Introduction

Low-cycle fatigue (LCF) is a type of fatigue failure that occurs in materials subjected to relatively high stress levels and a low number of cycles, typically less than 10⁴–10⁵ cycles. This phenomenon is common in components exposed to cyclic plastic deformation, such as those in aerospace, nuclear, and power generation industries.

To model and predict LCF damage, traditional stress-life (S-N) or strain-life (ε-N) methods have limitations, particularly when plasticity plays a significant role. An alternative and more physically meaningful approach is the hysteresis energy-based model, which considers the energy dissipated per cycle as a direct measure of fatigue damage.

Detailed Explanation: Hysteresis Energy Model for LCF

1. Fundamental Concept

The hysteresis energy approach is based on the idea that fatigue damage correlates with the energy dissipated in the material during each loading cycle. When a material is cyclically loaded beyond its elastic limit, it undergoes plastic deformation, creating a stress-strain hysteresis loop. The area within this loop represents the energy dissipated per cycle due to plastic deformation.

2. Calculation of Energy Dissipation

The hysteresis energy per cycle (W) is calculated as the area enclosed by the stress-strain loop:

Where:

• σ is the stress
• ε is the strain
• The integral is evaluated over one full load-unload cycle

This energy correlates with microstructural damage mechanisms such as crack initiation and propagation.

3. Energy-Based Fatigue Life Model

Fatigue life prediction using hysteresis energy typically follows a power-law form:

Where:

• Wf is the hysteresis energy per cycle
• Nf is the number of cycles to failure
• β, C are material constants obtained from experimental data

This equation implies that the higher the energy per cycle, the fewer the cycles to failure, making it suitable for LCF regimes where large plastic strains dominate.

4. Advantages of the Energy-Based Model

• Physically meaningful: Energy dissipation is directly related to material damage.
• Unified approach: Suitable for both uniaxial and multiaxial loading.
• Captures mean stress effects naturally.
• Good correlation with experimental results, especially in cases with complex loading.

5. Application Examples

• High-temperature turbine components are subjected to thermal and mechanical loads.
• Welded joints and notched components where local plasticity drives fatigue.
• Seismic design in civil engineering, where low-cycle, large-strain loads are expected (e.g., base isolators, dampers).

6. Considerations and Limitations

• Material-specific: Requires calibration with experimental data.
• Microstructure-sensitive: Cannot fully account for microcrack coalescence without additional modeling.
• Temperature effects: Must be accounted for separately in high-temperature environments.