HUANG et al:NANOSTRUCTURED Cu 1503 modate further deformation,especially when the ing,large subgrains may further divide into smaller strain path changes. subgrains.and the misorientation between subgrains Another salient feature of the deformation structure may increase to form low-angle GBs and high-angle is the DTZ,as shown in Figs 4(a)and 8.Such a DTZ GBs (>15).The above theory has worked pretty well may form cell structure through recovery.In fact, with rolling-deformation of metals with a medium to transformation of the DTZ to cell structure is in pro- high stacking fault energy such as Cu and Al [16,17, gress as shown in the area marked by a white square 19,26],although the formation of subgrain structure in Fig.4(a) from dislocation cells has not been experimentally observed. 4.2.Microstructural evolution During the rolling deformation,the work-piece Grain refinement is caused by dislocation gliding, is deformed in one direction (i.e.under constant accumulation,interaction,tangling and spatial strain path)with increasing strain.This is different rearrangement.Deformation in polycrystalline from the RCS process,in which the work-piece materials has been described by a number of mod- was rotated between consecutive RCS cycles, els,including Sach's zero constraint model [441. resulting in the change of strain path.To a certain Taylor's full constraint model [45]and relaxed con- extent,the rotation of work-piece makes the defor- straint model [46].For equiaxed grains,it is gener- mation mode of RCS process resemble that of ally agreed that the Taylor's model is most appro- fatigue.However,unlike fatigue,larger plastic priate [46,47].According to Taylor's model,slip is deformation is introduced to the work-piece during uniform within each grain and strain compatibility each RCS cycle. is achieved by simultaneous operation of at least The unique deformation mode in the RCS process five slip systems.As discussed below,the uniform is expected to affect the deformation microstructure deformation within each grain as hypothesized by and is indeed shown to do so in Fig.8.Similar to Taylor is often not followed in the deformation of rolling-induced microstructure,Fig.8 shows that the real materials.Consequently,the Taylor's model grains of Cu deformed by RCS are divided into CBs has been modified. and dislocation cells.However,new microstructural It has been observed in coarse-grained fcc features including UDWs,IDCs,and DTZs are also materials such as copper that each grain is divided observed.The UDWs and DTZs are,to some extent, into many volume elements during plastic defor- similar to dislocation structures observed in fatigued mation [16-27,48-52]and there are differences in polycrystalline Cu [40,41].In addition,unlike the the number and selection of active slip systems rolling-induced microstructure.the dislocation cells among neighboring volume elements [20,21].Each are not well networked. volume element deforms under a reduced number During the RCS process,even in the same CB or (less than 5)of slip systems,but a group of adjacent subgrain,slip systems will change when the strain volumes act collectively to fulfill the Taylor cri- path changes from one RCS cycle to the next.As a terion.Each volume element is usually subdivided consequence.the dislocations not only interact with into cells with dislocations forming cell boundaries. other dislocations in the current active slip systems, For this reason,the volume elements are referred but also interact with inactive dislocations generated as CBs.Dislocations from neighboring CBs meet in previous RCS cycles.This will promote the forma- at their boundaries and interact to form CB bound- tion of DTZs and IDCs.Liu et al.[40]proposed a aries.This type of boundary is named GNB since mechanism for the formation of dipolized dislocation they are needed to accommodate the misorientation tangle during fatigue.It is not clear if the same mech- in neighboring CBs.The dislocation cell bound- anism applies to the formation of DTZs in RCS-pro- aries are called incidental boundaries since they are cessed Cu. generated by statistical mutual tapping of glide dis- As marked by white triangles in Fig.8,dislocations locations [20].often supplemented by "forest"dis-may pile up on one side of DDWs to form UDWs. locations [36]. This indicates that DDWs formed first and dislo- The misorientations are very small across cell cations then piled up against the DDWs.The other boundaries but much larger across cell-block bound- type of UDWs was formed by the interaction of dislo- aries.With increasing strain,the misorientations cations from CBs on both sides (see the place marked across cell and CB boundaries increase,and the size by white squares).Both types of UDWs may sub- of the CBs become smaller due to further division. sequently transform to small dislocation cells.for- At a certain strain,the misorientation between ming two types of CSCWs.The former form CSCWs neighboring cells becomes so high that additional slip whose boundaries on one side are delineated by system may be triggered in the cells,which converts DDWs (see the place marked by a black triangle), incidental boundaries into GNBs and make the dislo-while the latter form CSCWs whose both boundaries cation cells act like CBs.Domains surrounded by are composed of rough,small cell boundaries (see the GNBs,such as CBs and CB-like dislocation cells are place marked by a black square). called subgrain structures,and the GNBs are also With increasing RCS strain (cycles),the IDCs may called subgrain boundaries [20].With further strain- become an isolated subgrain (e.g.Fig.5(a)).Also,HUANG et al.: NANOSTRUCTURED Cu 1503 modate further deformation, especially when the strain path changes. Another salient feature of the deformation structure is the DTZ, as shown in Figs 4(a) and 8. Such a DTZ may form cell structure through recovery. In fact, transformation of the DTZ to cell structure is in pro￾gress as shown in the area marked by a white square in Fig. 4(a). 4.2. Microstructural evolution Grain refinement is caused by dislocation gliding, accumulation, interaction, tangling and spatial rearrangement. Deformation in polycrystalline materials has been described by a number of mod￾els, including Sach’s zero constraint model [44], Taylor’s full constraint model [45] and relaxed con￾straint model [46]. For equiaxed grains, it is gener￾ally agreed that the Taylor’s model is most appro￾priate [46, 47]. According to Taylor’s model, slip is uniform within each grain and strain compatibility is achieved by simultaneous operation of at least five slip systems. As discussed below, the uniform deformation within each grain as hypothesized by Taylor is often not followed in the deformation of real materials. Consequently, the Taylor’s model has been modified. It has been observed in coarse-grained fcc materials such as copper that each grain is divided into many volume elements during plastic defor￾mation [16–27, 48–52] and there are differences in the number and selection of active slip systems among neighboring volume elements [20, 21]. Each volume element deforms under a reduced number (less than 5) of slip systems, but a group of adjacent volumes act collectively to fulfill the Taylor cri￾terion. Each volume element is usually subdivided into cells with dislocations forming cell boundaries. For this reason, the volume elements are referred as CBs. Dislocations from neighboring CBs meet at their boundaries and interact to form CB bound￾aries. This type of boundary is named GNB since they are needed to accommodate the misorientation in neighboring CBs. The dislocation cell bound￾aries are called incidental boundaries since they are generated by statistical mutual tapping of glide dis￾locations [20], often supplemented by “forest” dis￾locations [36]. The misorientations are very small across cell boundaries but much larger across cell-block bound￾aries. With increasing strain, the misorientations across cell and CB boundaries increase, and the size of the CBs become smaller due to further division. At a certain strain, the misorientation between neighboring cells becomes so high that additional slip system may be triggered in the cells, which converts incidental boundaries into GNBs and make the dislo￾cation cells act like CBs. Domains surrounded by GNBs, such as CBs and CB-like dislocation cells are called subgrain structures, and the GNBs are also called subgrain boundaries [20]. With further strain￾ing, large subgrains may further divide into smaller subgrains, and the misorientation between subgrains may increase to form low-angle GBs and high-angle GBs (>15°). The above theory has worked pretty well with rolling-deformation of metals with a medium to high stacking fault energy such as Cu and Al [16, 17, 19, 26], although the formation of subgrain structure from dislocation cells has not been experimentally observed. During the rolling deformation, the work-piece is deformed in one direction (i.e. under constant strain path) with increasing strain. This is different from the RCS process, in which the work-piece was rotated between consecutive RCS cycles, resulting in the change of strain path. To a certain extent, the rotation of work-piece makes the defor￾mation mode of RCS process resemble that of fatigue. However, unlike fatigue, larger plastic deformation is introduced to the work-piece during each RCS cycle. The unique deformation mode in the RCS process is expected to affect the deformation microstructure and is indeed shown to do so in Fig. 8. Similar to rolling-induced microstructure, Fig. 8 shows that the grains of Cu deformed by RCS are divided into CBs and dislocation cells. However, new microstructural features including UDWs, IDCs, and DTZs are also observed. The UDWs and DTZs are, to some extent, similar to dislocation structures observed in fatigued polycrystalline Cu [40, 41]. In addition, unlike the rolling-induced microstructure, the dislocation cells are not well networked. During the RCS process, even in the same CB or subgrain, slip systems will change when the strain path changes from one RCS cycle to the next. As a consequence, the dislocations not only interact with other dislocations in the current active slip systems, but also interact with inactive dislocations generated in previous RCS cycles. This will promote the forma￾tion of DTZs and IDCs. Liu et al. [40] proposed a mechanism for the formation of dipolized dislocation tangle during fatigue. It is not clear if the same mech￾anism applies to the formation of DTZs in RCS-pro￾cessed Cu. As marked by white triangles in Fig. 8, dislocations may pile up on one side of DDWs to form UDWs. This indicates that DDWs formed first and dislo￾cations then piled up against the DDWs. The other type of UDWs was formed by the interaction of dislo￾cations from CBs on both sides (see the place marked by white squares). Both types of UDWs may sub￾sequently transform to small dislocation cells, for￾ming two types of CSCWs. The former form CSCWs whose boundaries on one side are delineated by DDWs (see the place marked by a black triangle), while the latter form CSCWs whose both boundaries are composed of rough, small cell boundaries (see the place marked by a black square). With increasing RCS strain (cycles), the IDCs may become an isolated subgrain (e.g. Fig. 5(a)). Also