Problem $2$

The sample shown below is subjected to a uniaxial tensile test. The uniaxial yield

strength of the material is $600$ MPa $.$

$($a$)$ Will the sample neck in region I prior to yielding in region II$?$ Assume a plastic

constitutive law of

${}_{11}=k({)}^n$ with $n=0\mathrm{.}15,k=1300$MPa

The initial cross$-$sectional areas of region I and II$,A_{\text{I}}$ and $A_{II},$ are $12m{m}^2$ and $18m{m}^2,$

respectively.

$($b$)$ What is the limiting value of $A_{\text{I}}$ above which yielding will occur in region II prior to

necking in region I?