In modern engineering, steel casting nodes have become critical components in large-span structures due to their design flexibility and load-bearing efficiency. However, casting defects such as pores, inclusions, and shrinkage cavities significantly affect the fatigue performance of these nodes. This study systematically investigates the relationship between defect parameters and fatigue life through finite element modeling and numerical simulations.
1. Structural Modeling and Defect Characterization
A tubular truss bridge model with K-type steel casting joints was designed to evaluate defect-induced stress concentrations. Critical defect locations were identified at nine positions across the node geometry:
| Defect Position | Region | Typical Defect Type |
|---|---|---|
| ①-③ | Lower main tube | Subsurface porosity |
| ④ | Upper main tube | Surface shrinkage |
| ⑤-⑦ | Branch connections | Hot tearing |
| ⑧-⑨ | Branch interiors | Inclusion clusters |
2. Fatigue Assessment Methodology
The stress concentration factor (ασ) and fatigue safety coefficient (nσ) were calculated using:
$$ \alpha_{\sigma} = \frac{\sigma_{\text{max}}}{\sigma_0} $$
$$ n_{\sigma} = \frac{\sigma_{-1}}{\frac{K_{\sigma}}{\epsilon \beta}\sigma_a + \Psi_{\sigma} \sigma_m} $$
Where:
σ-1 = 202.8 MPa (fatigue limit)
Kσ = effective stress concentration factor
ε = size coefficient (Table 1)
| Position | ε | β |
|---|---|---|
| ① | 0.94 | 0.65 |
| ② | 0.91 | |
| ③ | 0.82 | |
| ④ | 0.92 | |
| ⑤ | 0.85 | |
| ⑥ | 0.83 | |
| ⑦ | 0.82 | |
| ⑧ | 0.92 | |
| ⑨ | 0.95 |
3. Multi-Defect Interaction Analysis
Eight defect configurations were evaluated under cyclic loading (Fmin=200 kN, Fmax=1,000 kN):
| Model | Defect Positions | Safety Factor |
|---|---|---|
| 1 | ①③④ | 3.46 |
| 2 | ①④⑤ | 3.54 |
| 3 | ②⑦⑧ | 3.29 |
| 4 | ①②④⑧ | 3.36 |
| 5 | ③④ | 4.38 |
| 6 | ① | 1.52 |
| 7 | ① | 1.37 |
| 8 | ⑧ | 2.69 |
The stress interaction between adjacent defects follows:
$$ \frac{\sigma_{\text{combined}}}{\sigma_{\text{isolated}}} = 1 + 0.5\left(\frac{d}{D}\right)^{1.8} $$
Where d = defect diameter, D = spacing between defects
4. Defect Tolerance Criteria
A modified Paris Law equation for steel casting defects:
$$ \frac{da}{dN} = C(\Delta K_{\text{eff}})^m $$
$$ \Delta K_{\text{eff}} = \Delta K \sqrt{\frac{2}{\pi} \tan^{-1}\left(\frac{a}{\rho}\right)} $$
Where ρ = defect tip radius (0.1-0.3 mm for typical steel casting defects)
5. Quality Assessment Framework
Proposed multi-defect evaluation matrix for steel casting nodes:
| Parameter | Weight | Evaluation Metric |
|---|---|---|
| Max Defect Size | 0.3 | a ≤ 2% wall thickness |
| Defect Clustering | 0.4 | D ≥ 5d between defects |
| Location Criticality | 0.3 | Stress gradient > 50 MPa/mm |
The comprehensive safety index (CSI) for steel casting nodes:
$$ CSI = \prod_{i=1}^n \left(1 – \frac{a_i}{t}\right)^{w_i} \times \frac{1}{1 + 0.1N_d} $$
Where:
ai = defect depth at position i
t = wall thickness
wi = position weight factor
Nd = number of defects in critical zones
6. Industrial Applications
Field data from 32 steel casting nodes in bridge applications shows:
| Defect Management Strategy | Fatigue Life Improvement |
|---|---|
| Single defect repair | 18-22% |
| Cluster defect mitigation | 41-47% |
| Full volumetric inspection | 63-69% |
The economic factor for steel casting quality control:
$$ E_{f} = \frac{C_{\text{inspection}}}{0.1 C_{\text{failure}}} \times \ln\left(\frac{N_{\text{cycles}}}{10^6}\right) $$
Justifying advanced NDT methods when Ef > 1.2
7. Future Development Directions
Emerging solutions for steel casting defect mitigation include:
- Real-time solidification monitoring with thermal cameras
- Machine learning-based defect prediction algorithms
- Hybrid additive-subtractive repair techniques
The complete fatigue life equation for steel casting nodes:
$$ N_{f} = \frac{1}{C} \int_{a_0}^{a_c} \frac{da}{(\Delta K(a))^m} \times \prod_{i=1}^n \left(1 – \frac{a_i}{t}\right) $$
Where a0 = initial defect size, ac = critical crack size