Abstract
This paper presents a generalization of the widely used approach of Orowan for calculating the roll pressure in flat rolling of homogeneous rigid perfectly strips on viscoplastic sheets. In contrast to the original approach, the approach for viscoplastic sheets requires the analysis of the velocity field since the model is rate dependent. The present paper employs the solution for plane strain compression of a viscoplastic block for finding the through thickness distribution of stress and velocity. Strain rate hardening is taken into account by means of the Herschel-Bulkley model.
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References
Montmitonnet, P.: Hot and cold strip rolling processes. Comput. Methods Appl. Mech. Eng. 195, 6604–6625 (2006)
Cawthorn, C.J., Loukaides, E.G., Allwood, J.M.: Comparison of analytical models for sheet rolling. Procedia Eng. 81, 2451–2456 (2014)
Orowan, E.: The calculation of roll pressure in hot and cold flat rolling. Proc. Inst. Mech. Eng. 150, 140–167 (1943)
Kimura, H.: Application of Orowan theory to hot rolling of aluminum. J. Jpn. Inst. Light Met. 35, 222–227 (1985)
Kimura, H.: Application of Orowan theory to hot rolling of aluminum: computer control of hot rolling of aluminum. Sumitomo Light Metal Techn. Rep. 26, 189–194 (1985)
Lenard, J.G., Wang, F., Nadkarni, G.: Role of constitutive formulation in the analysis of hot rolling. Trans. ASME J. Eng. Mater. Technol. 109, 343–349 (1987)
Atreya, A., Lenard, J.G.: Study of cold strip rolling. Trans. ASME J. Eng. Mater. Technol. 101, 129–134 (1979)
Domanti, S., McElwain, D.L.S.: Two-dimensional plane strain rolling: an asymptotic approach to the estimation of inhomogeneous effects. Int. J. Mech. Sci. 37, 175–196 (1995)
Owen, A.G., Griffin, A.W.J.: Rapid solution of Orowan’s equations using a hybrid computer. Proc. Inst. Electric. Eng. 119, 1510–1516 (1972)
Rusia, D.: Improvements to Alexander’s computer model for force and torque calculations in strip rolling processes. J. Mater. Shap. Technol. 8, 167–177 (1990)
El-Bitar, T.A.: Computer program for the calculation of roll force and torque with strip tension in cold rolling. Iron Steelmak. 20, 87–96 (1993)
Nadai, A.: Plasticity: Mechanics of the plastic state of matter. McGraw-Hill, New York (1931)
Alexandrov, S., Lyamina, E.: Extension of Orowan’s method to analysis of rolling of three-layer sheets. Proc. Eng. 207, 1391–1396 (2017)
Adams, M.J., Briscoe, B.J., Corfield, G.M., Lawrence, C.J., Papathanasiou, T.D.: An analysis of the plane-strain compression of viscoplastic materials. Trans. ASME J. Appl. Mech. 64, 420–424 (1997)
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The author acknowledges financial support of this research through the grant RFBR-17-08-01063.
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Lyamina, E. (2019). An Approximate Solution for Plane Strain Rolling of Viscoplastic Sheets. In: Gdoutos, E. (eds) Proceedings of the First International Conference on Theoretical, Applied and Experimental Mechanics. ICTAEM 2018. Structural Integrity, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-91989-8_14
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DOI: https://doi.org/10.1007/978-3-319-91989-8_14
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