A new approach for modeling of streamlined die operations based on a non-quadratic stream function

• Introduction of non-quadratic stream function for modeling of forming processes.
• Bi-metal extrusion and drawing were analyzed.
• Evaluation of effective plastic strain based on stream function approach.
• The flow pattern was predicted based on quadratic and non-quadratic stream function.
• The effect of die length on the shear component of strain was revealed.

Talbert and Avitzure introduced the implementation of a quadratic stream function for derivation of velocity field governing through streamlined die extrusion. In the present study, a non-quadratic stream function is introduced to model various streamlined die processes. In the modified formulation an exponent was designated to the stream function in order to obtain a generalized model. The quadratic stream function approach was restricted to processes with axial flow direction. In contrast, the modified model is capable to study the common forming processes i.e. simple and bimetal extrusion and drawing. The actual velocity field was derived from the generalized field by upper bound technique. The plastic flow was studied through distorted bands and elements that obtained by Eulerian description of motion. Subsequently, the modeling of extrusion and drawing proceed by the calculation of the effective plastic strain distribution. Streamlined die has been designed and proposed based on the fact that it requires less external power than the conventional operations and that deforming material encounters smoother plastic flow. The results revealed the length of die highly influences the deformation mode by affecting the shear component of strain. The capability of the modified stream function to capture various metal forming operations with streamlined die was investigated.