A carbon steel alloy E30106 psi specimen is undergoing a ten

A carbon steel alloy (E=30*10^6 psi) specimen is undergoing a tensile test. The initial gage length of the specimen is 5 in and the initial cross-sectional area is 2 in^2. When the specimen is stretched to an engineering strain of 0.009, a 45 ksi engineering stress is produced:

A) What are the true and the true strain?

B) For the true strain at this value of true stress, what portion of of it is elastic and thus recovered upon unloading, and what portion of it is plastic?

C) Repeat each of the above steps for a state where an engineering strain of 0.001 is accompanied by an engineering stress of 25 ksi.

Solution

true strain= ln L/L₀

L= 0.009*5= 0.045in

true strain= ln(0.045/5)= 9*10*^-3

true stress= 30*10^{6 *} 0.009=270ksi