Question

A H.R. Steel is subjected to a tension test at room temperature. Its tensile strength (max. strength) occurs at 100 MPa at strain of 0.3. Determine the true stress when the engineering strain is 0.4. The true stress-true strain of this steel follows the power law relationship σ-K (E)

Answer 1

Given, max. Strength, S_ut = 100 Mpa = sigma Engineering strain, element of = 0.4 let 'Element of _T' be true strain. Element of _T = l_n (1 + Element of) = l_n (1 + 0.4) = l_n (1.4) Implies Element of _T = 0.3365 Given power law is sigma = k (Element of ^n) For elastic body, n = 1 Implies At sigma = 100 Mpa and Element of = 0.3 100 = k (0.3)^' Implies K= 333.33 Now, at Element of _T = 0.3365 True Stress, sigma_T = k (Element of _ T)^n = 333.33 (0.3365)^1 Therefore True Stress, Sigma_T = 112.16 Mpa