Comprehensive Guide to Fatigue Analysis FEA: Ensuring Structural Integrity

Engineers designing machines and structures must ensure their products endure long-term use without damage. One of the most critical phenomena limiting the longevity of structures is material fatigue—the gradual formation of fatigue cracks under cyclic loads, even when these loads are significantly below the material’s static strength. It is estimated that fatigue accounts for ~90% of mechanical component failures during use. Worse, fatigue cracks develop stealthily—from microscopic fissures to sudden catastrophic failure—often without warning. Therefore, fatigue resistance analysis is a crucial aspect of mechanical design focused on safety. Fatigue analysis involves predicting how many cycles a specific part of a structure can endure before cracking. Today, this is conducted using computer simulations, combining Finite Element Analysis (FEA) with models describing material behavior under cyclic loads. Such fatigue life simulation allows engineers to identify critical points in a structure, prevent failures and cracks during the design phase, and optimize the structure for durability. Consequently, a well-conducted fatigue analysis helps avoid costly breakdowns or product recalls and, most importantly, enhances the safety and reliability of the product in operation.

What is Fatigue Analysis in FEA Calculations?

Traditional strength analysis (static) in FEA checks whether a structure can withstand a single, maximum load without plastic deformation or destruction. However, meeting static criteria does not guarantee long-term durability—a component may not break from a single load but may succumb to fatigue after repeated applications. Fatigue Analysis FEA complements FEA calculations by assessing the longevity of structures under repeated load cycles.

In engineering practice, this involves creating an FEA model of the component and performing FEA calculations for characteristic load cases (e.g., simulating driving on a bumpy road for a vehicle frame, wind gust loads for a wind turbine structure, etc.). FEA provides the distribution of stresses (and strains) throughout the model. These results are then combined with a material model that considers the material’s fatigue properties—typically in the form of an S-N curve (Wöhler curve) or fatigue strength parameters. Based on this, fatigue life is calculated: the number of cycles to crack initiation or the safety factor against fatigue at each point in the structure. These calculations can be performed within FEA software (in fatigue modules) or using specialized fatigue analysis tools. The result includes a map of areas most prone to cracking and an estimate of how many cycles will lead to failure. This informs the designer which areas of the structure require improvements to achieve the desired lifespan and safe operation.

Basic Methods for Fatigue Assessment

Several established approaches exist for fatigue calculations. The choice of method depends on factors such as the range of deformations (elastic or plastic), the number of cycles to failure, and the nature of the loads. The basic methods include:

• S-N Method (stress-life, Wöhler curve) – A classic stress-number of cycles approach based on graphs 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 samples are subjected to cyclic sinusoidal loading of varying amplitudes, and the number of cycles to crack each sample is recorded. This creates a graph (often in log-log scale) called the Wöhler curve, where lower stresses correspond to greater durability (more cycles to crack). The S-N method assumes elastic material behavior—it is mainly applicable for high-cycle fatigue, where stresses remain below the yield strength, and durability is measured in thousands to millions of cycles. It is assumed that above approximately 10^4 cycles (e.g., in ranges >10 thousand), the elastic range still dominates, so the S-N method provides reliable results. The S-N curve often has a horizontal segment at a high number of cycles—this corresponds to the endurance limit of the material, i.e., the amplitude below which steel samples can withstand an unlimited number of cycles without cracking. (Note: not all materials have a clear endurance limit—e.g., aluminum shows a gradual decrease in strength with increasing cycles, so fatigue strength is conventionally defined for 10^7 cycles instead of infinite durability).
• ε-N Method (strain-life, strain-based method) – When deformations are not elastic and local plasticizations occur (e.g., at notches, stress concentration areas), the accuracy of the S-N method decreases. In such cases, the strain-number of cycles method, also known as the Coffin-Manson approach, is used. The ε-N method sums elastic and plastic deformations during a cycle—defining the total strain amplitude as the sum of the elastic amplitude (Δε_e/2) and plastic amplitude (Δε_p/2). ε-N curves combine Basquin’s law (describing the elastic part of the stress-cycle relationship) and Coffin-Manson’s law (describing the plastic part) into one equation. The strain-based method is mainly used for low-cycle fatigue (when the number of cycles to failure is small, on the order of <10 thousand, but high stress amplitudes close to the material's yield strength occur). By considering plastic deformations, the ε-N method better predicts the lifespan of components operating under large deformations (e.g., during machine startups, thermal cycles causing thermal expansion, etc.).
• Mean Stress Effect – Goodman Diagram – Real loads are rarely fully variable symmetrically (from tension to compression). Often, there is cyclic loading with a static component (known as mean stress). Tensile mean stress is usually detrimental to fatigue life (accelerating crack initiation), while compressive stress can be beneficial (closing microcracks). To account for mean stress effects in calculations, corrections and constant life diagrams (such as Goodman, Gerber, Soderberg diagrams) are used. The most popular is the Goodman diagram—in a coordinate system, mean stress is plotted on the horizontal axis and variable stress amplitude on the vertical axis. The diagram defines the safe combinations of these values. The Goodman line connects the point Rm (ultimate tensile strength of the material at mean stress equal to Rm and zero amplitude) with the endurance limit point (maximum amplitude at zero mean stress). Any combination of mean and variable stress below the Goodman line indicates no crack formation in an infinite number of cycles, while points above indicate a risk of fatigue failure. In practice, engineers often correct the effective stress amplitude according to the Goodman formula (or Gerber for ductile materials) before using the S-N curve—this allows estimating durability at a given mean stress.
• Multiaxial Fatigue Criteria (e.g., Dang Van) – Many components are subjected to complex stress states (multiaxial)—e.g., a combination of bending and torsion in a shaft, or pressure + bending in a pipe. Classic S-N curves are based on nominally uniaxial stresses, so multiaxial fatigue assessment uses criteria that incorporate appropriate strength hypotheses. An example is the Dang Van criterion, especially used to assess the fatigue strength limit under complex loads. The Dang Van method assumes finding combinations of microshear stresses and hydrostatic pressure in the material that can initiate microcracks. The result of the Dang Van analysis is a safety factor against fatigue for an infinite number of cycles, not 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 for assessing the durability of suspension components, gearboxes, etc., where loads vary in multiple axes, and an unlimited lifespan of the component with an appropriate safety margin is required.
• Palmgren-Miner Rule (damage summation) – When a structural element experiences variable load amplitudes (known as a load spectrum), a single S-N curve is insufficient—the material suffers damage from cycles at different levels. The Miner’s rule is a simple and widely used hypothesis of linear fatigue damage accumulation. According to it, each cycle at a given amplitude consumes a portion of the material’s “life.” Despite simplifications, this method is widely used in engineering (automotive, aviation, offshore structures) for estimating fatigue life under complex variable loads. It allows summing the effects of, for example, thousands of different load measurements on a construction site into a simple fatigue life depletion indicator for the element.

Step-by-Step Fatigue Analysis Process

Fatigue Analysis FEA is an organized process that step by step allows assessing the durability of a structure and identifying critical areas. Below is a typical sequence of actions:

1. Problem Definition and FEA Model: The engineer defines the geometry of the element and load cases that best represent real operating conditions. At this stage, the type of cyclic loads to be analyzed is determined (e.g., sinusoidal loads, random vibrations, on/off cycles of the device, etc.). The element model is prepared using the finite element method—FEA mesh, material properties (elastic, plastic), and boundary conditions and loads corresponding to repetitive work cycles are established.
2. FEA Calculations for Cyclic Loads: FEA simulations (usually static or dynamic analyses) are conducted to determine stresses and deformations from the specified loads. In a simple case, this may be a single load cycle (e.g., maximum bending of a beam), while in more complex cases, a series of several cases representing different phases of the cycle or different load scenarios. If load history from measurements is available (e.g., strain gauge readings over time), techniques like 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 Stressed Areas: Even from the stress analysis in FEA, areas with the highest stresses or greatest stress concentrations (e.g., at notches, holes, weld notches, etc.) can be identified. These are likely locations for fatigue crack initiation. In fatigue analysis, these locations are particularly important—often, so-called fatigue hot-spots are defined, i.e., points for which durability will be calculated. FEA software can automatically detect elements with the worst variable stress factor, or the engineer selects them based on results and experience.
4. Selection of Fatigue Model and Material Data: In the next step, data on the fatigue resistance of the material must be provided. An appropriate S-N curve for the material is selected (with a specified safety factor, survival probability—e.g., 97.7%—and for the corresponding R range, i.e., the min/max stress ratio). If plastic deformations are anticipated, ε-N curves (Coffin-Manson parameters for the material) are used instead of S-N. Sources of this data can be industry standards, manufacturer test results, or fatigue databases. It is also necessary to determine whether mean stress correction is applied—e.g., a mean stress parameter for a given cycle is introduced, or the Goodman diagram is conservatively assumed (which in practice is equivalent to reducing the allowable amplitude of variable stresses with increasing mean stress). If necessary, corrections for notch sensitivity and surface quality are included, especially when S-N data comes from laboratory tests of smooth samples, and the actual element has a rough surface or welded joints.
5. Calculation of Durability or Damage: With the stress distribution from the load scenario and material data, the actual life prediction is performed. For each significant point (e.g., FEA mesh element in the hot-spot), its fatigue life is calculated. If there is a single dominant load cycle, the number of cycles to failure at an amplitude equal to the stress at that point and mean stress is read from the S-N curve. However, often there are many different load levels—then the Miner’s summation described above is used. Often, the result of fatigue analysis is also a safety factor—a multiple reserve relative to the assumed number of cycles or the minimum number of cycles divided by the required number of cycles. In the case of criteria like Dang Van, the result is directly given as a safety factor for infinite durability (e.g., information on whether a given location will withstand the required 10^6 cycles with a reserve of 1.5 or not).
6. Location and Evaluation of Cracks: The final step is interpreting the results. The analysis indicates specific areas of the structure with the lowest durability (or highest damage). These are where fatigue crack initiation may begin earliest. Reports usually present contour maps on the FEA model showing the distribution of the predicted number of cycles to failure or fatigue safety factor values. The engineer focuses on the elements that exhibit the most critical values. If the minimum predicted structure lifespan does not meet the assumptions (e.g., the component is supposed to withstand 1 million cycles, but the analysis indicates cracking after 200 thousand), design changes must be proposed: modifying geometry (rounding notches, increasing cross-section), changing the material to one more fatigue-resistant, improving surface quality, or applying hardening processes (e.g., shot peening) to extend lifespan.
7. Verification and Prototype Testing: Although Fatigue Analysis FEA provides valuable predictions, the best practice is to confirm its results with prototype testing. Fatigue tests of key components or entire assemblies (e.g., multi-million cyclic loading of a car suspension on a test rig) are often conducted and compared with simulation predictions. This allows the model to be calibrated, and the obtained experimental data enables better fitting of the material model (e.g., refining S-N curves for the actual material after welding or processing). Such a verification loop ensures that the final product has both simulation-confirmed and experimentally verified fatigue durability, increasing confidence in its safety.

Applications of Fatigue Analysis in Various Industries

Fatigue analyses are now standard in many industries, from automotive to energy. Wherever components are subjected to repeated loads, engineers use fatigue simulations to ensure sufficient durability and prevent failures. Here are some examples of applications in different industries:

• Automotive: Vehicle structures must withstand hundreds of thousands of kilometers of vibrations, impacts, and load changes. Fatigue analysis is used in designing chassis frames, suspension components, bodies, axles, wheels, and even engine parts. For example, a suspension arm experiences continuous bending cycles on road irregularities—fatigue simulation assesses whether it will not crack after a specified number of steering cycles. In engines, crankshafts and connecting rods are examined for material fatigue from millions of combustion cycles. Car manufacturers use both FEA calculations and test rigs (so-called durability testing) to ensure that, for example, the vehicle frame will not suffer fatigue cracks throughout its service life. Fatigue analyses also help optimize component weight—eliminating excessive over-dimensioning where a smaller cross-section still meets durability requirements, resulting in lighter and more fuel-efficient vehicles.
• Aerospace: The aviation industry, since the tragic De Havilland Comet jet accidents in the 1950s (caused by fatigue cracks in fuselage skins around windows), places great emphasis on material fatigue. Every passenger aircraft has a defined fatigue lifespan in takeoff-landing cycles and fuselage pressure cycles. Strength analyses of aircraft structures always include a fatigue section—e.g., calculations of how many pressure cycles will cause a crack in the skin or when a landing gear component may require replacement. Fail-safe and damage-tolerance philosophies are applied, assuming the existence of cracks and designing elements to prevent sudden or catastrophic failure (e.g., double spars in wings, regular defectoscopic inspections of critical zones). Fatigue life simulation determines inspection intervals—e.g., predicting that after 5000 flight cycles, a specific landing gear node should be inspected. This ensures aviation maintains a high level of safety, and aircraft components are optimally utilized (not replaced too early or too late).
• Industrial Machinery and Engineering Structures: In heavy industry, many devices operate cyclically—forge presses exert pressure thousands of times, cranes repeatedly lift and lower loads, bridges and cranes undergo cyclic loads from vehicle movement or wind. Fatigue analyses are used, for example, for crane booms (assessing weld durability at points of maximum bending moments), winch drums (number of winding cycles to crack), or high-rise building steel structures (swaying in the wind causes billions of stress cycles in structural elements). Fatigue is also studied in civil engineering—e.g., road bridges must withstand hundreds of thousands of truck crossings. Standards (e.g., Eurocode) require fatigue analyses for bridges, considering vehicle traffic as a series of load cycles. In rotating machinery, such as turbines or generators, fatigue is also crucial—steam turbine blades experience periodic force changes from steam flow, generator shafts experience torsional vibrations. Each such element is sensitive to fatigue cracks, so engineers analyze these phenomena during the design of mechanical structures to prevent failures during operation.
• Energy: In the energy sector, especially in renewable energy sources and power plants, fatigue issues play a significant role. For example, wind turbines are exposed to continuous variable wind loads—the rotor blades bend with each rotation and gust, resulting in millions of stress cycles over the 20-30 year lifespan of the turbine. Fatigue analysis predicts whether, for example, after 10^7 cycles, a crack will not appear in a critical blade location (at the root); based on this, the turbine’s design lifespan is determined, and periodic blade inspections are planned. In conventional thermal energy, there is the issue of low-cycle thermal fatigue—e.g., pipelines and boilers experience stress with each heating and cooling of the installation. The number of full start-up/shutdown cycles of a power plant is limited precisely by the material’s fatigue strength (FEA analyses determine how many such thermal cycles a boiler pipe will withstand before cracking). In nuclear power plants, strength analyses for fatigue of cooling and pressure system components are also mandatory. Fatigue simulations identify potential crack locations (e.g., nozzle roots, welds, pipe elbows) and allow planning NDT inspections of these areas during maintenance shutdowns before critical crack development occurs. In summary, in the energy sector, fatigue analysis is a tool ensuring both reliability of energy supply and infrastructure safety.

In conclusion, fatigue analysis is a powerful tool in the hands of a mechanical engineer. It complements traditional FEA calculations with the dimension of time and durability, providing a more complete picture of structural safety. In an era of increasing demands for product reliability, market competition, and user responsibility, the ability to predict fatigue behavior becomes crucial. Investing in thorough fatigue analysis during the design phase pays off multiple times during operation—trouble-free operation, lower service costs, and user satisfaction with a long-lasting product. Therefore, it is worth considering fatigue analyses as a standard element of engineering mechanical design projects, just like static or thermal analyses. Such a holistic approach ensures that our structures will be not only strong on paper but also durable in the real world.

FAQ: Fatigue Analysis FEA