A forensic failure analysis has revelaed that the mild structural steel under sc

Question

A forensic failure analysis has revelaed that the mild structural steel under scrutiny plastically deformed and therefore exceeded design tolerances. In a tension test of the steel using a circular cross-section specimen and an original diameter of D =0.36 inches, the following data points were found in the plastic range.
Load(lb) Diameter(inch)

4,900 0.342

6,400 0.328

Assuming that both data points fall on the straight line in a log-log plot of all true stress strain values, compute (sigma)o (strength coefficient) and n.

Explanation / Answer

True stress sigma1 = Load / instantaneous area = 4900 / (3.14/4*0.342^2) = 53367.2 psi

sigma2 = 6400 / (3.14/4*0.328^2) = 75781.4 psi

True strain 1, eps1 = ln A1/A0 = 2*ln (.342/.36) = 0.1026

eps2 = 2 ln(.328/.36) = 0.1862

sigma0 = yield stress

n = [log (sigma2 - sigma0) - log(sigma1 - sigma0)] / (log eps2 - log eps1)

log K = log(sigma1 - sigma0) - n*log eps1

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