Analytical Fatigue Life Prediction

When calculating the fatigue life of a technical component, material or system, an estimate is made of how long it will remain functional under specific conditions before failing or needing replacement. The dynamic load on the component, its material properties and the environmental conditions all play a significant role in this process.

Typical Applications

Whether in mechanical engineering, the automotive industry or medical technology – fatigue life calculations provide reliable insights into the durability of key components.
Examples include:
• Mechanical engineering: e.g. bearings, gears, springs
• Automotive industry: e.g. engine parts, chassis components
• Aerospace: e.g. turbine blades, structural parts
• Electronics: e.g. semiconductors, capacitors
• Medical devices: e.g. implants

Dynamic Loads

Dynamic loads arise from forces and movements that vary over time, placing additional stress on a component and potentially having a significant impact on its fatigue life.
• Stress and strain
• Cyclic loading (e.g. in rotating parts)
• Vibrations

Material Properties

Material properties
The fatigue life depends largely on the material used. The key factors are:
• Fatigue strength
• Fracture mechanics
• Corrosion behaviour

Environmental Conditions

In addition to mechanical stress, external factors also play an important role:
• Temperature – heat or cold affect material behaviour and strength.
• Humidity – can promote corrosion and alter material properties.
• Chemical influences – aggressive media accelerate ageing processes

Mathematical Models & Simulation

We use established methods to provide accurate analytical fatigue life predictions:
• Wöhler curves – the basis of fatigue analysis.
• Miner’s rule – calculation of damage accumulation under variable loads.
• Finite element analysis (FEA) – numerical simulation for evaluating complex loads

When is it necessary to predict the Fatigue Life?

When a finite element method (FEM) is performed, the results include the stresses and strains in the structure. The accuracy of the calculation is good and the deviations from reality are small when the FEM is used correctly. FEM is therefore a very reliable tool and helps the designer to understand how a component is loaded and where the critical points are.

For purely static stress, the calculated maximum stresses or strains can be compared with a reasonable limit, e.g. the yield strength. Due to the uncertainties in the load assumptions, the geometry deviations between model and reality and the manufacturing influences, a safety factor is applied and a purely static design can be performed.

The situation is completely different when the structure is subjected to dynamic stress, i.e. by a time-varying load (which can also be caused by a temperature changes). In this case, it is no longer the absolute value of the acting stresses that is decisive, but the amplitude of the stresses and their frequency.

The following figure illustrates this: A railway axle is stressed by a bending moment resulting from the axle loads. When the axle is stationary, the load is purely static, like a bending beam, and can be calculated very easily.

The upper side is stressed by compressive stresses, the lower side by tensile stresses. With the rolling axle, the particles now move from the compression side to the tension side and the number of these changes corresponds to the number of revolutions.

Forces, bending moment, stresses in the axle of a railway wagon


The stress amplitude that can be withstood by a material with a large number is much smaller than the yield strength. Furthermore, it is not the absolute value of the stress that is decisive, but the stress amplitude (or half the stress amplitude), which cannot be determined from a static calculation.

This also means that the location of the fatigue failure may no longer coincide with the location of a statically calculated maximum stress. A purely static design is therefore not suitable for physically correct recording of fatigue phenomena.

In the case of very small stresses, well below the fatigue strength, a so-called fatigue strength verification, which can be carried out with little effort, may be sufficient.

If the stresses exceed a critical level, they can cause a crack - usually on the surface - to propagate through the component, reducing the load-bearing area.  Depending on the number of load cycles, the load-bearing cross-sectional area becomes smaller and smaller until finally, usually at a peak load, a sudden fracture occurs.

This sudden failure is characteristic of fatigue problems and can be devastating. There are many examples of this throughout the history of technology: oil platforms, railways, aircraft and automobiles are all affected.

The discoverer of these fatigue phenomena is August Wöhler (1819 - 1914), who was the first to recognise these relationships during his research work on railway axles.

The S-N curves named after him are still a useful basis for estimating fatigue life.

Phases of Component Development: From Dimensioning to Analytical Fatigue Life Prediction

The development of a component goes through several phases. In the first step, dimensioning is carried out on the basis of the (rarely occurring) static maximum loads and, if applicable, a safety factor. The proof that the component does not fail under static loading is a prerequisite for all further verifications.
 

If the component is also subjected to dynamic loading, it must also be proven that this does not lead to failure. A comparatively simple proof, because it requires only a limited amount of data, is the endurance limit (infinite life) verification. If it can be shown that, under worst‑case assumptions, the stresses lie safely below the endurance limit, this result is initially sufficient.

In a later phase, when the structure is being optimised and more detailed information is available, the certification of fatigue strength under variable amplitude may be useful or even mandatory. The necessity  strongly depends on the consequences that a failure of the component could have. A crack propagation calculation can also be useful, for example, in determining inspection intervals.
 

The results of a fatigue life calculation have a comparatively large uncertainty. Therefore, absolute fatigue life from a calculation can only be predicted with significant scatter . The reason for this is simple: fatigue life depends logarithmically on the stress level (stress amplitude). If the stress changes by 5%, the fatigue life changes by a factor of 5 to 10. This phenomenon, which is easy to understand from a calculation point of view, is also a physical reality! Nevertheless, a fatigue life calculation is extremely helpful as it provides an accurate relative comparison of fatigue lives and identifies the critical point. This can significantly shorten the development process of a component.

For safety‑critical components, component testing is still required. The statistical nature of fatigue life requires a larger number of tests, which makes such
testing very time‑consuming. Computational fatigue life prediction helps to identify the key influencing factors, thereby reducing both the number of required tests and the test duration.
 
The combination of calculation, measurement, and damage analysis leads, in the long term, to a solid knowledge base. This makes the tool of computational fatigue analysis increasingly powerful, as experimental verification and the factor determined between calculation and measurement enable increasingly accurate quantitative predictions as the database grows.