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Introduction To Manufacturing Systems by Ed Red

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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
- Friction is an important factor in metal forming
- Strain rate and temperature are important factors in metal forming

Material Behavior in Metal Forming

Engineering Stress and Strain (used by engineering designers):

Engineering stress se = F/Ao

Engineering straine = (L - Lo)/Lo

Hooke's Law (elastic region):se = E e

Plastic region

Elastic region

Material Behavior in Metal Forming

Stress - strain diagrams (tensile and compression):

Ultimate strength

se

Yield strength

e

0.2% offset

Material Behavior in Metal Forming

Common parameter values: AlSteel

Epsi10 x 106 30 x 106

MPa 70 x 103 210 x 103

Yield strengthpsi400060,000

MPa 28400

Ultimate strengthpsi10,00090,000

MPa 70600

Material Behavior in Metal Forming

True Stress and Strain (used by manufacturing engineers):

True stress s = F/A

True straine = dL/L = ln(L/Lo)

Plastic region

Start of necking

Elastic region

s

e

Material Behavior in Metal Forming

Why do engineering designers base their design on engineering stress/strain, but manufacturing engineers use true stress-strain?

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.

Material Behavior in Metal Forming

Material Strength coeff, K Strain hardening exp, n

psi MPa

Aluminum30,000 2100.18

Steel125,000 8500.15

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)0400051806200650062004600

Length (in)5.0005.0095.255.605.886.126.40

Determine the yield strength Y, modulus of elasticity E, and tensile strength TS. Also determine the strength coefficient K and the hardening exponent n.

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

What have you learned?