Ultrafine Grained Materials III Edited by Y.T. Zhu, T.G. Langdon, R.Z. Valiev, S.L. Semiatin, D.H. Shin, and T.C. Lowe. TMS (The Minerals, Metals & Materials Society), 2004
MICROSTRUCTURE AND TEXTURE DEVELOPMENT IN COPPER AND ALUMINUM UNDER ECAP: NEW EXPERIMENTAL RESULTS AND MODELING Y. Estrin1*, R.J. Hellmig1, S.C. Baik2, H.S. Kim3, H.-G. Brokmeier4 and A. Zi1 1
IWW, Technische Universität Clausthal, Clausthal, D-38678, Germany 2 Pohang Iron and Steel Co. Ltd., Pohang, Korea 3 Department of Metallurgical Engineering, Chungnam National University, Daejeon, Korea 4 GKSS-Forschungszentrum Geesthacht GmbH, Geesthacht, D-21494, Germany
Abstract Copper and aluminum were processed by equal channel angular pressing (ECAP). The effect of the ECAP route and the number of passes on strength and ductility as well as on the dislocation cell structure and texture was studied for both materials. To investigate the stress distribution in ECAP deformed workpieces, hardness maps with small imprint spacing were produced for various sections of the workpieces. The experimental results were compared with the simulations based on a phase mixture model that combines a dislocation density evolution approach with crystal plasticity considerations. A good predictive capability of the model was confirmed. Keywords: ECAP, constitutive modeling, mechanical properties, texture, aluminum, copper.
Introduction Equal channel angular pressing has become a well established method for the production of bulk ultra fine grained (UFG) materials [1]. In this process, a high shear strain is imparted on the material by repetitive pressing of a workpiece through a die having two intersecting channels. In this process, the cross-sectional dimensions of the workpiece remain practically unchanged [2,3]. To facilitate multi pass processing, it is common to use a slightly reduced exit channel cross-section [1]. One of the possible scenarios of the formation of an ultra fine grained structure implies the evolution of dislocation cell boundaries and their transformation to high angle grain boundaries due to an ‘accumulation’ of the misorientation between adjacent cells with strain [4]. The use of models based on the dislocation density evolution and the variation of the dislocation cell size can thus shed light on the process of grain refinement. A dislocation density based constitutive model suitable for large strains (as occurs in ECAP) was suggested by Estrin et al.[5]. The model accounts for the strain hardening behavior of dislocation cell-forming crystalline materials. Details of a three dimensional version of this model, which was applied to aluminum [6] and copper [7], were given in [8]. This report provides an overview of the predictive capability of the model as applied to aluminum and copper, supported by additional experimental results. The calculations were performed using the finite element code ABAQUS. _______________________ *Corresponding Author:
[email protected]
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Experimental Procedures Technical purity (99.95%) copper specimens were heat treated at 450°C for two hours prior to ECAP processing. Route Cr, in which the specimens were rotated by 180° about their axis and turned upside down between two consecutive passes, was used. The specimens underwent up to 8 ECAP passes. The ECAP rig used had a split design, with the entire channel being contained within one part of the die. The angle Θ between the entrance and the exit channels was 90° and the die corner angle Ψ was 20°. This die geometry corresponds to a strain of approximately 1 per pass. To facilitate multi pass processing, the exit part of the channel was reduced in height and contained a slight extrusion step in the horizontal direction. For processing an INSTRON 8502 machine was used allowing an applied load up to 200 kN. A molybdenum disulphide grease was used as lubricant. The processing speed was 8 mm per minute. The same setup was used for the processing of pure (99.99%) aluminum having an initial grain diameter of 2 mm. Route Cr ECAP with a pressing speed of 4 mm per minute was employed. The average cell size of the deformed specimens was determined by transmission electron microscopy (TEM, Philips CM 200) combined with electronic image analysis. To determine the stress vs. strain behavior of the ECAP-processed specimens, uniaxial tensile tests were performed at a strain rate of 10-3 s-1. In addition, automated Vickers hardness measurements (Struers Duramin hardness tester) were performed on several sections of the specimens. A high imprint density was chosen (imprint spacing of 0.5 mm in transversal and 1 mm in pressing direction). Complete {111} pole figures were measured by neutron diffraction using 20 mm long samples cut from the homogeneous middle parts of the ECAP deformed workpieces. As the entire transverse section of a specimen was sampled in neutron diffraction experiments, the pole figures obtained represent the average texture of the specimen. Results and Discussion Stress and strain evolution Figure 1 shows the experimentally determined stress in dependence of the cumulative equivalent strain for the ECAP deformed copper and aluminum. The simulated curve in Figure 1 is in reasonable good agreement with the experimental data. 1st
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Figure. 1. Stress vs. strain behavior: comparison between simulation and experiment (left: copper, data from up to 8 pressings; right: aluminum, data for up to 4 pressings).
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Already after a single ECAP pass there was a strong increase in tensile strength, subsequent passes adding little to strength. The strain hardening rate decreased noticeably for the second pressing and beyond. This behavior is well reflected by the model.
Figure. 2. Equivalent strain distribution in copper obtained by finite element simulation of ECAP, Route Cr (left: 1 pass; right: 4 passes).
The simulated strain distribution in an ECAP deformed workpiece can be seen in Figure 2. In the middle part, the strain increases by about 1 per pass. After the first pass, the strain is predicted to be lower near the bottom of the specimen. The left picture of Figure 2 shows the formation of a die corner gap, which occurs due to large strain hardening and hence lower shear deformation in this region during the first ECAP pass [9,10]. Repetitive specimen rotation under route Cr reduces the differences between the top and the bottom parts of the workpiece, as seen in the right picture of Figure 2. After 4 ECAP passes the die corner gap is also reduced significantly, owing to a decrease in the strain hardening rate with strain.
ECA pressing direction Figure. 3. Vickers hardness maps of the specimen surface of a copper specimen (single ECAP pass). The hardness levels are represented by the grey scale (80 – 150 HV, as shown by the scale bar).
Figure 3 shows the measured Vickers hardness maps of the copper specimen surface after a single ECAP pass. The area of the measured surface corresponding to a homogeneous part of a pressed specimen was 26 mm x 10 mm. The pictures are arranged so as to reflect the adjacent surfaces. The bottom surface exhibits a lower overall hardness than the other surfaces. The left and the right sides also show a smaller hardness in the near-bottom area, which fits well with 3
the simulated results presented above. The larger hardness of the major parts of the side surfaces may also be caused by the additional extrusion through the exit channel of the ECAP die that compresses the specimen in the horizontal direction. For larger strains, the hardness measurements followed the model predictions: a slightly smaller hardness was observed at the top and the bottom surfaces as compared to the side surfaces.
Figure. 4. Vickers hardness maps of the middle cross-section (cut normally to the pressing direction) of a single pass copper specimen.
Figure 4 shows a hardness map for a cross-section of a single pass copper specimen cut in the middle normally to the pressing direction, where mainly homogeneous deformation was expected. A lower hardness was observed near the bottom, in an area whose size is comparable to the one predicted by the simulation. The rest of the area tested was quite homogeneous, which was also confirmed by additional measurements on other cross-sections. Altogether, the presented hardness maps show a good correlation with the calculated stress distribution (not shown here). Average cell size evolution The evolution of the dislocation cell size shows a similar behavior as the evolution of the equivalent stress. The average dislocation cell size was determined as follows. The area of the apparent dislocation cells observed in TEM was converted into an equivalent circle diameter; for each specimen several hundreds of dislocation cells were used to determine the log-normal cell size distribution yielding an average reported below. After a single pass the average cell size of both materials was significantly decreased and did not show much variation in subsequent pressings. This can be seen in Figure 5 for copper (left) and aluminum (right). A good correspondence between the experimental and the simulated curves is evident. The average dislocation cell size attained after several ECAP passes is about 200 nm for copper and around 1 µm for aluminum. This difference can be explained by the lower stacking fault energy of Cu, leading to a lower dynamic recovery rate for Cu [11]. A larger dislocation cell size found in ECAP processed Al [12] was also interpreted in terms of dynamic recovery being facilitated by its higher stacking fault energy. The differences in the tensile properties observed can also be accounted for on this basis. All features described above are correctly represented by the model used.
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Average cell size evolution in ECAP deformed copper (left) and aluminum (right).
Figure 6 shows typical bright field TEM pictures taken after four ECAP passes for Al and Cu. In the left micrograph, the dislocation cell structure of ECAP processed copper is seen. It exhibits a typical lamellar cell block structure with an average cell size of around 200 nm. The right picture shows the microstrucrture of aluminum, the average demonstrates the large difference in cell size between copper and aluminum, which is around 1 µm in the latter case. In aluminum the formation of lamellar bands was observed as well.
Figure. 6.
TEM pictures of ECAP deformed copper (left) and aluminum (right) after four passes.
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Texture evolution The texture evolution with increasing strain was analyzed using neutron diffraction. Below, (111) pole figures are presented, ED denoting the extrusion (here: ECAP pressing) direction and TD the transverse direction. In case of copper the undeformed material exhibits a very weak, almost random texture. Therefore, it was possible to use initially random texture in the simulations. To compare the simulated results with the experimentally determined texture, the calculated pole figure for an area in the middle of the specimen was taken as a representative average texture.
Figure. 7.
(111) pole figures for copper after a single ECAP pass (left: measured; right: simulation).
In Figure 7 a measured and a simulated (111) pole figure for a Cu specimen that underwent a single ECAP pass are juxtaposed. A good agreement between both figures can be seen, the main peaks in the simulation being fairly close to the experimentally determined positions. Due to the lower strain and strain variation in the bottom area of the specimens a non-uniform texture may be expected to occur in that area, but the volume fraction of this area turns out to be too low to influence the position of the main peaks in the experimentally determined pole figures. This confirms the adequacy of using the texture from the middle area far enough from the top or the bottom for a comparison between simulation and experimental data. Figure 8 shows measured and simulated (111) pole figures for a copper specimen that has been subjected to 4 ECAP passes. Again, a good accord between simulation and experiment is confirmed. For Al, good agreement between measured and simulated pole figures was obtained as well [13].
Figure. 8.
(111) pole figures for copper after four ECAP passes (left: measured; right: simulation).
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Conclusion Using a dislocation density based constitutive model it was possible to provide an adequate description of the evolution of stress, cell size and texture with the number of ECAP passes for both copper and aluminum. Acknowledgements Funding from the Deutsche Forschungsgemeinschaft through grant Es 74/9-1 is gratefully acknowledged. One of the authors (SCB) wishes to acknowledge support from the Ministry of Science and Culture of Lower Saxony. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
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