Table 1 Eight equations of traditional FCG rates prediction models
From: Crack Growth Rate Model Derived from Domain Knowledge-Guided Symbolic Regression
Model name | Equation |
|---|---|
Paris’ model | \(\ln C + m \cdot \ln \Delta K\) |
Forman’s model | \(\ln C + m \cdot \ln \Delta K - \ln \left[ {(1 - R) \cdot K_{{\text{C}}} - {\Delta }K} \right]\) |
Elber’s model | \(\ln C + m \cdot \ln \left( {\frac{\Delta K}{{1 - R}} - K_{{{\text{op}}}} } \right)\) |
Kujawski’s model | \(\ln C + m \cdot \alpha_{{\text{K}}} \cdot \ln \frac{\Delta K}{{1 - R}} + (1 - \alpha_{{\text{K}}} )m \cdot {\text{ln}}\Delta K^{ + }\) |
Huang’s model | \(\ln C + m \cdot \ln \Delta K + m \cdot \ln M\) |
Zhan’s model | \(\ln C + m \cdot \ln {\Delta }K + m \cdot \alpha_{{\text{Z}}} \cdot R\) |
NASGRO model | \(\ln C + {\text{m}} \cdot \ln \Delta K + {\text{m}} \cdot \ln \frac{1 - f}{{1 - R}} + p \cdot \ln (1 - \frac{{\Delta K_{{{\text{th}}}} }}{\Delta K}) - q \cdot \ln (1 - \frac{{K_{\max } }}{{K_{{\text{C}}} }})\) |
Simplified NASGRO model | \(\ln C + {\text{m}} \cdot \ln \Delta K + {\text{m}} \cdot \ln \frac{1 - f}{{1 - R}} + p \cdot \ln (1 - \frac{{\Delta K_{{{\text{th}}}} }}{\Delta K})\) |