Manufacturing Processes

• Forging
• Rolling
• Stamping
• Extruding
• Wire drawing

Strain Hardening (Cold Working)

When a metal is loaded into the plastic regime and then unloaded, it will have experienced permanent deformation (strain). This metal will have a new elastic regime with the same elastic modulus as before but beginning at an offset strain (residual plastic deformation) and with a higher yield strength.

After plastic deformation (manufacturing), the following changes to mechanical properties occur:

1. Yield strength increases —> hardness increases
2. Range of strain domain on stress-strain curve decreases —> ductility decreases

Strain hardening:

• Strain hardening (work/cold hardening)- the process of increasing strength of a material via plastic deformation
  • Plastic deformation = increased dislocation density —> dislocations prevent slip in material, thereby increasing strength
• Empirical form of true stress-strain relationship: $\sigma=K\epsilon^n$, where K is a strength coefficient and n is the strain-hardening exponent
  • n tells you how much hardening will occur: higher n —> higher hardening —> higher strength
  • n: HCP < BCC < FCC
    • Matches ductility: HCP < BCC < FCC
      • Plastic deformation is induced by dislocations, which are easier to form in more ductile materials
  • Very difficult to actually measure true strain
• Strain-rate sensitivity- most materials, including metals, become stronger at higher strain rates; $\sigma = C\dot{\epsilon}^m$
  • m- strain-rate sensitivity
    • Larger values are more desirable because that indicates that a material can resist necking, so it has better formability.
    • Typically, m<0.1 for metals and increases w/ temperature.
• Bauschinger Effect
  • Observed in cyclical tension-compression loading; empirical observation
  • During first loading cycle, dislocation move until they pile up, which is when plastic deformation occurs. This piling of dislocations is not energetically favorable because it is high in stress, so when loading is reversed, the dislocations more favorably move. Thus, not as much stress is required to induce plastic deformation as before.
    • I.e., yield strength required to induce plastic deformation in first tensile loading is less than the yield strength required to induce plastic deformation in the next compressive load.
• Note: there is little or no strain hardening in ceramics, covalent materials, and glasses.
  • Ceramics- can have some strain hardening, but dislocations are not very mobile because ceramics are brittle, not ductile; cold working is not usually possible.
  • Silicon- too brittle to strain harden appreciably
  • Glasses- amorphous, so no dislocations, so no strain hardening
• Polymers (thermoplastics) can be strengthened after deformation.
  • Polymers increase in strength after deformation because polymer chains align and/or crystallize upon deformation.
• Strain hardening is controlled by the amount of plastic deformation, aka the % cold work
  • % cold work is an easier parameter to measure deformation than $\epsilon$ in $\sigma=K\epsilon^n$
  • Wire drawing: $\%CW = [\dfrac{A_o-A_f}{A_o}]*100$
  • Plate rolling: $\%CW=[\dfrac{t_o-t_f}{t_o}]*100$
  • As % CW increases:
    • Yield strength increases
    • $%CW = [\dfrac{t_o-t_f}{t_o}]*100$Tensile strength increases
    • % elongation (ductility) decreases
• During rolling, grains rotate and elongate, which causes certain crystal directions/plans to become aligned in the rolling direction.
  • Causes anisotropy.