# Crack Initiation and Propagation Fatigue Life of Ultra High-Strength Steel Butt Joints
## 3 Optical Detection of Crack Initiation and Propagation
### Crack Detection and Tracking Procedure
#### 3.2.2 Crack Detection and Tracking  
This section deals with the identification of a crack and its tracing over the load cycle number based on the results of the digital image correlation procedure. This includes recognition of a newly initiated crack to an existing one, as well as the merging of two small cracks into a larger one. This part of the procedure is once again divided into two subsections; the first covers the detection of all cracks for each image separately. The second traces the growth with increasing load cycle number and determines possible merges, as well as initiation of new cracks.  
The identification of cracks in an image is performed utilizing the Matlab implemented image processing toolbox. Therefore, the gradient field is converted to a binary black-white image with an initial threshold value \(s^{\prime}_{y,thres}\) of two pixels/pixel. If the maximum gradient value of an image exceeds forty pixels/pixel, the threshold value is adapted to five percent of the maximum value. The reason for this lies in the enlargement of the plastic zone at the crack tip with increasing crack length [55], which is considered by this adaptive threshold setting. It has to be noted that the definition and the course of the threshold value is, besides the parameters of the image correlation, the primary influencing factor regarding the finally-measured crack length. Therefore, it plays a decisive role in the procedure's verification process (see Section 3.3). Figure 9 shows the black-white image related to Figure 8b with a threshold value of \(s^{\prime}_{y,thres}=2.39\). Figure 10 plots the result of crack identification process in the gradient field of Figure 8b.  
Based on the results of each image, crack tracking is performed over all of the images. At first, the last image before fracture is considered by identifying the number and positions of the final cracks before specimen failure. This information is essential, as all crack initiations will occur in these areas. However, due to this action, the procedure is not suitable for application during the test without any modification. Subsequently, a loop through all images assigns the respective cracks to a final crack.  
Figure 10: Gradient field \(s^{\prime}y\) of Figure 8 with marked results of the crack identification process.  
Figure 9: Binarized matrix of Figure 8 indicating crack regions.  
Additionally, the merging of cracks is noted at this point by a comparison to the previous image's state. Finally, the determined surface crack length is converted from pixels to millimetres.  
Figure 11 shows the procedures result, the surface crack length \(2c\) in mm with respect to the load cycle number. Crack number one actually initiated at two different positions and merged just a few thousand load cycles before final fracture. Figure 12a shows the image of the first step at 60,000 load cycles with marked crack number one in red and two in green dye. In this picture, the two separate initiations of crack one are visible, which will merge within further crack growth. Figure 12b depicts the image of the last step before fracture at 84,000 load cycles where crack one is already merged. The respective fracture surface after 85,039 load cycles in Figure 12c gives a good opportunity to verify the result. Here, the two initiation points within the left crack are clearly visible. Furthermore, all three crack initiation points are located at local undercuts, which are indicated in the figure.