Fatigue is the progressive weakening or failure of a material caused by repeated or cyclic loading over time. In fatigue conditions, materials can fail at stress levels well below their ultimate strength as small cracks initiate, grow, and eventually lead to sudden fracture. This makes fatigue a critical consideration in engineering design and materials testing, especially for components subjected to long-term or dynamic loading.
Why Do We Fatigue Test?
Stages of Fatigue Failure
Crack Initiation
Repeated stress cycles cause microscopic plastic deformation.
Crack Growth
The crack slowly grows with each load cycle.
Failure
The remaining cross-section can no longer support the load and fails.
To understand how fatigue develops, it’s important to look at the type of loading that causes it. Unlike static testing, fatigue occurs under repeated or fluctuating forces in a process known as cyclic loading, which gradually damages a material over time.
What is Cyclic Loading?
Cyclic loading is the repeated fluctuation of stress or strain between defined limits over time. Even at stresses below a material’s strength, these repeated cycles can accumulate damage, leading to crack initiation and eventual fatigue failure.
Types of Cyclic Loading
Fully Reversed Cycle
The stress alternates between equal positive (tensile) and negative (compressive) magnitudes.
R – Value = -1
Pulsating Cycle
The stress alternates between a maximum value and zero (or a minimum positive value. A common R-value is 0.1 for tension-tension loading or compression-compression loading.
R – Value = 0
Asymmetric Cycle
The load varies between two unequal tensile or compressive values, where the mean stress is not zero.
-1 < R – Value < 0
Random Cycle
Loads change in an unpredictable, irregular manner.
R – Value = σmax/σmin
Understanding a Loading Cycle
While loading can take many forms, fatigue behavior is defined by how each cycle is measured. A single loading cycle can be broken down into key parameters that describe its magnitude, range, and mean value.
Single Cycle Representation
Cycle Parameters
Maximum Stress (σmax )
Highest stress value reached in a cycle
Minimum Stress (σmin )
Lowest stress value in a cycle
Stress Range (𝚫σ)
The difference between maximum and minimum stress
σmax– σmin
Mean Stress (σm)
The average stress over a cycle
(σmax– σmin)/2
Stress Amplitude (σa)
The distance from the mean stress to the peak value
σa= 𝚫σ/2
Stress Ratio (R)
The ratio of minimum stress to maximum stress
R = σmin/σmax
S-N Curves & Stress-Life
Once a loading cycle is defined, fatigue performance can be expressed using an S–N curve. This relationship shows how stress amplitude (σₐ) affects the number of cycles to failure (N), providing a practical way to predict material life under repeated loading.
What is the Stress Life Method?
The stress-life method evaluates fatigue by relating applied stress to the number of cycles to failure. It is best suited for high-cycle fatigue where materials experience mostly elastic deformation, making it ideal for long-life performance analysis under lower stress levels.
How do I use an S-N Curve to Predict Fatigue Life?
To predict fatigue life using an S–N curve, start by identifying the stress amplitude your component will experience in service. Locate that stress level on the vertical (stress) axis of the curve, then move horizontally until you intersect the S–N curve. From that intersection point, drop down to the horizontal axis to find the corresponding number of cycles to failure (N).
This value represents the expected fatigue life under those loading conditions.
What is the Endurance Limit?
The maximum stress amplitude a material can withstand for an infinite number of cycles without experiencing fatigue failure. It is essentially the point at which a material reaches infinite life. This unique characteristic distinguishes steel from materials like aluminum, which do not have a distinct plateau and will eventually fail at even very low stress levels if cycled long enough
Strain-Life Curve
Alternatively, fatigue performance can be expressed using a strain-life (ε–N) curve. This relationship shows how strain amplitude (εₐ) affects the number of cycles to failure (N), capturing both elastic and plastic deformation to provide a more accurate prediction of material life under higher-stress, lower-cycle loading conditions.
Components of the Strain-Life Curve:
- Basquin Equation – Relates stress amplitude (σa) to the number of cycles to failure (Nf) in high-cycle fatigue, and only accounts for the elastic portion of fatigue. The Basquin equation is used to calculate the “slope” leading down to the endurance limit.
- Coffin-Manson Equation – Relates plastic strain amplitude (𝚫p/2) to low-cycle fatigue life, predicting that higher plastic deformation leads to fewer cycles until failure (Nf).
- Combined (Coffin-Manson-Basquin) – A comprehensive fatigue model that predicts the total strain-life of a material by combining plastic strain (Coffin-Manson) and elastic strain (Basquin) components. This combined component allows engineers to predict fatigue life across the entire range, from high-stress plastic deformation to low-stress elastic cycles.
When should I use Strain life over stress life?
The strain-life method is preferred when fatigue behavior involves plastic deformation, making it more accurate for low-cycle and high-strain applications. Unlike the stress-life (S–N) approach, which assumes primarily elastic behavior and is best suited for long-life fatigue, strain-life accounts for both elastic and plastic strain, capturing the mechanisms that drive crack initiation.
What is the difference between elastic and plastic deformation in fatigue?
Elastic deformation is reversible, so the material returns to its original shape when the load is removed. Plastic deformation is permanent, causing lasting changes in the material’s shape. In fatigue, elastic deformation dominates at low stress levels and high-cycle fatigue, while plastic deformation occurs at higher stress levels and contributes to crack initiation in low-cycle fatigue.
By: Hazel Salazar | Published on: May 4, 2026 | Last Updated: June 25, 2026
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