Fundamentals of Metal working
Z
50 MPa
30 MPa
100 MPa
Y
30 MPa
200 MPa
X
Classification of metal forming processes
Based on the type of force applied on to the
work piece:
• Direct-compression-type processes: The
applied force is normal to the direction of the
metal flow
• Indirect-compression processes:
The primary forces are frequently tensile,
with indirect compressive forces developed
by the reaction of the work piece. The metal
flow is therefore under the combined stress
state, i.e., extrusion, wiredrawing, tube
drawing.
Classification of metal forming processes
• Tension type processes:
The applied force is tensile, i.e., stretching forming.
• Bending processes:
The applied force involves the application of bending
moments to the sheet.
• Shearing processes:
The applied force involves the application of shearing
forces of sufficient magnitude to rupture the metal in the
plane of shear.
Classification of metal forming by subgroups
Metal Forming
Compression Tension Combined Type Bending Shear
Type Type (Tensile + Compressive) Type forming
• • Bending with linear • Joggling
• Rolling • Stretching Rolling
• tool motion. • Twisting
• Forging Extrusion
• • Bending with rotary • Blanking
• Indenting Deep drawing
• tool motion • Coining
• Pushing Spinning
through a die • Upset bulging
• Flange forming
Mechanics of metal working
Metal working occurs due to plastic deformation which is associated with
analysis of complex stress distribution. require simplification.
• Only (large) plastic strain is considered while elastic strain is very small and can be
neglected.
• Strain hardening is often neglected.
• Metal is considered to be isotropic and homogeneous.
Normally plastic deformation is not uniform and also have frictions, but we need to
simplify the stress analysis in order to determine the force required to produce a given
amount of deformation to obtain a product in a required geometry.
Mechanics of metal working
A0 A1 F
Required theory of plasticity, and for plastic deformation. Deformation
➢ Constant-volume relationship in plastic deformation. h0 h1
F
➢ In metalworking, compressive stress and strain are predominated. If a block of initial
height ho is compressed to h1, the axial compressive strain will be:
➢ True Strain:
➢ Engineering Strain:
Note: In compression the calculated strain would be negative.
Mechanics of metal working
Considering change in cross sectional area:
• The fractional reduction in area is
• From the constant volumetric relationship i.e. Aoho = A1h1
Mechanics of metal working
• Theory need to be develop which can describe the stress, strain and velocity at every points
of the deformed region. Such theory consists of three sets of eqn.
I. Static equilibrium of force
II. The Levy-Mises eqn.
III. The yield criteria.
• Methods of Analysis:
I. The Slab method
II. Uniform-deformation energy method
III. Slip-line field theory
IV. Upper and lower-bound solution
V. FEM
The Slab method
The Slab method
The Slab method
Uniform-deformation energy method
Uniform-deformation energy method
La
Lb
Ab
Aa
Ab
Aa
