Question 2.1: Calculation of Ultimate Tensile Strength This example shows ...

Because the necking strain corresponds to the maximum load, the necking strain for this material is

ε= n = 0.5,

the true ultimate tensile strength is

$\sigma =Kn^{n}=690(0.5)^{0.5}=488 \text{ }MPa$.

The true area at the onset of necking is obtained from

$ln(\frac{A_{o}}{A_{neck}})= n =0.5.$

Thus,

$A_{neck} =A_{o}\varepsilon ^{-0.5}$,

and the maximum load, P, is

$P=\sigma A_{neck}=\sigma A_{o}e^{-0.5}$,

where σ is the true ultimate tensile strength. Hence,

$P=(488)(0.606)(A_{o})=2900A_{o}\text{ }kg$.

Since UTS = P/$A_{o}$.

UTS = 296 MPa.