Fundamentals of Metal Working

Metal Forming

Metal FormingSyllabusUnit-IIElastic & plastic deformationYield criteriaHot working v/s cold workingAnalysis (equilibrium equation method) of forging process for load estimation with sliding frictionsticking friction and mixed condition for slab and discWork required for forgingHand, Power and Drop Forging

Elastic and Plastic DeformationDeformation is change in original dimensions of a solid body when it is subjected to external load.Deformation is elastic if the original dimensions are recovered when the load is removed.Permanent change in dimensions due to application of load is called plastic deformationMost of the metal forming processes involve large plastic deformation of the work piece.A metal forming or a metal working operation is a plastic deformation process in which the volume and mass of metal are conserved and the metal is displaced from one location to another.

During analysis of metal forming processes, only (large) plastic strain is considered while elastic strain is very small and can be neglected.

The strains that result from elastic deformation are described by Hookes law. There are similar relations for plastic deformation, called the flow rules.

Engineering stress-strain curveTrue stress-strain curve

Flow curves

Elastic plastic (power law of strain hardening)Rigid Plastic (power law of strain hardening)Rigid Plastic (linear strain hardening)Rigid Ideal Plastic

Mean flow stressSince flow stress is not constant and it increases with strain in cold working due to strain hardening, it is usual practice to use mean flow stress to calculate forming loads.

When the strain is increased from 1 to 2, mean flow stress is defined as

Yield Criterion:Yield criteria are mathematical descriptions of the combination of stresses necessary to cause yielding. ORA yield criterion is a postulated mathematical expression of the states of stress that will cause yielding.

Yielding in unidirectional tension test takes place when the stress = F/A reaches the critical value.

Yielding in multiaxial stress states is not dependent on a single stress but on a combination of all stresses.

There are two generally accepted criteria for prediction the onset of yielding in ductile metals

Von Mises yield criterion (Distortion energy criterion)

Tresca yield criterion (maximum shear stress)

Tresca Yield Criterion

Von Mises yield criterion

Therefore, from von Mises and Tresca yield criteria we have

Hot Working and Cold Working: