To develop this problem it is necessary to apply the concepts related to stress.
The calculation of maximum stress by definition is given by
[tex]\sigma_m = 2\sigma_0 \sqrt{(\frac{a}{\rho_i})}[/tex]
Where,
[tex]\sigma_0[/tex] = Nominal applied tensile stress
a = Length of a surface crack
[tex]\rho_i[/tex] = Radius of curvature tip of the internal crack
Now we can find the length of a surface crack,
[tex]a = \frac{3*10^{-3}}{2}[/tex]
[tex]a = 1.5*10^{-2}mm[/tex]
With this value we find now the ratio of [tex]\rho_t[/tex]
[tex]\frac{a}{\rho_t} =\frac{1.5*10^{-2}mm}{4.5*10^{-4}}[/tex]
[tex]\frac{a}{\rho_t} = 33.33[/tex]
Therefore the magnitud of the stress would be
[tex]\sigma_m = 2\sigma_0 \sqrt{(\frac{a}{\rho_i})}[/tex]
[tex]\sigma_m = 2(160Mpa) \sqrt{(33.33)}[/tex]
[tex]\sigma_m = 1847.42 Mpa[/tex]
Therefore the magnitude of the maximum stress is 1847.42Mpa.
