Rolling textures in nanoscale Cu/Nb multilayers
Introduction
Deformation behavior of nanostructured materials has received significant interest recently due to the extremely high strength observed in these materials. One can easily synthesize nanolayered metallic composites with nanometer-scale individual layer thickness using physical vapor deposition techniques such as electron beam evaporation or magnetron sputtering. While the evolution in hardness of these nanolayered metallic composites as a function of layer thickness has been studied [1], [2], [3], [4], little or no literature exists on the response of these materials to large plastic deformation. Previous work indicates that Hall–Petch type dislocation pile-up models are not applicable at nanoscale layer thicknesses. Rather, deformation may involve confined layer slip, in which single Orowan (hairpin) dislocation loops are confined to glide within individual layers, followed by either annihilation of dislocations at interfaces or transmission of single dislocations across interfaces [5], [6], [7], [8], [9], [10]. The deformation texture evolution in bulk metals where dislocation pile-up type deformation is active has been studied in great detail. However, corresponding studies have not been conducted in nanoscale materials where single rather than pile-up dislocation behavior may dominate.
Associated work on transmission electron microscopy of rolled multilayers [11] and theories for deformation and recovery [5], [7], [10], [12] indicate possible reasons to expect different textures. For thin layers, initial confined layer slip in the softer phase will deposit interfacial dislocation content until the load transfer eventually causes the harder phase to co-deform. During co-deformation, new interfacial area is created. Further, annihilation can take place at interfaces as they receive dislocation content from confined layer slip in both adjoining phases or as they receive dislocation content from one phase and transmit new content into the other phase. The efficiency of annihilation will depend on the relative orientation of slip systems on either side of the interface and on the uniformity of deposited slip, but work hardening ultimately ensues from imperfect annihilation. The individual layer thickness is expected to affect the efficiency of annihilation, as multilayers with smaller individual layer thickness are predicted to deposit more uniform, single slip content at interfaces than those with larger layer thickness [6].
There is a thermodynamic driving force to maintain a low energy Kurdjumov–Sachs interfacial orientation for the interface. Also, the above Orowan-loop-glide/interface-annihilation mechanism would tend to maintain a K–S interface if the slip within each phase were symmetrical, so that no crystal rotation occurred. Indeed, this mechanism would suggest that the favored orientation should be the K–S texture: ND || 〈1 1 0〉bcc || 〈1 1 1〉fcc and RD || 〈0 0 1〉bcc || 5° from 〈1 1 0〉fcc, where ND is the normal direction and RD is the rolling direction. Both of these effects contribute to the stabilization of this K–S texture during rolling. However, surface energy and recovery concepts typically are not directly incorporated in crystal plasticity modeling; so, there are two issues in the modeling. First, does the crystal plasticity itself favor the retention of the K–S texture? Second, can the crystal plasticity model be modified to emulate the surface energy/recovery aspects to see if the K–S texture is favored?
In this article, we report on the texture evolution in self-supported Cu–Nb multilayers deformed by room temperature rolling and develop a crystal plasticity model to interpret the new deformation textures in rolled nanoscale metals.
Section snippets
Experimental procedure
Cu–Nb multilayers were synthesized by d.c. magnetron sputtering at room temperature on Si or glass substrates. For the texture measurements presented, two layer thicknesses (i.e., one-half of the bilayer repeat length) were used: 75 nm and 4 μm. The total thicknesses of these two samples were 7.5 and 16 μm, respectively. After deposition, the multilayered thin foils could be peeled off the substrates easily. The specimens were cut into strips approximately 6.25 mm wide and 25 mm long,
Experimental results
Statistics concerning the texture strength (the square root of the texture index [18]) and the RP error of the ODF calculation [14] are presented for all samples in Table 1. Pole figures were recalculated from the ODF in order to display non-measured regions at sample tilt angles greater than 80°. The accuracy of these regions (both in the pole figures and in three-dimensional orientation distribution space) is dependent on the relative ODF error. For the nanolayer rolled Cu, the RP error for
Modeling
The objective of the modeling effort is to determine whether the experimentally observed in-plane texture in rolled Cu/Nb multilayers can be predicted and, if so, under what conditions or assumptions. The underlying strategy will be to determine for the Cu and Nb phases, the combination of slip activities requiring the minimum compressive rolling stress to deform them. To do so, the assumption is made that the Cu and Nb phases have the experimentally observed Kurdjumov–Sachs ND orientation
Rolling stress for a fixed orientation
We display the minimum compressive rolling stress as a function of texture angle θ for Cu in Fig. 9(a) and Nb in Fig. 9(b), assuming that the grains do not rotate with deformation (dω=0). Five curves are shown for each material, corresponding to different assumptions for the values of critical resolved shear stress on various slip systems (β). The reference analysis, R00, denotes a uniform critical resolved shear stress, τ0, on all slip systems listed in Table 2a and b. The remaining cases
Discussion
The crystal plasticity model appears to capture the experimentally observed primary texture, but not the weaker secondary texturing. In particular, if the driving forces Fθ from the Cu and Nb phases (see Fig. 10) are superimposed, the combined trend is for Cu and Nb grains in the angular range −90°<θ<−30° to rotate during rolling deformation to the interval −60°<θ<−54.7°. This corresponds to the experimental K–S texture that RD is approximately parallel to Cu and [0 0 1]Nb. Combined
Conclusions
Experimental observations of the rolling texture in sputter-deposited Cu/Nb multilayered thin films indicate that when the initial individual layer thickness is 2–4 μm or larger, a bulk rolling texture forms during a 50% thickness reduction, but when the initial individual layer thickness is 75 nm, a unique rolling texture results. The unique K–S texture is characterized by polycrystalline layers which reduce uniformly in thickness during rolling and columnar grains which rotate around the
Acknowledgements
PMA gratefully acknowledges the support of the Air Force Office of Scientific Research Metallic Materials Program (F49620-01-1-0092), the National Science Foundation Mechanics & Materials and Metallic Materials Programs, and a Matthias Scholar position from Los Alamos National Laboratory while on sabbatical there. This research program at Los Alamos National Laboratory is funded by the Department of Energy, Office of Science, Office of Basic Energy Sciences. The authors acknowledge discussions
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