The true stress (σ) - true strain ( ε ) diagram of a strain hardening material is shown in figure. First, there is loading up to point A, i.e., up to stress of 500 MPa and strain of 0.5. Then from point A, there is unloading up to point B, i.e., to stress of 100 MPa. Given that the Young’s modulus E = 200 GPa, the natural strain at point B (ε_B ) is _________ (correct to three decimal places).

Answer :

0.498

We know that Slope of AB line is E

                                                               E =  AC/BC

                                                                200*10³ MPa = (500-100)MPa/BC

                                                                                    BC = 400/(200*10³ ) = 0.002

                                                                                      ε_{B =} 0.5 - 0.002 = 0.498