# Manufacturing Processes - MFRG 315 - 3.2.4 Friction in Metal Forming

Frequently deformation is brought about during contact between a tool and a workpiece. This inevitably results in friction if there is any tangential force at the contacting surfaces. For tangential forces which give rise to shear stresses below the yield shear stress of the workpiece, the friction force and the normal force can be related by the coefficient of friction defined as:

Coeff. of friction = Tangential force / Normal force = shear stress / normal stress, or: The coefficient of friction is reasonably constant (provided environment and surface conditions remain constant).

In some metal forming operations the coefficient of friction is high and the interface shear stress may reach the flow shear stress (often assumed to be equal to 0.5 times the flow stress). At this point the workpiece will start to deform by shearing within its body. Even if the normal pressure between the tool and workpiece continues to rise the shear stress will not and the term 'coefficient of friction' is no longer meaningful.

In calculations it is appropriate to denote the interface shear stress as a fraction of the yield shear stress, m* the frictional shear factor (sometimes also referred to as m). For perfect lubrication m* = 0, for sticking friction, m* = 1.

For most metals it is often assumed that the flow shear stress is 0.5 x direct (uniaxial) flow stress.

The uniaxial yield strength is sometimes called Y.

The above assumption (for large scale yielding) should be contrasted with the results from torsion tests, as in accordance to the von Mises failure criterion, the onset of plastic flow occurs at a shear stress k = 0.577 Y.

In cold working, lubrication is often effectively used and the coefficient of friction may be quite low - typically 0.03 to 0.2. This causes an increase of the forces required to carry out the process of up to about 20% or more (depending upon which process is being used) above the levels that would be needed if friction was zero.

However when hot working lubrication is more problematic and the coefficient of friction will often be much higher and may well become meaningless as the interface shear stress exceeds the flow shear stress.

Friction increases the pressures and forces between the workpiece and the tool and may limit the attainable reduction.

The effects of friction can be visualised by considering the axial upsetting of a cylinder:

If there were no friction between the circular ends and the platens of the press then the cylinder would reduce in height and remain cylindrical in shape. The normal pressure would be constant over the contact circles.

When friction is present, the outward movement of the material in contact with the platens is restricted, hence the cylinder bulges (and if excessive bulging is allowed to occur, the periphery may start to crack). The friction force opposes the outward flow of the material, meaning that a higher stress must be generated near the centre of of the contact zone to move the material outwards. This gives rise to the so called 'friction hill', the term 'hill' describing the profile of the flow stress across a diameter of the cylinder, see diagram below. The derivation below shows how the expression for the form of the 'friction hill' may be derived, assuming the coefficient of friction is below that which causes sticking.

This analysis considers at a sector of a cylinder while subjected to axisymmetric compression.  References:
1. 'Introduction to Manufacturing Processes', J A Schey, McGraw-Hill International, 1987.
2. 'Mechanical Metallurgy' G E Dieter, McGraw-Hill International, 1988.