An accurate upper bound solution for plane strain extrusion through a wedge-shaped die

Area of Science:

• Mechanical Engineering
• Materials Science
• Applied Mathematics

Background:

• Plane strain extrusion is a critical metal forming process.
• Accurate modeling of material flow, especially under high friction, is essential for process optimization.
• Existing methods may not fully capture the complex velocity fields near friction surfaces.

Purpose of the Study:

• To develop a novel upper bound method for analyzing plane strain extrusion through wedge-shaped dies.
• To incorporate the asymptotic singular behavior of velocity fields near maximum friction surfaces.
• To validate the accuracy of the proposed method.

Main Methods:

• Derivation of an upper bound method for plane strain extrusion.
• Construction of kinematically admissible velocity fields.
• Satisfying exact asymptotic singular behavior at maximum friction surfaces.
• Comparison with established slip-line solutions.

Main Results:

• Two specific upper bound solutions were obtained using the new method.
• The derived solutions demonstrated very high accuracy.
• The method effectively models velocity fields near maximum friction surfaces.

Conclusions:

• The new upper bound method provides a highly accurate approach for plane strain extrusion analysis.
• The technique successfully accounts for complex velocity behaviors at critical friction zones.
• This method offers a valuable tool for predicting and optimizing extrusion processes.