Calculating Nominal strain at which Necking Occurs

[50Cent]

Homework Statement

Given two wires of gauge length 100mm and 200mm
They are loaded to fracture in tension
The 100mm sample extends by 15mm
The 200mm sample extends by 25mm.

I need to use this information to calculate the nominal strain at which necking commences in the wires

Homework Equations

These are the relavent equations i can find in my notes relating to necking, stress/strain, true stress/strain

we are also told, the true stress/strain curve generally represented by,

where n is the work-hardening exponent

"necking" in a sample started when the value of the true strain is equal to the work hardening exponent, i.e.,

The Attempt at a Solution

Im not so sure where to start with this as there are no forces given or areas. I assume we have to use the two sets of data to equated these terms and cancel them out.

 

[Astronuc]

Im not so sure where to start with this as there are no forces given or areas. I assume we have to use the two sets of data to equated these terms and cancel them out.

Assuming that the wires are the same material and have the same cross-section, a starting point would be to realize that the ultimate tensile strength, which coincides with uniform elongation, when/where necking starts is the same between the wires.

https://www.admet.com/effect-specimen-geometry-tensile-testing-results/

Note: As the gauge length increases, the percent elongation decreases.

And, after fracture, one measures the resulting 'total' elongation.