## 4 Analysis of Fatigue Crack Propagation Test Results
### Effect of Semi-Ellipsoidal Notch Depth on Crack Propagation Rate
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Numbering** & **Crack Front Marking Technique** & _a_/mm** & _c_/mm** & _a_/_c_ & \(N\) \\ \hline \multirow{8}{*}{D-1} & Crack front marking 1 & 0.210 & 1.050 & 0.200 & 35,000 \\  & Crack front marking 2 & 0.420 & 1.680 & 0.250 & 51,000 \\  & Crack front marking 3 & 0.735 & 2.205 & 0.333 & 67,000 \\  & Crack front marking 4 & 0.945 & 2.520 & 0.375 & 83,000 \\  & Crack front marking 5 & 1.208 & 3.150 & 0.383 & 99,000 \\  & Crack front marking 6 & 1.628 & 4.200 & 0.388 & 115,000 \\  & Crack front marking 7 & 2.415 & 5.985 & 0.403 & 121,000 \\ \hline \multirow{8}{*}{D-2} & Crack front marking 1 & 0.424 & 1.802 & 0.235 & 20,000 \\  & Crack front marking 2 & 0.583 & 2.226 & 0.262 & 30,000 \\  & Crack front marking 3 & 0.848 & 2.968 & 0.286 & 40,000 \\  & Crack front marking 4 & 1.166 & 4.028 & 0.289 & 50,000 \\  & Crack front marking 5 & 1.484 & 4.770 & 0.311 & 60,000 \\  & Crack front marking 6 & 2.332 & 5.512 & 0.423 & 70,000 \\ \hline \multirow{8}{*}{D-3} & Crack front marking 1 & 0.371 & 1.484 & 0.250 & 20,000 \\  & Crack front marking 2 & 0.795 & 2.862 & 0.278 & 30,000 \\ \cline{1-1}  & Crack front marking 3 & 1.272 & 3.180 & 0.400 & 40,000 \\ \cline{1-1}  & Crack front marking 4 & 1.643 & 4.558 & 0.360 & 50,000 \\ \cline{1-1}  & Crack front marking 5 & 2.544 & 6.572 & 0.387 & 60,000 \\ \hline \multirow{8}{*}{D-4} & Crack front marking 1 & 0.412 & 1.545 & 0.267 & 20,000 \\ \cline{1-1}  & Crack front marking 2 & 0.876 & 2.472 & 0.354 & 30,000 \\ \cline{1-1}  & Crack front marking 3 & 1.391 & 3.811 & 0.365 & 40,000 \\ \cline{1-1}  & Crack front marking 4 & 2.060 & 5.047 & 0.408 & 50,000 \\ \cline{1-1}  & Crack front marking 5 & 2.987 & 6.489 & 0.460 & 58,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Test data of steel wire crack propagation with notches of different depths. Figures 18 and 19 show the change of crack depth and width with fatigue loading numbers obtained according to the data in Table 1. It can be seen that the crack propagation rate is slow at first, but gradually accelerates. The deeper the initial depth of the notch, the faster the rate of crack propagation. It can also be seen from Figures 18 and 19 that both crack depth and crack width show a law which are similar to linear propagation with the change of fatigue loading numbers. In order to distinguish the influence of initial notch depth on crack propagation, the _a-N_ curve and _c-N_ curve were linear fitted, \(a=A\times N+B\), \(a=A^{\prime}\times N+B^{\prime}\). The specific results are shown in Table 4. It can be seen that the slope of the fitting line corresponding to the specimen with a larger notch depth is higher. That is, the deeper the notch depth is, the higher the crack propagation rate is. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Numbering**} & **Fitting Curve** & **Coefficient A (10\({}^{-4}\))** & **Coefficient B** & **Fitting Curve** & **Coefficient A’ (10\({}^{-4}\))** & **Coefficient B’** \\ \hline D-1 & _a-N_ & 0.220 & \(-\)0.718 & _c-N_ & 0.481 & \(-\)0.951 \\ D-2 & _a-N_ & 0.359 & \(-\)0.475 & _c-N_ & 0.778 & 0.048 \\ D-3 & _a-N_ & 0.519 & \(-\)0.753 & _c-N_ & 1.187 & \(-\)1.018 \\ D-4 & _a-N_ & 0.655 & \(-\)1.048 & _c-N_ & 1.293 & \(-\)1.249 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Coefficient table. Figure 19: Variation of crack width with cyclic numbers. Figure 18: Variation of crack depth with cyclic numbers.