Effect of Grain Size and Hardness

It has been shown in the previous section how inclusions size plays a role in fatigue life. But inclusion are normally contained in grains. In carbon steels yield strength Cy is related to ferritic grain size d by the well-known Fetch equation [30] 

This fatigue limit is much lower than the plain fatigue limit that would be measured with a mirror-polished specimen without surface inclusions. For example, 1800 MPa tensile strength steel in ideal conditions has a fatigue limit of about 800 MPa, see Fig. 3.34, but it would fail under cyclic stress at 380 MPa if an inclusion of just 5-10 micron would be present on a surface grain. The equation of the average grain size d or inclusion size I, solid curve of Fig. 3.36, is 

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