Fatigue refers to weakening of the material when subjected to repeated loads. In real life scenario, take a paperclip which is robust and strong at the beginning of its life. But when it is used repeatedly, you observe that it becomes easier and easier to bend. It might eventually break at a force far less than that required to permanently deform. This softening and eventual breaking due to application of repeated loads is due to fatigue in the material. When load is applied on a structure, it causes the rearrangement of the localized discontinuities causing microcracks. After the crack is initiated, continuous application of the cyclic loads will cause the micro crack to slowly grow and become catastrophic to the integrity of the structure. When the crack is big enough, it causes the structure to fail under the applied load. This failure occurs suddenly, and the surface of the broken structure is typically smooth without any evidence of plastic deformation. To read some catastrophic historical fatigue failure events, please refer to here.
Representation Of Cyclic Load
Cyclic loading is the primary factor influencing fatigue behavior of a component. Lets first understand some of the terms important for defining cyclic loads. The figure below shows a uniaxial stress cycle. The mean stress (σm ) and stress amplitude (σa ) are expressed in terms of maximum stress (σmax ) and minimum stress (σmin) as,
σm = (σmax + σmin )/2
σa = (σmax – σmin )/2
Stress ratio (R) is defined as,
R = σmin /σmax
The load ratio determines the characteristic stress range experienced by the material. The table below outlines the different R values and their significance.
| R Value | Load State | Notes |
| 0<R<1 | This represents a fluctuating tensile loading scenario with non-zero minimum stress. | Stress goes from being tensile (at σmin) to tensile (at σmax ) in the structure and σm is always positive. |
| R=0 | This represents a repeating tensile loading cycle. | Stress goes from being 0 (at σmin ) to tensile (at σmax ) in the structure and σm is always positive. |
| -1<R<0 | This represents a repeating loading scenario with non-zero minimum stress. | Stress goes from being compressive (at σmin) to tensile (at σmax ) in the structure and σm is always positive. |
| R=-1 | This represents fully reversed cyclic loading. | Stress goes from being compressive (at σmin) to tensile (at σmax ) in the structure and σm= 0. σmax = – σmin |
| -∞<R<-1 | This represents a repeating loading scenario with non-zero maximum stress. | Stress goes from being compressive (at σmin) to tensile (at σmax ) in the structure and σm is always negative. |
| R=∞ | This represents a repeating compressive loading cycle. | Stress goes from being compressive (at σmin ) to 0 (at σmax ) in the structure and σm is always negative. |
| 1<R<∞ | This represents a fluctuating compressive loading scenario with non-zero maximum stress. | Stress goes from being compressive (at σmin) to compressive (at σmax ) in the structure and σm is always negative. |
Effect Of Mean Stress
The above figure shows the load cycles with different mean stress values. A non-zero mean stress can significantly affect fatigue life. It introduces a constant component to the loading cycle which can enhance or reduce materials fatigue life. If the mean stress is tensile, it generally reduces the fatigue life whereas compressive mean stress increases the fatigue life as shown in the figure below. Compressive stress causes the discontinuities to move closely inhibiting the process of crack formation while the tensile stresses pull the discontinuities apart providing favorable conditions for the formation of cracks thus reducing the fatigue life.
As the crack almost always initiates on the surface of the material or near a stress concentration region such as weld zone, efforts must be made to enhance surface properties of a components when needed. Several processes such as carburizing, nitriding, and shot peening induce residual compressive stresses in the surface and subsurface regions of a structure thereby improving the fatigue properties. Processes such as smoothing and polishing can be used to dampen the stress risers.
Accounting For Mean Stress In Fatigue Life Prediction
To calibrate fatigue curves, standard experiments with fully reversed cyclic loads are used. But in real life scenarios mean stress is not always zero. Indeed, as previously mentioned, compressive mean stresses are induced in the material to improve fatigue life properties. Therefore, mean stress correction has to be used to account for the non-zero mean stresses in the analysis of structures, either by hand or with tools such as fe-safe. There is no single mean stress correction method that works in all cases as fatigue damage can occur either due to development of microcracks in shear or tensile planes. The table below summarizes different mean stress correction methods available and their applications.
| Mean Stress Correction Model | Fatigue Approach | Crack Type | Additional Notes |
| Goodman | S-N | Tensile | Ignores compressive mean stress giving a conservative result |
| FKM | Tensile | Stress ratio is used to correct stress amplitude | |
| Findley | Shear | Used for finite long life fatigue cases | |
| Morrow | E-N | Tensile | Gives realistic results for predominantly compressive loads |
| Smith Watson Topper (SWT) | Tensile | Gives conservative life for predominantly tensile loads | |
| Fatemi-Socie | Shear | Shear strain life constants capture mean stress and non-proportional hardening effects | |
| Brown-Miller | Shear | Combined shear and normal strain to calculate fatigue life |
Final Thoughts
Fatigue is a critical failure mechanism that leads to the cracking of structural components under repeated cyclic loading. It must be carefully considered during the design process, as failure can occur even at stress levels significantly below the material’s yield point.
Hopefully this article has given good insights into the fatigue load cycles and the significance of mean stress correction while evaluating fatigue life of structure. We are always here to help, so if you have concerns in your design for fatigue, don’t hesitate to reach out to our expert team!
