Answer:
7.7 kN
Explanation:
The capacity of a material having a crack to withstand fracture is referred to as fracture toughness.
It can be expressed by using the formula:
[tex]K = \sigma Y \sqrt{\pi a}[/tex]
where;
fracture toughness K = 137 MPa[tex]m^{1/2}[/tex]
geometry factor Y = 1
applied stress [tex]\sigma[/tex] = ???
crack length a = 2mm = 0.002
∴
[tex]137 =\sigma \times 1 \sqrt{ \pi \times 0.002 }[/tex]
[tex]137 =\sigma \times 0.07926[/tex]
[tex]\dfrac{137}{0.07926} =\sigma[/tex]
[tex]\sigma = 1728.489 MPa[/tex]
Now, the tensile impact obtained is:
[tex]\sigma = \dfrac{P}{A}[/tex]
P = A × σ
P = 1728.289 × 4.5
P = 7777.30 N
P = 7.7 kN
