Fatigue Assessment through the Effective Critical Plane Factor

An insight into the novel fatigue assessment method using the Effective Critical Plane (ECP) factor.

Introduction

Fatigue failures in structural components often result from stress concentrations caused by geometric irregularities such as notches or welds. Various methods like the Notch Stress Approach (NSA), Theory of Critical Distances (TCD), and Strain Energy Density (SED) have been used for fatigue strength assessment. However, these methods may not capture the full complexity of the stress-strain field near stress concentrators.

We introduce a novel approach, the Effective Critical Plane (ECP) method, which enhances fatigue life prediction by averaging the stress-strain field over a small volume around the critical point, preserving the tensorial characteristics of the field. The size of this averaging volume is determined as a material parameter and optimized through experimental data.

Methodology

The ECP method focuses on calculating critical plane parameters starting from an averaged stress or strain tensor over a control volume . The main steps include:

1. Finite Element Analysis (FEA): Linear elastic simulations identify the critical node, i.e., the node with the maximum CP factor.
2. Stress-Strain Averaging: The stress and strain tensors are averaged over a spherical volume (3D) or circular area (2D) around the critical node.
3. Control Radius Optimization: The radius of this control volume, denoted as $r_c$, is determined through a best-fit process against fatigue test data from notched specimens.
4. Critical Plane Factor Calculation: Using the averaged stress-strain values, the FS and SWT ECP factors are computed for varying values of rc. The optimal rc is identified by minimizing scatter between predicted and experimental fatigue lives.

Key Equations

• Fatemi-Socie (FS) Factor: \(FS = \frac{\Delta \gamma_{max}}{2} \left(1 + k \frac{\sigma_n}{\sigma_y}\right)\) Where \(\Delta \gamma_{max}\) is the maximum shear strain amplitude, \(\sigma_n\) is the normal stress, and \(k\) is a material constant.

• Smith-Watson-Topper (SWT) Factor: \(SWT = \frac{\Delta \varepsilon_{max}}{2} \sigma_n\) Where \(\Delta \varepsilon_{max}\) is the maximum normal strain amplitude and \(\sigma_n\) is the maximum normal stress.

Implementation in MATLAB

The method is implemented through a MATLAB script (included as supplementary material). The script performs the following steps:

1. FEA to determine stress-strain tensors at critical nodes.
2. Averaging these tensors over a control volume.
3. Computing the ECP factors \(\widetilde{FS}\) and \(\widetilde{SWT}\) for each load cycle and control radius.

Applications

The ECP approach has been validated using experimental data from low carbon steel specimens subjected to various notches and loading conditions. Two geometries—U-notched and V-notched specimens—were used in simulations to derive the optimal control radius $r_c$ for the material. The results were compared with traditional methods like NSA, TCD, and SED.

Results and Discussion

The optimal control radii were found to be:

• Fatemi-Socie (FS): \(r_c = 0.20 \, mm\)
• Smith-Watson-Topper (SWT): \(r_c = 0.25 \, mm\)

For each geometry, the FS and SWT factors were computed and plotted against the number of cycles to failure. The comparison with experimental data showed that the FS model better describes the fatigue process for ductile materials, as it accounts for shear cracking.

A supplementary Matlab® script implementing the method is available on GitHub: ECP.