Commonly used mechanical fatigue analysis methods

Commonly used mechanical fatigue analysis methods

Summary of Common Mechanical Fatigue Analysis Methods

This article summarizes common mechanical fatigue analysis methods, including: Nominal Stress Method, Local Stress-Strain Method, Energy Method, Stress Field Intensity Method, Fracture Mechanics Method, Reliability Design Method, and Probabilistic Fracture Mechanics.

1. Nominal Stress Method

The nominal stress method is based on the nominal stress of a structure for testing and life estimation. It uses the rain-flow method to extract independent stress cycles and combines them with the material’s S-N curve to estimate structural fatigue life based on the linear cumulative damage theory.

Basic Assumptions:

For any component (or structural detail/element), if the stress concentration factor \(K_T\) and load spectrum are the same, their fatigue lives will be identical. Nominal stress is the control parameter in this method. It considers the effects of load sequence and residual stress, making it simple and easy to implement.

Limitations:

• It studies fatigue within the elastic range and does not account for local plastic deformation at notch roots, leading to large calculation errors when estimating fatigue life for structures with stress concentration.
• Determining the equivalence between standard specimens and actual structures is challenging, as this relationship depends on factors such as structural geometry, loading mode, size, and material properties.

Due to these drawbacks, the nominal stress method has low accuracy in predicting fatigue crack initiation. Additionally, it requires S-N curves under different stress ratios R and stress concentration factors \(K_T\), which demands substantial investment in material data acquisition. Thus, it is only suitable for high-cycle fatigue calculations under low stress levels and for notch-free structures. Recent developments include the Stress Severity Factor (S.ST) method, effective stress method, and Design Rating Factor (DRF) method.

2. Local Stress-Strain Method

The core idea of the local stress-strain method is to analyze local stress at notches using nominal stress history, then estimate fatigue life by combining local stress at notches with the component’s S-N curve, material’s cyclic stress-strain curve, ε-N curve, and linear cumulative damage theory.

Basic Assumptions:

If the stress-strain history at a critical location (point) of a component is identical to that of a smooth small specimen, their fatigue lives will be the same. Local stress-strain is the control parameter here.

Applications and Advantages:

This method is primarily used for low-cycle fatigue under high strain conditions and fatigue life estimation of notched structures. Its key advantage is converting nominal stress on a structure to local stress and strain at notches through analysis and calculation. It can detailedly analyze the nonlinear relationship between local stress and strain at notches and considers the effects of load sequence and residual stress on fatigue life. Thus, it is currently a relatively effective fatigue life estimation method that overcomes the main limitations of the nominal stress method.

Limitations:

• It does not consider stress gradients near notch roots or multiaxial stress effects.
• Fatigue life calculations are highly sensitive to the fatigue notch factor K.

In practice, accurately determining K for structures is difficult, which reduces the accuracy of life estimation. Additionally, the method relies on material ε-N curves, which are obtained from strain-controlled fatigue tests—data that is less readily available compared to S-N curves, limiting its application.

3. Energy Method

Basic Assumptions:

Components (elements or structural details) made of the same material will have the same fatigue crack initiation life if their critical fatigue zones experience identical local strain energy histories.

The material properties required for the energy method include cyclic stress-strain curves and cyclic energy consumption-life curves. Existing energy methods assume linear additivity of energy consumption per cycle, but in reality, energy consumption The total amount is nonlinear with the number of cycles due to the expansion of internal damage interfaces during cyclic loading. This critical issue hinders the practical engineering application of the energy method, making it less promising for widespread use.

4. Stress Field Intensity Method

Basic Assumptions:

Components (elements or structural details) made of the same material will have the same fatigue life if their fatigue failure zones undergo identical stress field intensity histories. Stress field intensity is the control parameter here. Predicting fatigue crack initiation life using this method requires cyclic stress-strain curves and S-Nf (or ε-Nf) curves, involving complex analysis and calculations.

Selection of Methods Based on Scenarios:

From the characteristics of the four methods above, different approaches are chosen based on available conditions:

• The nominal stress method is suitable for connectors or structural parts with abundant material fatigue data.
• The local stress-strain method, especially when combined with transient cyclic curves and ε-Nf curves, is ideal for structures with complex geometries under complex loads.
• The stress field intensity method uses the same material fatigue data as the local stress-strain method, i.e., cyclic stress-strain curves and S-Nf (or ε-Nf) curves.

5. Fracture Mechanics Method

Fracture mechanics is based on the fact that materials inherently contain defects or cracks. It uses deformation mechanics to study the propagation, instability, and arrest of defects or cracks. By quantitatively analyzing fracture surfaces, it determines the fatigue crack growth rate in actual service (the widely used Paris formula for fatigue crack growth rate) to reasonably estimate component fatigue life, identify crack initiation time, evaluate manufacturing quality, and facilitate accident analysis. This method addresses many catastrophic low-stress brittle fracture issues in engineering, It makes up for the shortcomings of conventional design methods,and has has become a key method in failure analysis.

Fatigue fracture is the primary failure mode of structural components. Statistics show that 85%-90% of major accidents caused by structural failure are related to fatigue fracture. From a fracture mechanics perspective, fatigue failure of metal structures occurs when the main crack expands to a critical size, and structural life depends on crack initiation and propagation at critical locations.

Stages of Fatigue Fracture:

1. Initial crack formation: Under alternating loads, initial cracks form (typically defined as 0.5-1mm, though no unified standard exists).
2. Crack propagation: Cracks expand to form large macroscopic cracks.
3. Catastrophic fracture: Cracks expand rapidly, leading to immediate failure. This stage has a very short life and is generally not evaluated in engineering.

By time sequence, the first stage is called initiation life, and the second stage is propagation life (often referred to as residual life). Life is typically measured by the number of cyclic load cycles. Fracture mechanics recognizes the existence of a fatigue limit: if the cyclic load amplitude is below the material’s fatigue limit, the component will not fail due to cracking, meaning its fatigue life is theoretically infinite. Fatigue life is also related to load frequency, distinguishing between high-cycle and low-cycle fatigue.

The nominal stress method and local stress-strain method focus on initiation life, while residual life research remains complex, with no universally accepted evaluation method in engineering. Despite significant advancements, fracture mechanics is still 不完善，as the mechanisms of fracture failure are not fully understood. Developing simple, accurate, and reliable fatigue life prediction formulas remains a future goal.

6. Reliability Design Method

The reliability design method applies reliability theory and statistical data of design parameters to design components, equipment, or systems under specified reliability targets. Its goal is to identify potential risks and weak points, then improve inherent reliability through prevention and optimization. However, reliability research for mechanical systems is immature, and this method cannot solve the problem of fatigue residual life assessment.

7. Probabilistic Fracture Mechanics

Fracture mechanics uses deterministic parameters for estimation, while probabilistic fracture mechanics treats parameters such as crack size, fracture toughness, stress intensity factor, and crack growth rate as random variables for reliability analysis. This improves the reliability of engineering analysis using fracture mechanics.

Limitations:

• Random variables and numbers are mainly generated using normal distribution or three-parameter Weibull distribution, which cannot fully reflect real-world scenarios.
• Insufficient experimental data restricts its practical application.

Recently, some studies have used fuzzy mathematics and statistical simulation to comprehensively evaluate the technical status of metal structures and estimate residual life. The reliability of these methods depends not only on mathematical approaches but also on subjective human factors.

8. Theoretical Basis for Fatigue Life Assessment of Metal Structures

Experimental research focuses on selecting practical measurement methods for engineering metal structures, identifying applicable evaluation criteria, and accurately assessing life. Computer virtual technology is used to enhance the processing of measured data, establish expert systems for metal structural components, evaluate fatigue residual life and other technical indicators, and develop artificial intelligence systems for structural design, manufacturing, and technical transformation.

Experts agree that future research in metal structure fatigue life assessment should focus on:

• Studying system critical states, multi-critical state optimization, and first-order second-moment methods under multi-criteria conditions.
• Developing effective methods to verify critical failure models.
• Improving fatigue strength theory and fracture mechanics methods.
• Establishing more suitable probabilistic failure models and optimizing fracture probability calculation methods.
• Advancing reliability calculation methods.
• Investigating sensitivity parameters affecting systems, particularly parameter sensitivity analysis methods, to systematically handle sensitivity indicators.

Source: Finite Element Technology Alliance

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