Question

A 356 cast aluminum test bar is tested in tension. The initial gage length as marked on the sample is 50mm and the initial diameter is 13.1mm. After fracture, the gage length is 53.7mm and the final diameter is 12.6mm. What is the UTS?

Answer 1

Answer

given,

l₀ = 50 mm

d₀ = 13.1 mm

l₁ = 53.7 mm

d₁ = 12.6 mm

Area of cross section

$A = \dfrac{\pi}{4}d_0^2$

$A = \dfrac{\pi}{4} \times 13.1^2$

A = 134. 782 mm²

The strain is

$\epsilon = \dfrac{l_f-l_0}{l_0}$

             $= \dfrac{53.7-50}{50}$

             = 0.074

the tensile modulus of A356 aluminium is

E = 72.4 GPa

The stress is

σ = εE

  = 72.4 × 10⁹ × 0.074

  = 5357.6 × 10⁶ Pa

σ = 5357.6 MPa

$UTS = \dfrac{ultimate\ load}{cross\ sectional\ area}$

$UTS = \dfrac{ultimate\ load}{134.782}$