Pumps & Systems, June 2007

Shaft failures do not happen everyday, but when they do, it can be a challenge to determine the cause of failure. Here's a technical explanation of what happens when the shaft bends or breaks.

To understand shafts and why they fail, you need to understand the relationship between stress and strain for steel.

Stress is the force carried by a material per unit area, measured in psi (pounds per square inch) or Mpa (Megapascals or Mega Newtons per square meter). If a material is under tension, the stress is acting to pull apart the molecules that make it up, making it longer; if the material is under compression, the stress is pushing the molecules together, causing the material to get shorter (and fatter as the compressed material “bulges” outward) if enough stress is applied (see Figure 1).

Figure 1, left. Simplified model of the distortion of molecules under stress: (A) Material in neutral state. (B) Material under tension. (C) Material under compression.

Strain is the change in the length, or elongation per unit length, of a material under a tensile stress.

Most shafts are made of hot-rolled carbon steel, but for more specialized loads or environments, you may see shafts that are made of alloyed or stainless steel. When a tensile stress is added to a material, the material begins to deform at a certain level of stress. This applies to steel, wood, concrete or any other “engineering” material. In the case of a motor shaft, the material is steel.

Glossary of Terms

• Stress – The force carried by a material per unit area normal to the force direction.
• Strain – The elongation per unit length of a material. Œ = ∆L/L where Œ is the strain and L is the original length of the material.
• Tension – A stress that produces an elongation of an elastic physical body.
• Compression – A force that attempts to push molecules of a material closer together.
• Elastic Material – An object behaves elastically if it returns to its original shape after a force is applied and then removed. (If an applied force causes a permanent deformation, the behavior is termed plastic.)
• Plastic Deformation – Deformation that remains after the load causing it is removed. It is the permanent part of the deformation beyond the elastic limit of a material.
• Maximum Tensile Strength – The maximum stress that a material can withstand. In tensile testing, the ratio of maximum load to original cross sectional area. Also called Ultimate Tensile Strength.

The deformation due to the tensile stress is elastic until the stress reaches its yield strength point for the steel (typical carbon steel = 73000-psi or 503-Mpa). The yield strength will vary with the material. For example, a 416 stainless steel shaft, while offering corrosion resistance, will actually have slightly lower yield strength than a typical 1045 hot-rolled carbon steel.

Effects of Deformation

If the stress applied to a shaft is below the yield strength, when the stress is removed there is no permanent change in the molecules of steel. Elastic deformation simply means that the steel shaft will return to its original shape and dimensions when the force is removed. In other words, if you apply enough force to deflect the shaft, and release the force, it will spring back to the original position.

Strain is measured by the percent of deformation, and the yield strength is the point where the strain is equal to 0.2 percent deformation. If the applied stress is greater than the yield strength, then the deformation becomes plastic and the steel will not return to its original shape. That is, if you bend it past the yield strength, it remains bent.

Even if the shaft is straightened, it will still be weaker than before it was bent. This is why we should always consider the application before deciding whether to straighten a shaft or replace it. The maximum (or ultimate) tensile strength is the point at which the material is just about to fracture.

Tensile vs. Brittle Strength

Materials can be classified as ductile or brittle. A material that undergoes extensive plastic deformation before fracture is called ductile. This simply means that it can bend (as opposed to it “snapping”) before it finally breaks.

Figure 2 shows a stress-strain diagram for an elastic material. Point A is the yield strength, Point B is the maximum tensile strength, and Point C is the point at which the material breaks. Even if the stress between points A and B remains stable, the strain will continue to cause deformation, where the molecules are changing position and forming new bonds within the material.

Figure 2, left. Stress-strain diagram for an elastic material.

A brittle material can undergo only a small amount of plastic deformation before breaking. A glass rod is a good example of a brittle material. You cannot bend it, but if enough force is applied, it snaps. A perfectly brittle material will break exactly at the yield stress point, as shown in Figure 3.