Multiaxial Fatigue
Multiaxial Fatigue: Theoretical Foundations
What is Multiaxial Fatigue?
Professor, what is multiaxial fatigue?
Standard S-N methods assume uniaxial stress, but in real structures, stresses in multiple directions fluctuate simultaneously. This is multiaxial fatigue.
Multiaxial Fatigue Criteria
| Criterion | Parameter | Characteristics |
|---|---|---|
| von Mises Equivalent Stress | $\sigma_{vm}$ | Simplest. For proportional loading only. |
| Critical Plane Method | Plane with maximum damage | Applicable to non-proportional loading |
| Fatemi-Socie | $\gamma_{max}(1+k\sigma_{n,max}/\sigma_y)$ | Shear strain based |
| Smith-Watson-Topper | $\sigma_{max} \cdot \Delta\varepsilon/2$ | Normal stress based |
| Dang Van | Mesoscopic stress | High-cycle multiaxial fatigue |
Is the Critical Plane Method the most common?
For non-proportional loading (multiaxial stresses with phase shifts), the Critical Plane Method is essential. The von Mises equivalent can be non-conservative.
Summary
The Problem von Mises Couldn't Solve
Directly applying uniaxial fatigue theory to a multiaxial stress field can lead to dangerously optimistic predictions. Evaluating with von Mises equivalent stress can predict a fatigue limit up to 40% higher for biaxial stress with a 180° phase difference. The Brown-Miller criterion (1973) solved this by evaluating the combination of maximum shear strain and maximum principal strain, achieving accuracy within 15% of experimental data.
Computational Methods for Multiaxial Fatigue
FEM for Multiaxial Fatigue
1. Calculate time histories of all stress components via FEM ($\sigma_x(t), \sigma_y(t), \tau_{xy}(t)$)
2. Search for the critical plane using fatigue software (scan all directions)
3. Perform rainflow counting and damage calculation on the critical plane
nCode, fe-safe support the Critical Plane Method for multiaxial fatigue.
Summary
Calculation Procedure for the Critical Plane Method
In the Critical Plane Method for multiaxial fatigue, the crack initiation parameter is calculated for all directions, and the plane giving the maximum value (the critical plane) is identified. In implementation, it's common to calculate for 18 directions in 10° increments from 0° to 180°. Implementing this as an FEM post-processing step takes a few seconds for a solid model with 10,000 elements, but its versatility is high, applicable to both proportional and non-proportional loading.
Multiaxial Fatigue in Practice
Multiaxial Fatigue in Practice
Components where multiaxial stress dominates, such as crankshafts, vehicle axles, nozzle connections on pressure vessels, etc.
Practical Checklist
Multiaxial Evaluation of a Turbofan Engine Disk
Aircraft engine compressor disks are a typical field of multiaxial fatigue where centrifugal force (tension) and thermal stress (compression) act simultaneously. For the CFM56 engine disk, life predicted by multiaxial fatigue criteria was 30% shorter than uniaxial evaluation, forming the basis for early overhaul scheduling.
Multiaxial Fatigue: Software & Solver Comparison
Tools
Capability of FEMFAT Multiaxial Module
FEMFAT by Austrian company ECS implements the Critical Plane Method, Integral Method, and Equivalent Stress Method in its Multiaxial module, and is used by AB company for certification analysis of engine mount brackets. Direct import from FEM is possible, supporting ABAQUS/ANSYS/Nastran. Full-direction critical plane search for a 10,000-element model completes within 3 minutes.
Advanced Technologies
Advanced Multiaxial Fatigue: Modern Research & Trends
Relationship Between Non-Proportional Hardening and Fatigue Life
Under multiaxial stress with phase differences, materials undergo additional hardening (non-proportional hardening), leading to 20-40% shorter life than uniaxial fatigue predictions. For stainless steel SUS304, hardening is maximum at a 90° phase difference, and fatigue life can be less than half even at the same equivalent stress amplitude. The Itoh-Katakoke model developed in the 2000s can quantitatively handle this phenomenon.