Introduction To Manufacturing Systems by Ed Red. 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
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
Material Behavior in Metal Forming
Stress - strain diagrams (tensile and compression):
Common parameter values: Al Steel
E psi 10 x 106 30 x 106
MPa 70 x 103 210 x 103
Yield strength psi 4000 60,000
Ultimate strength psi 10,00090,000
True Stress and Strain (used by manufacturing engineers):
True stress s = F/A
True strain e = dL/L = ln(L/Lo)
Start of necking
Why do engineering designers base their design on engineering stress/strain, but manufacturing engineers use true stress-strain?
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.
Material Strength coeff, K Strain hardening exp, n
Aluminum 30,000 210 0.18
Steel 125,000 850 0.15
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.
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