Deformation banding and its influence on deformation textures formation

It is shown by a crystallographic etching technique that deformation banding is an important deformation mode in copper. In a cold rolled coarse grain copper, deformation banding forms in a three dimensional manner dividing grains into a large number of bands of different orientations. The influence of this important, but long ignored deformation mode, is studied by incorporating it into the Taylor model. The predicted textures from the new model are better than those from other existing models in mainly two aspects. Firstly, the present model predicts the co-existence of the three major FCC rolling texture components, namely {123)<634> or S component, {112)<111> or C and {110}<112> or B. The existing models are deficient in that they predict either C and S or B, but not their co-existence. The second point is that textures predicted by the existing models are always too sharp compared to the experimental textures. The deformation banding model predicts texture peaks with larger spread and hence more realistic texture sharpness. Introduction Deformation bandinq is a process in which different reqions of a deforming crystal gradually rotate to different orientations as deformation proceeds. Its importance to the deformation process has been repeatedly emphasized by Barrett et. al. [I-31 and Chin [4]. However, only a limited amount of work has been done recently [5-81 mainly on single crystals or for recrystallisation studies. The purpose of the present work has been to investigate the influence of this deformation mode in polycrystalline materials. Experimental Results and Discussions High purity copper (99.99%) of two different grain sizes, 40 and 3000pm, with weak initial textures were cold rolled to various strains up to 92% reduction. The behaviour of the two materials has been confirmed to be typical by various standard techniques including X-ray diffraction, optical and transmission electron microscopy. The results shown in this paper were obtained by a crystallographic etching technique recently developed by Kohlhoff et al. [9]. By etching electropolished surfaces of copper in concentrated nitric acid, the {Ill) planes within grains are preferentially exposed. As a result, different etching patterns are observed in grains of different orientations. The general cold rolled microstructure as revealed by the Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:19937323 2028 JOURNAL DE PHYSIQUE IV crystallographic etch is shown in figure 1. Figure la shows a longitudinal section of the coarse grained copper after 85% reduction. The most remarkable feature is the unexpected thickness of the layered structure. The thickness of the layers each with different orientations ranges from about 1 to 50 pm and has an average value of 17.2 pm (measured by a linear intercept method at 4 different locations in two specimens containing over 100 layers). This value is much smaller than the average grain thickness after 85% reduction, which is about 3000~0.15 or 450pm. It therefore follows that each grain deforms to give on the average about 26 (=450/17.2) layers. Fig. 1. a) SEM micrograph of crystallographically etched longitudinal section of coarse grained copper after 85% cold rolling; b) Rolling plane section of coarse grained copper after 70% reduction. The grain splits into alternative bands of complementary B orientations (i.e. (110)[1i2] and (llO) [i12]); c) Schematic diagram of the etching patterns of (110) [112], (110) [I123 AND (110) [OOl] when observed in the rolling plane. Possible deformation processes which would subdivide a grain into regions of different orientation, include mechanical twinning, martensitic transformation and deformation banding. The operation of the first two processes is excluded for two reasons. Firstly, transmission electron microscope studies have not revealed any evidence of twinning or martensitic transformation in copper deformed at room temperature. Furthermore, both processes would produce lattice regions of new orientation having sharp boundaries with the matrix. Both diffuse and sharp boundaries are observed in the present studies. Diffuse boundaries are more common at low strains (~50% reduction) and sharp boundaries at high strains (>85% reduction). It is therefore believed that deformation banding is responsible for the observed subdivision of the grains. Figure lb is a micrograph taken from the rolling plane section of the coarse grained copper after 75% reduction. It clearly shows that a grain is divided into bands of two symmetrically related {110)<112> orientations (i.e. (110) [li2] and (110) [i12]) with (110) [OOl] in between, fig. lc) . The average band width in the rolling plane section is measured to be 120 pm. This is again much narrower than the original grain width of 3000pm, suggesting that on the average each grain is divided into 25 (=3000/120) regions by banding with boundaries parallel to the longitudinal planes. It therefore appears that banding of at least two different geometries is operating simultaneously, namely banding with planes parallel to the rolling and longitudinal planes respectively. As a consequence, grains are three dimensionally subdivided and on the average, each grain will give over 600 (25x26, assuming that the two banding geometries are independent) bands in three dimensions. Deformation banding was also observed in the fine grained copper but not as pronounced as in the coarse grained copper. From the measurement of the longitudinal section, each grain gives an average of 2.4 layers. This value together with the corresponding one from the coarse grained copper agrees reasonably well with a recent prediction by Lee et al. [lo] that the average number of bands (in one dimension) formed in a grain is proportional to the square root of the grain size. No measurements have been carried out on the rolling plane of the fine grained copper because satisfactory etching cannot be achieved due to the small layer thickness in the normal direction. Because of these important microstructural changes, it is likely that deformation banding also significantly affects the development of the deformation texture. It has been believed for many years that copper deformed at room temperature does so mainly by homogeneous slip processes. Deformation models based on homogeneous slip have indeed predicted deformation textures similar to those observ,ed experimentally [ll-121. However, these predicted textures have a major difference from the experimentally determined textures. The {110}<112> orientation is one of the major stable rolling texture component in copper but is predicted by neither the Full Constraint (FC) nor the Relaxed Constraint (RC) Taylor models [13]. Calculation with these models shows that {110}<112> is stable only if shear in the rolling plane is allowed (fig. 2a). However, relaxing this shear constraint in the deformation not only produces a severe incompatible shape change with the surrounding, but also destroys other experimentally observed stable texture components, namely {123)<634> and {112)<111>. An earlier analysis by Aernoudt and Stuwe [14 3 affords a possible solution in suggesting that if grains of (110) [1i2] and (110) [I121 orientations are put side by side, the opposite shears will then be cancelled out (fig. 2b) . While they made no further suggestion on how the special microstructural arrangement forms, it is clear from f ig-are 2 that this structure which stabilises the {110)<112> orientation could be produced by deformation banding. Modellinu of Deformation bandinq It is clear from the above discussion that the deficiency of the current deformation models is mainly due to their failure to address the significance of deformation banding. In order to study its influence on the deformation processes, a texture simulation model (DB model) is developed by incorporating deformation banding into the Taylor model. This is done by assuming that all grains behave macroscopically as "Taylor grainsg1, whether deformation banding occurs or not. In the original Taylor model, it is assumed that the strain in each grain equals the macroscopic external strain. If deformation banding occurs, this assumption becomes: The average strain over different regions of a banded grain should equal the macroscopic external strain. Thus, the microscopic deformation within each segment can be different from the macroscopic one, so long as their average strain is compatible to themselves and JOURNAL DE PHYSIQUE IV