The effect of plastic strain incompatibility on intragranular slip in zinc bicrystals at elevated temperatures

Suipta~caetM

Vol. 32, No. 12,

Pergamon 0956-716x(95)ooo48-?3

THE EFFECT OF PLASTIC STRAIN INCOMPATIBILITY ON INTRAGRANULAR SLIP IN ZINC BICRYSTALS AT ELEVATED TEMPERATURES A. D. Sheikh-Ali and R.Z. Valiev Institute for Metals Superplasticity Problems of Russian Academy of Sciences,Khaltu.rina 39, Ufa, 45000 1, Russian Federation (Received November 16,1994) (Revised January 10,1995) . IntroductloQ

It is well known that plastic strain incompatibility at grain boundaries (GBs) is an important factor which determines deformation behavior of crystalline materials (l-4). At low temperatures plastic incompatibility significantly retards the development of intragranular deformation (3,4). However at elevated temperatures the grain bou&ary participating in grain boundary sliding (GBS) process can play the role of additional slip plane and compensate the dilference in strain of neighbouring grains, thus making easy the development of nearboum&y intragranular defbrmation (5). Besides, plastic incompatibility influences GBS process itself, resulting in its spatial non-umformity (6,7). Recently this problem has been specially studied on incompatible zinc bicrystals with symmetrical tilt boundary which are deformed under creep (7). At the same time the chat-a&r ofchange ofthe distribution of GBS vahte along the GB in time and different intensity of slip traces near the GB and far from it, which are observed in the work (7) can testify to the possibility of impediment to the action of intragranular slip at elevated temperatures. Thus, the studies of the deformation behavior of plastically incompatible bicrystals are of direct interest for solving an important problem: whether grain boundaries are able to strengthen materials at elevated temperatures and if so, why. The purpose of the present work is the quantitative study of the regularities of intragranular slip at hightanperature creep of compatible and incompatible zinc bicrystals with the same symmetrical 45” tilt boundary and analysis of the experimental data on the basis of consideration of the interaction between intragmnular slip and GB at the dislocation level. Zinc bicrystals of these types have preferential (basal) slip system and seem to be the most convenient model objects for investigation of tbis problem. Exmvimental

Deb&

Zinc bicrystals (99.97%) of two types containing a 45” symmetrical tilt boundary were used (figure 1). This boundary is close to the boundary with the following special cry&allographic descriptors: the misorientation angle 8 = 44.41°
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graphite boat by the Bt@man method. Samples of two types were spark cut from a bicrystal plate at an angle of 45” and 90”with respect to the boundary line. The damaged layer adjacent to the surfaces was removed by chemical polishing on the acid-resistant cloth. Final polishing was performed electrolytically. On the polished bictystal surfaces, the marker lines to be used for measuring intragranular deformation and GBS were scratched by a needle with a diamond point along and across the tensile axis. Lines normal to the tensile axis were scratched at an average interval 100 urn. Elongations in different grain areas were determined by measuring the length changes ofsegments formed by the intersection of a family of lines normal to the tensile axis with the marker line running along the tensile axis in the middle of the sample. The values of intragranular strain were converted into the values of shear strain. The samples were tensile strained under a constant load at 553 K (0.8T,,,& Deformation was achieved with the aid of independent and freely movable grips. Tests were performed at two values of initial tensile stress: oN.62 MPa and o=O.7 1 MPa, which corresponded to the values of shear stress along the basal planes: 2,,=0.22 MPa and ri,._=0.25MPa and along the boundary: 2=0.3 1 MPa and ~=0.36 MPa. Figure 1 shows bicrystals with three orthogonal axes X, Y and Z. The requirements of compatibility (1,2) are not fulfilled for type I bicrystals in which basal slip in grains A and B operates:

and are completely fulfilled for type II bictystals:

For providing deformation near the boundary in both grains of type I bicrystals the shear along the axis X should ooxr. Thus, according to the classical deli&ion (1,2) the type I bicrystals are incompatible and type II bicrystals are compatible. The orientations of biuystals are such that under the action of applied stresses, dislocation loops generated in the grain interior reach the boundary with their edge components and the surfaces normal to the boundary with their screw components. Since this paper is primarily concerned with the loop components interacting with the boundary, the geometry of deformation can be represented by a two-dimensional model shown in figures 1(b) and 1(d).

Figure 2 shows surface areas in the vicinity of the boundary and the border of the sample a&r testing. In type I bicrystals, the intensity of slip lines continued on the surfaces of grains is substantially higher and they are mom w than the lines ending at the boundary In type II bicrystals the same picture of distribution of slip lines is observed but the dilTerence in intensity of slip lines reaching the boundary and those continuing onto the side surfaces is noticeably lower. Figure 3 illustrates shear strains as a function of distances travelled along the tensile axis for bicrystals of both types. The intragranular shear measured near the GB of type I bicrystals is si@cantly lower than that in type II bicrystals at the same straining conditions. This dit&rence is inherent for bicrystals strained at high (o=O.71 Mpa) and at low (o=O.62MPa) stmsses.Bicrystals of both types tend to larger strains as the distance from GB increases. The strain considerably increases during the transition from an area with slip lines terminating in the grain boundaty to an area with slip lines continued onto the crystal surfaces. In type II bicaystaltested under o=O.62 MPa, a certain asymmetty can be observed: in grain B the value of local strain first decreases and then grows as the distance from the boundary increases, which is not exactly the case in grain A (figure 3(b)). In type I bicrystals the siguiticant GBS is observed. There is spatial non-un%ormity of sliding: the increase of the sliding value tiorn the point 0 to the point C (7). In bictystal tested under the tensile stress o=O.62 MPa

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andstrainingtims:~22minthevalueofGBSnwKthepointOis12~andnearthepointCis3O~.Intype II bicrystal tested under the same straining conditions there is small GBS which do not exceed a few microns.

The experimental data obtained show that in type I bicrystals more significant difliculty occurs for the developmentofnearbour&y&agrauulardeformationthanin type II bicrystals. In type I bicrystals intensive GBS is observed which opera& non-uuifii along the boundary. Both types of bicrystals are characterized by the increase of the value of intragranular deformation at the transition from the near botmdary region to single crystal one. For the analysis of obtained results we consider the interaction between intragranular deformation and grain boundary at two di%rent structural levels: macro- and microscopic ones. Figure 4 presents the schemes of deformation of bicrystals at macroscopic level. The case of deformation of type I bicrystal is consistent with the presence of grain boundary shear and intragranular one (figure 4(a)). The interaction between these shears leads to the spatial non-uniformity of GBS (increase of the sliding value from the point 0 to the point C) which can be considered a superposition of the GB shear S, caused by the applied stress and the GB shear S induced by the intragranular one (7). The ideal case of deformation of type IIbicrystalis con&tent with the pmsence of iniragrauular shear and the absence of grain boundary one (figure 4(b)). Apparently the cause of small GBS observed in the bicrystals tested at cr=O.62MPa is the di%rence of Formation of neighbouring grains changing the orientation of boundary plane with respect to the tensile axisandttle appearance of extemal shear stress along the GB. Thus, the comparison of macroscopic schemes of deformation shows that the existence of GB shear compensating plastic incompatibility is the main difference of the straining of type I bicrystals from the straining of type II bicrystals. However, at elevated temperatures GBS process is significantly facilitated and macroscopic analysis does not allow to understand the cause of strong influence of plastic strain incompatibility on the development of intragranular slip. At the microscopic level the development of deformation is associated with the motion of lattice dislocations (IDS) in grain interior, their interaction with GB and the motion of the interaction products along GB. Numerous investigations(lo,1 1) have shown that the ID-GB interaction leads to forming grain boundary dislocations (GBDs). The simple geometry of used bicrystals enable to analyse possible dislocation reactions at the boundary. Let us suppose basal dislocations enter the boundary and dissociate into glissile and sessile GBDs. The directions of the Burgers v&ors of edge IDS slipping along the basal planes can be derived t&n the diagram illustrating the geometry of dislocation slip in the bicrystals (figures 1(b) and 1(d)). In the case of type I bicrystak the dissociation of LDs arriving from grains A and B in GB yields glissile GBDs with the same sign and sessile GBDs with opposite signs (figure 5(a)). Atkcted by the external shear stresses applied along the GB, the slip of glissile GBDs occurs in one direction (in the direction of point C). Glissile GBDs are able to accumulate in GB because the length of their run is large and comparable with the length of the boundary. Besides, undissociated IDS would impede the movement of GBDs (figure 6). The climbing of sessile GBDs results in their mutual annihilation. At the straining of type II bicrystal entering the boundary basal IDS dissociate into glissile GBDs of d&rent signs and sessile GBDs of the same sign (figure 5(b)). The motion of glissile GBDs due to their mutual attraction must result in their annihilation. Sessile GBDs are accumulated during the deformation and increase the boundary misorientation angle. Thus, IDS entering the GB results in the gene&on and accumulationof GBDs of predominantly the same sign: glissile GBDs in type I biuystals and sessile ones in type II bicrystals. Other modes of the interaction of LDs with GBs (transmission of LDs across GB, emission of L.Ds Tom GB) should yield the same GBDs as in the case of IDS entering the GB. Apparently, the processes of grain boundary recovery operate faster in type II bicrystals than in type I bicrystals since the length of climb of sessile GBDs from the sites of their appearance to their equilibrium positions is significantlylower than the length of run of glissile GBDs from the sites of their generation to the sites of their disappearance. Aboundary containing dislocationscan possess a significant field of elastic stresses and therefore we turn to the consideration of stress fields associated with the arrays of edge GBDs in the cases of d&rent types of

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bicrystals. Let us suppose inhite GBs containing equal-spaced dislocations: glissile GBDs in the case of deformation of type I bicrystals and sessile GBDs in the case of deformation of type II bicrystals. For determining stress fields near GB we use expressions suggested by Cottrell and Hirth (12,13) which were obtained by summing the contributions of individual GBDs. Figure 7(a) presents the distribution of shear stmsses along basal planes near the infinite GB containing equal-spaced glissile GBDs. As the distance from the boundary increases, the stresses induced by glissile GBDs tend to the value of 0.707ub/2D( 1-v) where l.t is the shear modulus, b is the GBDs Burgers vector, D is the spacing between GBDs, and v is Poisson coefficient. The distribution of shear stresses associated with the arrays of sessile GBDs is shown in figure 7(b). It can be seen that as the distance from grain boundary increases, the stresses tend to zero. Thus, GB in type I bicrystal unlike the boundary of type II bicrystal possesses a significant field of long range elastic stresses. It is important to note that our approach to the determination of the Burgers vectors of GBDs with the longest period of life and of fields of stmsses associated with these dislocations is qualitative. Nevertheless, thiSdlOWStOunderstand the signifkant difference in the deformation behavior of ditkrent types of bicrystak. Assuming that the driving force. of intragranular slip corresponds to the effective stress z, = z - ziwhere z is the external stress, zi is the internal stress, a drop in the intragrauular slip rate observed during the transition from the vicinity of the boundary of type II bicrystals to that of type I bicrystals and from a single crystal portion of the sample to the boundary area can be associated with the increase of zi. The zi can be interpreted as a back stress counteracting a LD in its slip, these stresses being induced predominantly by GBDs. In type 11bicrystals the marked decrease of the rate of intragmuularslip at the transition from the single crystal portion to the boundary area is observed. At the same time according to the calculation there are no long range elastic stresses (figure 7(b)). Apparently, the equal-space position of GBDs, which was used as the basis for the expressions of Cottrell(l2,13) can be reached at uniform and mutually co-ordinated dislocation tilling free sites in the boundary. In a real material such situation is unlikely to be realized and the boundary containing non-uniformly distributed sessile GBDs possesses long range stress fields which are more weak than in the case of glissile GBDs (14). Conclusions

1) The study of the deformation behavior under creep of zinc bicrystals of two types (compatible and incompatible) testifies that plastic strain incompatibility may significantly impede the development of near boundary intragranular slip at elevated temperatures. 2) The grain boundary strengthening at elevated temperatures revealed in incompatible bicrystak can be explained by non-effectiveness of gram boundary recovery processes, i.e., low rates of disappearance of glissile grain boundary dislocations of the same sign and lattice dislocations impinged into the boundary, and hence by a significant counteraction of long range stresses associated with these dislocations to the development of intragrauular slip. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

J.J.HauserandB. Cluhers,Acru met&! 9,802 (1961). J.P.Hirth,A4etd. Trans. 3,3047 (1972). K. Maruyama,M. AkaboriandS. Karahh, Trans. Jupn Inst. Metals 22,723 (1981). K Maruyama,M. Ahbori andS. Kardha, Truns.Japan Inst. M&k 22,899 (1981). K Maruyama, Y. WatatmbeandH. Oikawa, Groin Boundary Structure undRel.utedPhenomenu (edited by Y. Idida), Suppl. 27, p. 899. Traus.JapanIa& Metals(1986). P. Mussot,C. Rey andA Zaoui, ResMechunicu 14,69 (1985). AD. She&h-AliandRZ. Vdiev, Scrtptu met& m&x 31,170s (1994). R Botmet, E. Cousineauand D. H. Wiwiugtq Acru crystull. A37.184 (1981). E.R ChenandAH. King.Philos. Mug. ASI, 431 (1988). D.A Smith,J. dePhysique 43, C6-225 (1982).

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11. M. Elkajbaji and J. Thibault-Desmux, Phi&x. Mug. A%,325 (1988). 12. AH. Coitrell, Dislocations andPlasticHow in Crystals, p. 94, Fair Lawn (1958). 13. J.P. Hirtb and J. L.&e, Theory ofDi&xations, p. 669, McGraw-Hill (1968). 14. AA Nazarov, AE. Romanov and RZ. Valiev, Acta metalL mater. 41.1033 (1993).

TYPE II BICRYSTAL

TYPE I BICRYSTAL

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Figure 1. ‘Ihe geuwhy ofbicrystalline samples (a&) and inirqaaular slip (b,d). Lattice dislocations slip towards the boundary. Double arrowsindicatethedirectionofshearstressesalongbasalplanesandtbeboundary;a-theappliedstress.

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