What is Fatigue Analysis? | Abaqus Fatigue, Fatigue Life Prediction, Cyclic Loading Types

1. What is Fatigue Damage and Fatigue Analysis?

Fatigue failure can occur in three main stages:

• Crack initiation: Small imperfections or stress concentrations (like surface roughness, voids, or notches) begin to develop into micro-cracks after repetitive loading.
• Crack propagation: These micro-cracks expand with each loading cycle, growing slowly across the material’s surface or internally.
• Final fracture: Once the cracks reach a critical size, the material can no longer withstand the stress, leading to sudden and often catastrophic failure.

The process of fatigue is complex because it depends on various factors such as load amplitude, mean stress, material properties, surface conditions, and environmental influences (e.g., corrosion). Fatigue can occur in metals, polymers, ceramics, and composites under cyclic loading conditions. Let’s examine some real examples of the fatigue phenomenon.

1.1. Real examples of Fatigue | Fatigue Analysis Example

• Shoes: Over time, the soles of shoes wear down due to the repetitive compressive and tensile forces experienced during walking or running. The materials used in shoes undergo fatigue, which leads to degradation and eventual failure.
• Bridges: Bridges experience cyclic loading from vehicles passing over them. The repeated stresses can cause fatigue cracks in the steel or concrete structure. For example, a bridge in the United States, the Silver Bridge collapse in 1967 was attributed to the fatigue of an eyebar, a critical load-bearing component of the bridge. This was another fatigue analysis example to understand why fatigue analysis is important.
• Rotating Machinery: Components like turbine blades, gears, and axles experience cyclic stresses during their operation. Over time, these stresses can cause fatigue cracks. The failure of a turbine blade due to fatigue in jet engines can lead to catastrophic engine failure.

Fatigue is crucial in engineering design because it can lead to unexpected failures if not properly accounted for. Designers must predict the fatigue life of a component and ensure it can withstand the expected number of load cycles throughout its operational life. This is especially important for structures or components subjected to repeated or fluctuating stresses. In the next sections, we will examine the important issues of the fatigue phenomenon together.

Figure 1: Failure of a crank arm due to fatigue

2. Types of Fatigue Loading (Cyclic Loading)

Fatigue damage is caused by cyclic loading, where repeated or fluctuating stresses act on a material over time. There are several types of cyclic loading patterns that contribute to fatigue analysis. Each type can have different effects on the material, leading to various fatigue failure behaviors. The most common cyclic loading types that can lead to fatigue are:

2.1. Fully Reversed Cyclic Loading

In fully reversed cyclic loading, the stress alternates between positive (tensile) and negative (compressive) stress. The magnitude of tension and compression is equal. Here is stress-time diagram:

Figure 2: Fully Reversed Cyclic Loading stress-time curve

For example, Crankshafts in internal combustion engines are subjected to fully reversed cyclic loading as they rotate, alternating between tension and compression with each revolution.

To calculate the mean stress, stress amplitude, and stress range, the following equations, respectively labeled as 1 to 3, are used:

2.2. Asymmetric Cyclic Loading

Asymmetric cyclic loading has stresses that do not alternate equally between tension and compression. The minimum stress is greater than zero (it never reaches the compressive range), and the mean stress is not zero. This type of loading is common in many real-world applications where loads fluctuate but don’t reverse entirely.

Figure 3: Asymmetric Cyclic Loading stress-time curve (The minimum stress is greater than zero)

If the minimum stress is less than zero (reaches the compressive range) and the average stress is not zero, the loading is the asymmetric cyclic loading type.

Figure 4: Asymmetric Cyclic Loading stress-time curve (minimum stress is less than zero)

2.3. Repeated Cyclic Loading

In repeated cyclic loading, the stress oscillates between a maximum positive stress and a zero or minimum positive stress. The stress does not alternate to negative values (compression), meaning the material is primarily under tension.

Figure 5: Repeated Cyclic Loading stress-time curve

2.4. Random Cyclic Loading

In random cyclic loading, the stress varies in an unpredictable manner with both amplitude and frequency fluctuating randomly. It often occurs in components subjected to varying loads with no fixed pattern, making fatigue prediction more challenging. For example, wind turbine blades undergo random cyclic loading due to the variable nature of wind speeds and directions. These random loads cause stresses on the blades, leading to fatigue over time.

Figure 6: Random Cyclic Loading stress-time curve

3. Fatigue Analysis Crack Growth

The fatigue process consists of several stages that describe how damage accumulates in a material due to cyclic loading. Understanding these stages is critical for predicting in fatigue analysis when a component will fail due to fatigue.

As we explained before, crack initiation is the first stage of the fatigue process, where micro-cracks form in the material. Crack initiation usually occurs in areas of high-stress concentration, such as surface defects, inclusions, or sharp notches. The cyclic loading leads to microscopic defects like grain boundary separations. After crack initiation, the crack begins to grow with each loading cycle. The rate at which the crack grows depends on the material properties, the applied load, and the environment. In this stage, the crack propagates incrementally with each stress cycle, and the size of the crack increases, leading to a reduction in the material’s load-carrying capacity.

As the crack grows, it passes through three different phases based on the rate of crack growth:

3.1. Threshold Region

In this region, the stress intensity factor range ΔK is very low, and the crack growth rate is negligible. There is a threshold value of ΔK called ΔK_th​ below which no crack growth occurs. The stress intensity factor range (ΔK) is introduced by the equation below.

Where:

•  is the cyclic stress range.
•  is the crack length.
•  is a constant.

3.2. Stable Crack Growth Region

In this region, the crack growth rate follows a steady, predictable pattern. The rate of crack propagation is typically proportional to a Paris Law. This is the most important region for engineers because most of the component’s life is spent in this stage.

3.3. Rapid Fracture Region

As the crack reaches a critical size, the stress intensity factor increases rapidly, and the crack propagation rate accelerates. The crack grows uncontrollably until the material fractures.

3.3.1. Paris Law: A Crack Growth Theory

One of the most widely used theories for predicting fatigue crack growth is Paris Law, which describes the relationship between the crack growth rate and the applied cyclic stress intensity factor. It is applicable in the second region of the crack growth process, where the crack growth rate is stable. Paris Law is given by the following equation:

Where:

•  is the crack growth rate (i.e., the crack extension per load cycle).
•  is the stress intensity factor range, which represents the difference between the maximum and minimum stress intensity factors during a loading cycle.
• C and m are material constants that are determined experimentally. They depend on the material and the environment.

As the crack length “” increases, the stress intensity factor range (ΔK) increases, leading to faster crack growth. Paris Law helps in predicting how fast a crack will grow under given cyclic loads and when it will reach a critical size, causing failure.

Using Paris Law, engineers can predict the number of cycles a component can endure before failure. By integrating the Paris Law equation, the remaining fatigue life can be calculated based on the initial crack size ​, the final critical crack size ​, and the material constants C and m.

Where:

• N_f is the number of cycles to failure.
•  is the initial crack size.
•  is the critical crack size.

This equation allows for the prediction of when a crack will grow to a dangerous size and enables engineers to design maintenance schedules or preventive measures accordingly.

Figure 7: Typical fatigue fracture surface

4. Fatigue Cycle Number

Fatigue cycle number refers to the number of load cycles a material can endure before a fatigue crack leads to failure. It is a crucial concept in fatigue analysis and helps determine the lifetime of components subjected to cyclic loading. Fatigue life is typically expressed as the total number of cycles a material can withstand before failure, denoted by N.

The fatigue life of a material is categorized based on the number of cycles to failure. These categories help to distinguish between different types of fatigue behavior, which vary depending on the magnitude of applied stress, material properties, and environmental conditions.

4.1. Low-Cycle Fatigue (LCF)

Low-cycle fatigue occurs when the material experiences high cyclic stresses, which induce significant plastic deformation in each cycle. The material undergoes fewer load cycles before failure in this kind of fatigue analysis(typically fewer than 10,000 cycles).

4.2. High-Cycle Fatigue (HCF)

High-cycle fatigue occurs when the material is subjected to lower stress levels, typically within the elastic range. The cyclic stresses are lower, meaning the material can endure a large number of load cycles before failure. For this type of fatigue, lifetime is typically in the range of 10,000 to 1,000,000 cycles or more.

There are also two other types of fatigue analysis known as Very High-Cycle Fatigue (VHCF) and Very Low-Cycle Fatigue (VLCF). In Very High-Cycle Fatigue, due to the very low stress level, the number of cycles can reach over one billion cycles (10⁹ cycles), but Very Low-Cycle Fatigue is an extreme form of low-cycle fatigue where very few cycles (often fewer than 10) are required to initiate and propagate cracks. These types of fatigue occur less frequently.

5. Fatigue Life (S-N curve) | Fatigue Life Prediction

• Fatigue Life

Fatigue life is the total number of stress cycles a material can endure before failure occurs due to fatigue. It represents the lifetime of a component under repeated cyclic loading. Fatigue life is often denoted as N, which refers to the number of cycles to failure. Fatigue life prediction is crucial for ensuring the long-term durability and safety of components subjected to cyclic stresses, especially in fields like aerospace, automotive, and civil engineering.

• Fatigue Life Curve (S-N Curve)

The S-N curve is a graphical representation that shows the relationship between the stress amplitude (S) and the number of cycles to failure (N). It is widely used to predict fatigue life under constant amplitude loading. The S-N curve is typically plotted on a logarithmic scale, with stress amplitude on the vertical axis and the number of cycles to failure on the horizontal axis.

Some materials, particularly ferrous metals (such as steel), exhibit an endurance limit. This is the stress amplitude (S_e) below which the material can theoretically endure an infinite number of cycles without failing.

Figure 8: Fatigue life curve (S-N curve)

5. How to do a Abaqus Fatigue Analysis?

To perform Abaqus fatigue analysis, you need to follow a structured approach that involves selecting the appropriate fatigue analysis method, preparing your model, and gathering the necessary input data. Here’s a detailed guide on how to get started.

5.1. Input Data Required for Fatigue Simulation

The following data is needed for a fatigue simulation:

1. Stress/Strain History: The stress and strain results from a structural analysis under cyclic loading. These can be obtained from static or dynamic simulations in Abaqus.
2. Material Fatigue Properties: These include:

• S-N Curve (Stress-Life Curve): Shows the relationship between the stress amplitude and the number of cycles to failure.
• Strain-Life Curve: For low-cycle fatigue simulations, you need strain-life data.
• Fatigue Strength Coefficient (σf’) and Exponent (b): For predicting high-cycle fatigue life.
• Fatigue Ductility Coefficient (εf’) and Exponent (c): For low-cycle fatigue prediction.
• Coffin-Manson Relation: For strain-based fatigue simulations.
• Crack Growth Data (Paris Law Parameters): If you’re performing crack propagation analysis.

3. Loading Conditions:

• Cyclic loading can be time-based (e.g., fluctuating stresses over time) or load-based (variable loading magnitudes over cycles).
• You may need the load history or spectrum if the loading is complex.

4. Mean Stress Correction (Optional): If the load includes a mean stress, a correction factor like Goodman or Gerber may be needed to account for the effect of mean stress on fatigue life.
5. Environmental Factors (Optional): For more advanced fatigue simulations, environmental factors like temperature or corrosion may be considered.

5.2. Types of Abaqus Fatigue Simulation

Abaqus Fatigue simulations can be broadly categorized into several methods, each suitable for different loading conditions:

1. High-Cycle Fatigue (HCF):

• High-cycle fatigue occurs when the structure undergoes many cycles (typically >10,000 cycles) with low to moderate stress levels.
• Abaqus stress analysis results can be used with a Stress-Life (S-N) curve to predict fatigue life. Typically done when elastic deformation is predominant.

2. Low-Cycle Fatigue (LCF):

• Low-cycle fatigue happens under high stress or strain levels, where plastic deformation is significant, with fewer cycles (typically <10,000 cycles).
• You would use Strain-Life (ε-N) curves to predict life.
• The analysis focuses on regions with plastic deformation.

3. Cumulative Damage Analysis:

For situations where the loading is variable or random, the Palmgren-Miner Rule can be used to estimate fatigue life based on damage accumulation. This approach sums the damage caused by each load cycle to estimate the total life.

4. Crack Initiation and Propagation:

• Abaqus can simulate crack initiation and growth under fatigue using XFEM (Extended Finite Element Method) or Paris Law for crack growth.
• You can predict where the crack starts and how it propagates due to cyclic loading.

5. Thermo-Mechanical Fatigue (TMF):

In applications where cyclic mechanical loading is coupled with temperature variations, TMF simulations are done to predict the impact of thermal stresses on fatigue life.

6. Vibration Fatigue:

In some applications, like automotive or aerospace, components are subjected to vibrational loading. Fatigue analysis can be performed based on the frequency response and stress/strain results from harmonic or random vibration analysis.

6. Conclusion

In this article, we explored the concept of fatigue damage, focusing on how materials fail under cyclic loading. Fatigue is important to understand because it affects the lifespan and reliability of materials, which is critical in industries like aerospace, automotive, and civil engineering. Proper fatigue analysis prediction can prevent unexpected failures, ensuring the safety and longevity of components in these fields.

In this article we started by defining fatigue and discussing real-life cases such as shoe wear, bridge collapses, and machine failures. Then, we covered types of cyclic loading, including fully reversed and asymmetric, which are essential for predicting fatigue behavior. The crack growth process, the use of Paris Law for crack propagation, and fatigue life prediction through S-N curves were explained to provide a clearer understanding of how engineers estimate material life. Also, we have learned where to start Abaqus Fatigue analysis.

Overall, this article highlighted the importance of recognizing fatigue damage early, the mechanisms behind it, and how different loading conditions impact material failure. Understanding these principles helps in designing more resilient components and improving safety in various industries.

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You can always learn more about Abaqus fatigue analysis from Abaqus Documentation.