(Solved): 4- A ductile metal wire of uniform cross-section is loaded in tension until it just begins to neck. ...

4- A ductile metal wire of uniform cross-section is loaded in tension until it just begins to neck. The curve of true stress $?$ vs. true strain $?$ for this wire approximates to: $?=235{?}^{0.37}\mathrm{MPa}$ a- Assuming that the volume is conserved, derive a differential equation relating the true stress to the true strain at the point of necking. b- Estimate the ultimate tensile strength of the metal and the work required to take $0.1{\mathrm{m}}^3$ of the wire to necking.