Calculate the Engineering Ultimate Tensile Strength and the maximum load in tension testing of an annealed copper specimen with an original diameter of 5 mm. Assume that the strain hardening coefficient for annealed copper is 0.50 and that the true stress at necking is 290 MPa.

Original diameter = 5mm

d = 0.005m. r=0.0025m

True stress (σ) = 290MPa

Coefficient of annealing copper (n) = 0.5

True stress is given as force/area

σ=F/A

Ao=πr^2

Ao=1.963*10^-5m2

F=σ * A

F=290*10^6 * π * (0.0025) ^2

F = 5694.13N

Given that

σ=Kε^n

290=Kε^0.5

n=ε=0.5 at necking

Therefore

290=K*0.5^0.5

K=410.12MPa

ε=In (Ao/A)

0.5=In (π*0.0025^2/A)

exp (0.5) = 1.96*10^-5/A

A=1.96*10^-5/exp (0.5)

A = 1.2*10^-5m2

This is the new area

Then the Ultimate Tensile Stress

σ=F/A

σ=5694.13/1.2*10^-5

σ=4.75*10^8Pa

σ=475MPa

Therefore,

The ultimate tensile stress is 475MPa.

The maximum tension is

Fo/Ao=F/A

F = (Fo/Ao) * A

F = (5694.13/1963*10^-5) * 1.2*10^-5

F = 3479.99

F=3480N.