Effect of plastic incompatibility on grain boundary sliding in zinc bicrystals

Pergamon

Scripta Metallurgica et Materialia. Vol. 31, No. 12, pp.1705-1710, 1994 Copyright © 1994 ElsevierScienceLid Printed in the USA. All rights reserved 0956-716X/94 $6.00 + 00

EFFECT OF PLASTIC INCOMPATIBILITY ON GRAIN BOUNDARY SLIDING IN ZINC BICRYSTALS A. D. Sheikh-Ali and R . Z . Valiev t ( ([a Slate Aviation Technical l hm'ersity, Marksa 12, Ufa, 450025, Russia t Institute for Metals Superplaslicity Problems of Russian Academy of Sciences, Khalturina 39, Ufa, 450001, Russia

(Received March 21, 1994) (Revised July 25, 1994) Introduction Grain boundary sliding (GBS) in polycrystalline materials can act independently under the effect of applied stresses and can be induced by intragranular slip (IS) for compensating plastic strain incompatibility of neighbouring grains (1,2). The phenomenology of these different types of GBS was investigated separately on specially prepared model objects bi- and tricrystals (3,4). However, the regularities of simultaneous operation of these types of GBS in the same boundary which is the usual case during high-temperature deformation of polycrystals, and micromechanisms of their interactions are still unknown. This paper describes the effect of interaction of two types of GBS in incompatible zinc bicrystals with symmetrical tilt boundary and presents the analysis of mechanism of this interaction. The investigated type of zinc bicrystal has a simple crystallography and geometry of IS and GBS, which significantly facilitates the identification of deformation mechanisms. Experimental Details Zinc bicrystals (99.97%) with a 450+ 0.5°<10]'0> symmetrical tilt boundary were used (figure 1). This boundary is close to the boundary with the following special crystallographic descriptors: the misorientation angle 0=44.4 I°<10T0>, (c/a)2=27/8 where c and a are the h.c.p, lattice parameters, the reverse coincident site density E=21 (5). Following Chen and King (6), this grain boundary is termed a constrained coincident-siterelated boundary. A bicrystalline plate was grown from the melt in a horizontal graphite boat by the Bridgman method. Samples were spark cut from a bicrystal plate at an angle of 450 with respect to the boundary line. The sample size was 30 x 4 x 2 mm3. The damaged layer adjacent to the surfaces was removed by chemical polishing on the acid-resistant cloth in a water solution of nitric acid. Final polishing was performed electrolytically in the solution 40% H3PO4 + 60% CH3OH. On the polished bicrystal surfaces, the marker lines to be used for measuring GBS were scratched by a needle with a diamond point. The samples were tensile strained under a constant load at 553K (0.8Tmelt). Deformation was achieved with the aid of independent and freely movable grips which could rotate with the ends of the bicrystalline sample during changing its form. These loading conditions decreased the additional incompatibility stresses or fully excluded their appearance and also excluded the appearance of stresses counteracting the operation of GBS. Tests were performed at two values of initial tensile stress: c~=0 32 MPa and c~=0.62 MPa, which corresponded to the values of shear stress along the boundary: x=016 MPa and x=0.31 MPa and along the basal planes: Xbas=0. ] 1 MPa and ~bas=0.22 MPa. Figure l(a) shows a bicrystal with three orthogonal axes X, Y and Z If the boundary ability for sliding is neglected, then one of the conditions of compatibility (7-9) is not fulfilled: gxxA~xx B, gz.zA=gzz.B, E)GA=E;~ B . For providing deformation in both grains the sliding should occur along the axis X. The orientation of bicrystals is such that under the action of applied stresses, dislocation loops generated in the grain interior reach the boundary with their edge components and surfaces normal to the boundary with their screw components. Since this paper is primarily concerned with the loop component interacting with the boundary, the geometry of deformation can be represented by a two-dimensional model shown in figure I(b). 1705

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Experimental Results Figure 2 shows surface areas in the vicinity of tile boundary and sample border. The main feature of deformation relief of the bicrvstal tested at a tensile stress ~=032 MPa and straining time t=97 rain is tile absence of slip lines reaching" the boundary. (figure 2(a)). There are only slip lines continuing onto the side surface of grain A. In the bicrystal tested at a=0.62 MPa and t=42 min, slip lines reach the boundary (figure 2(b)) The intensity of slip lines continuing on the c~stal surfaces is substantially higher and they are more frequent than lines ending at the boundary. At the begmning of the creep, the s.lip lines continuing to the side crystal surfaces are formed and then lines ending at the boundary appear, t.e., intragranular deformation gradually spreads from the single crystal portion to the bicrystal one and from the borders to the interior of the sample. Figure 3 illustrates the dependencies of the amount of GBS S on the distance along the boundary L. As shown in this figure, the oscillation of the GBS value at short distances along the boundary (<- 0.5 ram) is inherent for bicrystals tested at a=0.32 MPa and a=0.62 MPa In the bicrystal tested at a=0.32 MPa there is no significant change in the GBS value at large segments which is comparable with the length of the boundary (figure 3(a)). Macroscopic spatial non-uniformity of GBS is observed in the bicrystal tested at a=0.62 MPa: sliding value increases from point O to point C (figure 3(b)). As shown in figure 3(b), at the early stage of the deformation, the S-L curve has a plateau the length of which diminishes with time and which disappears at the end of the test. Discussion Figure 4 presents the scheme of interactions between intragranular and grain boundary shears. The existing grain boundary shear and the absence of the intragranular one (figure 4(a)) correspond to the case of deformation of the bicrystal at a=0.32 MPa. The existence of both types of shears and spatial non-uniformity of GBS induced by the interaction of the shears (increasing GBS value from point O to point C) relate to the case of deformation of bicrystal at a=0.62 MPa (figure 4(b)). The spatial non-uniformity of sliding can be considered a superposition of the GB shear Se caused by the applied stress and the GB shear Si induced by the intragranular one. In our experiments, the rate of the former shear was higher than the rate of the latter (Se > Si). If the rates of the shears are equal to each other the value of the resulting shear should increase from zero at the point O to the value (Se + Si) at the point C. If Se < Si the value of the resulting shear in the point O becomes negative (Se - Si) and point C remains positive and equal to (Se + Si). Probably the appearance of negative GBS observed by Giannuzzi and King (10) relates to the case of prevalence of the rate of sliding induced by IS over the rate of GBS caused by applied stress. In any case, the value of GBS in the centre of the boundary should be equal to So. In our case, the GBS value is Se along the middle boundary portion, the length of which is equal to that of the plateau in the S-L curve (figure 3(b)), i.e., in the middle boundary portion GBS caused by applied shear stress develops without operation of GBS induced by incompatibility of intragranular deformation. For better understanding of the nature of the interaction of different types of GBS one must consider deformation at the microscopic level, i.e., the level of separate dislocations Recent investigations reveal that GBS is realized by the motion of grain boundary dislocations (GBDs) which possess a glissile component of the Burgers vector (11,12). In the case of the absence oflS or intragranular shear ("pure" GBS (1,3,12)), the generation of GBDs occurs in the boundary plane. Figure 5(a) shows glissile GBDs of opposite signs, generated by grain boundary sources. Under the conditions of unconstrained shear along a macroscopically flat boundary, a quantitative balance between GBDs of opposite signs should exist. A number of sources of GBDs can be considered to be uniformly distributed along the boundary. Therefore it is difficult to expect the appearance of macroscopic non-uniformity of pure GBS Usually a real boundary contains irregularities such as steps and/or facets, which are barriers for the movement of GBDs (figure 5(b)). Evidently, the appearance of GBD pile-ups near some of these irregularities may lead to the noticeable local non-uniformity of sliding along the boundary~ Lattice dislocations interact with GBs during IS operation. This interaction results in forming GBDs (13-15), Lattice dislocations (LDs) which entered the boundary dissociate into GBDs which in their turn interact with GBDs generated in the boundary plane. As shown in figure 6(a), the result of the interaction between GBDs is the annihilation of a part of glissile GBDs of one sign and concentration of glissile GBDs of the other sign. Transmission of LDs across the boundary also leads to appearing glissile GBDs of one sign, interacting with GBDs of the opposite sign and, as a result, increasing the number of GBDs of one sign (figure 6(b)). The interaction between LDs and GBs may take place in the form of emission of LDs from the boundary As shown in figure 6(c), glissile GBDs generated by GB sources and driven by external shear stresses "are forced to the steps. This creates a concentration of stresses, which is necessary for the generation of LDs. As l_Ds :~rc ,:mitred. sessile GBDs of opposite signs are left on the steps. Preferentially, GBDs of the same ~i'.zn ar,.' ~.', d ' , ~'~,~it l.Ds imo different grains, which result in tile accumulation of glissile GBDs of ~hc~pi'~;:.,~c ~,=. . . . . . . ,:,, a~, ,~i~cmcntioned types of interaction between lattice dislocations and GBs result ..

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breaking the balance between the glissile GBDs of opposite signs and accumulation of GBDs of the same sign The movement of these GBDs under the action of applied shear stresses should occur in the direction of the point C and lead to the spatial non-uniformity of GBS (increasing GBS value from point O to point C) Possible cases of other relationships between the two types of GBS may be also described from the point of view of GBDs. If the number of GBDs appearing in the boundary as a result of LD-GB interaction increases, then the influence of internal mutual repulsion stresses on the GBD motion also increases and they may stand or move in the direction opposite to the direction of applied shear stresses Such a dislocation behavior results in the absence of GBS or in the appearance of negative GBS. In this work, we established that the intensity of slip lines continuing to the surfaces of the sample is significantly higher than that of the lines ending in the boundary. Besides, intragranular deformation gradually spreads either from the single crystal portion to the bicrystal one or from the borders of the sample to its middle portion during creep and the distribution of GBS value along the boundary changes (the length of the plateau in the S-L curve decreases during the test), These facts testify to the existence of a noticeable effect of plastic strain incompatibility on the development of IS at high temperatures at which GBS operates easily For the study of the problem, the macroscopic approach is not fruitful and dislocation analysis should be used. However, this problem needs further study and is beyond the scope of this paper.

Conclusions 1) The interaction of intragranular slip and grain boundary sliding in incompatible bicrystals results in the appearance of a spatial non-uniformity of grain boundary sliding comparable with the length of the boundary. This non-uniformity can be well understood considering the deformation at different structural levels: macro- and microscopic ones. 2) Local spatial non-uniformity of grain boundary sliding along the boundary observed in this study testifies to the dislocation nature of the grain boundary sliding process. 3) The character of the distribution of basal slip lines, the gradual spreading of intragranular strain either from the single crystal portion to the bicrystal one or from the borders of the sample to its middle portion and the character of changing the distribution of grain boundary sliding along the boundary during creep show that an effect of plastic strain incompatibility on intragranular deformation exists at high temperatures.

References 1. H. Gleiter and B. Chalmers, Prog. Mater. Sci., 1__6, 1 (1972). 2. V M. Rosenberg, Creep of Metals, MetallurgiyaPublishing, Moscow (1967). 3. O A. Kaibyshev, V. V. Astanin, R. Z. Valley and V. G. Khairullin, Fizika Metallov i Metallovedenie, 51, 193 (1981). 4. P. Mussot, C. Rey and A. Zaoui, Res Mechanica, 1_44, 69 (1985). 5. R. Bonnet, E. Cousineau and D.H. Warrington, Acta Crystallogr. A., 37, 184 (1981). 6. E R.. Chert and A.H. King, Philos. Mag. A., 52, 431 (1988). 7. J.D. Livingston and B. Chalmers, Acta MetalL, 5., 322 (1957). 8. J.J. Hauser and B. Chalmers, Acta MetalL, 9__, 802 (1961). 9. J.P. Hirth, Metall. Trans., 3, 3047 (1972). 10 L. A Giannuzzi and A. H. King, ScriptaMetall., 1__99,291 (1985). 11. S. E Babcock and R. W. BaUuffi, ActaMetalL, 37, 2357 (1989). 12. R. Z. Valiev, V. G. Khairullin and A.D. Sheikh-All, Structure and Property Relationships for blterfaces, ed. by J. L. Walter, A. H. King and K. Tangri, p. 309, ASM Publication (1991). 13. D. A. Smith, J, de Physique, 43, C6-225 (1982). 14. M. Elkajbaji and J. Thibault-Desseaux, Philos. Mag. A, 5_88, 325 (1988). 15. X Baillin, J. Pelissier, A. Jacques and A. George, Philos. Mag. A, 6__11,329 (1990).

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FIG. 1. The geometry ofbicrystalline samples (a) and intragranular slip (b). Lattice dislocations slip towards the boundary. Double arrows indicate the direction of shear stresses along basal planes and the boundary; o - the applied stress.

a b FIG. 2. Slip lines nearthe grain boundary and sample edge in the bicrystalline sample

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12 o I-'mm~m" m- m

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DISTANCE ALONG BOUNDARY (mm)

FIG. 3. Variation of the sliding value along the boundary of the bicrystalline sample strained at: a) 0=0.32 MPa and b) o=0.62 MPa.

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FIG. 4 The response to axial loading. The appearance of grain boundary shear during the absence of intragranular shear (a). The combination of grain boundary shear with intragranular one (b). Grey arrows show the tension of grain A and the compression of grain B along the boundary.

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c FIG. 6. Modes of the interaction of lattice dislocations with the boundary. Formation of GBDs as a result of LDs entering GB (a) and LDs transmission across GB (b). Breaking balance between glissile GBDs of opposite signs due to the emission of LDs in the grain interior (c).