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

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- Received:
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DOI: 10.1007/s11665-009-9571-y

- Cite this article as:
- Pishbin, H., Parsa, M.H. & Dastvareh, A. J. of Materi Eng and Perform (2010) 19: 936. doi:10.1007/s11665-009-9571-y

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## Abstract

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.

### Keywords

clad sheet bondingcold rollingcladdingmodeling of bimetallic stripupper bound theorem### Nomenclature

*V*_{01}initial velocity of upper layer

*V*_{02}initial velocity of lower layer

*V*_{f}final velocity of bimetal strip

- Δ
*V* amount of velocity discontinuity on each surface of velocity discontinuity

- ω
_{R} rotational velocity of roller

- ω
rotational velocity of each rigid zone

*U*linear velocity of roll

*t*_{si}initial thickness of upper layer

*t*_{hi}initial thickness of lower layer

*t*_{sf}final thickness of upper layer

*t*_{hf}final thickness of lower layer

*t*_{f}final thickness of strip

*R*_{0}roller radius

*R*radius of cylindrical surface of velocity discontinuity

*r*reduction in area

*m*_{a}coefficient of friction between roller and strip

*m*_{b}coefficient of friction between layers

- \( \Upgamma \)
surface of velocity discontinuity

*S*area of the surface of velocity discontinuity

*W*shear power of the surface of velocity discontinuity

- σ
_{s}or*S*_{S} flow stress of upper layer

*σ*_{h}or*S*_{h}flow stress of lower layer

*F*rolling force

*L*contact length

*J*rolling power

- θ
angle between motion direction and

*X*-axis