INTERACTION BETWEEN LATTICE AND GRAIN BOUNDARY DISLOCATIONS AND THEIR ROLE IN MECHANICAL PROPERTIES OF INTERFACES

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INTERACTION BETWEEN LATTICE AND GRAIN BOUNDARY DISLOCATIONS AND THEIR ROLE IN

MECHANICAL PROPERTIES OF INTERFACES

L. Lim, R. Raj

To cite this version:

L. Lim, R. Raj. INTERACTION BETWEEN LATTICE AND GRAIN BOUNDARY DISLOCA-

TIONS AND THEIR ROLE IN MECHANICAL PROPERTIES OF INTERFACES. Journal de

Physique Colloques, 1985, 46 (C4), pp.C4-581-C4-595. �10.1051/jphyscol:1985464�. �jpa-00224716�

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JOURNAL DE PHYSIQUE

Colloque C4, supplément au n°4, Tome 46, avril 1985 page C4-581

INTERACTION BETWEEN LATTICE AND GRAIN BOUNDARY DISLOCATIONS AND THEIR ROLE IN MECHANICAL PROPERTIES OF INTERFACES

L . C . Lira and R. Raj

Department of Materials Science and Engineering, Bard Hall, Cornell University, Ithaca, NY 14853, U.S.A.

Résumé. - Cet article est une brève revue des propriétés mécaniques liées à la structure des interfaces cristallines. Une étude antérieure menée sur des bi-cristaux d'orientations différentes avait montré qu'une telle corrélation existait. Plus récemment, une meilleure compréhension de la structure des joints de grains a permis de spécifier la structure et d'établir un lien

avec les propriétés mécaniques. Les rudiments de caractérisation de la structure des joints de grains sont discutés. Les propriétés mécaniques des interfaces sont décrites en termes de cavitation intergranulaire induite par glissement, continuité de bandes de glissement à travers les interfaces et de limite élastique. Les auteurs insistent sur la nécessité d'autres travaux dans cet

important domaine.

Abstract - This paper is a brief review of the relationship between the structure and the mechanical properties of grain interfaces. Early work had inferred that such a correlation exists from experiments with bicrystals of different orientations. More recently, the advances in the understanding of grain boundary structure have allowed specifying the structure and then studying how it relates to mechanical behavior. The rudiments of grain boundary structure characterization are discussed. The mechanical properties of interfaces are described in terms of slip induced intergranular cavitation, continuity of slip bands across interfaces and the "yield strength" of interfaces. The need for much more work in this important area is emphasized.

1. INTRODUCTION

Mechanical properties of polycrystals are often limited by grain interfaces. The yield strength of pure materials depends on the grain size because interfaces act as barriers to crystal slip. The ductile to brittle transition in metals has so far not been studied in terms of interface structure, yet it is possible that structure plays a significant role in slip induced fracture at interfaces. For example, the stress concentration produced at the interface by a pile up of lattice dislocations may be relaxed by the dissociation of lattice dislocations into boundary dislocations and the diffusion of the boundary dislocations away from the site of the stress concentration. It is possible to hypothesize that the temperature at which the boundary dislocations become mobile enough to relax the stress concentration at the grain boundary, is related to the ductile to brittle transition temperature. These are mere ideas at this point but they do emphasize that the understanding of grain boundary structure can lead to new insights into the mechanism of interface controlled mechanical behavior.

At temperatures near one half of the melting points, interfaces generally ex- hibit special properties such as grain boundary sliding and intergranular cavitation. The mechanisms which have been successful in explaining such behavior invoke the idea of matter transport by grain boundary diffusion. The concept of sliding by

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985464

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C4-582 JOURNAL DE PHYSIQUE

diffusional accommodation [I], and of the g;owth of cavities by transport of atoms away from the cavity surface and into the adjacent grain boundaries [2] are examples of ideas which build on processes which occur only in the grain boundary such as boundary diffusion. These processes are, therefore, independent of the yield strength of single crystals since they can occur even without any deformation in the grain matrix. For the purpose of this paper, we specifically exclude the considera- tion of these high temperature processes since we wish to limit the discussion to those effects which are caused by the interaction between lattice and grain boundary dislocations.

At high temperatures and at high strain rates, the impingement of lattice dislocation at boundaries can lead to the formation of fresh grains. This phenomenon, known as dynamic recrystallization, is important in the forming and shaping of ma-

terials at high temperatures. But considering the rather inadequate current state of fundamental understanding of the reactions between lattice dislocations and grain boundaries, a discussion of dynamic recrystallization will be beyond the scope of the paper.

The discussion in this paper will be limited, therefore, to temperatures rang- ing from the ambient up to a temperature just below where grain boundary sliding begins to become dominant. The upper limit of the temperature is strain-rate dependent since sliding is a highly strain-rate sensitive process. An attempt has been made to characterize this upper bound locus of strain-rate and temperature with the use of internal friction data for grain boundary sliding [3, 41. The results by Gandhi and Raj [ 4 ] for polycrystalline nickel, having a grain size of 100 pm, showing the region in a field of strain-rate and temperature in which large scale grain boundary sliding is not expec edlto be significant is reproduced in Fig. 1. Note that for a strain-rate of LO-'s- sliding effects are not expected to be significant until T reaches 0.4 T or about 700K. The point is that mechanical properties can be dominated by the izteraction between lattice dislocations and the grain boundaries up to fairly high temperature, which in this case is about 700K. Most of the attention in the literature on the study of interaction between lattice dislocations and grain boundaries has focussed on ambient temperature. We wish to emphasize the need for studies at intermediate temperatures where the mobility of grain boundary dislocations may be high, yet grain boundary sliding may not be significant.

The present paper is a concise review of the work in the literature pertaining to the interaction between lattice dislocations and grain boundaries. Most of the work at this point is phenomenological because the detailed understanding of the structure of grain boundaries is much more recent than the experimental work on mechanical behavior. Yet, the importance of the structure of interfaces was recog- nized by Chalmers in 1937, in experiments of crystal slip and yield strength with bicrystals of different orientation. He conjectured that if grain boundaries are

"amorphous" then the mechanical properties would be iridependent of the misorientation. He discovered that this was not the case and inferred that grain boundaries have structure and that deformation in the bicrystal can be influenced by that structure. Yet, even today, our understanding of a correlation between structure and mechanical properties of interfaces is in its infancy. But with the recent advances in the understanding of structure of interfaces, the research in the mechanical properties of interfaces is likely to advance rapidly.

In following sections, we begin with a summary of grain boundary structure.

Next, some of the significant early results on deformation of bicrystals at ambient temperature are described. This is followed by a summary of our recent work on nickel at intermediate temperature (573 K). Finally, some simple concepts based on reactions between lattice and grain boundary dislocations are suggested which may be helpful in interpreting the experimental results.

2. GRAIN BOUNDARY STRUCTURE

In recent years significant advances have been made in the understanding of

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grain boundary structure. Here we shall review the simple and basic concepts which have a bearing on the interaction between interfaces and lattice dislocations. An in depth review can be formed in the proceedings of a conference on grain boundary structure and kinetics [5].

NO- SLIDING

w

GRAIN BOUNDARY

@

^SLIDING

Separation of sliding and no- sliding regimes for polycrystalline nickel based on internal friction data [ 4 ] . E,v

--

elastie constants

u

--

applied tensile stress Ts

--

time constant for grain

boundary sliding, from grain boundary peak in internal friction.

Nickel

1.1

The building blocks for describing grain boundary structure are the Coinci- dence Site Lattice (CSL), the "0" lattice and the Displacement Shift Complete (DSC) lattice. The CSL is the super-lattice formed by the coincidence lattice points when two crystal lattices with a given misorientation are superimposed, much like the Moire interference pattern. The frequency with which the super lattice points occur

is denoted by a number 1, which is defined as the number of lattice points in the single crystal lattice for each lattice point in the super-lattice. For example, the CSL formed by the first twinning operation in f.c.c. structure, i.e. by rotating one crystal lattice an angle of 60' about a common <Ill> axis with respect to the other, has a value C = 3 or 13. A single crystal is simply 11. It is easily shown by overlaying two grids of points and rotating one set with respect to the other that particularly low valugs of .Z occur at certain discrete misorientations. We call these the exact .Z or C orientations.* In the case when the two cr stal lat- tices are rotated by an angle

e

about < 0 0 P in simple cubic structure, is obtained at the discrete angles g i v ~ n in Table I. The examples for 25 and 2 1 7 are shown in Fig. 2. Note that higher C leads to a larger unit cell of the CSL.

In addition to CSL the concept of "0" lattice, put forward by Bollmann 161 is useful. The "0" lattice is constructed from points in the CSL which can serve as

*The

2

notation is being used for boundaries at the exact coincidence and for those which are a little off coincidence but mav be described in terms of C and GBD accommodating network having Burgers vectors pertaining to the DSC lattice for that CSL.

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C4-584 JOURNAL DE PHYSIQUE

Table I. CSLs generated by rotation of 8 degrees about [001]

in a simple cubic structure

the origin for CSL rotations. These points are also "crystallographically" equivalent with respect to both component single crystal lattices. It can be shown that the walls of Wigner-Seitz cells, constructed around the "0"-lattice points, are the regions of worst matching between the two crystals. On relaxation, these worst- matching regions will become localized and form dislocations with lattice Burgers vector.

So far we have considered only special boundaries, which have a high degree of coincidence sites. A high degree of coincidence is characterized by a low value of

CSL

a

DSC Lattice

,DSC Lattice

Fig. 2

-

CSL and DSC lattices formed Ftg. 3

-

Dissociation of a lattice by interpenetrating (001) planes of dislocation into GBDs in a X29 boundary simple cubic lattices rotated with [161.

respect to one another by angle 8 around [OOl]. (a) 8 = 36.9' (2 = 5).

(b) 8 = 28.1"

(2

= 17). The primitive DSC vectors are shown at the center of each diagram [ 7 ] .

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A

C, and occur only at particular misorientations (see Table I). The question then arises about the change in structure of a boundary when the misorientation is increased continuously. Bollmann[6] showed that the concept of arrays of lattice dislocations to describe low angle boundaries in single crystals (Cl) may be extended to higher C boundaries. The only difference is that whereas the structure of low angle boundaries may be described in terms of lattice dislocations, the structure of higher C boundaries must be described in terms of grain Boundary Dislocations(GBDs).

The Burgers vector of these GBDs is given by the Displacement Shift Complete vectors which are uniquely defined by the CSL and the component single crystal lattices.

The DSC vectors are translation vectors such that if one crystal is translated re:a- tive to the other by that vector than the CSL is recovered. The DSC lattice for C5 and 217 CSLs are shown i~ Fig. 2. Note that the magnitude of the primitive DSC vectors becomes smaller as C increases [8].

Just as the concept of low angle boundary begins to breakdown when the misorientation becomes so large that the cores of the array of lattice dislocations begin to overlap, the concept of low angle boundaries relative to CSLs using GBDs to accommodate the misfit is valid only up to a critical misorientation, A@,. It has been suggested that A@ is related to C by the following equation [9,101.

A@ (in degrees) = - 15 (1)

The existence of accommodating GBD network having DSC vectors has in fact been experimentally verified by Balluffi et al. [ll] and by Cosandey and Bauer [12] for boundaries related to 15, 213 and C17 CLSs in [001] twist and tilt boundaries in gold bicrystals.

Using Eq. (I), all boundaries can be described either as CSL-related or general, depending on if the misfit deviation from an exact C misorientation is smaller or larger than the critical deviation, ABc. In addition, as the misorientation angle increases, both the spacing and the strain field of the accommodating GBD network varies in a continuous manner as one goes from one low C misorientation to the next low C misorientation [13-151.

3. FORMULATION OF DISLOCATION REACTIONS

Since the Burgers vector of a lattice dislocation is always equal to the vector sum of primitive DSC vectors, and since the magnitude of the primitive DSC vectors is always smaller than the magnitude of the lattice Burgers vector, the energy of a lattice dislocation can be decreased by its dissociating into several, smaller GBDs. Experimental evidence for such dissociation has been reported by several investigators [16-191. Fig. 3 contains an example from the literature 1161.

At sufficiently high temperatures GBDs can move along the interface, to form complex arrays in the boundary [20-231. The development of the arrays is likely to be related to the shape of the boundary since points where boundary changes its angle can serve as obstructions to the movement of GBDs. For example an edge GBD which can move by pure glide in a certain grain boundary plane, must also climb if the boundary plane changes its orientation. Thus, whereas the Burgers vector of GBDs can be defined only in terms of C, the mobility of the GBDs is likely to depend also on the orientation of the grain boundary plane.

In order to exactly define the reactions between lattice and grain bouniary dislocations, the Burgers vector of lattice dislocations in the two crystals b and

and the GBD,

g ,

must be consistently defined. For example, we can assume tBat tge direction of the axis of the Burgers circuit in all three instances is chosen such that all the directions converge toward the point of intersections of the three Cartesian axes. The Burgers circuits may then be defined in a self consistent way relative to the axes, by choosing the right handed screw convention. Note that the

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C4-586 JOURNAL DE PHYSIQUE

Burgers circuit for the lattice dislocations is constructed in the single crystal lattice but the Burgers vector of the GBD is constructed in the DSC lattice.

When $ and

<

enter the grain boundary then a residual dislocation, br, will 4

be left in tie interface. The residual may be expressed as a vector sum of n GBDs, 2

A a 2 A

To specify b

,

in terms of b and b2 we must specify the direction of motion of b and

b

with $espect to the boundary. We define a quantity 1 J such that J = +1 if +eh! lattice dislocation moves towards the boundary and J 2 = -1 if it moves away from the boundary. Then the following equation may be written:

As an application of Eq. ( 3 ) consider the dislocation reaction between edge dislocation2 in bicrystal containing a symmetrical tilt boundary. As shown in Fig.

4, if both bl and b move t2ward the boundary then the resLdual will be sessile in the boundary planesfbut if b moves into the boundary and b2 away from the boundary then the residual will be gldssile in the boundary plane.

Note that in contrast to edge dislocations, screw dislocations, if they are parallel to each other and to the grain boundary plane, can cross the interface with a zero residual GBD if one dislocation moves into and the other out of the grain boundary. Alternatively if the screw dislocations in the two crystal have positive and negative Burgers vectors, then they can annihilate each other completely by moving into the grain boundary. Thus, at least in simple situations, it would be easier for screw dislocations than for edge dislocations to intersect the grain boundary without leaving a residual dislocation at the interface.

Case I Case I1

Both Dislocations Moving Toward the Boundary

One Dislocation Toward & The Other Away From the Boundary Fig. 4

-

The Burgers vector of the residual dislocation left in the boundary depends not only on the Burgers vector of the two lattice dislocations intersecting the boundary, but also on their relative direction of motion.

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4. STRUCTURE DEPENDENT MECHANICAL BEHAVIOR OF INTERFACES (a) Change of Misorientation with Deformation

If the intersection of slip from the two adjacent crystal is such that a residual dislocation,

g ,

is left behind in the interface then that would change the misorientation betwee; the two crystals (this can be visualized by considering a low angle boundary; as more dislocations are added to the boundary, the two crystals will rotate relative to each other).

Experimental evidence for the above was provided by experiments on symmetrical tilt bicrystals of germanium by Bacmann, Gay and Tournemine [24]. The bicrystal was symmetrically stressed so that equivalent slip systems were activated in both crystals. The intersection of these slip systems led to residual dislocations in the boundary which increased the misorientation between the two crystals. The increase in misorientation was physically apparent. A picture of their deformed specimen is reproduced in Fig. 5.

(b) Continuity of Slip at Coherent Twin Boundaries

In a recent study Lim [25] examined the continuity of slip, and the Schmid factor for the slip systems which were activated in a polycrystal of nickel at 573 K under conditions of low cycle fatigue. The study of Coherent p i n Boundaries (symmetrical E3 boundaries) was particularly interesting. Altogether twenty-seven twins were studied. Two results emerged from this study:

(i) With one exception, CTBs are effective barriers to crystal slip. The excep- tional situation arises when the dislocations crossing the interface are screws with Burgers vectors

%<Oil>

which can cross-slip across the CTB since the boundary plane itself serves as a glide plane for these dislocations; in this case no residual slip vector is left behind in the interface.

(ii) The Schmid factor is not necessarily the only criterion which determines which slip system is activated in a polycrystal. The residual slip vector remaining at the interface when the slip vectors from the adjacent grains enter the grain boundary, also plays a role. For example, we find that a slip system which has a zero residual slip vector is preferred even though other slip systems may have a higher Schmid factor.

It must be kept in mind that the above results are probably valid only when the temperature is high enough, and the applied strain rate is slow enough that it is kine- tically possible for lattice dislocations to dissociate into small GBDs. The kine- tic barrier will be particularly important if one of the GBDs has a climb component in the boundary plane.

(c) Multiple Slip near Grain Interfaces and the Influence of Grain Boundaries on the Yield Strength of Bicrystals at Ambient Temperature

A large number of experiments with bicrystals have been reported in the literature. In the 1930s, Chalmers [26] studied the effect of misorientation on the yield strength of symmetrical bicrystals of tin. He found that the yield strength increased with misorientation. Later work on aluminum [27,28] showed that in addition to the yield stress, the rate of work hardening also increased with the angle of misorientation. Gilman 1291, working with the symmetric bicrystals of Zn found, however, that the yield behavior of single crystal and bicrystals were nearly exactly alike up to 20% strain. This dichotomy in fact is not surprising because the effect of the interface on yield stress will be felt only if the length of the pile- up of dislocations against the interface is of the same order as the size of the specimen. Generally speaking, not enough attention has been given to the importance of specimen size effects in experiments with bicrystals.

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C4-588 JOURNAL DE PHYSIQUE

Perhaps a better indication of the effectiveness of the grain-boundary as a barrier to crystal slip is the physical observation of the induction of secondary slip near the interface. Experiments with low angle grain boundaries have consistently shown if the misorientation is less than some critical value, usually about

15', then slip lines are continuous across the interface [30,31]. The experiments

on large angle, symmetrical grain boundaries are not quite in agreement, although many investigators report a lack of multiple slip at grain boundaries, especially if

the applied strain is kept small [32,33].

The relative influence of symmetrical and non-symmetrical boundaries on the yield and strain hardening behavior of bicrystals was studied by Fleischer and Back- ofen [34]. Single crystals of aluminum were oriented such that the Schmid factor on the primary slip plane, in all cases, was 0.5. Three different types of bicrystal were prepared by rotating the single crystals about the tensile axis. The stress- strain curves for two of their bicrystals, one symmetrical and the other non- symmetrical, are shown in Fig. 6. Note that in symmetrical case, the yield and

Fig. 5 Fig. 6

8 = 0'. 180' e = 03 90"

SYMMETRICAL NON-SYMMETRICAL

h 1600

N

E E ^I200

\

-

0) ₈₀₀

D 400

0 .o

Fig. 5 (top)

-

The pictures from Ref. 24 showing the increase in the misorientation of a bicrystal of germanium as a result of applied plastic strain.

Fig. 6 (right)

-

The stress-strain behavior of symmetrical bicrystals is nearly the same as that of the component single crystals but the non-symmetrical bicrystals have a

higher flow stress. Note that the O o 1.0 2.0 3.0 4.0 5.0 6.0 7.0

critical resolved shear stress is

the same in all cases [34]. ^&( % I

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strain hardening for the bicrystal and the single crystal are nearly identical. In contrast, the behavior is quite different for the non-symmetrical case. We may infer from the above comparison that non-symmetrical boundaries offer a stronger barrier to crystal slip than symmetrical boundaries.

(d) Influence of C on Slip Induced Intergranular Cavitation

In section (b) we summarized an experiment by Lim [ 2 5 ] where he demonstrates that grain boundaries can act as traps for lattice dislocations. The energy poten- tial well arises from the dissociation of a lattice dislocation into smaller grain boundary dislocations.

The dissociated and trapped dislocations in the boundary will lead to internal stress at the interface. The magnitude of the stress would likely rise as more plastic strain is applied, or as the density of the trapped dislocations increases.

One consequence of the misfit stresswillbe to nucleate small cavities at the grain interfaces. Evidence of such cavities was found by Lim and paj 1351. However, they also found that the extent of cavitation in a polycrystal differed from one boundary to another. The severity of cavitation could not be correlated to the physical orientation of the boundary with respect to the loading axis. Experiments were then carried out to investigate a possible correlation between the C value and the cavitation behavior of grain boundaries [ 3 6 ] . The specimens which were tested in low- cycle-fatigue under fully revised plastic strain range of 1.35%, were interrupted at increasing life fraction and examined for cavitation. The results at 6%, 8% and 14%

of life are shown in Figs. 7a,b and c. Note that at 6% life only the high C boundaries showed any evidence for cavitation (Fig. 7a). With increasing deformation, boundaries with smaller C's and A 0 < A 8 began to cavitate, as shown by the progres- sive increase in cavitation in Figs. 7bcani c. At even higher life fractions, all grain boundaries except the coherent twin C3 boundaries, developed cavities.

5. DISCUSSION

The study of the mechanical effects of grain boundaries in terms of reactions between lattice and grain boundary dislocations is in its infancy. Specific experiments to identify various types of reactions and their consequence on mechanical behavior have yet to be carried out. Nevertheless, the published literature does point towards some interesting effects which have been discussed in the preceding section and are summarized below:

(i) Grain boundaries are effective traps for lattice dislocations. As greater plastic strain is applied to che two adjacent crystals, the density of the dislocations trapped in the boundary increases. The residual dislocation can then lead to different effects.

(ii) In a symmetrical tilt boundary the residual dislocations can change the misorientation between the two crystals.

(iii) It appears that in the case of low angle boundaries, and to a certain extent, in the case of symmetrical tilt boundaries, the slip traces are continuous across the interface provided that equivalent slip systems are activated at equal critical-resolved-shear-stress in the two crystals.

(iv) Symmetrical and non-symmetrical boundaries appear to behave differently.

Thus not only C, but the orientation of the boundary plane can also influence slip-boundary interaction. It appears that non-symmetrical boundaries offer greater resistance to the passage of crystal dislocations, thereby having a greater effect on the yield strength.

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(v) At moderately high temperature, 573K or 0 . 3 3 T for nickel, the accumulation of residual dislocation in the grain interfacemleads to slip induced cavitation. The amount of plastic strain required to nucleate cavities is greater for boundaries with a lower value of Z.

(vi) At 5 7 3 K in nickel even the coherent twin 1 3 boundaries are effective barriers to slip, except in the case of screw dislocations which can cross slip across the boundary, using the boundary plane itself as a glide plane. In this special case, the screw dislocations domot leave behind any residual dislocation in the boundary.

The understanding of the subject matter at the present time is not advanced enough to provide a clear explanation for the effects described above. Indeed, some of the observations themselves have yet to be corroborated by further experimenta- tion. Therefore, the explanations given here must necessarily be regarded as con- ceptual.

The grain boundaries act as traps for lattice dislocations because they can dissociate into smaller GBDs (the primitive vectors in the DSC lattice are always smaller than those in the single crystal lattice). Since the energy of the dislocations scales as the square of their Burgers vector, the dissociation is energeti- cally favorable. The dislocations produced in the boundary by dissociation can be of three types: screw, glide edge, and climb edge. The glide GBDs will have their Burgers vector parallel to the boundary plane and the climb dislocations not parallel to the boundary plane. No systematic study on the kinetics of climb of GBDs has yet been reported. The experiments by Lim and Raj [ 2 5 , 3 5 , 3 6 ] were done at

573K in Ni; at this temperature, the mobility of climb type GBDs was sufficiently

high to allow dissociation of lattice dislocations [ 3 7 ] .

2 2

If the lattice dislocations, bl and b

,

are not equal then, according to equation ( 3 ) , residual dislocations will accumufate in the gb with increasing applied strain. The residual may have different consequences: it may lead to cavitation, migration, nucleation and growth of new grains [ 3 6 ] , or a change in the misorientation between the two grains [ 2 4 ] . In order to appreciate how residual dislocations may lead to different effects, we consider a simple array of GBDs shown in Fig. 8.

They are climb type and arrange in a low energy configuration. They differ from the classical picture of a low angle grain boundary because (a) their Burgers vector is smaller than the lattice dislocation vector and (b) the array is superimposed on an exact C CSL instead of being imposed on a'single crystal. The advantage of using an array like this is that many properties of small angle grain boundaries may be carried forth to the CSL boundaries.

Some of the physical consequences of the dislocation array are illustrated in Figs. 8a, b and c. In (a), an increase in the density of the GBDs is shown to change the misorientation between the adjacent grains. The density can be increased by increasing the applied plastic strain.

In Fig. 8(b), the possibility is raised that the coalescence of GBDs can lead to the nucleation of cavities. In 8(c) it shows that the application of a shear stress can exert a force on the dislocation wall, thus providing an additional driving force for grain boundary migration.

ACKNOWLEDGMENT

We appreciate the support received from the National Science Foundation though the Materials Science Center at Cornell University.

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JOURNAL DE PHYSIQUE

GBD Superimposed on

f

CSL I

CSL boundary

(a, Increase the Density of GBDs

in the misorientation between adlacent crystals

. I

Cb) Coalescence of GBDs can Lead to Cavity Formation

CC) Movement of GBDs Perpendicular to the Boundary Plane Additional driving force

,

;"r boundary migration

Fig. 8

-

^{A CSL}boundary containing an array of grain boundary dislocations can result in various effects as shown in (a), (b) and (c).

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2,

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28. K.T. Aust and N.K. Chen, Acta M e t a l l .

2,

632 (1954).

29. J . J . Gilman, Acta M e t a l l .

1,

426 (1953).

30. N. K r a t o c h v i l o v a and B. S e s t a k , Phys. S t a t . S o l .

5,

345 (1964).

31. S. Miura, K. Kamashima and K.T. A u s t , Acta M e t a l l . 28, 1591 (1980).

32. J.D. L i v i n g s t o n and B. Chalmers, Acta M e t a l l . 5 , 3 2 2 (1957).

33. K.G. Davis, E. Teghtsoonian and A. Lu, Acta M e t a l l .

u,

1677 (1966).

34. R.L. F l e i s c h e r and W.A. Backofen, Trans. M e t a l l . Soc. AIME

3,

243 (1960).

35. L.C. Lim and R. R a j , Acta M e t a l l . 32, 727 (1984).

36. L.C. Lim and R. R a j , Acta m e t a l l . 32, 1183 (1984).

37. P.H. Pumphrey and H. G l e i t e r , P h i l . Mag.

30,

593 (1974).

DISCUSSION

M.W. Grabski: What w i l l happen when t h e r e a r e c o n s t r a i n t s on your b i c r y s t a l s o t h a t it cannot change t h e m i s o r i e n t a t i o n when d i s l o c a t i o n s a r e running i n t o t h e boundary? I am t h i n k i n g i n terms o f p o l y c r y s t a l i n t h e c a s e when c a v i t i e s cannot be formed. Actually g r a i n boundaries a r e acquiring then a s o r t of flnon-equilibrium" s t r u c t u r e .

R. Raj: There is a s t r o n g p o s s i b i l i t y t h a t a c o n s t r a i n t c r y s t a l r o t a t i o n l e a d s t o long range i n t e r n a l s t r e s s , one o f t h e consequences o f which is c a v i t a t i o n . Other

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C4-594 JOURNAL DE PHYSIQUE

p r o p e r t i e s which may be influenced by t h e i n t e r n a l s t r e s s a r e strain-hardening behaviour i n f c c m e t a l s o r i n t e r g r a n u l a r and c r y s t a l cleavage i n bcc, i o n i c and c o v a l e n t m a t e r i a l s .

P. Neum- What do you t h i n k i s t h e c r i t i c a l temperature f o r t h e e f f e c t s you observed? They a r e p a r t i a l l y observed a l s o a t lower temperatures.

R. Raj: All our work s o f a r was done a t 573K (0.33 Tm f o r n i c k e l ) where t h e GBDs appear t o be q u i t e mobile (even t h e climb t y p e ) . We a r e now beginning t o study p r o p e r t i e s such a s slip-processes and c a v i t a t i o n a t even lower temperatures. Our p l a n s a l s o i n c l u d e experiments with a BCC m a t e r i a l t o s e e i f t h e m o b i l i t y o f g r a i n boundary d i s l o c a t i o n s is r e l a t e d t o t h e d u c t i l e t o b r i t t l e t r a n s i t i o n .

P.

A s t : ( i ) I n S i , one s e e s experimentally t h a t when t h e secondary d i s l o c a t i o n c o n t e n t exceeds a c r i t i c a l value, t h e =3, coherent twin llshedslf its g r a i n boundary d i s l o c a t i o n c o n t e n t i n t h e form o f a r e g u l a r small angle g r a i n boundary, which s p l i t s o f f . Did you s e e experimentally a s i m i l a r process i n Ni? Could such a mechanism account f o r t h e 3 0 0 ' ~ r e c r y s t a l l i z a t i o n ? ( i i ) Residual GB d i s l o c a t i o n s o f sub DSC s i z e can e x i s t i n g r a i n boundaries. For example i n z = 3 coherent twin, you can g e n e r a t e r e s i d u a l GB d i s l o c a t i o n s with b=

2

^n127,^{i . e .} ^1/3o f t h e DSC value. The p h y s i c a l reason f o r t h i s is t h a t due t o t h e d i f f e r e n t s t a c k i n g sequence a t t h e twin, t h e l o c a l symmetry i s hcp, i . e . d i f f e r e n t from f c c .

R. Raj: ( i ) We have seen s l i p induced migration and s l i p induced dynamic r e c r y s t a l l i z a t i o n i n N i a t 573 K. I am n o t s a t i s f i e d t h a t we understand t h e phenomenon o f dynamic r e c r y s t a l l i z a t i o n w e l l enough, m e c h a n i s t i c a l l y , t o d i s t i n g u i s h between t h e c r e a t i o n o f small a n g l e and l a r g e a n g l e boundaries by s l i p impingement a t GBs. ( i i ) J u s t l i k e i n s i n g l e c r y s t a l s , a g r a i n boundary d i s l o c a t i o n may d i s s o c i a t e i n t o p a r t i a l s w i t h Burgers v e c t o r s m a l l e r than a DSC vector. But a l l t h e p a r t i a l s , composed t o g e t h e r , should be e q u a l t o one DSC vector.

M. Riihle: You observed no c a v i t a t i o n only a t t = 3 boundaries. Can you g e n e r a l i z e your r e s u l t t h a t low boundaries show no c a v i t a t i o n ?

R. Raj: We found t h a t a l l boundaries, except t h e symmetrical c o h e r e n t z = 3 boundaries, developed c a v i t i e s , b u t t h a t t h e s t r a i n r e q u i r e d t o induce c a v i t a t i o n increased a s

Z

decreased.

V. Gerold: How l a r g e is t h e i n f l u e n c e o f t h e o r i e n t a t i o n o f t h e g r a i n boundaries w i t h r e s p e c t t o t h e s t r e s s a x i s on t h e n u c l e a t i o n o f - c a v i t i e s ? This o r i e n t a t i o n should i n f l u e n c e t h e d i r e c t i o n o f

4

with r e s p e c t t o t h e boundary?

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R. Raj: I n t h e p o l y c r y s t a l experiments we did n o t f i n d a s i g n i f i c a n t c o r r e l a t i o n between c a v i t a t i o n and t h e o r i e n t a t i o n o f t h e GB r e l a t i v e t o t h e s t r e s s a x i s . However, I a g r e e t h a t w e l l c o n t r o l l e d experiments with b i c r y s t a l s a r e needed t o answer your question.

You s a i d t h a t t h e Burgers vector o f t h e r e s i d u a l GB d i s l o c a t i o n a f t e r d i s l o c a t i o n r e a c t i o n through a GB should s p l i t i n t o d i s l o c a t i o n s w i t h Burgers v e c t o r s belonging t o t h e DSC l a t t i c e . Do you t h i n k t h i s is a necessary dondition?

I r e f e r t o previous experimental evidence f o r r e s i d u a l GB d i s l o c a t i o n s with no DSC Burgers vector.

R . Bonnet: Clear experimental e x i s t a n c e was found by Forward and Clarebrough

(1981) f o r s l i p c o n t i n u i t y a c r o s s a high a n g l e boundary i n s t a i n l e s s s t e e l , involving a remanant non-DSC e x t r i n s i c d i s l o c a t i o n and p r i s m a t i c g l i d e o f segments o f t h e g l i d i n g matrix d i s l o c a t i o n .

R. Raj: There is no rigorous theory which s p e c i f i e s t h a t GBDs should belong t o t h e DSC l a t t i c e . But it is c o r r e c t t o say t h a t DSC Burgers v e c t o r s a r e more commonly observed than non-DSC Burgers vector. I t h i n k t h a t t h e non-DSC can a r i s e where t h e g r a i n boundary plane makes abrupt changes i n d i r e c t i o n s .