Question $2$

An Fe$-0\mathrm{.}1$C $($in wt$.\%)$ binary alloy undergoes a tensile test with repeated loading and unloading cycles, as shown in Figure Q$2,$ to measure the evolution of yield strength due to work hardening in the material. The Fe$-0\mathrm{.}1$C steel is a martensitic alloy with an equi$-$axed subgrain structure. Table Q$2$ presents the microstructure and hardening parameters for the Fe$-0\mathrm{.}1$C steel.

$($a$)$ If the initial yield strength, $\backslash$sigma $\_($y$,0),$ is $570$ MPa and the yield strength can be approximated by Kock's root mean square model, estimate the initial dislocation density of the material prior to testing.

$[9]$

$($b$)$ Using the Kocks$-$Mecking$-$Estrin $($KME$)$ model, predict the evolution of dislocation density for points A and B in Figure Q$2.$

$($c$)$ Hence, estimate the evolution of yield strength due to work hardening under the assumption that the solute and hierarchical grain structure does not evolve during the test.

$[7]$

Figur

test.

Table Q$2$: Model parameters for Fe$-0\mathrm{.}1$C$.$