Finite Element Method (FEM) fatigue analysis

Engineers who design machines and structures must ensure that their products can withstand long-term operation without damage. One of the most dangerous phenomena limiting structural service life is material fatigue—the gradual formation of fatigue cracks under load cycles, even when the loads are well below the material’s static strength. It is estimated that fatigue accounts for ~90% of mechanical component failures during service. Worse still, fatigue cracks develop stealthily—from microscopic fissures to sudden catastrophic failure—often without warning. For this reason, fatigue resistance assessment is a crucial part of safety-focused mechanical structure design. In practice, fatigue analysis involves predicting after how many cycles a given location in a structure may crack. Today, it is carried out using computer simulations, combining FEM strength calculations (finite element method) with models that describe material behavior under cyclic loading. Such a fatigue life simulation enables engineers to identify critical points in the design, prevent failures and cracking already at the design stage, and optimize the structure for durability. As a result, a properly performed fatigue analysis helps avoid costly defects or product recalls and, above all, increases the product’s safety and reliability in operation.

What does fatigue analysis involve in FEM calculations?

Traditional strength analysis (static) in FEA checks whether a structure can withstand a single, maximum load without plastic deformation or failure. However, meeting static criteria does not guarantee long-term durability—an element may survive a one-time load, yet still fail due to fatigue after that load is repeated many times. Fatigue analysis therefore complements FEA calculations by assessing the service life of the structure under repeated loading.

In engineering practice, it typically works like this: first, an FEA model of the component is created and FEA calculations are run for representative load cases (e.g., simulating driving on a rough road for a vehicle frame, wind-gust loading for a wind turbine structure, etc.). FEA provides the distribution of stresses (and strains) throughout the entire model. Next, a material model is applied to these results, accounting for the material’s fatigue properties—most often in the form of an S–N (Wöhler) curve or fatigue strength parameters. Based on this, fatigue life is calculated: that is, the number of cycles to crack initiation or the fatigue safety factor at each point in the structure. These calculations can be performed within the FEA software itself (in fatigue modules) or using specialized tools for fatigue analysis. The output includes, among other things, a map of the areas most susceptible to cracking and an estimate of how many cycles it will take for damage to occur. This allows the designer to see which areas of the structure need improvement in order to achieve the intended service life and safe operation.

Basic methods for assessing material fatigue

There are several well-established approaches to fatigue calculations. The choice of method depends, among other things, on the strain range (elastic or plastic), the number of cycles to failure, and the nature of the loading. The main methods include:

• S–N method (stress–life, Wöhler curve) – The classic stress–number of cycles approach is based on plots showing the relationship between stress level and the number of cycles to failure. The S–N curve for a given material is determined experimentally: material specimens are subjected to sinusoidal cyclic loading at different amplitudes, and the number of cycles to fracture is then recorded for each specimen. This produces a plot (often on a log–log scale) known as the Wöhler curve, where lower stresses correspond to longer life (more cycles to fracture). The S–N method assumes elastic material behavior—it is mainly applicable to high-cycle fatigue, where stresses remain below the yield strength and life is counted in thousands up to millions of cycles. It is assumed that above about 10^4 cycles (e.g., in ranges >10,000), elastic behavior still dominates, so the S–N method provides reliable results. The S–N curve often includes a horizontal segment at high cycle counts—this corresponds to the material’s fatigue limit (endurance limit), i.e., an amplitude below which steel specimens can withstand an unlimited number of cycles without cracking. (Note: not all materials have a distinct fatigue limit—for example, aluminium shows a gradual reduction in strength as the number of cycles increases, so by convention its strength is defined at 10^7 cycles instead of infinite life).
• ε-N method (strain-life, strain-based method) – When strains are no longer purely elastic, local plastic deformation occurs (e.g., at notches, stress concentration sites), and the accuracy of the S-N method decreases. In such cases, the strain–number of cycles approach is used, also known as the Coffin–Manson methodology. The ε-N method adds elastic and plastic strains over a cycle, defining the total strain amplitude as the sum of the elastic amplitude (Δε_e/2) and the plastic amplitude (Δε_p/2). ε-N curves combine Basquin’s law (describing the elastic part of the stress–cycle relationship) and the Coffin–Manson relation (describing the plastic part) into a single equation. The strain-based method is used mainly for low-cycle fatigue (when the number of cycles to failure is small, on the order of
• Effect of mean stress – the Goodman diagram – Real-world loads are rarely fully symmetric, fully reversed (from tension to compression). More often, the loading is cyclic with a certain static component (the so-called mean stress). A tensile mean stress (in tension) is generally detrimental to fatigue life (it accelerates crack initiation), whereas compressive stress can be beneficial (by closing microcracks). To account for the effect of mean stress in calculations, correction methods and constant-life plots are used (the so-called Goodman, Gerber, Soderberg diagrams). The most common is the Goodman diagram—in a coordinate system, mean stress is plotted on the horizontal axis and the alternating stress amplitude on the vertical axis. The diagram defines the region of safe combinations of these values. The Goodman line connects the point Rm (the material’s ultimate strength at a mean stress equal to Rm and zero amplitude) with the fatigue limit point (maximum amplitude at zero mean stress). Any combination of mean and alternating stress that lies below the Goodman line indicates that cracks will not form over an infinite number of cycles, while points above it indicate a risk of fatigue failure. In practice, engineers often correct the effective stress amplitude using the Goodman equation (or Gerber for ductile materials) before applying the S–N curve—this makes it possible to estimate life for a given mean stress.
• Multiaxial fatigue criteria (e.g., Dang Van) – Many components are subjected to loads with a complex (multiaxial) stress state—for example, a combination of shaft bending and torsion, or pressure + bending in a pipe. Classic S–N curves are based on nominally uniaxial stresses, so to assess multiaxial fatigue, criteria are used that incorporate appropriate strength (failure) hypotheses. One example is the Dang Van criterion, used especially to evaluate the fatigue endurance limit under complex loading. The Dang Van method assumes searching for combinations of micro shear stresses and hydrostatic pressure in the material that can initiate microcracks. The result of a Dang Van analysis is a safety factor with respect to fatigue at an infinite number of cycles, rather than a specific number of cycles to failure. Applying this criterion requires special material parameters (determined from uniaxial and biaxial material tests). It is used, for example, in the automotive industry when analyzing the durability of suspension components, gear transmissions, etc., where loads vary along multiple axes and an unlimited service life of the component is required with an appropriate safety margin.
• Palmgren–Miner rule (damage accumulation) – When a structural component is subjected to variable load amplitudes (a so-called load spectrum), a single S–N curve is not sufficient—the material accumulates damage from cycles at different levels. Miner’s rule is a simple and widely used hypothesis of linear accumulation of fatigue damage. According to it, each cycle at a given amplitude consumes a certain fraction of the material’s “life”. Despite its simplifications, this method is widely used in engineering (automotive, aviation, offshore structures) for approximate assessment of fatigue life under complex variable loading. It makes it possible to sum the effect of, for example, thousands of different measured loads from a construction site into a simple indicator of the component’s fatigue life consumption.

Step-by-step fatigue analysis process

MES fatigue analysis is a structured, step-by-step process used to assess a structure’s durability and identify critical areas. Below is a typical sequence of activities:

1. Problem definition and FEM model: The engineer defines the component geometry and the load cases that best reflect real operating conditions. At this stage, the type of cyclic loads to be assessed is determined (e.g., sinusoidal loading, random vibration, equipment on/off cycles, etc.). The component model is then prepared using the finite element method—FEM mesh, material properties (elastic, plastic), and boundary conditions and loads corresponding to the repeated duty cycles.
2. FEA calculations for cyclic loading: FEA simulations (most often static or dynamic analyses) are performed to determine stresses and strains resulting from the specified loads. In a simple case, this may be a single load cycle (e.g., maximum bending of a beam); in more complex cases, it is a series of several cases representing different phases of the cycle or different loading scenarios. If a measured load history is available (e.g., strain-gauge time histories), cycle-counting techniques such as the Rainflow algorithm are used to reduce the variable load signal to a set of cycle blocks with defined amplitudes and means.
3. Identification of highly stressed areas: Even a basic FEM stress analysis can be used to pinpoint regions with the highest stresses or the greatest stress concentrations (e.g., at notches, holes, weld toes, etc.). This is where fatigue crack initiation is most likely to occur. In fatigue analysis, these locations are particularly important—so-called fatigue hot spots are often defined, i.e., points for which the service life will be calculated. FEM software can automatically detect elements with the worst alternating-stress factor, or the engineer selects them based on the results and experience.
4. Selecting the fatigue model and material data: The next step is to provide data on the material’s fatigue strength. An appropriate S–N curve is selected for the material (with the required safety factor, survival probability—e.g., 97.7%—and for the corresponding R range, i.e., the min/max stress ratio). If plastic strains are expected, ε–N curves are used instead of S–N (the material’s Coffin–Manson parameters). These data may come from industry standards, the material manufacturer’s experimental results, or fatigue databases. It is also necessary to determine whether a mean stress correction is applied—for example, by entering the mean stress parameter for a given cycle or, conservatively, by using the Goodman diagram (which in practice is equivalent to reducing the allowable alternating stress amplitude as mean stress increases). Where needed, corrections for the notch sensitivity factor and surface finish are included, especially when the S–N data come from laboratory tests on smooth specimens while the actual component has a rough surface or welded joints.
5. Durability or damage calculation: With the stress distribution from the load scenario and the material data in hand, we move on to the actual life prediction. For each relevant point (e.g., an FEA mesh element at a hot spot), its fatigue life is calculated. If there is a single dominant load cycle, the S–N curve is used to read off the number of cycles to failure at an amplitude equal to the stress at that point (and the mean stress). Often, however, there are multiple different load levels—in that case, the Miner’s summation described above is applied. The fatigue analysis result is also often a safety factor—either a multiplicative margin relative to the assumed number of cycles, or the minimum number of cycles divided by the required number of cycles. For criteria such as Dang Van, the result is given directly as a safety factor for infinite life (e.g., information on whether a given location will withstand the required 10^6 cycles with a margin of 1.5 or not).
6. Locating and assessing cracks: The final step is interpreting the results. The analysis identifies specific areas of the structure with the lowest durability (or the highest level of damage). These are the locations where fatigue crack initiation may begin first. Reports typically include contour plots on the FEA model showing the distribution of the predicted number of cycles to failure or the fatigue safety factor values. The engineer focuses on components that show the most critical values. If the minimum predicted service life of the structure does not meet the assumptions (e.g., the component is expected to withstand 1 million cycles, but the analysis indicates cracking after 200,000), design changes should be proposed: modifying the geometry (rounding notches, increasing the cross-section), switching to a material with better fatigue strength, improving surface quality, or applying hardening processes (e.g., shot peening) to extend service life.
7. Prototype verification and testing: Although FEA fatigue analysis provides valuable predictions, best practice is to confirm its results with prototype testing. Fatigue tests are often performed on key components or entire assemblies (e.g., multi-million-cycle cyclic loading of a car suspension on a test rig) and then compared with the simulation predictions. This allows the model to be calibrated, and the resulting experimental data makes it possible to better tune the material model (e.g., by refining S–N curves for the actual material after welding or machining). This verification loop ensures that the final product has fatigue durability confirmed both by simulation and by experiment, increasing confidence in its safety.

Applications of fatigue analysis across different industries

Fatigue analyses are now standard practice across many industries, from automotive to power generation. Wherever components are subjected to repeated loading, engineers use fatigue simulations to ensure adequate durability and prevent failures. Below are a few examples of applications across industries:

• Automotive: Vehicle structures must withstand hundreds of thousands of kilometers of vibration, impacts, and changing loads. Fatigue analysis is used when designing load-bearing frames, suspension components, body structures, axles, wheels, and even engine parts. For example, a suspension control arm undergoes continuous deflection cycles when driving over uneven road surfaces—fatigue simulation makes it possible to assess whether it will crack after a specified number of torsional cycles. In engines, crankshafts and connecting rods are evaluated for material fatigue resulting from millions of combustion cycles. Car manufacturers use both FEA calculations and bench tests (so-called durability testing) to ensure that, for instance, the vehicle frame will not develop fatigue cracks throughout its service life. Fatigue analyses also help optimize component weight—eliminating excessive overdesign where a smaller cross-section still meets durability requirements, resulting in lighter, more fuel-efficient vehicles.
• Aviation: The aviation industry has placed enormous emphasis on material fatigue ever since the tragic De Havilland Comet jet accidents in the 1950s (caused by fatigue cracking of the fuselage skin around windows). Every passenger aircraft has a defined fatigue life, expressed in takeoff–landing cycles and fuselage pressurization cycles. Strength analyses for aircraft structures always include a fatigue section—for example, calculations of how many pressurization cycles it will take before a crack appears in the skin, or when a landing-gear component may need replacement. The fail-safe and damage-tolerance philosophies are used, meaning cracks are assumed to exist and components are designed so that failure is neither sudden nor catastrophic (e.g., double spars in wings, regular non-destructive inspections of critical areas). Fatigue durability simulation makes it possible to set inspection intervals—for example, predicting that after 5000 flight cycles a given landing-gear joint should be inspected. This is how aviation maintains a high level of safety, while aircraft structural components are used optimally (they are not replaced too early or too late).
• Industrial machinery and engineering structures: In heavy industry, many devices operate in cycles—forge presses apply force thousands of times, overhead cranes repeatedly lift and lower loads, and bridges and cranes are subjected to cyclic loads from vehicle traffic or wind. Fatigue analyses are used, for example, for crane booms (assessing weld life in areas with the highest bending moments), winch drums (the number of rope-winding cycles until fracture), or the steel structures of high-rise buildings (wind-induced sway causes billions of stress cycles in structural members). Fatigue is also studied in civil engineering—for instance, road bridges must withstand hundreds of thousands of truck crossings. Standards (e.g., Eurocode) require fatigue analyses for bridges, treating vehicle traffic as a series of load cycles. In rotating machinery such as turbines or generators, fatigue is also critical—steam turbine blades experience periodic force changes from steam flow, and generator shafts are subjected to torsional vibrations. Each such component is susceptible to fatigue cracking, which is why, already at the mechanical design stage, engineers analyze these phenomena to prevent failures during operation.
• Energy: In the energy sector—especially in renewable energy and power plants—fatigue-related issues play a major role. For example, wind turbines are subjected to continuous, variable wind loads: the rotor blades flex with every rotation and gust, which translates into millions of stress cycles over 20-30 years of turbine operation. Fatigue analysis makes it possible to predict whether, for instance, after 10^7 cycles a crack will not appear at a critical location on the blade (at the root); on this basis, the turbine’s design life is defined and periodic blade inspections are planned. In conventional thermal power generation, in turn, there is the issue of low-cycle thermal fatigue—for example, pipelines and boilers experience stresses each time the system heats up and cools down. The number of full plant start-up/shut-down cycles is limited precisely by the material’s fatigue strength (FEA analyses determine how many such thermal cycles a boiler tube can withstand before it cracks). Also in nuclear power plants, strength analyses focused on fatigue of cooling-system and pressure-system components are mandatory. Fatigue simulations identify locations of potential cracking (e.g., nozzle roots, welds, pipe elbows) and make it possible to plan NDT inspections of these areas during an outage, before a critical crack develops. In summary, in the energy sector, fatigue analysis is a tool that ensures both reliability of energy supply and infrastructure safety.

In summary, fatigue analysis is a powerful tool in a mechanical engineer’s toolkit. It complements traditional FEA calculations by adding the dimension of time and durability, providing a more complete picture of structural safety. With growing demands for product reliability, market competition, and responsibility toward the end user, the ability to predict fatigue behavior is becoming essential. Investing in a thorough fatigue analysis at the design stage pays off many times over during operation—through trouble-free performance, lower service costs, and satisfied users who receive a long-lasting product. It is therefore worth treating fatigue analyses as a standard part of engineering mechanical structural design from the very start of projects, just like static or thermal analyses. This holistic approach ensures that our designs are not only strong on paper, but also durable in the real world.