In real world designs, parts are rarely simple in geometry and this may lead to areas of stress concentrations. They are also sometimes known as stress risers and can occur whenever there are abrupt changes in geometry or due to the presence of cracks in a material. These abrupt changes in geometry are due to the presence of features such as holes, notches, grooves and threads among many others. Finite element analysis software can be used to detect areas of stress concentrations and determine stress values.

The stresses at regions where stress concentrations occur are much higher than at other regions. If these are not taken into consideration during the design stage, the material may yield and fail prematurely.

Stress concentrations can occur upon application of different types of loads whether axial, bending or shear loads.
The theoretical stress concentration factor $$k_t$$ can be used as a measure of stress concentration. It is also known as the form factor and is given by the following equation

$$k_t = \sigma_{max}/\sigma_{nom}$$ or in the case of shear loads,
$$k_{ts} = \tau_{max}/\tau_{nom}$$
Where,
$$\sigma_{max}$$ and $$\tau_{max}$$ are the maximum stresses in the part
$$\sigma_{nom}$$ and $$\tau_{nom}$$ are the reference stresses in the part

Approximations
In some cases where cracks or defects are present in a part, it might be reasonable to use an approximation for calculating the stresses. For example, a crack that is very similar to a hole can be approximated by the latter of a chosen radius.

Peterson’s Stress Concentration Factors is a great resource that contains K values for various shaped elements and is recommended for those wishing to have a closer look at stress concentrations phenomena.

Stress concentration factor
Stress concentration kt