Notch Sensitivity

The relationship between $K_t$ for static loading and $K_f$ for dynamic loading is defined by notch sensitivity, $q$. This value ranges from 0 (not sensitive) to 1 (full notch sensitivity).

• For normal stress:

$$K_f=1+q(K_t-1)$$

• For shear stress:

$$K_{fs}=1+q_s(K_{ts}-1)$$

Notch sensitivity is typically determined experimentally.

It has been shown that notch sensitivity can be described as a function of the notch radius and a material characteristic length dimension $a$. This characteristic length is several times the size of a single microstructure grain, and can be thought of as near the size of the material’s natural internal imperfections. It is often shown in the form of the Neuber constant, $\sqrt{a}$, such that:

$$q=\frac{1}{1+\frac{\sqrt{a}}{\sqrt{r}}}⟶K_f=1+\frac{K_t-1}{1+(\sqrt{a}/\sqrt{r})}$$

where $r$ is the notch radius.

The Neuber constant is experimentally determined for each material. For steels, it correlates with the ultimate strength, and can be represented with the following curve-fit equations in both U.S. customary and SI units.