# Crack Initiation and Propagation Fatigue Life of Ultra High-Strength Steel Butt Joints
## 3 Optical Detection of Crack Initiation and Propagation
### Validation of the Procedure
#### 3.3.2 Fracture Surfaces  
The second part of the method's validation utilizes separate, not-through base plate thickness cracks in the fracture surface. The fracture-causing crack itself is not suitable for a comparison with the calculated value, as the transition zone from stable crack propagation to rupture is vague. This inhibits a precise measurement of the final surface crack length. The number of such separated, not-through cracks is limited and takes place preferably in high load levels, where the tendency for multi-crack initiation is higher. However, two suitable fracture surfaces are available for validation within the present test series (see Figure 14).  
The measurement of the actual crack length in the fracture surface is performed utilizing a Matlab(r)-tool introduced in [25]. The script fits a semi-ellipse to a number of points manually selected in the image using a non-linear fitting algorithm. Figure 15 displays the result of the fitting procedure for both specimens including the crack measures. Hereby, the shape of the crack in Figure 15a fits the semi-ellipse quite well, whereas the smaller crack in Figure 15b deviates from the semi-elliptical shape considerably. However, the surface length is assessed properly.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Beach Mark**} & \multicolumn{2}{c}{**Measured Crack**} & \multicolumn{2}{c}{**Assessed Crack**} & \multicolumn{1}{c}{**Deviation**} \\ \hline
**No.** & **N (-)** & **Length 2\(c\) (mm)** & **Length 2\(c\) (mm)** & **(\%)** \\ \hline
1 & 740,000 & 17.94 & 18.23 & 1,62 \\
2 & 700,000 & 11.98 & 11.97 & \(-\)0,08 \\
3 & 660,000 & 9.52 & 9.52 & 0 \\
4 & 620,000 & 8.00 & 7.92 & \(-\)1.00 \\
5 & 580,000 & 6.84 & 6.72 & \(-\)1.75 \\
6 & 540,000 & 6.00 & 6.00 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison between the measured and assessed surface crack length.  
Figure 14: Fracture surfaces used for validation of the calculated crack length: (**a**) Specim 1; \(\Delta\sigma_{n}\) = 400 MPa, \(N_{f}\) = 85,039; (**b**) specimen 2; \(\Delta\sigma_{n}\) = 600 MPa, \(N_{f}\) = 30,871.  
Due to the strategy of the presented crack detection procedure, the measurement of the surface crack length cannot be performed at burst fracture. Thus, quadratic extrapolation from the last four measurement results up to the number of load cycles at burst fracture is performed. This assumption could lead to an underestimation of the actual crack length. However, it delivers sufficient accuracy and does not require any local material parameters affecting the extrapolation.  
Table 4 presents the calculated surface crack length with respect to load cycle numbers for both investigated cracks including the extrapolated values at burst fracture. The measured values originating from the fracture surface are listed as well for direct comparison. Hereby, the actual surface crack length exceeds the extrapolated values of about 2% in both cases. This, once more, validates the approach and the determined parameters of the crack detection and tracking procedure.