Journal of Materials Engineering and Performance

, Volume 19, Issue 7, pp 936–941 | Cite as

An Analytical Modified Model of Clad Sheet Bonding by Cold Rolling Using Upper Bond Theorem



In this paper, clad sheet bonding by cold rolling was investigated using the upper bond theorem. Plastic deformation behavior of the strip at the roll gap was investigated, unlike previous methods; distinctive angular velocities are used for different zones in roll gap in present model and absolute minimum of rolling power function is achieved. Rolling power, rolling force, and thickness ratio of the rolled product affected by various rolling condition such as flow stress of sheets, initial thickness ratio, roller radius, total thickness reduction, coefficient of friction between rollers and metals and between components layer, roll speed, etc., are discussed. It was found that the theoretical prediction of the thickness ratio of the rolled product, rolling force, and rolling power are in good agreement with the experimental measurement.


clad sheet bonding cold rolling cladding modeling of bimetallic strip upper bound theorem 



initial velocity of upper layer


initial velocity of lower layer


final velocity of bimetal strip


amount of velocity discontinuity on each surface of velocity discontinuity


rotational velocity of roller


rotational velocity of each rigid zone


linear velocity of roll


initial thickness of upper layer


initial thickness of lower layer


final thickness of upper layer


final thickness of lower layer


final thickness of strip


roller radius


radius of cylindrical surface of velocity discontinuity


reduction in area


coefficient of friction between roller and strip


coefficient of friction between layers

\( \Upgamma \)

surface of velocity discontinuity


area of the surface of velocity discontinuity


shear power of the surface of velocity discontinuity

σs or SS

flow stress of upper layer

σh or Sh

flow stress of lower layer


rolling force


contact length


rolling power


angle between motion direction and X-axis


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Copyright information

© ASM International 2009

Authors and Affiliations

  1. 1.Faculty of Metallurgy and Material Science Engineering, College of EngineeringUniversity of TehranTehranIran

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