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A modified method for lateral spread in thin strip rolling
Journal of Materials Processing Technology 124 (2002) 77±82
A modi®ed method for lateral spread in thin strip rolling M. Abo-Elkhier* Faculty of Engineering, Department of Production Engineering and Mechanical Design, Menou®a University, Shebin El-Kom 32511, Egypt Received 18 April 2001; accepted 2 January 2002
Abstract A rolling method to increase the width of the metal would have advantages in multi-pass strip production, giving high productivity and control of texture or planar anisotropy. In conventional ¯at rolling, however, it is dif®cult to produce metal ¯ow in the lateral direction. A new method for spread rolling has been proposed in the literature, in which several portions of strip width were rolled between a roll that has many circumferential grooves and a ¯at roll. In the present work, new modi®cations in roll pro®le and numbers of grooves are introduced. The advantages of the new modi®cations are evaluated through rolling of commercially pure aluminum strips. It was found that a strip of 70 mm wide and 1 mm thickness have been widened by up to 3.1% for a reduction of 35%. It was also found that the planar anisotropy decreases. A special purpose nonlinear ®nite element program has been developed to deal with continuous change of contact between the roll and the strip in each rolling pass. The calculated strain tensor was utilized to investigate the localized necking. # 2002 Published by Elsevier Science B.V. Keywords: Spread rolling; Planar anisotropy; Finite element modeling
1. Introduction The continuous casting process of thin sheets has been employed in industry recently and the demand for changing the width of produced strips by rolling is growing. However, in conventional ¯at rolling, the material elongates in the rolling direction without any deformation in the lateral direction. This is due to the fact that the resistance of deformation in the rolling direction is smaller than that in the lateral direction [1]. As a result, the mechanical properties and the microstructure along the rolling direction are essentially different from those in the lateral direction. In order to change the width of produced strips, it is required to change the width of the mold caster. This modi®cation needs a high level of investment in equipment and leads to a decrease in productivity. On the other hand, the spread rolling method can introduce strain in the lateral direction as well as in the rolling direction. It also has an advantage of giving high productivity and control of mechanical properties [2]. Cross rolling [3] or intermittent pressing [4] has been proposed as a spread rolling method which showed less planar anisotropy, although they have problem of productivity.
*
Present address: Department of Mechanical Engineering, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia. Fax: 996-1-467-6652. 0924-0136/02/$ ± see front matter # 2002 Published by Elsevier Science B.V. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 0 4 3 - 2
Recently, Saito et al. [5] and Utsunomiya et al. [6] proposed a new method for spread rolling in thin strip using three-pass rolling operations. In the ®rst pass, the strip is rolled between a roll having many regular trapezoidal circumferential grooves and a ¯at roll. Several portions of the strip width which get in contact with the grooved roll are reduced , whilst the other portions bulge in the grooves. In the second and the third passes, strips are ¯attened between ¯at rolls. They have used the plasticine (clay) to examine the spread-ability of the proposed method. It was found that, strips of 1 mm thickness and 100 mm wide increased in width by 5 mm for a reduction of 30%. When aluminum strips were rolled in the above sequence [7], some defects such as: necking and fracture occurred near edges under certain rolling conditions. Therefore, the achieved lateral spread was limited by the occurrence of these defects. In order to avoid these defects, the method has been improved to ®vepass: the ®rst and the third passes utilized the grooved roll against the ¯at roll, whilst, in the rest of passes ¯at rolls are utilized to ¯atten strips. In Ref. [8] Utsunomiya et al. modi®ed the shape of the circumferential grooves to half circle and adopted the same rolling sequence and used delivery guide to obtain wide and sound strips. They utilized tapercrown rolls as upper ones in the second and fourth passes. The effect of the spread rolling method on the mechanical properties of the rolled strips was investigated. The spread rolling method is further employed for a copper alloy to verify the capability of spreading and control of texture [9].
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M. Abo-Elkhier / Journal of Materials Processing Technology 124 (2002) 77±82
The present study includes two parts. The ®rst part introduces new modi®cations such as: roll pro®le, circumferential groove pro®le and number of grooves, which have great effect on the lateral spread. A portable rolling device was designed and manufactured. Special rolls of 100 mm diameter and 130 mm width were machined with the new groove geometry. Commercial annealed aluminum (1050) strips of 1 mm thickness and width of 30, 50 and 70 mm were rolled. The advantages of the proposed spread rolling method as compared with the ¯at rolling are investigated by evaluating the mechanical properties and the planar anisotropy of the rolled strips. In the second part, a special purpose nonlinear ®nite element program has been developed based on the incremental updated Lagrangian formulation. The program takes
into account the geometrical (large strain) and the material nonlinearities as well as the continuous change in contact between the rolls and the strip. Comparisons between the obtained values of lateral spread and the measured ones are made. The calculated strain tensor was utilized to investigate the localized necking. 2. Experimental work 2.1. Principle of the spread rolling method Fig. 1 schematically illustrates the sequence set up of the spread rolling method used by Utsunomiya et al. [8] and the present model. In the ®rst pass, the thickness of several
Fig. 1. Diagrammatic representation of spread rolling arrangements: (a) Utsunomiya et al. [8], (b) present model.
M. Abo-Elkhier / Journal of Materials Processing Technology 124 (2002) 77±82
portions of the strip width are reduced due to rolling between a roll having circular circumferential grooves and a ¯at one. Portions not in contact with upper roll bulge into the grooves. In the present model, the dimensions of the circumferential grooves are reduced to one-half and their number is doubled to avoid surface defects and necking, see Fig. 1. The second pass is a roll-forming pass, where the bulged portions are ¯attened. In order to increase the lateral spread, an over-cambered roll with a ¯at one are employed in this pass, instead of using a taper-crown roll in the work of Utsunomiya et al. [8] as shown in Fig. 1. It is believed that employing the over-cambered roll can enhance the metal ¯ow along the lateral direction. In the third pass, the grooved roll is used as the bottom roll. The bulged parts in the ®rst pass are rolled in this pass and vise versa. The over-cambered roll is used as the bottom roll in the fourth pass. Two ¯at rolls are used to ¯atten the strips in the ®fth pass. 2.2. Rolling experiments A portable rolling device was designed and manufactured. Four rolls; two ¯ats, one with the half circular circumferential grooves and ®nally the over-cambered roll were machined from stainless steel. All rolls are of 100 mm diameter and of 130 mm width. The pro®le of the circular grooves was designed with a pitch of 10 mm and a curvature radius of 2.5 mm as shown in Fig. 1. These dimensions were chosen to avoid surface defects and necking. The diameter of the over-cambered roll is 100 mm in the middle whilst at both ends it equals 98 mm. It was found that the overcambered roll is effective not only in the achieved lateral spread but also in the strip shape after rolling. Commercial annealed aluminum (1050) strips of thickness of 1 mm and width of 30, 50 and 70 mm were used to investigate the spread-capability of the introduced modi®cations. The strips were annealed for 4 h at 450 8C. The prime reason of choosing the material and the dimensions was to compare the obtained results with those presented by Utsunomiya et al. [8]. Strips were processed with total reduction in thickness of 35%, whilst the reduction in the ®rst, in the third and in the ®fth passes are 20, 20 and 35% of the initial thickness, respectively. The lateral spread was measured by comparing the projected width after rolling with the initial strip width in each pass. Conventional three-pass ¯at rolling was also conducted for the sake of comparison. The mechanical properties as well as the planar anisotropy of the spread rolled and the ¯at rolled strips, for the same reduction ratio, were evaluated by conducting tensile tests. In both cases, three tensile test specimens were cut from the rolled strips; with the ®rst, second and third specimens at angles of 08, 458 and 908 to the rolling direction, respectively. The gauge length of the specimen was taken 10 mm with width of 5 mm. The offset yield strength s0.2 and the ultimate strength su were recorded for each case.
79
3. Finite element modelling As stated above, the developed nonlinear ®nite element program takes into account geometrical (large strain) and the material nonlinearities as well as the continuous change in contact between the roll and the strip. The analysis was carried out based on the incremental updated Lagrangian formulation. At each increment, the stress and the strain tensors are transformed to the present state (last calculated one) according to the continuum mechanics basis. The material behavior was approximated as 150e0:2 s
(1)
(MPa) and e are the effective stress and effective where s strain, respectively. The resulting deformed strip shape and the ®eld variables such as stress and strain tensors at the exit from a pass are used as input to the subsequent pass model. In the ®nite element modeling, only one-half of the strip width was modeled due to symmetry. A mesh of 30705 elements was utilized in the longitudinal, lateral and through the thickness directions, respectively. The friction layer technique was employed to model the friction effect at the roll/strip interface [10]. In this technique, an imaginary layer of elements is added at the roll/strip interface to model the friction effect. The friction factor m at the roll/strip interface is calculated as m
mP k
(2)
the mean pressure where m is the coef®cient of friction, P and k the yield shear strength. 4. Results and discussions 4.1. Spread rolling The percentage of lateral spread, during the spread rolling, measured in the present investigation as well as the predictions of ®nite element model are shown in Fig. 2. In addition, the results of the present ¯at rolling process for the same reduction ratio are plotted. Also, included in the ®gure, for the purpose of comparison, the data of Utsunomiya et al. [8]. For the case of Utsunomiya et al. [8], the lateral spread in the ®rst pass is negative because the edge folded and the projected width decreased. This is not the case in the present results because the dimensions of the grooves are reduced to one-half of those used in Ref. [8]. On the other hand, the spread in ¯at rolling is negligibly small. It is clear from the ®gure that employing the presented sequence has signi®cant effect on the lateral spread, which increases from 1.6 (Utsunomiya et al.) to 3.1% (present results). Fig. 3 shows the percentage of longitudinal elongation of the strip plotted against the pass number. The elongation in the spread rolling is considerably smaller than that of the ¯at rolling.
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M. Abo-Elkhier / Journal of Materials Processing Technology 124 (2002) 77±82
Fig. 2. Variation of percentage lateral spread of the strip during rolling.
The elongation from the ®rst to the fourth passes is small as compared to ®nal ¯at rolling pass. This is because of the unrolled portions bulge into the grooves in the ®rst and the third passes. Fig. 4 depicts the percentage lateral spread in case of strip width of 30, 50 and 70 mm where it can be seen that the percentage lateral spread decreases as the initial width increases. Fig. 5 depicts the ®nite element predictions of the strip cross-section after each pass. In the ®rst and the third passes, unrolled portions of the strip width bulged in the roll grooves, whilst in the second and the fourth passes, the strip has been ¯attened and widened. In the ®fth pass, ¯at rolling has straightened out the bulged edges of the strip leading to the increase in the strip width. 4.2. Mechanical properties The measured mechanical properties in case of 70 mm strip width are shown in Table 1. The offset yield strength
Fig. 3. Variation of percentage longitudinal elongation of the strip during rolling.
s0.2 of the as spread rolled material is higher than that of the ¯at rolled strip. This may be due to redundant deformation introduced by bulging and ¯attening. The average strain state through the thickness is utilized to investigate the localized necking. The critical strain for localized necking eL3 is given by [11] eL3 r
n 1r
e_ 2 e_ 1
(3) (4)
where n is the strain hardening exponent, and e_ 1 and e_ 2 the strain rates in the rolling and in the lateral direction. The calculated average critical strain eL3 through the thickness using the above formula is compared with the average strain e3 obtained from the ®nite element program. It is found that the average strain eL3 is lower than e3 which means that there is no necking.
Fig. 4. Variation of percentage lateral spread as a function of the initial width.
M. Abo-Elkhier / Journal of Materials Processing Technology 124 (2002) 77±82
81
Fig. 5. Finite element predictions of strip cross-section for a strip of 70 mm width.
Table 1 Mechanical properties of the spread rolled and the flat rolled strips Spread rolled
s0.2 (MPa) su (MPa)
Flat rolled
08
458
908
08
458
908
78 103
73 95
76 97
76 101
71 91
66 83
had been widened up to 3.1% for a reduction of 35%. The mechanical properties of the spread rolled material was slightly work hardened and with less planar anisotropy. A special purpose nonlinear ®nite element program has been developed based on the incremental updated Lagrangian formulation. The calculated strain tensor is utilized to investigate the localized necking. The proposed rolling method is found to be effective to obtain wide and mechanically sound strips. Acknowledgements
Fig. 6. The ratio between the induced lateral and the longitudinal strains.
Fig. 6 depicts the ratio between the induced lateral and the longitudinal strains. It is shown that the lateral spread rolling method induces appreciable lateral strain as compared to the longitudinal one. 5. Conclusions In this study, new modi®cations such as roll pro®le and number and dimension of the grooves have been introduced to the proposed spread rolling in the literature. Portable rolling device was designed and manufactured. The advantages of proposed modi®cations were examined through the rolling of commercial pure aluminum strips. The proposed modi®cations show a remarkable spread-ability, where it was found that a strip of 1 mm thickness and 70 mm width
The author would like to acknowledge the assistance of the staff of the Material Testing Laboratory, Department of Mechanical Engineering, King Saud University, Riyadh, Saudi Arabia, in conducting the tensile test experiments. References [1] Z. Wusatawski, Fundamentals of Rolling, Pergamon Press, Oxford, 1969, p. 55. [2] H. Utsunomiya, Y. Saito, T. Saka, K. Morita, J. Jpn. Inst. Met. 59 (1995) 191. [3] Y. Shinizu, J. Seino, M. Siato, K. Miyaji, T. Ichikaya, S. Ohno, J. Jpn. Inst. Light Met. 38 (1988) 717. [4] T. Takamachi, K. Yamada, S. Ogawa, M. Ataka, Proceedings of the 41st Japanese Joint Conference for Technology of Plasticity, 1990, p. 117. [5] Y. Saito, H. Utsunomiya, S. Matsueda, T. Sekino, T. Sakai, Proceedings of the Australiasia-pacific Forum on Intelligent Processing and Manufacturing of Materials, Goldcost, Australia, 1997, p. 1104. [6] H. Utsunomiya, Y. Saito, S. Matsueda, J. Mater. Proc. Technol. 87 (1999) 207. [7] H. Utsunomiya, Y. Saito, T. Sakai, S. Matsueda, T. Sekino, J. Jpn. Inst. Light Met. 48 (1998) 581 (in Japanese).
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M. Abo-Elkhier / Journal of Materials Processing Technology 124 (2002) 77±82
[8] H. Utsunomiya, Y. Saito, K. Hirata, T. Saka, Proceedings of the Seventh International Conference on Steel Rolling, Cheba, Japan, 1998, p. 816. [9] Y. Saito, H. Utsunomiya, S. Kaneko, T. Saka, T. Kanzaki, Proceedings of the Sixth International Conference on Advanced Technology of Plasticity, Vol. II, 1999, p. 927.
[10] G.W. Rowe, C.E.N. Sturgess, P. Hartly, I. Pillinger, Finite Element Plasticity and Metal Forming Analysis, Cambridge University Press, Cambridge, 1991. [11] P.F. Thomason, Ductile Fracture of Metal, Pergamon Press, Oxford, 1990, p 179.
A modi®ed method for lateral spread in thin strip rolling M. Abo-Elkhier* Faculty of Engineering, Department of Production Engineering and Mechanical Design, Menou®a University, Shebin El-Kom 32511, Egypt Received 18 April 2001; accepted 2 January 2002
Abstract A rolling method to increase the width of the metal would have advantages in multi-pass strip production, giving high productivity and control of texture or planar anisotropy. In conventional ¯at rolling, however, it is dif®cult to produce metal ¯ow in the lateral direction. A new method for spread rolling has been proposed in the literature, in which several portions of strip width were rolled between a roll that has many circumferential grooves and a ¯at roll. In the present work, new modi®cations in roll pro®le and numbers of grooves are introduced. The advantages of the new modi®cations are evaluated through rolling of commercially pure aluminum strips. It was found that a strip of 70 mm wide and 1 mm thickness have been widened by up to 3.1% for a reduction of 35%. It was also found that the planar anisotropy decreases. A special purpose nonlinear ®nite element program has been developed to deal with continuous change of contact between the roll and the strip in each rolling pass. The calculated strain tensor was utilized to investigate the localized necking. # 2002 Published by Elsevier Science B.V. Keywords: Spread rolling; Planar anisotropy; Finite element modeling
1. Introduction The continuous casting process of thin sheets has been employed in industry recently and the demand for changing the width of produced strips by rolling is growing. However, in conventional ¯at rolling, the material elongates in the rolling direction without any deformation in the lateral direction. This is due to the fact that the resistance of deformation in the rolling direction is smaller than that in the lateral direction [1]. As a result, the mechanical properties and the microstructure along the rolling direction are essentially different from those in the lateral direction. In order to change the width of produced strips, it is required to change the width of the mold caster. This modi®cation needs a high level of investment in equipment and leads to a decrease in productivity. On the other hand, the spread rolling method can introduce strain in the lateral direction as well as in the rolling direction. It also has an advantage of giving high productivity and control of mechanical properties [2]. Cross rolling [3] or intermittent pressing [4] has been proposed as a spread rolling method which showed less planar anisotropy, although they have problem of productivity.
*
Present address: Department of Mechanical Engineering, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia. Fax: 996-1-467-6652. 0924-0136/02/$ ± see front matter # 2002 Published by Elsevier Science B.V. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 0 4 3 - 2
Recently, Saito et al. [5] and Utsunomiya et al. [6] proposed a new method for spread rolling in thin strip using three-pass rolling operations. In the ®rst pass, the strip is rolled between a roll having many regular trapezoidal circumferential grooves and a ¯at roll. Several portions of the strip width which get in contact with the grooved roll are reduced , whilst the other portions bulge in the grooves. In the second and the third passes, strips are ¯attened between ¯at rolls. They have used the plasticine (clay) to examine the spread-ability of the proposed method. It was found that, strips of 1 mm thickness and 100 mm wide increased in width by 5 mm for a reduction of 30%. When aluminum strips were rolled in the above sequence [7], some defects such as: necking and fracture occurred near edges under certain rolling conditions. Therefore, the achieved lateral spread was limited by the occurrence of these defects. In order to avoid these defects, the method has been improved to ®vepass: the ®rst and the third passes utilized the grooved roll against the ¯at roll, whilst, in the rest of passes ¯at rolls are utilized to ¯atten strips. In Ref. [8] Utsunomiya et al. modi®ed the shape of the circumferential grooves to half circle and adopted the same rolling sequence and used delivery guide to obtain wide and sound strips. They utilized tapercrown rolls as upper ones in the second and fourth passes. The effect of the spread rolling method on the mechanical properties of the rolled strips was investigated. The spread rolling method is further employed for a copper alloy to verify the capability of spreading and control of texture [9].
78
M. Abo-Elkhier / Journal of Materials Processing Technology 124 (2002) 77±82
The present study includes two parts. The ®rst part introduces new modi®cations such as: roll pro®le, circumferential groove pro®le and number of grooves, which have great effect on the lateral spread. A portable rolling device was designed and manufactured. Special rolls of 100 mm diameter and 130 mm width were machined with the new groove geometry. Commercial annealed aluminum (1050) strips of 1 mm thickness and width of 30, 50 and 70 mm were rolled. The advantages of the proposed spread rolling method as compared with the ¯at rolling are investigated by evaluating the mechanical properties and the planar anisotropy of the rolled strips. In the second part, a special purpose nonlinear ®nite element program has been developed based on the incremental updated Lagrangian formulation. The program takes
into account the geometrical (large strain) and the material nonlinearities as well as the continuous change in contact between the rolls and the strip. Comparisons between the obtained values of lateral spread and the measured ones are made. The calculated strain tensor was utilized to investigate the localized necking. 2. Experimental work 2.1. Principle of the spread rolling method Fig. 1 schematically illustrates the sequence set up of the spread rolling method used by Utsunomiya et al. [8] and the present model. In the ®rst pass, the thickness of several
Fig. 1. Diagrammatic representation of spread rolling arrangements: (a) Utsunomiya et al. [8], (b) present model.
M. Abo-Elkhier / Journal of Materials Processing Technology 124 (2002) 77±82
portions of the strip width are reduced due to rolling between a roll having circular circumferential grooves and a ¯at one. Portions not in contact with upper roll bulge into the grooves. In the present model, the dimensions of the circumferential grooves are reduced to one-half and their number is doubled to avoid surface defects and necking, see Fig. 1. The second pass is a roll-forming pass, where the bulged portions are ¯attened. In order to increase the lateral spread, an over-cambered roll with a ¯at one are employed in this pass, instead of using a taper-crown roll in the work of Utsunomiya et al. [8] as shown in Fig. 1. It is believed that employing the over-cambered roll can enhance the metal ¯ow along the lateral direction. In the third pass, the grooved roll is used as the bottom roll. The bulged parts in the ®rst pass are rolled in this pass and vise versa. The over-cambered roll is used as the bottom roll in the fourth pass. Two ¯at rolls are used to ¯atten the strips in the ®fth pass. 2.2. Rolling experiments A portable rolling device was designed and manufactured. Four rolls; two ¯ats, one with the half circular circumferential grooves and ®nally the over-cambered roll were machined from stainless steel. All rolls are of 100 mm diameter and of 130 mm width. The pro®le of the circular grooves was designed with a pitch of 10 mm and a curvature radius of 2.5 mm as shown in Fig. 1. These dimensions were chosen to avoid surface defects and necking. The diameter of the over-cambered roll is 100 mm in the middle whilst at both ends it equals 98 mm. It was found that the overcambered roll is effective not only in the achieved lateral spread but also in the strip shape after rolling. Commercial annealed aluminum (1050) strips of thickness of 1 mm and width of 30, 50 and 70 mm were used to investigate the spread-capability of the introduced modi®cations. The strips were annealed for 4 h at 450 8C. The prime reason of choosing the material and the dimensions was to compare the obtained results with those presented by Utsunomiya et al. [8]. Strips were processed with total reduction in thickness of 35%, whilst the reduction in the ®rst, in the third and in the ®fth passes are 20, 20 and 35% of the initial thickness, respectively. The lateral spread was measured by comparing the projected width after rolling with the initial strip width in each pass. Conventional three-pass ¯at rolling was also conducted for the sake of comparison. The mechanical properties as well as the planar anisotropy of the spread rolled and the ¯at rolled strips, for the same reduction ratio, were evaluated by conducting tensile tests. In both cases, three tensile test specimens were cut from the rolled strips; with the ®rst, second and third specimens at angles of 08, 458 and 908 to the rolling direction, respectively. The gauge length of the specimen was taken 10 mm with width of 5 mm. The offset yield strength s0.2 and the ultimate strength su were recorded for each case.
79
3. Finite element modelling As stated above, the developed nonlinear ®nite element program takes into account geometrical (large strain) and the material nonlinearities as well as the continuous change in contact between the roll and the strip. The analysis was carried out based on the incremental updated Lagrangian formulation. At each increment, the stress and the strain tensors are transformed to the present state (last calculated one) according to the continuum mechanics basis. The material behavior was approximated as 150e0:2 s
(1)
(MPa) and e are the effective stress and effective where s strain, respectively. The resulting deformed strip shape and the ®eld variables such as stress and strain tensors at the exit from a pass are used as input to the subsequent pass model. In the ®nite element modeling, only one-half of the strip width was modeled due to symmetry. A mesh of 30705 elements was utilized in the longitudinal, lateral and through the thickness directions, respectively. The friction layer technique was employed to model the friction effect at the roll/strip interface [10]. In this technique, an imaginary layer of elements is added at the roll/strip interface to model the friction effect. The friction factor m at the roll/strip interface is calculated as m
mP k
(2)
the mean pressure where m is the coef®cient of friction, P and k the yield shear strength. 4. Results and discussions 4.1. Spread rolling The percentage of lateral spread, during the spread rolling, measured in the present investigation as well as the predictions of ®nite element model are shown in Fig. 2. In addition, the results of the present ¯at rolling process for the same reduction ratio are plotted. Also, included in the ®gure, for the purpose of comparison, the data of Utsunomiya et al. [8]. For the case of Utsunomiya et al. [8], the lateral spread in the ®rst pass is negative because the edge folded and the projected width decreased. This is not the case in the present results because the dimensions of the grooves are reduced to one-half of those used in Ref. [8]. On the other hand, the spread in ¯at rolling is negligibly small. It is clear from the ®gure that employing the presented sequence has signi®cant effect on the lateral spread, which increases from 1.6 (Utsunomiya et al.) to 3.1% (present results). Fig. 3 shows the percentage of longitudinal elongation of the strip plotted against the pass number. The elongation in the spread rolling is considerably smaller than that of the ¯at rolling.
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M. Abo-Elkhier / Journal of Materials Processing Technology 124 (2002) 77±82
Fig. 2. Variation of percentage lateral spread of the strip during rolling.
The elongation from the ®rst to the fourth passes is small as compared to ®nal ¯at rolling pass. This is because of the unrolled portions bulge into the grooves in the ®rst and the third passes. Fig. 4 depicts the percentage lateral spread in case of strip width of 30, 50 and 70 mm where it can be seen that the percentage lateral spread decreases as the initial width increases. Fig. 5 depicts the ®nite element predictions of the strip cross-section after each pass. In the ®rst and the third passes, unrolled portions of the strip width bulged in the roll grooves, whilst in the second and the fourth passes, the strip has been ¯attened and widened. In the ®fth pass, ¯at rolling has straightened out the bulged edges of the strip leading to the increase in the strip width. 4.2. Mechanical properties The measured mechanical properties in case of 70 mm strip width are shown in Table 1. The offset yield strength
Fig. 3. Variation of percentage longitudinal elongation of the strip during rolling.
s0.2 of the as spread rolled material is higher than that of the ¯at rolled strip. This may be due to redundant deformation introduced by bulging and ¯attening. The average strain state through the thickness is utilized to investigate the localized necking. The critical strain for localized necking eL3 is given by [11] eL3 r
n 1r
e_ 2 e_ 1
(3) (4)
where n is the strain hardening exponent, and e_ 1 and e_ 2 the strain rates in the rolling and in the lateral direction. The calculated average critical strain eL3 through the thickness using the above formula is compared with the average strain e3 obtained from the ®nite element program. It is found that the average strain eL3 is lower than e3 which means that there is no necking.
Fig. 4. Variation of percentage lateral spread as a function of the initial width.
M. Abo-Elkhier / Journal of Materials Processing Technology 124 (2002) 77±82
81
Fig. 5. Finite element predictions of strip cross-section for a strip of 70 mm width.
Table 1 Mechanical properties of the spread rolled and the flat rolled strips Spread rolled
s0.2 (MPa) su (MPa)
Flat rolled
08
458
908
08
458
908
78 103
73 95
76 97
76 101
71 91
66 83
had been widened up to 3.1% for a reduction of 35%. The mechanical properties of the spread rolled material was slightly work hardened and with less planar anisotropy. A special purpose nonlinear ®nite element program has been developed based on the incremental updated Lagrangian formulation. The calculated strain tensor is utilized to investigate the localized necking. The proposed rolling method is found to be effective to obtain wide and mechanically sound strips. Acknowledgements
Fig. 6. The ratio between the induced lateral and the longitudinal strains.
Fig. 6 depicts the ratio between the induced lateral and the longitudinal strains. It is shown that the lateral spread rolling method induces appreciable lateral strain as compared to the longitudinal one. 5. Conclusions In this study, new modi®cations such as roll pro®le and number and dimension of the grooves have been introduced to the proposed spread rolling in the literature. Portable rolling device was designed and manufactured. The advantages of proposed modi®cations were examined through the rolling of commercial pure aluminum strips. The proposed modi®cations show a remarkable spread-ability, where it was found that a strip of 1 mm thickness and 70 mm width
The author would like to acknowledge the assistance of the staff of the Material Testing Laboratory, Department of Mechanical Engineering, King Saud University, Riyadh, Saudi Arabia, in conducting the tensile test experiments. References [1] Z. Wusatawski, Fundamentals of Rolling, Pergamon Press, Oxford, 1969, p. 55. [2] H. Utsunomiya, Y. Saito, T. Saka, K. Morita, J. Jpn. Inst. Met. 59 (1995) 191. [3] Y. Shinizu, J. Seino, M. Siato, K. Miyaji, T. Ichikaya, S. Ohno, J. Jpn. Inst. Light Met. 38 (1988) 717. [4] T. Takamachi, K. Yamada, S. Ogawa, M. Ataka, Proceedings of the 41st Japanese Joint Conference for Technology of Plasticity, 1990, p. 117. [5] Y. Saito, H. Utsunomiya, S. Matsueda, T. Sekino, T. Sakai, Proceedings of the Australiasia-pacific Forum on Intelligent Processing and Manufacturing of Materials, Goldcost, Australia, 1997, p. 1104. [6] H. Utsunomiya, Y. Saito, S. Matsueda, J. Mater. Proc. Technol. 87 (1999) 207. [7] H. Utsunomiya, Y. Saito, T. Sakai, S. Matsueda, T. Sekino, J. Jpn. Inst. Light Met. 48 (1998) 581 (in Japanese).
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M. Abo-Elkhier / Journal of Materials Processing Technology 124 (2002) 77±82
[8] H. Utsunomiya, Y. Saito, K. Hirata, T. Saka, Proceedings of the Seventh International Conference on Steel Rolling, Cheba, Japan, 1998, p. 816. [9] Y. Saito, H. Utsunomiya, S. Kaneko, T. Saka, T. Kanzaki, Proceedings of the Sixth International Conference on Advanced Technology of Plasticity, Vol. II, 1999, p. 927.
[10] G.W. Rowe, C.E.N. Sturgess, P. Hartly, I. Pillinger, Finite Element Plasticity and Metal Forming Analysis, Cambridge University Press, Cambridge, 1991. [11] P.F. Thomason, Ductile Fracture of Metal, Pergamon Press, Oxford, 1990, p 179.