Analysis of Bonding Behavior and Critical Reduction of Two-Layer Strips in Clad Cold Rolling Process

  • H. Maleki
  • S. Bagherzadeh
  • B. Mollaei-Dariani
  • K. Abrinia


In recent years, two-layer metallic sheets have been increasingly used in various industries to create combined functions. Among cladding methods, the cold rolling is most widely used in producing bimetallic sheets. In this research, to thoroughly provide guidelines for cold rolling of bimetal strip, an attempt has been made to develop an analytical model based on upper bound method. Also, the bonding strength and critical reduction were calculated using upper bound theorem and the finite element simulation was used for Al/St bimetallic strip. Finally, an experimental study was run for our model to be verified analytically and numerically. Results show that the bonding strength of strips increases with increasing the total thickness reduction of bimetal strips and because of subsequent occurrence of strips bonding in roll gap, increasing the yield strength of base layer gives rise to critical reduction. Through the study, it becomes clear that the proposed analytical model is applicable for simulating the cold rolling process of the two-layer strips and is capable to broaden our knowledge in manufacturing and production of bimetal strips and sheets.


analytical model clad rolling critical reduction FEM two-layer strip upper bound 


ti, mm

Initial thickness of bimetal strips

tf, mm

Final thickness of bimetal strips

t0, mm

Initial thickness of composite

ts0, mm

Initial thickness of clad layer

th0, mm

Initial thickness of base layer

tsf, mm

Final thickness of clad layer

thf, mm

Final thickness of base layer

V01, mm/s

Initial velocity of clad layer

V02, mm/s

Initial velocity of base layer

Vf, mm/s

Final velocity of bimetal strip

V, mm/s

Linear velocity of roll

\( V^{\prime}_{01} ,V^{\prime}_{02} \), mm/s

Linear velocity in (V) and (VI) regions

ωR, 1/s

Rotational velocity of roll

ωi, 1/s

Rotational velocity of each rigid zone


Strain hardening exponent


Surface of velocity discontinuity

R0, mm

Radius of roll

Ri, mm

Radius of cylindrical surface of velocity discontinuity

ξi and λi

Velocity ratio in the rigid zones

ΔVi, mm/s

Amount of velocity discontinuity on each surface of velocity discontinuity


Shear power of the surface of velocity discontinuity


Total shear power


Friction factor between roll and strips


Constant friction factor between layers

σ0S, MPa

Yield stress of clad layer (outer layer)

σ0h, MPa

Yield stress of base layer (inner layer)

Τ, MPa

Shear stress

K′, MPa

Bonding strength between two layers

Copyright information

© ASM International 2012

Authors and Affiliations

  • H. Maleki
    • 1
  • S. Bagherzadeh
    • 2
  • B. Mollaei-Dariani
    • 1
  • K. Abrinia
    • 2
  1. 1.Department of Mechanical EngineeringAmirkabir University of TechnologyTehranIran
  2. 2.Department of Mechanical Engineering, College of EngineeringUniversity of TehranTehranIran

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