1. Strain Hardening & Annealing
Ch. 8
MSC101: Eyres

2. Chapter Learning Objectives
Quantify the strain hardening of a metal and explain why strain hardening may significantly increase the force required to deform a metal
Quantify the strain rate sensitivity of a metal and explain why strain rate sensitivity may influence the force required to deform a metal
Explain how materials properties of a cold-rolled polycrystalline material will change due to annealing (recovery, recrystallization, grain growth) and deformation and how this affects mechanical behavior
Design processes to produce metal sheet with desired dimensions and mechanical properties using combinations of working and annealing treatments
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3. Relationship of Cold-Working to the Stress-Strain Curve
By applying a stress that exceeds the original yield strength of a metallic material, we strain hardened (cold worked) it
This stress, called the flow stress, causes the specimen to flow deform plastically or “flow”
Each time we apply a higher stress, flow stress and tensile strength increase (see Figure 8-1)
We eventually strengthen the material until its flow stress, tensile, and breaking strengths are equal (zero ductility)
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5. Deformation Processing & Strain Hardening Exponent
Many techniques for deformations processing are used to simultaneously shape and strengthen a material.
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6. Strain-Rate Sensitivity and Springback
The response of metal to cold working can be quantified by the strain hardening exponent n
The relationship between true stress σ, true strain ε, and the strain hardening exponent n:
𝜎=𝐾 ε 𝑛
Notice the relationship between n and crystal structure!
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7. Need to find:
True stress
True strain
Graph of ?????? Vs ??????

8. True strain
True stress (MPa)
448.98
643.81
794.89
Ln(true stress)
Find K and n
Then
Compare to table
Ln(true strain)

9. Strain-Rate Sensitivity and Springback
Strain-rate sensitivity (m) of stress σ is defined as:
𝒎= 𝝏 𝐥𝐧 𝝈 𝝏 𝐥𝐧 𝓔
m describes how flow stress changes with strain rate, important for shaping and how well the material will perform under high-impact loading
Springback is the elastic strain that is recovered after a material has been plastically deformed
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10. Strain-Hardening Mechanisms
We strengthen a metallic material during deformation by increasing the number of dislocations
When we apply stress greater than the yield strength, dislocations begin to slip. Eventually, dislocations encounter obstacles, which cause them to change shape and even generate new dislocations
This mechanism for generating new dislocations is called a Frank- Read source
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11. Strain-Hardening Mechanisms
Thermoplastics (polymers) have strengthen by a different mechanism, the alignment of their chainlike molecules
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12. Properties versus Percent Cold Work
We normally measure the amount of deformation by defining percent cold work
For the case of cold-rolling, the percent reduction in thickness is used as the measure of cold work
The effect of cold work on commercially pure copper: As cold work increases, both yield and tensile strengths increase, but ductility decreases and approaches zero
Copper
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Which Equation and Why
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14. What is the first thing to consider?
Copper
What is the first thing to consider?

15. UNITS!
Copper
65000 𝑝𝑠𝑖=65000 𝑙𝑏 𝑖𝑛 𝑁 𝑙𝑏 𝑖𝑛 𝑐𝑚 𝑐𝑚 2 𝑚 2
65000 𝑝𝑠𝑖=4.48𝑥 10 8 𝑃𝑎=448𝑀𝑃𝑎
60000 𝑝𝑠𝑖=4.14𝑥 10 8 𝑃𝑎=414𝑀𝑃𝑎

16. UNITS!
Copper
65000 𝑝𝑠𝑖=65000 𝑙𝑏 𝑖𝑛 𝑁 𝑙𝑏 𝑖𝑛 𝑐𝑚 𝑐𝑚 2 𝑚 2
65000 𝑝𝑠𝑖=4.48𝑥 10 8 𝑃𝑎=448𝑀𝑃𝑎
60000 𝑝𝑠𝑖=4.14𝑥 10 8 𝑃𝑎=414𝑀𝑃𝑎

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Copper
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18. Example 8-4
Design a process to produce 0.5 cm diameter copper wire.
Choose any starting diameter

19. Example 8-4
Design a process to produce 0.5 cm diameter copper wire.
Choose any starting diameter
% 𝑐𝑜𝑙𝑑 𝑤𝑜𝑟𝑘= Δ𝐴 𝐴 0 =67.3%
Copper
510 MPa
𝐹=𝑆∙𝐴
𝑆= 9140𝑁 𝜋 𝑚 2 2
𝐹=152𝑀𝑃𝑎∙𝜋 𝑚 2 2
152 MPa
𝑆=465𝑀𝑃𝑎
𝐹=9140 𝑁
It Does NOT break!

20. Isotropic vs. anisotropic
Iso: The same An: Not
Isotropic: Same properties in every direction
Anisotropic: different properties in different directions.

21. Microstructure, Texture Strengthening, and Residual Stresses
During deformation, grains rotate & elongate, causing certain crystallographic directions and planes to become aligned with the direction of applied stress
This phenomenon is responsible for the fiber texture of materials that undergo wire drawing and extrusion as well as the sheet texture of those that undergo rolling
The strengthening that occurs by the development of anisotropy or of a texture is known as texture strengthening
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Residual Stress
A small portion of the applied stress is stored in the form of residual stresses within the structure as a tangled network of dislocations
This may not be desirable and can be undone by a heat treatment known as a stress-relief anneal
Residual stresses affect the ability of a part to carry a load. This can be a benefit. For instance, a part with a residual compressive stress can withstand a larger tensile load
Total stress = Residual stress + applied stress
Compressive stress is negative
Tension stress is positive
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23. Residual Stress and Glasses
Residual stresses can also strengthen materials that are prone to fatigue failure.
Hence, sometimes components that are subject to fatigue failure are bombarded with steel shot propelled at high velocity to introduce compressive stresses. This process is called shot peening

24. Residual Stress and Glasses
Glasses can be rid of their residual stresses with annealing, a high temperature heat treatment
Raise to a high temperature and (annealing point) and let it cool slowly
Inside and outside cool at same rate
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25. Residual Stress and Glasses
Tempering
puts compressive stresses on the surface of the glass
Improves strength and inhibits the growth of cracks, but with a large enough impact the glass shatters
Glass is also sometimes laminated to minimize the injuries or damages that might result from its failure
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26. Characteristics of Cold-Working
Advantages and limitations to strengthening a metallic material.
Advantages
Limitations
We can strengthen the material and produce the desired final shape at the same time
Some metals are brittle at room temperature. Cold-working does little for these
We can get excellent dimensional tolerances and surface finishes by cold-working
Ductility, electrical conductivity, and corrosion resistance are impaired by cold working
Cold-working can be an inexpensive method for producing large numbers of small parts
Residual stresses can greatly impair materials properties if not properly controlled
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28. The Three Stages of Annealing
Annealing is a heat treatment used to eliminate some or all, depending on the temperature, of the effects of cold working
You might want to do this, for example, because of loss of ductility or development of undesirable residual stresses
There are three stages to annealing:
Recovery
Recrystallization
Grain Growth
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29. Recovery, Recrystallization, and Grain Growth
Recovery: low temperature treatment, provides the thermal energy for tangled dislocations to move and form the boundaries of a polygonized subgrain structure, removes residual stresses
Above recrystallization temperature: recovery occurs quickly, new grains nucleate the boundaries of the polygonized structure, eliminates dislocations (reducing strength). This process is called recrystallization
At even higher annealing temperatures, both recovery and recrystallization occur rapidly and grain growth occurs, with favored grains consuming smaller ones
Cold worked
Recovery
Recrystallization
Grain growth
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8-7 Control of Annealing
To design an annealing heat treatment, we need to know the recrystallization temperature, which is the temperature at which the grains in the cold-worked microstructure begin to transform into new, equiaxed, dislocation-free grains
The recrystallization temperature is influenced by a variety of processing variables, such as amount of cold work, initial grain size, purity, annealing time, and melting point
Recrystallization grain size is affected by some of the same factors
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