Deforming process for materials

Cold working is plastic deformation of a metal below its recrystallisation temperature, so that the grains are deformed and strengthened without recrystallising.

Types of cold working

• Cold rolling (sheets, strips)
• Wire/bar drawing and tube drawing
• Cold forging and extrusion
• Bending, deep drawing and spinning of sheet
• Shot peening (surface cold work)

Strain hardening

During cold work, the dislocation density rises from about $10^{6}$-$10^{8}$ cm$^{-2}$ to $10^{10}$-$10^{12}$ cm$^{-2}$. Dislocations multiply (Frank-Read sources), tangle and block each other, so a higher stress is needed to move them. Hence the metal becomes stronger and harder as it is deformed. This is also called work hardening. The flow curve is $\sigma_T = K\varepsilon_T^{\,n}$.

Effect of % cold work

$$\%\,CW = \frac{A_0 - A_d}{A_0}\times 100$$

 property
  |         tensile strength
  |       _..---
  |   _.-'
  |  /       yield strength lower than UTS
  |  \_
  |    `-._ ductility (% EL)
  +----------------------> % cold work

• Yield strength, tensile strength and hardness increase (yield strength rises faster, approaching the UTS).
• Ductility (% elongation, % RA) decreases.
• Electrical conductivity falls slightly; corrosion resistance is reduced; grains elongate along the working direction and residual stress is introduced.

A heavily cold-worked metal can be restored by annealing.

Formula: with $A_0$ the original and $A_d$ the deformed cross-section area,

$$\%\,CW = \frac{A_0 - A_d}{A_0}\times 100 = \left(1 - \frac{d_d^{\,2}}{d_0^{\,2}}\right)\times 100$$

(a)

$$\%\,CW = \left(1 - \frac{(10.2)^2}{(12.7)^2}\right)\times 100 = \left(1 - \frac{104.04}{161.29}\right)\times 100 = 35.5\%$$

(b)

$$0.30 = 1 - \frac{d_d^{\,2}}{15^2} \ \Rightarrow\ d_d^{\,2} = 0.70 \times 225 = 157.5$$ $$d_d = \sqrt{157.5} = 12.55\ \text{mm}$$

(c)

Cold drawing makes the wire stronger and harder (higher yield strength and UTS) but less ductile, because dislocation density increases.

Answer: (a) 35.5% cold work; (b) final diameter 12.55 mm.

Annealing is heating a cold-worked metal to a suitable temperature, holding, and cooling slowly to remove strain hardening, relieve residual stress and restore ductility.

Stages

1. Recovery (low temperature, below about $0.3\,T_m$)

• Point defects annihilate and dislocations rearrange into low-energy arrangements (polygonisation).
• Internal stresses are relieved; electrical conductivity partly recovers.
• Hardness, strength and ductility change very little; grain structure stays deformed.

2. Recrystallisation (about $0.3$-$0.5\,T_m$)

• New strain-free equiaxed grains nucleate at high-energy sites (grain boundaries, slip bands) and grow, consuming the deformed grains.
• Dislocation density drops sharply; strength and hardness fall, ductility rises to near the annealed values.

3. Grain growth (higher temperature or longer time)

• Large grains grow at the expense of small ones to reduce grain-boundary energy.
• Strength and hardness fall further and the surface may look rough (orange peel).

 property
  |\ strength
  | \_______
  |  |       \___
  |  |   |       `--- 
  |  |   | ductility ___--
  |__|___|_____..--'
  +--|---|----------------> temperature
   Rec. Recryst. Grain growth

Recrystallisation temperature

It is the temperature at which a cold-worked metal completely recrystallises in about one hour. For pure metals it is about $0.3$-$0.5\,T_m$ (absolute), e.g., about 200 °C for copper, 450 °C for iron, near room temperature for lead.

Factors affecting it: (i) larger prior cold work gives a lower temperature; (ii) smaller initial grain size lowers it; (iii) higher purity lowers it, since alloying atoms and impurities impede boundary movement; (iv) longer holding time lowers it.

Importance

Annealing permits further cold work without cracking, since ductility is restored. Working above the recrystallisation temperature is called hot working; below it, cold working.