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Philosophical Magazine Letters, Vol. 85, No. 12, December 2005, 613 623 Dislocation evolution in twins of cyclically deformed copper X. L. GUO, L. LU* and S. X. LI Shenyang National Laboratory for Materials Science, Institute of Metal Research Chinese Academy of Sciences, Shenyang 110016, China (Received 26 September 2005; in final form 21 October 2005) The evolution of dislocation structure in twins of different thicknesses has been investigated in polycrystalline copper fatigued at room temperature under constant plastic axial strain amplitude control. The dislocation structure and its evolution strongly depend on twin thickness. Three critical thicknesses must be distinguished, i.e. (i) characteristic size of fatigue dislocation structures, about 1 mm; (ii) critical height of stable dislocation wall structure, about 200 nm; (iii) critical spacing of dislocation dipole, about 20 nm. It is considered that the size effect is mainly caused by twin boundaries (TBs) which play different roles on slip behaviors in twins. 1. Introduction Investigations on annealing twins under cyclic deformation have been mainly focused on fatigue crack initiation at twin boundaries (TBs) in Cu [1 5]. Local stress concentrations are believed to arise near TBs as a result of crystal misorientation and anisotropy [6 8]. Early secondary slip is favored, generating significant hardening near TBs, which encourages the nucleation of persistent slip bands (PSBs) [9]. In cyclically deformed polycrystalline Cu, PSB formation mainly proceeds in the vicinity of TBs [2, 3, 10, 11]. TBs and adjacent regions are preferential sites for PSB formation and subsequent crack initiation. Most of the TB-containing materials studied so far consist of bicrystals or of polycrystalline materials with large grain sizes, usually larger than 10 mm twin. In those twins, the density is usually larger than 1 mm with a twin density that is too low to permit an extensive microstructural investigation in the twin interior and near TBs. Recently, Lu et al. [12] pointed out that pure copper samples with nanoscale growth twins could be prepared by means of pulsed electro-deposition technique. The Cu samples show a tensile strength about 10 times higher than that of conventional coarse-grained copper, while retaining an electrical conductivity comparable to that of pure copper. In a previous study [13], a high purity copper sample with an average grain size of 5 mm and a high density of growth twins, with thicknesses varying from several micrometers to tens of nanometers, was synthesized by electro-deposition. Systematic fatigue tests were performed and the cyclic *Corresponding author. Email: llu@imr.ac.cn Philosophical Magazine Letters ISSN 0950 0839 print/issn 1362 3036 online ß 2005 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/09500830500437450
614 X. L. Guo et al. deformation behavior was investigated. The present paper is a continuation of the investigation focusing on microstructural characteristics during cyclic deformation in twins with different thicknesses. 2. Experimental procedure A high-purity copper sample with a high density of grown-in twins was synthesized by means of a DC electro-deposition technique with an electrolyte of CuSO 4 [12]. Plane-view transmission electron microscopy (TEM) observations in the as-deposited Cu sample indicate that grain shape is essentially irregular (figure 1). The average grain size measured by standard lineal intercept method (excluding the twins) is about 5 mm. Each grain contains a high density of grown-in twins of {111}/h112i type. The twin lamella thicknesses show a wide distribution from 4 5 mm to about 10 nm, with twin length being grain size limited based on TEM observations with the beam axis along [110]. Symmetrical push pull fatigue tests were conducted on a servo-hydraulic Shimadzu 1 kn testing machine at room temperature in air under constant axial plastic strain amplitude control from 1.1 10 4 to 3.9 10 3. Fatigue specimens were cut from the as-deposited Cu sheet with an electro-spark machine. The size of the gauge section was 6 2 2mm 3. Thin foils for TEM observation were prepared by cutting slices with a thickness of about 0.4 mm parallel to the upper surface in the gauge section. The foils were mechanically thinned down to 50 mm and then twin-jet polished at 10 C. Dislocation structures were investigated by using a JEOL-2000FXII TEM at 200 kv. 3. Experimental results 3.1. Features of TBs and slip systems The twin plane and the possible slip planes, indicated as the double Thompson tetrahedron, are schematically shown in figure 2. The common face, ABC, of the Figure 1. TEM observation of the typical microstructure in the as-deposited Cu sample.
Dislocation evolution in twins of cyclically deformed copper 615 (a) matrix twin (b) Figure 2. The geometry relations of possible slip planes (activated slip planes are noted by the shaded planes) in twins for f.c.c. materials, including a double Thompson tetrahedron and two twin boundaries (a) the slip plane parallel to TBs and (b) the slip plane oblique to TBs tetrahedra corresponds to the twin plane (111). Here, the slip planes and the slip directions may be either parallel or oblique to TBs. Three types of slip pattern can be classified: (1) the slip plane is parallel to TB, as the shaded plane ABC in figure 2a; (2) the slip plane is oblique to TB, but the slip direction parallel to TB, for example (ABD 0 )[AB] in figure 2b; (3) both plane and direction are oblique to TB, e.g. (ABD 0 )[AD 0 ] or (ABD 0 )[BD 0 ] in figure 2b. In the following, these three types of slip systems will be dubbed parallel to TB, partially parallel to TB and oblique to TB, respectively. For convenience, the small part will be regarded as the twin and the other as the matrix. 3.2. Dislocation structures in twins The samples contain grown-in twins with thicknesses varying from micrometers to nanometers, which have given rise to different dislocation configurations during cyclic deformation. Based on microstructural observations, several ranges of twin thickness can be defined. 3.2.1. Twin thickness W t ` 1 km. Figure 3 shows dislocation configurations in twins with thickness larger than 1 mm, containing wall and labyrinth structures. From previous investigations on cyclic dislocation configurations in Cu single
616 X. L. Guo et al. (a) g = 020 A B (b) g = 220 Figure 3. Dislocation patterns in twins with thickness larger than 1 mm. (a) Parallel wall structures and labyrinth formed in twins, in sample fatigued at a plastic strain amplitude of 1.83 10 3 (activated slip systems are oblique to TBs in grain A and second slip pattern occurs in grain B) and (b) wall structure perpendicular to TBs found in twins, where activated slip systems parallel to TBs, in sample fatigued at a plastic strain amplitude of 4.1 10 4. crystals [14 16], the dislocation slip directions in wall structure are always perpendicular to the wall plane, based on which slip behaviours can be approximately estimated. In the thick twin (indicated by A in figure 3a), where labyrinth structures formed, the activated slip systems are oblique to TBs. The dislocation structures become more irregular near TBs. In grain B, walls are well formed, TBs seem to have no effects on the dislocation structures and the partially oblique system is activated. In figure 3b, most of the walls observed are perpendicular to TBs and only parallel slip systems are activated near TBs. Some cells are occasionally found in the thick twin.
Dislocation evolution in twins of cyclically deformed copper 617 PSB-like a b TB structure wall g = 111 matrix g = 111 twin wall twin matrix c A D Slip direction C B Wall Figure 4. Dislocation patterns in twins with thickness between about 1 mm and 200 nm. (a) PSB-like structure formed in a thin twin where activated slip systems are parallel to TBs, in sample fatigued at a plastic strain amplitude of 3.9 10 3 and (b) almost no dislocation substructures found in a thin twin, and slip systems oblique to TBs are activated in the matrix, in sample fatigued at a plastic strain amplitude of 1.83 10 3. (c) Schematic of wall structure and slip direction in the matrix of (b). 3.2.2. Twin thickness W t between 1 km and 200 nm. A PSB-like structure, similar to PSBs in fatigued single-slip-oriented Cu single crystals, is found in some thin twins (as shown in figure 4a). The walls (ladders) are perpendicular to TBs. A cell structure and tangled dislocations are found in the matrix beside the thin twin. In figure 4b, however, there is almost no characteristic dislocation substructure in the marked thin twin. At the same time, regular wall structures are formed in the matrix. From the orientation analysis (figure 4c), the wall plane is considered to be ð 110Þ which is oblique to twin planes. 3.2.3. Twin thickness W t between 200 and 20 nm. When the twin thickness decreases further down to a range from about 200 to 20 nm, the dislocation pattern characteristic of cyclic deformation is no longer found in the twins. Only some dislocation debris adhering to TBs can be seen whether or not slip systems are parallel to TBs (figure 5a, b). Most of the dislocations are considered as geometrically necessary dislocations (GNDs) [17]. On both sides of a given twin, the deformation behaviour in the matrix is similar, but the wall structure is not necessarily in registry (figure 5b). 3.2.4. Twin thickness W t _ 20 nm. Large amounts of very thin twins with thickness <20 nm have been encountered. During cyclic deformation, glissile dislocations would glide freely in the matrix and adhere to TBs when they encounter the thin twins. Most of the dislocation traces observed near thin twins are considered to be
618 X. L. Guo et al. (a) g = 111 GND (b) GND g = 111 Figure 5. Dislocation patterns in twins with thickness between about 200 and 20 nm. (a) When dislocation walls perpendicular to TBs and (b) when dislocation walls oblique to TBs in sample fatigued at a plastic strain amplitude of 1.83 10 3. Black arrows show the GNDs, i.e. geometrically necessary dislocations, adhering to TBs. A wall with different direction is seen adhering to the twin end, reflecting a stronger strain concentration. interfacial dislocations lying in TBs (figure 6). The intense contrast near thin twins in the TEM micrograph is mainly due to large strain incompatibility resulting from extrinsic interfacial dislocations. Some of the interfacial dislocations may be GNDs, the same as those considered in Section 3.2.3. In the interior of twins, however, no crystal dislocations could exist anymore. 4. Discussion In this work, stimulating the parallel slip systems to operate, and depressing the oblique slip systems to operate near the twin boundary, will lead to a
Dislocation evolution in twins of cyclically deformed copper 619 ThinTwins Wall g = 111 Figure 6. Crystal individual dislocations in the matrix and interfacial dislocations adhering to twins with thickness <20 nm in sample fatigued at a plastic strain amplitude of 1.83 10 3 ; dislocation loop bowing out of a thin twin is marked by hollow arrow. TB g = 220 Figure 7. Twin boundary affected zones (illustrated by black arrows) are found near TBs, with a width of about 1 mm, where strain is enhanced and dislocation evolutions proceed, in sample fatigued at a plastic strain amplitude of 4.1 10 4. The typical dislocation arrangements in the bottom-left corner are loop patches, and some parallel wall structures are formed in the regions near TBs. TB twin boundary affected zone (TBAZ) in which various dislocation substructures can be found to appear earlier than other structures in the interior due to higher stresses which could exist over there (for example, figure 7). The width of TBAZ, i.e. W TBAZ, is about 1 mm, consistent with the characteristic size of fatigue dislocation structures. In some other materials with small physical dimensions or grain sizes, evolution of characteristic fatigue dislocation structures also will be affected by size effects. For example, in thick Cu films and grains of at least 3.0 mm in diameter,
620 X. L. Guo et al. dislocation of wall and cell structures occurred; whereas, in thin films or in small diameter grains, no clearly defined dislocation structures were found [18]. In cyclically deformed pure nickel, conventional fatigue dislocation structures were absent for grain sizes below 1 mm [19]. Similarly, the slip patterns and dislocation configurations near TBs will be different in twins with different thicknesses. In the following sections, dislocation evolution in twins with different thicknesses will be discussed in detail. When the twin thickness W t is >1 mm, the slip systems with larger initial Schmid factors will operate more easily. Slip activities parallel to TBs in TBAZ are more favorable if the applied stress is suitable. The TB influence in the interior of twins is small and can be ignored, where veins, walls, labyrinths or even cells could be developed with increasing applied strain amplitudes (figure 3). In this case, TBs behave almost the same as conventional grain boundaries. However, because of the planar character of TBs, the affected zones near TBs are found more commonly and distinctly than possible affected zones near grain boundaries. When the twin thickness reduces to between about 1 mm and 200 nm, only parallel slip systems can operate without too much impediment, leading to PSB-like structure (figure 4a). Dislocations gliding on other slip systems oblique to TBs, would be blocked by TBs. A PSB-like structure in twins has also been found in the work of Kawazoe and co-workers [20, 21]. It is indicated that slip systems that are not coplanar with the twin boundary are suppressed in thin twins. When the local stress distribution is not suitable, however, none of the slip systems is preferred and no characteristic dislocation structures could be found (figure 4b). During cyclic deformation, edge dislocations are mainly generated from grain boundaries at twin terminals, and then glide into the twin interior developing into wall structures, forming a PSB-like structure (figure 4a). Screw dislocations between the parallel walls (ladders) could glide back and forth carrying a large plastic strain (figure 8). PSB-like structures in twins are all confined in grains and cannot traverse the whole sample, which can be thought of as a special wall structure with comparatively stable state. TB g = 111 Dislocation debris (GNDs) Wall ends Screw dislocations Figure 8. Screw dislocations between the walls of PSB-like structures and dislocation debris (mainly geometrically necessary dislocations, GNDs) adhering to TBs, in sample fatigued at a plastic strain amplitude of 3.9 10 3.
Dislocation evolution in twins of cyclically deformed copper 621 Figure 9. Model of wall (ladder) structure with condensed edge dislocation dipoles, some size parameters including the wall spacing s, the wall height h, the wall length l and the wall width w, are noted. PSB-like structures may be promoted to form in the twins thicker than 200 nm and less than 1 mm. In the work of Zhang et al. [18], however, no clearly defined dislocation structures were found in thin films or in small diameter grains with size <3.0 mm. The difference is mainly due to the different character between grain boundaries and twin boundaries. Twins always show a lamellar shape and most of the twins with PSB-like structures have lengths of several micrometers and thicknesses of 200 1000 nm. In this case, the effect of TBAZ can be enhanced due to the overlap of the TBAZ (about 1 mm). In other words, the dislocation motion parallel to TB can be enhanced and a PSB-like structure can finally be formed. This is quite different from that of curved grain boundaries. If the twin thickness is <200 nm, the stable PSB-like structure or the wall structure cannot exist in the twins. From previous results [16, 22], it is known that an aspect ratio of a wall (i.e. the ratio of height over width of a wall, noting that the definition of width of a wall w is different from the spacing between two walls s, as shown in figure 9) can evolve from about 12 to about 1 as cyclic deformation proceeds. No aspect ratio <1 can stably exist for walls. In the present experiment, the width of a wall in the PSB-like structure is about 150 nm (figure 8). Therefore, a stable wall structure can exist in a twin with a wall height >150 nm, that is, the twin thickness must be >150 nm for the formation of a wall structure, in accordance with the observed results (200 nm). When the twin thickness reduces to below 20 nm, the interaction between crystal dislocations and TBs are increased dramatically. Reactions between dislocations and TBs become more frequent, and most of the dislocations observed in twins are considered interfacial dislocations. A dislocation loop was accidentally found to bow out of TB, which is somewhat special because of the low energy of coherent TB. Because of the fewer crystal dislocations, such thin twins may be considered as second phases to block dislocation motions out of them and therefore can strengthen the material, particularly when strain amplitude is large (>10 3 ). The strengthening effect will be more significant when the twin thickness decreases and the volume fraction of those thin twins increases, in accordance with the results of Lu et al. [12].
622 X. L. Guo et al. 5. Summary During cyclic deformation, twin thickness plays a crucial role on slip activity and different dislocation patterns are formed: (i) when the twin thickness W t >1mm, corresponding with the characteristic size of dislocation substructures in cyclically deformed Cu, slip systems with large Schmid factor are preferentially activated without much effects of twin boundaries. Walls with different directions relative to TBs and labyrinths are found in twins, similar to that in single crystals; (ii) when the twin thickness lies in the range of 1 mm>w t > 200 nm, slip systems oblique to TBs are restricted in the vicinity of TBs. Only slip systems parallel to TBs can operate intensively and PSB-like structures are finally formed; (iii) when the twin thickness lies in the range of 200 nm > W t > 20 nm, no characteristic dislocation substructures can be formed any more. Only some dislocation fragments are found to impinge TBs irregularly, most of which are considered as geometrically necessary dislocations (GNDs) as a result of strain incompatibility near TBs; (iv) when the twin thickness W t < 20 nm, no crystal dislocations can be clearly observed in the interior of the twins. However, some interfacial dislocations are found adhering to TBs, resulting from dislocation interactions with TBs or GNDs. Acknowledgements This work was financially supported by National Natural Science Foundations of China (No. 50201017, No. 50021101 and No. 50271075). References [1] N. Thompson, in Fracture, edited by B.L. Averbach, D.K. Felbeck, G.T. Hahn and D.A. Thomas (J. Wiley, New York, 1959). [2] L. Llanes and C. Laird, Mater. Sci. Engng. A157 21 (1992). [3] L. Llanes, A.D. Rillett and C. Laird, et al., Acta metall. Mater. 41 2667 (1993). [4] L. Llanes and C. Laird, Mater. Sci. Engng A161 1 (1993). [5] T. Luoh and C.P. Chang, Mater. Sci. Engng A256 18 (1998). [6] Z.R. Wang and H. Margolin, Metall. Trans. A16 873 (1985). [7] A. Heinz and P. Neumann, Acta metall. mater. 38 1933 (1990). [8] P. Gopalan and H. Margolin, Mater. Sci. Engng A142 11 (1991). [9] P. Peralta, L. Llanes and J. Bassan, et al., Phil. Mag. A70 219 (1994). [10] A.T. Winter, O.B. Pedersen and K.V. Rasmussen, Acta Metall. 29 735 (1981). [11] H. Mughrabi and R. Wang, in Deformation of Polycrystals: Mechanisms and Microstructures, edited by N. Hansen, A. Horsewell and T. Leffers, et al. (Roskilde, Denmark, Risoe National Laboratory, 1981). [12] L. Lu, Y.F. Shen and X.H. Chen, et al., Science 16 422 (2004). [13] X.L. Guo, L. Lu and S.X. Li, Mater. Sci. Engng A405 239 (2005). [14] E.E. Laufer and W.N. Roberts, Phil. Mag. 14 67 (1966). [15] P.J. Woods, Phil. Mag. 28 155 (1973). [16] S.X. Li, Y. Li and G.Y. Li, et al., Phil. Mag. A82 867 (2002). [17] M.F. Ashby, Phil. Mag. A21 399 (1970).
Dislocation evolution in twins of cyclically deformed copper 623 [18] G.P. Zhang, R. Schwaiger and C.A. Volkert, et al., Phil. Mag. Lett. 83 477 (2003). [19] E. Thiele, C. Holste and R. Klemm, Z. Metallkunde 93 730 (2002). [20] H. Kawazoe, M. Yoshida and Z.S. Basinski, et al., Scripta mater. 40 639 (1999). [21] H. Kawazoe and M. Niewczas, Phil. Mag. 84 381 (2004). [22] P. Neumann, Mater. Sci. Engng 81 465 (1986).