Introduction To
Manufacturing Systems
by
Ed Red
ME 582 - Manufacturing Systems
Fundamentals of Metal Forming
• Metal forming is plastic deformation of metals into
desired shapes
• Deformation stresses may be tensile or compressive
(usually compressive)
• Metals must exhibit certain properties to be formed efficiently
• Friction is an important factor in metal forming
• Strain rate and temperature are important factors in
metal forming
ME 582 - Manufacturing Systems
Material Behavior in Metal Forming
Engineering Stress and Strain (used by engineering designers):
Engineering stress
se = F/Ao
Engineering strain
e = (L - Lo)/Lo
Hooke's Law (elastic region):
se = E e
ME 582 - Manufacturing Systems
Material Behavior in Metal Forming
Stress - strain diagrams (tensile and compression):
Ultimate strength
se
Plastic region
Yield strength
Elastic region
0.2% offset
ME 582 - Manufacturing Systems
e
Material Behavior in Metal Forming
Common parameter values:
E
Yield strength
Ultimate strength
ME 582 - Manufacturing Systems
Al
Steel
psi
10 x 106
30 x 106
MPa
70 x 103
210 x 103
psi
4000
60,000
MPa
28
400
psi
10,000
MPa
70
90,000
600
Material Behavior in Metal Forming
True Stress and Strain (used by manufacturing engineers):
True stress
s = F/A
True strain
e=
s
Start of necking
Plastic region
Elastic region
ME 582 - Manufacturing Systems
e
dL/L = ln(L/Lo)
Material Behavior in Metal Forming
Why do engineering designers base their design
on engineering stress/strain, but manufacturing
engineers use true stress-strain?
ME 582 - Manufacturing Systems
Material Behavior in Metal Forming
Strain hardening - Resistance to increasing strain. Stress-strain
can be related in the plastic region by the form
s = K en
where K is the strength coefficient and n is the hardening
exponent. A log-log diagram will show the linear behavior
expected for a curve of this form.
Note: The greater the n, the greater the strain hardening
effect. Necking for many ductile materials begins
approximately when the true strain reaches a value equal to n.
ME 582 - Manufacturing Systems
Material Behavior in Metal Forming
Material
Strength coeff, K
psi
MPa
Aluminum
Steel
ME 582 - Manufacturing Systems
30,000
125,000
210
850
Strain hardening exp, n
0.18
0.15
Material Behavior Example
The following data are collected during a tensile test in which
the initial gage length is 5 in. and the cross-sectional area is 0.1
in2:
Load (lb)
0
4000
5180
6200
6500
6200
4600
Length (in)
5.000
5.009
5.25
5.60
5.88
6.12
6.40
Determine the yield strength Y, modulus of elasticity E, and
tensile strength TS. Also determine the strength coefficient K
and the hardening exponent n.
ME 582 - Manufacturing Systems
Some relations you need to know
s = se (1 + e)
e = ln (1 + e)
Also note that it is often necessary to use a constant volume
relationship for modeling process phenomena. In the case of a
tensile test, the appropriate equation would be
AL = Ao Lo
ME 582 - Manufacturing Systems
What have you learned?
ME 582 - Manufacturing Systems