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The purpose of this paper is to develop a mathematical solution to estimate the deformation pattern and required power in cold plate rolling using coupled stream function method and upper bound theorem.

In the first place, an admissible velocity field and the geometry of deformation zone are derived from a new stream function. Then, the optimum velocity field is obtained by minimizing the corresponding power function. Also, to calculate the adiabatic heating during high speed rolling operations, a two-dimensional conduction-convection problem is sequentially coupled with the mechanical model. To verify the predictions, rolling experiments on aluminum plates are conducted and also, a finite element analysis is performed by Abaqus/Explicit. The predicted deformation zone is then compared with the experimentally measured region as well as with the results of the finite element analysis.

The results show that the predicted deformation zone and the temperature distribution fit reasonably with the experimental data while much lower computational cost needs comparing to the fully finite element analysis.

A new stream function is proposed to properly describe the velocity field and deformation pattern during plate rolling considering the neutral point. Furthermore, the employed algorithm can be simply coupled with the thermal finite element analysis.

The purpose of this paper is to study the kinetics of static recovery in cold-rolled aluminum alloy under different heating rates.

Deformation modeling was first performed to assess the distributions of plastic strain and stress within the deformed alloy. In the next stage, thermal analysis and the rate equation of static recovery were employed to determine the progress of static recovery under non-isothermal conditions. Accordingly, a thermal finite element analysis and the Runge-Kutta method were utilized to handle the transient heat conduction and the progress of static recovery. Finally, low temperature annealing heat treatments were conducted to verify the model predictions. Accordingly, the tensile tests were conducted to measure the yield stresses of cold-rolled plates subjected to the subsequent annealing treatment at different temperatures and durations.

The results indicate that the employed algorithm can be used as an appropriate predictive tool for designing a low temperature heat treatment schedule to achieve the desired yield stress.

The kinetics of non-isothermal recovery and resulting yield stress are well predicted under practical annealing conditions.