Development and application of constitutive equations for the multiple-stand hot rolling of Al-alloys

The dominant tasks for a confident use of a rolling process simulation is the determination of material data in the required accuracy and the formulation of material models which incorporate all important material features. The first aspect is the measurement and mathematical treatment of flow stress data, where the main issue is the compensation of adiabatic heating, friction and heterogeneous deformation. A procedure for performing these corrections is presented in this paper. The second aspect is the development of a physically based constitutive model, capable of tracing characteristic variables of state trough a multiple-pass rolling schedule in order to fully describe the forming history of a given material element. A four-internal-state-variable model (4IVM) is developed which computes the development of edge and screw dislocations both in the cell walls and interiors during forming and during holding times at elevated temperature. The magnitude of flow stress is derived from these internal variables. Furthermore, the current dislocation density is taken as driving force for recrystallisation, causing a coupling of recovery and recrystallisation mechanisms. Recrystallised fractions, originated at different points of time, are treated as individual substructures in subsequent deformation steps. Thus, the interactions of strain hardening, dynamic and static recovery and recrystallisation are formulated and collectively affect the flow stress. The effect of using the derived constitutive model within the thermal and mechanical simulation of rolling operations is shown by application to rolling trials on a laboratory mill and on an industrial four-stand mill by the example of alloy AA3104.