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Asymmetric flow during plane strain compression testing of aluminum alloys
Materials Science and Engineering A256 (1998) 220 – 226
Asymmetric flow during plane strain compression testing of aluminum alloys A. Duckham, R.D. Knutsen * Department of Materials Engineering, Uni6ersity of Cape Town, Department of Materials Engineering, Rondesbosch, 7700, South Africa Received 15 June 1998
Abstract The development of an asymmetric flow pattern during plane strain compression (PSC) testing of aluminum alloys is analyzed. The flow behavior is related to the occurrence of a minor lateral offset of the compression platens during high strain deformation. Variation in the rate of indentation of the platens as a consequence of the offset causes the specimen to rotate and an oscillatory flow pattern evolves. The influence of the resultant inhomogeneous strain distribution on texture evolution during post-deformation annealing is examined. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Aluminum alloys; Asymmetric flow; Plane strain compression
1. Introduction Plane strain compression (PSC) testing is now a commonly accepted means of simulating the rolling deformation of ductile metals, both at ambient and elevated temperature working conditions. The PSC test was first suggested by Orowan [1] as a modified compression test which might simulate the yield conditions in rolling, and thereby obviate the factor by which the homogeneous yield stress must be increased to allow for inhibited lateral spread. The inhibited lateral spread, giving rise to the plane strain condition, results in a measured yield stress equal to 1.155 s0 (where s0 is the yield stress for homogeneous compression) according to the von Mises criterion. This test technique was later successfully implemented by Ford [2] in connection with the determination of rolling loads during cold rolling of steels, and is sometimes referred to as the Ford PSC test. More recent work [3] has established that PSC testing is a valuable technique for deriving flow stress data under conditions which simulate the constraints of hot rolling of aluminum alloys, on condition that several corrections are made for factors such as machine compliance, lateral spread, and friction. The necessity to understand and control grain size and * Corresponding author. Tel.: +27 21 6503172; fax: + 27 21 6897571; e-mail: [email protected]
texture evolution during thermomechanical processing requires a reproducible laboratory scale technique which also simulates the strain history appropriate to commercial rolling processes. The analysis of deformation patterns during PSC testing was originally proposed by making a distinction between compression between parallel rough platens [4], and compression between parallel smooth platens [5]. Both these approaches contributed to the understanding of slip-line field theory and it has been demonstrated that different slip-line fields develop for friction conditions as opposed to frictionless conditions. The most simple slipline field arises when there is no friction, and the platen width (w) to specimen thickness (h) ratio is an integral value. In this case, the slip-lines in the specimen meet the platen surfaces at 45° and the field consists of a series of straight line crosses which intersect in the specimen mid-thickness plane. The number of crosses increases according to the w/h integral value, starting with a single cross when w/h is unity. Significant advances have been made on the basic understanding of slip-line field theory, and it has been demonstrated that accurate plane strain finite element analysis can be used to correct the friction and lateral spread effects, which provides a solution much better than classical slip-line analysis [6]. Research carried out by Beynon and Sellars [7] has shown that the flow behavior of commercial purity
0921-5093/98/$ - see front matter © 1998 Elsevier Science S.A. All rights reserved. PII S0921-5093(98)00811-9
A. Duckham, R.D. Knutsen / Materials Science and Engineering A256 (1998) 220–226
aluminum during PSC testing approximates the slip-line field predictions for frictionless conditions. In view of the need to obtain a more or less uniform strain distribution during PSC testing in order to simulate commercial rolling practice, Beynon and Sellars [7] proposed that conditions of larger w/h ratio provide more homogeneous strain distributions than do specimens of smaller ratio, although the strain distribution is generally always non-uniform. Timothy et al. [8] worked around this problem by firstly, minimizing the effect by selecting the appropriate specimen geometry according to the suggestions by Beynon and Sellars [7], and secondly, by consistently carrying out the metallographic examinations close to the center of the sectioned specimens, away from regions where local strain changes rapidly with position. In this way they were able to satisfactorily reproduce the partially recrystallized microstructures of the subsurface and center regions of a hot rolled aluminum slab by PSC simulation of their deformation histories. In all cases mentioned above which deal with slip-line field solutions, the conditions refer to perfectly aligned parallel platens. Although every effort is made to avoid any misalignment during actual PSC simulations, this situation can become difficult at high strain and/or high w/h ratio. Platen offset with respect to the compression axis will alter the slip-line field and thereby influence the material flow behavior. Johnson and Kudo [9] have described the slip-line field which develops during the compression of plastic-rigid material between rough parallel platens of unequal width. This condition is similar to the situation which arises when the platens become offset during normal PSC testing, except that the condition described by Johnson and Kudo [9] is symmetrical about the compression axis. The present paper demonstrates that even very minor offsets can lead to noticeable asymmetric flow when the w/h ratio becomes large as a consequence of high strain deformation. An experimental account of the development of the asymmetric slip-line pattern is given and a speculative analysis of the origin of the slip-line field is described. Furthermore, the possible influence of the asymmetric flow on microstructural evolution is indicated.
2. Experimental Procedure The PSC apparatus employed in this study was purpose built to fit a 250 kN load frame on an electroservo hydraulic (ESH) universal testing machine. The compression platens provide a contact area measuring 13 mm (platen width= w) ×52 mm which is sufficient to minimize lateral spread in order to generate a plane strain condition. All tests were performed at room temperature and at a constant strain rate equivalent to
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1 s − 1. Specimens were machined to produce a blank geometry measuring 10 mm (specimen height= h)×33 mm×52 mm. Two different aluminum alloy compositions were used, namely Al–1Mg and Al–1Mg–1Mn (figures indicate wt%). In both cases the starting microstructure was fully recrystallized. Friction conditions were reduced during testing by applying a graphite based lubricant to all the contact surfaces. The tendency for lateral offset of the compression platens to occur during loading was determined by mounting several displacement dial gauges at strategic locations. The specimens were annealed in a salt bath at a temperature of 420°C for a period of 3 min following deformation to produce a fully recrystallized grain structure. In order to observe the flow patterns following deformation, the grain morphology in the plane perpendicular to the transverse direction was examined using polarized light microscopy. The specimens were mechanically polished in a colloidal silica suspension, and then anodized in Barker’s reagent to reveal the microstructure. The texture of the as deformed and recrystallized Al–1Mg specimens was determined by bulk X-ray diffraction. Specimen sections corresponded to the mid-thickness plane and only included the final area between the platens. Orientation distribution functions (ODFs) were calculated using the series expansion method, and the volume fraction of texture components was calculated by integration over 15° around the corresponding peaks in the ODF. For this analysis, the texture components considered were: (a) cube {100}001; (b) brass {110}112; (c) Goss {110}001; (d) copper {112}111; (e) S {123}634; (f) P {011}122; and (g) Q {013}231.
3. Results and discussion
3.1. Microscopy analysis of flow patterns The longitudinal view of specimens in situ after a deformation event is depicted in a schematic illustration in Fig. 1. In each case the specimen cross section is a true representation of the shape after logarithmic strains of 2.1. Fig. 1a demonstrates the desirable ‘dog bone’ shape which is symmetrical about both the normal direction (ND) and rolling direction (RD) axes and it is expected that this condition will lead to symmetrical flow between the compression platens. The cross section in Fig. 1b displays an overall shape which is asymmetric about the same axes. Both tests were performed under identical conditions using fully recrystallized Al–1Mg specimens. The specimens were sectioned parallel to the ND–RD plane (ie the plane containing the ND and RD) at a point midway across the transverse direction (TD) to produce longitudinal views of the specimen segment in contact with the compression
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The development of the asymmetric flow pattern presented in Fig. 2b was traced by sectioning PSC specimens after fixed amounts of strain. Fig. 3 depicts the flow patterns in Al–1Mg–1Mn after logarithmic strain values of 0.48, 0.84, 1.40 and 1.90. It was generally found that the overall shape of the specimen remained symmetrical up to strains of : 1.40 with resultant symmetrical flow patterns as shown in Fig. 3a, b, c. However, a sharp contrast in the symmetry of the flow pattern develops at strains greater than 1.40 (Fig. 3d). A further point of interest is that although asymmetric flow was not always detected, even at strains up to 2.1, there was a greater tendency for asymmetric flow to occur in the Al–1Mg–1Mn alloy compared to the Al–1Mg alloy. This observation is given more attention in the following section.
3.2. Lateral offset of compression platens
Fig. 1. Schematic representation of deformed specimens in relation to platens for (a) symmetrical and (b) asymmetrical deformation.
platens at the end of the test (Fig. 2). Each section is a montage of light micrographs and illustrates the flow pattern which is highlighted by the elongated grain morphology. As expected, a symmetrical flow pattern (Fig. 2a) has developed in the specimen depicted in Fig. 1a. After deformation, the w/h ratio is :10 and consequently the strain distribution is uniform across most of the ND – RD plane, particularly in the midthickness plane. For the specimen whose external shape is asymmetric (Fig. 1b), the flow pattern between the compression platens is also asymmetric as shown in Fig. 2b. In this case the strain distribution is notably inhomogeneous across the ND – RD plane and the selection of a region of uniform strain is very limited.
Although the PSC rig is perfectly aligned when the specimen is removed and the platens are brought into contact, the geometric change in the specimen when asymmetric flow takes place suggests that either lateral offset of the platens occurs during loading, or an uneven frictional increase develops at some points of contact. After performing several PSC tests whilst monitoring the lateral displacement of the platens, it was found that a maximum lateral displacement of 0.20 mm is detected when a test results in asymmetric flow as shown in Fig. 1b. When considering the width of the platens, this translates to a maximum offset of only 1.5%. In addition, the lateral offset was noted to occur at a critical load which suggests a limit in the machine compliance. However, the fact that lateral offset sometimes does not occur even when the loading conditions are identical, as illustrated in Fig. 1, indicates that friction may exacerbate the situation. An increase in friction locally will inhibit lateral flow of material and therefore exert a lateral force on the platens. In view of the higher flow stress intrinsic to the Al–1Mg–1Mn alloy compared to the Al–1Mg alloy, the critical load is more easily exceeded with the former material, and
Fig. 2. Light micrographs displaying longitudinal views of two Al – 1Mg specimens deformed to logarithmic strains of 2.1: (a) symmetric deformation; (b) asymmetric deformation.
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Fig. 3. Flow pattern development during incremental straining of an Al – 1Mg – 1Mn specimen: (a) strain =0.48; (b) strain =0.84; (c) strain =1.40; (d) strain= 1.90.
consequently there is a greater tendency for asymmetric flow to occur in this alloy at high strains. Not surprisingly, it was also noted that the critical strain for the onset of asymmetric flow was generally lower for the Al–1Mg–1Mn alloy.
3.3. Analysis of asymmetric flow The slip-line field for a plastic-rigid material deformed between parallel platens is usually described by expecting that plastic zones will be initiated at the sharp edges of the platens and will spread inwards until they meet in the geometric center of the block [5]. The slip-lines meet a smooth surface at 45°, whereas a perfectly rough surface is cut orthogonally by one family of slip-lines. In view of the complications which
arise when trying to define accurately a slip-line field when friction conditions are somewhat intermediate between smooth and perfectly rough interface conditions, it is not the intention in this paper to develop a complete slip-line field for the two situations depicted in Fig. 1. However, it is important to focus on the plasticrigid boundary between the deforming material and the overhanging material as the material flows outwards from the indentation region. Hill et al. [4] have shown that for rough platens this boundary is a straight line, which intersects the center-line at 45° for any value of w/h ratio on condition that the platens are of equal width and the indentation is symmetrical. When platens of unequal width are considered it has been found necessary to modify this slightly by assuming the plastic-rigid boundary to be two straight lines of equal
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Fig. 4. Schematic representation of the plastic–rigid exit boundaries for (a) perfectly aligned platens, and (b) lateral platen offset equal to D.
length, starting from the edge of the platens and perpendicular to each other [9]. In this way the slip-line field can always be started by having a right-angled isosceles triangle between the edges of the two platens. Green [5] has shown that the plastic-rigid boundary for compression between smooth platens can be described in the same way as that for perfectly rough platens when w/h is an integral value. This analogy has been employed by Johnson and Kudo [9] when dealing with compression between partly rough dies of unequal width, but attention is drawn to the fact that the assumption that the plastic-rigid boundary sliplines are straight must be discarded for certain w/h ratios. This complicates the analysis in the present study, but some consolation can be drawn from the fact that when the strain is high, with resultant high values of w/h ratio, several integral values of w/h are derived for relatively small increments in strain. For example, w/h has an integral value when h =2.2 mm and again when h = 1.85 mm. Thus it is at least reasonable to consider slip-line conditions for integral values of w/h when attempting to establish the influence of lateral platen offset on material flow. A further factor influencing the present choice of plastic-rigid boundary is the nature of friction at the interface. Thomason [10] has reported that when viscous lubricants are used, the uneven distribution of lubricant which is likely to arise will lead to a much higher than average friction at the edges of the platen, whereas the friction might approach zero at the center of the platen. This means that the slip-line field at the platen edge is more likely to resemble the field for rough platens than for smooth platens, and consequently a straight line boundary is more likely. On the basis of the aforementioned arguments, the plastic-rigid boundaries for the situations shown in Fig. 1 are presented in Fig. 4. When the platens are perfectly aligned (Fig. 4a), then the plastic-rigid exit boundaries define the start of a symmetrical flow pattern about both the horizontal axis (specimen midthickness) and the vertical axis. On the other hand,
when the platens are offset by some value D, then it is obvious that an asymmetric flow pattern will develop from the plastic-rigid boundaries. In this case both boundaries have rotated clockwise, where the amount of rotation is related to the lateral offset D. Johnson and Kudo [9] have shown that for platens of unequal width, the velocity of indentation of the narrower platen is increased significantly with respect to the wider platen, despite only a very small difference in the total compressive force between the two platens (B 1%). In fact it is reported that when D is equal to or greater than the specimen thickness (f=0 in Fig. 4), then the velocity of the wider platen is zero and indentation from this platen ceases. The situation in Fig. 4b can thus be described in the following way. If the velocity (V) of the platen at the edges is considered with respect to the specimen, then VA \VB and VA% B VB%. In other words, the rate of indentation is higher at A and B% than at their respective opposite edges B and A%. However, there is no rotation of the platens and therefore the specimen has to rotate in order to satisfy the above velocity condition. The rotation of the specimen and the higher rate of indentation at A and B% causes the geometry in Fig. 1b to arise, and the rotation of the plastic-rigid exit boundaries causes the flow pattern shown in Fig. 2b, Fig. 3d to develop. An analogy to this situation is the condition where material is compressed between parallel rotating platens [11,12]. An asymmetric flow pattern is described with particular reference to the changing plastic-rigid exit boundaries. The situation is contrasted with that which arises during actual cold rolling of metals, and Collins [11] suggests that one might expect that the strain-rate field might have the same oscillatory nature in the two incidences. An interesting point which develops here is that although homogeneous strain is being sought during PSC testing, the influence of lateral platen offset may have more direct implications for studying certain situations which arise during actual cold rolling.
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Fig. 5. Light micrographs revealing shear bands in Al–1Mg after a logarithmic strain of 2.1 for (a) symmetric and (b) asymmetric flow patterns.
3.4. Influence of asymmetric flow on microstructure Large strain plastic deformation in Al – Mg alloys is known to promote the formation of grain scale or copper type shear bands [13 – 15]. This type of shear banding is localized to one or a few adjacent grains and is distinguished from sample scale or brass type shear banding. The strength of formation and also the density of copper type shear bands is dependent on the amount of strain experienced. A current study involves the analysis of the influence of shear bands on nucleation during recrystallization and the resultant texture evolution in the Al–1Mg alloy [16]. Since it is important to correlate microstructure development with applied
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strain, the achievement of homogeneous strain within a specimen is very important. Thus the influence of asymmetric flow on shear band development and texture evolution is required to be understood if specimens which demonstrate asymmetric flow are to be used in the study. Higher magnification views of the microstructures shown in Fig. 2 are presented in Fig. 5 for the Al–1Mg alloy. A comparison of the two specimens demonstrates a higher density of shear bands in the asymmetric specimen (Fig. 5b) compared to the more homogeneously deformed specimen (Fig. 5a). This has been found to be particularly more evident in the regions close to the plastic-rigid exit boundaries where the flow lines indicate more intense deformation. The deformation texture for these two specimens is presented in Table 1. It has been reported that shear banding results in an increase in the Goss and Brass orientations after deformation [15]. In spite of the significant difference in deformation flow patterns and the apparent difference in shear band density, the measured differences in volume fractions for the various texture components are within experimental error, and in particular there is no difference for the Goss and brass orientations. When comparing the actual ODFs, however, the texture is notably sharper for the symmetrical condition. Texture analysis of the fully recrystallized specimens following a post-deformation annealing treatment also reveals similar textures for the two specimens (Table 1). Although the deformation texture has been altered during recrystallization, both specimens depict the same trend in texture evolution. In particular there is no difference in the Goss, P and Q orientations that might be expected due to preferred nucleation of grains with these orientations at or near shear bands [15]. This result suggests an insignificant effect of asymmetric flow on the development of preferred orientations during recrystallization, despite the obvious differences in flow pattern and shear band density. However, it must be noted that only the texture in the specimen mid-plane has been analyzed and variations could still be detected through the thickness (ND) of the specimens, for instance at the specimen quarter plane where the difference in shear band density is more pronounced. Hence the approach for selective sampling adopted by Timothy et al. [8] is emphasized, and researchers are cautioned to be aware of the nature of the flow pattern
Table 1 Volume fraction of texture components for deformed and recrystallized specimens Specimen
Cube
Goss
Copper
Brass
S
P
Q
Symmetric-deformed Asymmetric-deformed Symmetric-recrystallized Asymmetric-recrystallized
0.04 0.04 0.08 0.09
0.07 0.08 0.03 0.02
0.23 0.21 0.11 0.10
0.32 0.29 0.05 0.05
0.55 0.52 0.25 0.23
0.03 0.02 0.01 0.01
0.07 0.08 0.14 0.14
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during PSC testing. It is logical to assume that the situation might become more critical as the amount of lateral offset (D) increases.
4. Summary During high strain PSC deformation, the platen width to specimen thickness ratio (w/h) increases in such a way that even very minor lateral offset of the two compression platens can significantly influence the pattern of material flow. The offset causes the plasticrigid exit boundaries to rotate and an asymmetric slipline field is initiated. The overall shape change of the specimen is ascribed to a variation in indentation velocity at the platen edges, with resultant rotation of the specimen between the compression platens and the development of an oscillatory flow pattern. Comparison of the texture of the symmetric and asymmetric conditions for both the deformed and recrystallized microstructures demonstrates no significant influence of asymmetric flow on texture evolution when only the mid-plane of the specimen is considered.
Acknowledgements The authors wish to acknowledge the financial support provided by Hulett Aluminium (Pietermaritzburg,
.
RSA) and the Foundation for Research Development (Pretoria, RSA). Gratitude is also extended to the technical and administrative staff at the University of Cape Town for their ongoing assistance. Finally, the authors are grateful for the texture measurements provided by MINTEK (Randburg, RSA).
References [1] E. Orowan, Proc. Inst. Mech. Eng. 150 (1943) 140. [2] H. Ford, Proc. Inst. Mech. Eng. 159 (1948) 115. [3] H. Shi, A.J. Mclaren, C.M. Sellars, R. Shahani, R. Bolingbroke, J. Test. Eval. 25 (1997) 61. [4] R. Hill, E.H. Lee, S.J. Tupper, J. Appl. Mech. 18 (1951) 46. [5] A.P. Green, Phil. Mag. 42 (1951) 900. [6] J.C. Gelin, O. Ghouati, R. Shahani, Int. J. Mech. Sci. 36 (1994) 773. [7] J.H. Beynon, C.M. Sellars, J. Test. Eval. 13 (1985) 28. [8] S.P. Timothy, H.L. Yiu, J.M. Fine, R.A. Ricks, Mater. Sci. Technol. 7 (1991) 255. [9] W. Johnson, H. Kudo, Int. J. Mech. Sci. 1 (1960) 336. [10] P.F. Thomason, Int. J. Mech. Sci. 14 (1972) 279. [11] I.F. Collins, Int. J. Mech. Sci. 11 (1969) 971. [12] I.F. Collins, Quart. J. Mech. Appl. Math. 23 (1970) 329. [13] K. Morii, H. Mecking, Y. Nakayama, Acta Metall. 33 (1985) 379. [14] A. Korbel, J.D. Embury, M. Hatherly, P.L. Martin, H.W. Erbsloh, Acta Metall 34 (1986) 1999. [15] K. Lu¨cke, O. Engler, Mater. Sci. Technol. 6 (1990) 1113. [16] A. Duckham, Ph.D. thesis, University of Cape Town, South Africa, submitted August 1998.
Asymmetric flow during plane strain compression testing of aluminum alloys A. Duckham, R.D. Knutsen * Department of Materials Engineering, Uni6ersity of Cape Town, Department of Materials Engineering, Rondesbosch, 7700, South Africa Received 15 June 1998
Abstract The development of an asymmetric flow pattern during plane strain compression (PSC) testing of aluminum alloys is analyzed. The flow behavior is related to the occurrence of a minor lateral offset of the compression platens during high strain deformation. Variation in the rate of indentation of the platens as a consequence of the offset causes the specimen to rotate and an oscillatory flow pattern evolves. The influence of the resultant inhomogeneous strain distribution on texture evolution during post-deformation annealing is examined. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Aluminum alloys; Asymmetric flow; Plane strain compression
1. Introduction Plane strain compression (PSC) testing is now a commonly accepted means of simulating the rolling deformation of ductile metals, both at ambient and elevated temperature working conditions. The PSC test was first suggested by Orowan [1] as a modified compression test which might simulate the yield conditions in rolling, and thereby obviate the factor by which the homogeneous yield stress must be increased to allow for inhibited lateral spread. The inhibited lateral spread, giving rise to the plane strain condition, results in a measured yield stress equal to 1.155 s0 (where s0 is the yield stress for homogeneous compression) according to the von Mises criterion. This test technique was later successfully implemented by Ford [2] in connection with the determination of rolling loads during cold rolling of steels, and is sometimes referred to as the Ford PSC test. More recent work [3] has established that PSC testing is a valuable technique for deriving flow stress data under conditions which simulate the constraints of hot rolling of aluminum alloys, on condition that several corrections are made for factors such as machine compliance, lateral spread, and friction. The necessity to understand and control grain size and * Corresponding author. Tel.: +27 21 6503172; fax: + 27 21 6897571; e-mail: [email protected]
texture evolution during thermomechanical processing requires a reproducible laboratory scale technique which also simulates the strain history appropriate to commercial rolling processes. The analysis of deformation patterns during PSC testing was originally proposed by making a distinction between compression between parallel rough platens [4], and compression between parallel smooth platens [5]. Both these approaches contributed to the understanding of slip-line field theory and it has been demonstrated that different slip-line fields develop for friction conditions as opposed to frictionless conditions. The most simple slipline field arises when there is no friction, and the platen width (w) to specimen thickness (h) ratio is an integral value. In this case, the slip-lines in the specimen meet the platen surfaces at 45° and the field consists of a series of straight line crosses which intersect in the specimen mid-thickness plane. The number of crosses increases according to the w/h integral value, starting with a single cross when w/h is unity. Significant advances have been made on the basic understanding of slip-line field theory, and it has been demonstrated that accurate plane strain finite element analysis can be used to correct the friction and lateral spread effects, which provides a solution much better than classical slip-line analysis [6]. Research carried out by Beynon and Sellars [7] has shown that the flow behavior of commercial purity
0921-5093/98/$ - see front matter © 1998 Elsevier Science S.A. All rights reserved. PII S0921-5093(98)00811-9
A. Duckham, R.D. Knutsen / Materials Science and Engineering A256 (1998) 220–226
aluminum during PSC testing approximates the slip-line field predictions for frictionless conditions. In view of the need to obtain a more or less uniform strain distribution during PSC testing in order to simulate commercial rolling practice, Beynon and Sellars [7] proposed that conditions of larger w/h ratio provide more homogeneous strain distributions than do specimens of smaller ratio, although the strain distribution is generally always non-uniform. Timothy et al. [8] worked around this problem by firstly, minimizing the effect by selecting the appropriate specimen geometry according to the suggestions by Beynon and Sellars [7], and secondly, by consistently carrying out the metallographic examinations close to the center of the sectioned specimens, away from regions where local strain changes rapidly with position. In this way they were able to satisfactorily reproduce the partially recrystallized microstructures of the subsurface and center regions of a hot rolled aluminum slab by PSC simulation of their deformation histories. In all cases mentioned above which deal with slip-line field solutions, the conditions refer to perfectly aligned parallel platens. Although every effort is made to avoid any misalignment during actual PSC simulations, this situation can become difficult at high strain and/or high w/h ratio. Platen offset with respect to the compression axis will alter the slip-line field and thereby influence the material flow behavior. Johnson and Kudo [9] have described the slip-line field which develops during the compression of plastic-rigid material between rough parallel platens of unequal width. This condition is similar to the situation which arises when the platens become offset during normal PSC testing, except that the condition described by Johnson and Kudo [9] is symmetrical about the compression axis. The present paper demonstrates that even very minor offsets can lead to noticeable asymmetric flow when the w/h ratio becomes large as a consequence of high strain deformation. An experimental account of the development of the asymmetric slip-line pattern is given and a speculative analysis of the origin of the slip-line field is described. Furthermore, the possible influence of the asymmetric flow on microstructural evolution is indicated.
2. Experimental Procedure The PSC apparatus employed in this study was purpose built to fit a 250 kN load frame on an electroservo hydraulic (ESH) universal testing machine. The compression platens provide a contact area measuring 13 mm (platen width= w) ×52 mm which is sufficient to minimize lateral spread in order to generate a plane strain condition. All tests were performed at room temperature and at a constant strain rate equivalent to
221
1 s − 1. Specimens were machined to produce a blank geometry measuring 10 mm (specimen height= h)×33 mm×52 mm. Two different aluminum alloy compositions were used, namely Al–1Mg and Al–1Mg–1Mn (figures indicate wt%). In both cases the starting microstructure was fully recrystallized. Friction conditions were reduced during testing by applying a graphite based lubricant to all the contact surfaces. The tendency for lateral offset of the compression platens to occur during loading was determined by mounting several displacement dial gauges at strategic locations. The specimens were annealed in a salt bath at a temperature of 420°C for a period of 3 min following deformation to produce a fully recrystallized grain structure. In order to observe the flow patterns following deformation, the grain morphology in the plane perpendicular to the transverse direction was examined using polarized light microscopy. The specimens were mechanically polished in a colloidal silica suspension, and then anodized in Barker’s reagent to reveal the microstructure. The texture of the as deformed and recrystallized Al–1Mg specimens was determined by bulk X-ray diffraction. Specimen sections corresponded to the mid-thickness plane and only included the final area between the platens. Orientation distribution functions (ODFs) were calculated using the series expansion method, and the volume fraction of texture components was calculated by integration over 15° around the corresponding peaks in the ODF. For this analysis, the texture components considered were: (a) cube {100}001; (b) brass {110}112; (c) Goss {110}001; (d) copper {112}111; (e) S {123}634; (f) P {011}122; and (g) Q {013}231.
3. Results and discussion
3.1. Microscopy analysis of flow patterns The longitudinal view of specimens in situ after a deformation event is depicted in a schematic illustration in Fig. 1. In each case the specimen cross section is a true representation of the shape after logarithmic strains of 2.1. Fig. 1a demonstrates the desirable ‘dog bone’ shape which is symmetrical about both the normal direction (ND) and rolling direction (RD) axes and it is expected that this condition will lead to symmetrical flow between the compression platens. The cross section in Fig. 1b displays an overall shape which is asymmetric about the same axes. Both tests were performed under identical conditions using fully recrystallized Al–1Mg specimens. The specimens were sectioned parallel to the ND–RD plane (ie the plane containing the ND and RD) at a point midway across the transverse direction (TD) to produce longitudinal views of the specimen segment in contact with the compression
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The development of the asymmetric flow pattern presented in Fig. 2b was traced by sectioning PSC specimens after fixed amounts of strain. Fig. 3 depicts the flow patterns in Al–1Mg–1Mn after logarithmic strain values of 0.48, 0.84, 1.40 and 1.90. It was generally found that the overall shape of the specimen remained symmetrical up to strains of : 1.40 with resultant symmetrical flow patterns as shown in Fig. 3a, b, c. However, a sharp contrast in the symmetry of the flow pattern develops at strains greater than 1.40 (Fig. 3d). A further point of interest is that although asymmetric flow was not always detected, even at strains up to 2.1, there was a greater tendency for asymmetric flow to occur in the Al–1Mg–1Mn alloy compared to the Al–1Mg alloy. This observation is given more attention in the following section.
3.2. Lateral offset of compression platens
Fig. 1. Schematic representation of deformed specimens in relation to platens for (a) symmetrical and (b) asymmetrical deformation.
platens at the end of the test (Fig. 2). Each section is a montage of light micrographs and illustrates the flow pattern which is highlighted by the elongated grain morphology. As expected, a symmetrical flow pattern (Fig. 2a) has developed in the specimen depicted in Fig. 1a. After deformation, the w/h ratio is :10 and consequently the strain distribution is uniform across most of the ND – RD plane, particularly in the midthickness plane. For the specimen whose external shape is asymmetric (Fig. 1b), the flow pattern between the compression platens is also asymmetric as shown in Fig. 2b. In this case the strain distribution is notably inhomogeneous across the ND – RD plane and the selection of a region of uniform strain is very limited.
Although the PSC rig is perfectly aligned when the specimen is removed and the platens are brought into contact, the geometric change in the specimen when asymmetric flow takes place suggests that either lateral offset of the platens occurs during loading, or an uneven frictional increase develops at some points of contact. After performing several PSC tests whilst monitoring the lateral displacement of the platens, it was found that a maximum lateral displacement of 0.20 mm is detected when a test results in asymmetric flow as shown in Fig. 1b. When considering the width of the platens, this translates to a maximum offset of only 1.5%. In addition, the lateral offset was noted to occur at a critical load which suggests a limit in the machine compliance. However, the fact that lateral offset sometimes does not occur even when the loading conditions are identical, as illustrated in Fig. 1, indicates that friction may exacerbate the situation. An increase in friction locally will inhibit lateral flow of material and therefore exert a lateral force on the platens. In view of the higher flow stress intrinsic to the Al–1Mg–1Mn alloy compared to the Al–1Mg alloy, the critical load is more easily exceeded with the former material, and
Fig. 2. Light micrographs displaying longitudinal views of two Al – 1Mg specimens deformed to logarithmic strains of 2.1: (a) symmetric deformation; (b) asymmetric deformation.
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Fig. 3. Flow pattern development during incremental straining of an Al – 1Mg – 1Mn specimen: (a) strain =0.48; (b) strain =0.84; (c) strain =1.40; (d) strain= 1.90.
consequently there is a greater tendency for asymmetric flow to occur in this alloy at high strains. Not surprisingly, it was also noted that the critical strain for the onset of asymmetric flow was generally lower for the Al–1Mg–1Mn alloy.
3.3. Analysis of asymmetric flow The slip-line field for a plastic-rigid material deformed between parallel platens is usually described by expecting that plastic zones will be initiated at the sharp edges of the platens and will spread inwards until they meet in the geometric center of the block [5]. The slip-lines meet a smooth surface at 45°, whereas a perfectly rough surface is cut orthogonally by one family of slip-lines. In view of the complications which
arise when trying to define accurately a slip-line field when friction conditions are somewhat intermediate between smooth and perfectly rough interface conditions, it is not the intention in this paper to develop a complete slip-line field for the two situations depicted in Fig. 1. However, it is important to focus on the plasticrigid boundary between the deforming material and the overhanging material as the material flows outwards from the indentation region. Hill et al. [4] have shown that for rough platens this boundary is a straight line, which intersects the center-line at 45° for any value of w/h ratio on condition that the platens are of equal width and the indentation is symmetrical. When platens of unequal width are considered it has been found necessary to modify this slightly by assuming the plastic-rigid boundary to be two straight lines of equal
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Fig. 4. Schematic representation of the plastic–rigid exit boundaries for (a) perfectly aligned platens, and (b) lateral platen offset equal to D.
length, starting from the edge of the platens and perpendicular to each other [9]. In this way the slip-line field can always be started by having a right-angled isosceles triangle between the edges of the two platens. Green [5] has shown that the plastic-rigid boundary for compression between smooth platens can be described in the same way as that for perfectly rough platens when w/h is an integral value. This analogy has been employed by Johnson and Kudo [9] when dealing with compression between partly rough dies of unequal width, but attention is drawn to the fact that the assumption that the plastic-rigid boundary sliplines are straight must be discarded for certain w/h ratios. This complicates the analysis in the present study, but some consolation can be drawn from the fact that when the strain is high, with resultant high values of w/h ratio, several integral values of w/h are derived for relatively small increments in strain. For example, w/h has an integral value when h =2.2 mm and again when h = 1.85 mm. Thus it is at least reasonable to consider slip-line conditions for integral values of w/h when attempting to establish the influence of lateral platen offset on material flow. A further factor influencing the present choice of plastic-rigid boundary is the nature of friction at the interface. Thomason [10] has reported that when viscous lubricants are used, the uneven distribution of lubricant which is likely to arise will lead to a much higher than average friction at the edges of the platen, whereas the friction might approach zero at the center of the platen. This means that the slip-line field at the platen edge is more likely to resemble the field for rough platens than for smooth platens, and consequently a straight line boundary is more likely. On the basis of the aforementioned arguments, the plastic-rigid boundaries for the situations shown in Fig. 1 are presented in Fig. 4. When the platens are perfectly aligned (Fig. 4a), then the plastic-rigid exit boundaries define the start of a symmetrical flow pattern about both the horizontal axis (specimen midthickness) and the vertical axis. On the other hand,
when the platens are offset by some value D, then it is obvious that an asymmetric flow pattern will develop from the plastic-rigid boundaries. In this case both boundaries have rotated clockwise, where the amount of rotation is related to the lateral offset D. Johnson and Kudo [9] have shown that for platens of unequal width, the velocity of indentation of the narrower platen is increased significantly with respect to the wider platen, despite only a very small difference in the total compressive force between the two platens (B 1%). In fact it is reported that when D is equal to or greater than the specimen thickness (f=0 in Fig. 4), then the velocity of the wider platen is zero and indentation from this platen ceases. The situation in Fig. 4b can thus be described in the following way. If the velocity (V) of the platen at the edges is considered with respect to the specimen, then VA \VB and VA% B VB%. In other words, the rate of indentation is higher at A and B% than at their respective opposite edges B and A%. However, there is no rotation of the platens and therefore the specimen has to rotate in order to satisfy the above velocity condition. The rotation of the specimen and the higher rate of indentation at A and B% causes the geometry in Fig. 1b to arise, and the rotation of the plastic-rigid exit boundaries causes the flow pattern shown in Fig. 2b, Fig. 3d to develop. An analogy to this situation is the condition where material is compressed between parallel rotating platens [11,12]. An asymmetric flow pattern is described with particular reference to the changing plastic-rigid exit boundaries. The situation is contrasted with that which arises during actual cold rolling of metals, and Collins [11] suggests that one might expect that the strain-rate field might have the same oscillatory nature in the two incidences. An interesting point which develops here is that although homogeneous strain is being sought during PSC testing, the influence of lateral platen offset may have more direct implications for studying certain situations which arise during actual cold rolling.
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Fig. 5. Light micrographs revealing shear bands in Al–1Mg after a logarithmic strain of 2.1 for (a) symmetric and (b) asymmetric flow patterns.
3.4. Influence of asymmetric flow on microstructure Large strain plastic deformation in Al – Mg alloys is known to promote the formation of grain scale or copper type shear bands [13 – 15]. This type of shear banding is localized to one or a few adjacent grains and is distinguished from sample scale or brass type shear banding. The strength of formation and also the density of copper type shear bands is dependent on the amount of strain experienced. A current study involves the analysis of the influence of shear bands on nucleation during recrystallization and the resultant texture evolution in the Al–1Mg alloy [16]. Since it is important to correlate microstructure development with applied
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strain, the achievement of homogeneous strain within a specimen is very important. Thus the influence of asymmetric flow on shear band development and texture evolution is required to be understood if specimens which demonstrate asymmetric flow are to be used in the study. Higher magnification views of the microstructures shown in Fig. 2 are presented in Fig. 5 for the Al–1Mg alloy. A comparison of the two specimens demonstrates a higher density of shear bands in the asymmetric specimen (Fig. 5b) compared to the more homogeneously deformed specimen (Fig. 5a). This has been found to be particularly more evident in the regions close to the plastic-rigid exit boundaries where the flow lines indicate more intense deformation. The deformation texture for these two specimens is presented in Table 1. It has been reported that shear banding results in an increase in the Goss and Brass orientations after deformation [15]. In spite of the significant difference in deformation flow patterns and the apparent difference in shear band density, the measured differences in volume fractions for the various texture components are within experimental error, and in particular there is no difference for the Goss and brass orientations. When comparing the actual ODFs, however, the texture is notably sharper for the symmetrical condition. Texture analysis of the fully recrystallized specimens following a post-deformation annealing treatment also reveals similar textures for the two specimens (Table 1). Although the deformation texture has been altered during recrystallization, both specimens depict the same trend in texture evolution. In particular there is no difference in the Goss, P and Q orientations that might be expected due to preferred nucleation of grains with these orientations at or near shear bands [15]. This result suggests an insignificant effect of asymmetric flow on the development of preferred orientations during recrystallization, despite the obvious differences in flow pattern and shear band density. However, it must be noted that only the texture in the specimen mid-plane has been analyzed and variations could still be detected through the thickness (ND) of the specimens, for instance at the specimen quarter plane where the difference in shear band density is more pronounced. Hence the approach for selective sampling adopted by Timothy et al. [8] is emphasized, and researchers are cautioned to be aware of the nature of the flow pattern
Table 1 Volume fraction of texture components for deformed and recrystallized specimens Specimen
Cube
Goss
Copper
Brass
S
P
Q
Symmetric-deformed Asymmetric-deformed Symmetric-recrystallized Asymmetric-recrystallized
0.04 0.04 0.08 0.09
0.07 0.08 0.03 0.02
0.23 0.21 0.11 0.10
0.32 0.29 0.05 0.05
0.55 0.52 0.25 0.23
0.03 0.02 0.01 0.01
0.07 0.08 0.14 0.14
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during PSC testing. It is logical to assume that the situation might become more critical as the amount of lateral offset (D) increases.
4. Summary During high strain PSC deformation, the platen width to specimen thickness ratio (w/h) increases in such a way that even very minor lateral offset of the two compression platens can significantly influence the pattern of material flow. The offset causes the plasticrigid exit boundaries to rotate and an asymmetric slipline field is initiated. The overall shape change of the specimen is ascribed to a variation in indentation velocity at the platen edges, with resultant rotation of the specimen between the compression platens and the development of an oscillatory flow pattern. Comparison of the texture of the symmetric and asymmetric conditions for both the deformed and recrystallized microstructures demonstrates no significant influence of asymmetric flow on texture evolution when only the mid-plane of the specimen is considered.
Acknowledgements The authors wish to acknowledge the financial support provided by Hulett Aluminium (Pietermaritzburg,
.
RSA) and the Foundation for Research Development (Pretoria, RSA). Gratitude is also extended to the technical and administrative staff at the University of Cape Town for their ongoing assistance. Finally, the authors are grateful for the texture measurements provided by MINTEK (Randburg, RSA).
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