1. Metal Forming
Metal forming includes a large group of manufacturing processes in which plastic deformation is used to change the shape of metal work pieces
Plastic deformation: a permanent change of shape, i.e., the stress in materials is larger than its yield strength
Usually a die is needed to force deformed metal into a shape of the die so that the product has the same cross area as the die
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2. Metal Forming
Metal with low yield strength and high ductility is in favor of metal forming
One important difference between plastic forming and metal forming is:
Plastic: solids are heated up to be polymer melt
Metal: solid remains a solid state in the whole process
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3. Metal Forming Metal forming is divided into (1) bulk and (2) sheet
Bulk: (1) there is a significant deformation
(2) there is a massive shape change
(3) surface area to volume of the work is small
Sheet: Surface area to volume of the work is large
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4. Bulk deformation processes Forging Rolling
Traditionally Hot
Extrusion
Drawing
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5. Sheet deformation processes (Press working/ Stamping)
Drawing
Bending
Shearing
Actually Cutting
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6. In the following series of lecture, we discuss:
For general metal forming process, general mechanics principle / law / effect
For individual processes:
- mechanics principles
- design for manufacturing (DFM) rules
- equipment
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7. 1. General mechanics principle
The underlying mechanics principle for metal forming is the stress-strain relationship; see Figure 1.
Figure 1
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8. True strain: Instantaneous elongation per unit length of the material
True Stress: Applied load divided by instantaneous value of cross-section area
True strain: Instantaneous elongation per unit length of the material
L0: the initial length of a specimen
L: the length of the specimen at time t
the true strain at time t
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9. Plastic deformation region
In the forming process we are more interested in the plastic deformation region (Figure 1)
Plastic deformation region
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10. K= the strength coefficient, (MPa)
The stress-strain relationship in the plastic deformation region is described by
Called FLOW CURVE
Where
K= the strength coefficient, (MPa)
 = the true strain, σ=the true stress
n= the strain hardening exponent,
The flow stress (Yf) is used for the above stress (which is the stress beyond yield)
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11. FLOW STRESS
As deformation occurs, increasing STRESS is required to continue deformation
Flow Stress: Instantaneous value of stress required to continue deforming the material (i.e., to keep metal “flowing”):
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12. AVERAGE FLOW STRESS
For many bulk deforming processes, rather than instantaneous stress, average stress is used (extrusion)
The average flow stress can be obtained by integrating the flow stress along the trajectory of straining, from zero to the final strain value which defines the range of interest:
Strength Coefficient
Max. strain during deformation
Average flow stress
Strain hardening exponent
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13. Example 1:
Determine the value of the strain-hardening exponent for a metal that will cause the average flow stress to be three-quarters of the final flow stress after deformation.
Solution: According to the statement of the problem, we have of
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14. Temperature up  The (yield) strength down and ductility up
The above analysis is generally applicable to the cold working, where the temperature factor is not considered.
The metal forming process has three kinds in terms of temperature: (1) cold, (2) warm, (3) hot
In the case of warm and hot forming, the temperature factor needs to be considered, in particular
Temperature up  The (yield) strength down and ductility up
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15. h Strain rate (related to elevated temperatures)
Rate at which metal is strained in a forming process
Such a strain rate can affect the flow stress
Instantaneous height of work-piece being deformed
Speed of deformation (could be equal to velocity of ram)
Strain Rate h h
Flow stress
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16. Strength coefficient but not the same as K
where
C  strength constant
m  strain-rate sensitivity exponent
C and m are determined by the following figure which is generated from the experiment
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