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# Cyclic stress

Cyclic stress in engineering refers is an internal distribution of forces (a stress) that changes over time in a repetitive fashion. As an example, consider one of the large wheels used to drive an aerial lift such as a ski lift. The wire cable wrapped around the wheel exerts a downward force on the wheel and the drive shaft supporting the wheel. Although the shaft, wheel, and cable move the force remains nearly vertical relative to the ground. Thus a point on the surface of the drive shaft will undergo tension when it is pointing towards the ground and compression when it is pointing to the sky. Because the wheel rotates many times during the use of the machine, this cycle of tension and compression is repeated many times — hence the name cyclic stress.

## Types of cyclic stress

Cyclic stress is frequently encountered in rotating machinery where a bending moment is applied to a rotating part. This is called a cyclic bending stress and the aerial lift above is a good example. However, cyclic axial stresses and cyclic torsional stresses also exist. An example of cyclic axial stress would be a bungee cord (see bungee jumping), which must support the mass of people as they jump off structures such as bridges. When a person reaches the end of a cord, the cord deflects elastically and stops the person's descent. This creates a large axial stress in the cord. A fraction of the elastic potential energy stored in the cord is typically transferred back to the person, throwing the person upwards some fraction of the distance he or she fell. The person then falls on the cord again, inducing stress in the cord. This happens multiple times per jump. The same cord is used for several jumps, creating cyclical stresses in the cord that could eventually cause failure if not replaced.

Cyclical torsional stresses are stresses repetitively applied tangent to an axis. As an example, consider a compact disc drive. Each time a disc is inserted into the drive, a motor applies torque to the disc via a drive shaft. Once disc reaches the desired rotational velocity, relatively little torque is required to maintain the speed. Thus the torque varies over time as the drive spins up a disc and slows it down. Unlike the ski lift example above where the torque is relatively constant but the load due to cable tension created a bending moment, compact disc drive shafts have little to no bending moment applied but have a torque that varies significantly over time.

## Cyclic stress and material failure

When cyclic stresses are applied to a material, even though the stresses do not cause plastic deformation, the material may fail due to fatigue. Fatigue failure is typically modeled by decomposing cyclic stresses into mean and alternating components. Mean stress is the time average of the principal stress. Alternating stress is the difference between the mean and the maximum or the mean and the minimum value the principal stress takes on. Engineers try to design mechanisms whose parts are subjected to a single type (bending, axial, or torsional) of cyclic stress because this more closely matches experiments used to characterize fatigue failure in different materials.