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Percent cold work of a drawn wire

Short answer

%CW = (1 - d_d²/d_0²)×100. (a) d0=12.7, dd=10.2 → 35.5% CW. (b) Desired 30% CW, d0=15 mm, solve d_d = 15√(1-0.30) = 12.55 mm. (c) Strength and hardness increase, ductility decreases.

(a) A copper wire of diameter 12.7 mm is cold drawn to 10.2 mm diameter. Calculate the percentage cold work. (b) A 15 mm diameter rod is to be given 30% cold work by drawing. Find the final diameter. (c) State what happens to its strength and ductility.

Formula: with A0A_0 the original and AdA_d the deformed cross-section area,

% CW=A0−AdA0×100=(1−dd 2d0 2)×100\%\,CW = \frac{A_0 - A_d}{A_0}\times 100 = \left(1 - \frac{d_d^{\,2}}{d_0^{\,2}}\right)\times 100

(a)

% CW=(1−(10.2)2(12.7)2)×100=(1−104.04161.29)×100=35.5%\%\,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−dd 2152 ⇒ dd 2=0.70×225=157.50.30 = 1 - \frac{d_d^{\,2}}{15^2} \ \Rightarrow\ d_d^{\,2} = 0.70 \times 225 = 157.5 dd=157.5=12.55 mmd_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.

✓ Answer checked by Claude Opus 5.5 (high effort)

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