An Upper Bound Solution for the Compression of an Orthotropic Cylinder

Area of Science:

• Solid mechanics
• Materials science
• Tribology

Background:

• Determining the force required for upsetting solid cylinders is crucial in metal forming processes.
• Existing models often simplify friction and material behavior, limiting predictive accuracy.
• The upper bound theorem and Hill's quadratic yield criterion provide a framework for such analyses.

Purpose of the Study:

• To develop a method for estimating the force required to upset a solid cylinder.
• To investigate the influence of friction, including sticking, on the calculated upsetting force.
• To provide a computationally efficient estimation for various geometric and material parameters.

Main Methods:

• Application of the upper bound theorem combined with Hill's quadratic yield criterion.
• Development of a kinematically admissible velocity field that incorporates singular behavior near friction surfaces.
• Inclusion and analysis of the sticking regime in the velocity field and its effect on the upper bound limit load.

Main Results:

• A method for estimating the upsetting force of solid cylinders was established.
• The analysis revealed that including the sticking regime can lead to a lower upper bound estimate compared to analyses without sticking.
• The developed approach provides a quick estimation of the compression force for diverse parameters, overcoming the limitations of exhaustive parametric analysis.

Conclusions:

• The upper bound theorem, coupled with Hill's criterion and consideration of friction/sticking, offers a viable method for estimating cylinder upsetting forces.
• The sticking regime significantly impacts the upper bound limit load, potentially reducing the required force.
• This method provides a valuable tool for rapid force estimation in engineering applications involving solid cylinder deformation.