Question

If a steel cylindrical specimen is stressed nominally to 70 MPa, what stress level exists at the tip of an elliptical surface flaw, whose length is 5. 3 microns and radius of curvature is 1,074 nanometers

Answer 1

Step-by-step explanation:

To determine the stress level at the tip of the elliptical surface flaw, we can use the stress concentration factor (Kt) which is a dimensionless factor that accounts for the local increase in stress around the flaw. For an elliptical flaw with a length (2a) and a radius of curvature (ρ), the stress concentration factor can be estimated using the following equation:

Kt = 1 + 2(a/ρ)^1/2 + 0.5(a/ρ)

In this case, a = 5.3 microns = 5.3 x 10^-6 meters and ρ = 1,074 nanometers = 1.074 x 10^-6 meters. Substituting these values into the equation, we get:

Kt = 1 + 2(5.3 x 10^-6 / 1.074 x 10^-6)^1/2 + 0.5(5.3 x 10^-6 / 1.074 x 10^-6)

= 3.70

The stress concentration factor of 3.70 indicates that the stress at the tip of the elliptical surface flaw is 3.70 times higher than the nominal stress of 70 MPa. Therefore, the stress level at the tip of the flaw is:

σ = Kt x σ_nominal

= 3.70 x 70 MPa

= 259 MPa

So, the stress level at the tip of the elliptical surface flaw is 259 MPa. It is important to note that this is an estimate and actual stress levels can vary based on factors such as the material properties, the size and shape of the flaw, and the applied load.