. It is known that the twin boundaries slide very much more slowly than the grain boundaries, a s would also be expected from results such a s Lagarde and Biscon- di's. However, a twin boundary can scarcely slide unless it contains dislocations with a Burgers vector component parallel to the twin interface. As is shown by transmission electron microscopy, twin boundaries are transparent t o dislocations ; of the dislocations which strike each twin boundary during plastic deformation, scarcely any remain in the twin boundary t o contribute t o shear. Grain boundaries, on the other hand, are mostly opaque to disloca- tions, which therefore do remain in a grain boundary when they strike it and can contribute to shear.
7. Conclusions.
-
I " The cohesion of grain boundaries in metals is criticaI and often marginal.One consequence is that improved purity is fre- quently worthwhile.
2O Over the whole experimental range ( l W 5 to 100 pm in sliding distance and lo4 to G in stress) the experimental data about sliding is reasonably self-consistent).
D. Mc LEAN
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DISCUSSION
B. BAUDELET : Vous montrez que la vitesse de X... : Les cassures des bicristaux de Molybdkne glissement au joint dCpend fortement de la nature sont-elles intergranulaires pour les faibles dksorien- du joint (de macle ou quelconque), de la nature du tations ?
matkriau (bicristal ou polycristal) et de I'intensitC A. KoByLANsKI Les cassures des bicristaux de du tenseur des contraintes appliquk (frottement, Molybdbne de haute p u r e t ~ (<
ppm et
intkrieur ou fluage). Ne pensez-vOus pas que < 10 ppm 02) SOnt intergranulaireS dans le domaine
l'interprktation de ces diffkrences nkcessite de de faibles et de fortes d ~ ~ ~par centre ~ i ~ ~ ~ ~ ~ i ~ ~ ~ .
considkrer B la fois le glissement aux joints et les t r o u v ~ que ~ 'de teneur en ~ ~ ~ ~ ~ ~ ~ ~ ~ i ~ ~
mkcanismes qui accompagnent (klastique ou plasti-
c
(deso
ppm) consolide le joint (dans les que) pour accomoder ledissement
aux joints ? faibles et fortes dCsorientations) et on obtient des Suivant Ies cas, le glissement pourrait &re contr6lk cassures par ,-livage ou des cassures mixtes.soit par la dkformation dans les grains de part et
d'autre des joints soit par le glissement au joint H. F. MATARE : Considering the bicrystal rupture lui-m&me. results by Prof. Goux, is it possible to assume that for higher values of 8 or high grain boundary energies, the stress lowering is caused by weaken- D. M c LEAN : There is certain to be interaction ing of the bonds at the interface monocrystal - between sliding at the grain boundaries and grain grain boundary rather than by weakening (rupture) interior deformation. As the controlling (not the of the bonds within the boundary ?
only) interaction, I favour the idea that sliding in The argument here is that a high-energy zone polycrystals is caused basically by dislocations with a multiplicity of free bonds will weaken the which hit the boundary and then glide along them a interface by a strain-differential and cause breakage certain distance before disappearing. The attraction there rather than within the high-energy zone of this idea is that, if the mean distance of glide in (compare grain-boundary sliding experiments).
the grain is y, it is only necessary to suppose that D. M c LEAN : I prefer the simpler explanation
x l y is constant to explain the very general result advanced in my paper, as working hypotheses until,
that, in creep, syb (YEtotal to quite a good accuracy. or unless, they are both proved wrong.
