Question

For a plane strain extrusion process shown in the figure, the knowns are: the initial and final thickness of the workpiece t0 and t1, (the width w is much larger than the thickness), the wedged die semi angle α, the deformation zone is from section a to section b of known x-coordinate Columbian friction coefficient of the workpiece-die is μ, and the workpiece yield strength from uniaxial tension is Y (ignore elastic strain)

 A.  Determine the extrusion force F if we ignore friction work and redundant work.

 B. If we consider the friction effect, use slab analysis method to determine the extrusion force F.

 1. Draw all stress components and establish the force balance equation for a slab shown (shadowed);

 2. establish differential equation that contains only one stress component and one coordinate parameter, i.e. Ox and x (ignore second-order small terms);

 3. what is the boundary condition;

 4. solve the differential equation and obtain the extrusion stress and force equations. 

Answer 1