True and Engineering, Stress and Strain

Q. The maximum reduction in cross-sectional area per pass (R) of a cold wire drawing process is

R = $1-e^{-(n+1)}$

where n represents the strain hardening coefficient. For the case of a perfectly plastic material, R is

1. 0.865
2. 0.826
3. 0.777
4. 0.632

Q. The relationship between true strain $\left({ϵ}_T\right)$ and engineering strain $\left({ϵ}_E\right)$ in a uniaxial tension test is given as

1. ${ϵ}_E=ln(1+{ϵ}_T)$
2. ${ϵ}_E=ln(1-{ϵ}_T)$
3. ${ϵ}_T=ln(1+{ϵ}_E)$
4. ${ϵ}_T=ln(1-{ϵ}_E)$

Q. In open-die forging, a disc of diameter 200 mm and height 60 mm is compressed without any barreling effect. The final diameter of the disc is 400 mm. The true strain is

1. 1.986
2. 1.686
3. 1.386
4. 0.602

Q. Engineering strain of a mild steel sample is recorded as 0.100% The true strain is

1. 0.010%
2. 0.055%
3. 0.099%
4. 0.101%

Q. By application of tensile force, the cross-sectional area of bar P is first reduced by 30% and then by an additional 20%. Another bar Q of the same material is reduced in the cross-sectional area by 50% in a single step by applying tensile force. After deformation, the true strain in bar P and bar Q will, respectively be

1. 0.5 and 0.5
2. 0.58 and 0.69
3. 0.69 and 0.69
4. 0.78 and 1.00