What is the magnitude of the maximum stress that exists at the tip of an internal crack having a radius of curvature of 2.5 × 10−4 mm and a crack length of 2.5 × 10−2 mm when a tensile stress of 170 MPa is applied (in MPa)

Respuesta :

Answer:

2404 MPa

Explanation:

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The maximum stress that exists at the tip of the internal crack is 3,400 Mpa.

The given parameters;

  • radius of the internal crack, r = 2.5 x 10⁻⁴ mm
  • crack length, l = 2.5 x 10⁻²
  • tensile stress, σ = 170 MPa = 170 x 10⁶ N/m²

The maximum stress that exists at the tip of the internal crack is calculated as follows;

[tex]\sigma _{max} = 2\sigma \times \sqrt{(\frac{l}{r} )} \\\\\sigma _{max} = 2 \times 170 \times 10^6 \times \sqrt{(\frac{2.5\times 10^{-2}}{2.5 \times 10^{-4}})} \\\\\sigma _{max} = 3.4 \times 10^{9} \ Pa\\\\\sigma _{max} = 3,400\ Mpa[/tex]

Thus, the maximum stress that exists at the tip of the internal crack is 3,400 Mpa.

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