Explanation:

Die angle is a crucial factor in metal extrusion process. It is the angle at which the die is cut and determines the shape of the extruded metal product. The die angle also affects the extrusion force required to produce the desired shape.

When the die angle increases, the required extrusion force initially decreases and then increases again. This is due to the following reasons:

1. Reduction in contact area:

As the die angle increases, the contact area between the billet and the die decreases. This reduction in contact area leads to a decrease in the frictional force between the billet and the die. As a result, the required extrusion force initially decreases.

2. Increase in shear stress:

The increase in die angle leads to an increase in the shear stress on the billet. This shear stress is maximum at the center of the billet and decreases towards the edges. As a result, the metal near the center of the billet starts to deform and flow outwards. This leads to a reduction in the effective area of the billet, which in turn increases the extrusion force required.

3. Increase in bending stress:

As the die angle increases, the billet experiences an increase in bending stress. This bending stress is maximum at the edges of the billet and decreases towards the center. This leads to a redistribution of stresses within the billet, which results in an increase in the extrusion force required.

Conclusion:

In summary, when the die angle increases, the required extrusion force initially decreases due to a reduction in contact area and then increases again due to an increase in shear stress and bending stress. Therefore, it is important to select the optimal die angle based on the desired shape of the extruded product and the available extrusion force.