A cylindrical specimen of a cold-worked brass has a ductility (%EL) of 27%. If its cold-worked radius is 14 mm, what was its radius before deformation?

Initial radius of cylindrical specimen

ri = 15.46mm

Explanation:

Cw = [(A1 - A2)/A1] * 100% ...equation 1

Where CW = cold worked percentage gain  for( 27% EL) ductile

A2 = final area of cylindrical specimen = pai * r²

Where r = final radius of cylindrical specimen

So therefore expanding equation 1 will give

A1 * Cw = (100 * A1) - (100 * A2)

Cw = 18% from attached graph

A2 = area of cylindrical specimen after cold work = pai * 14² = 615.75mm²

So therefore

18A1 = 100A1 - (100 * 615.75)

-82A1 = -61575.22

A1 = 750.92mm²

So solving for initial radius from initial area of specimen

r1 = (A1/pai)^½

r1 = (750.92/pai)^½

r1= 15.46mm

answer:

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