# 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
#### 3.2.1 Local Distortion Field of the Specim's Surface  
A crack in a structure leads to a local reduction of the stiffness along with a significant increase of local displacement in case of a load perpendicular to the crack surface. Therefore, the change in local displacement is a suitable parameter for the detection of surface cracks. Hereby, digital image correlation is an appropriate tool in order to measure this parameter using the images acquired during the fatigue tests. Digital image correlation is a camera-based toolbox to acquire full field displacements by cross-correlation. Usually, speckle patterns are applied to the measured surface in order to increase the surface contrast. However, in the present case the texture of the specimens' surface itself turned out to be sufficient for correlation in the desired regions. This is a great advantage compared to other crack detection methods as any surface modification could lead to a change in the weld's crack initiation and propagation behaviour. The image correlation procedure compares each image at a certain number of load cycles with the reference image acquired at the beginning of the fatigue test. In order to exclude any effects coming from optical distortion due to the camera lens, the Matlab(c) built-in _Camera Calibrator_ is applied to estimate the geometric parameters of the utilized lens. Subsequently, the distortion effects are removed of the acquired images. Figure 7 shows the grayscale images prepared for image correlation of Reference (a) and last image (b) of the exemplary specimen. Here, the \(x\)-axis corresponds to the horizontal and the \(y\)-axis to vertical direction. The last image already shows a large crack at the upper weld toe leading close to burst fracture. However, the actual size of the crack is not visible. In order to increase the correlation speed, parts of the image are excluded from correlation which do not contain relevant information, such as the areas to the left and right of the specimen. Here, Figure 7a shows the processed net surface as a red rectangle. The correlation procedure requires a set of parameters affecting its quality and accuracy as well as the calculation time which are described in the documentation of the code (see [59]). Hereby, a suitable set of parameters for the current images is invoked using the documented approach and further empirical investigations. One of the most sensitive parameters is the grid spacing defining the distance in pixels between two adjacent control points. At these points, the output distortion is computed. Therefore, the grid spacing represents the resolution quality of the result directly linked to computation time. For example, an image with a size of \(6000\times 4000\) pixels and a grid spacing of 15 pixels results in a distortion field of \(400\times 267\) entries. Here, a large grid spacing gives a rather coarse distortion field whereas a fine grid spacing leads to a disproportional long calculation time of several hours per image and increases the risk of poor correlation results. Thus, a grid spacing between 15 and 20 pixels is recommended. A more detailed insight on the correlation procedure and its parameters is given in [60]. The result of the image correlation procedure for N = 84,000 is depicted in Figure 8a as the vertical displacement field \(s_{y}\) in the load direction of the specimen. This outcome includes the local displacement as well as a potential global movement of the specimen due to a small amount of sliding in the clamping area. Therefore, the vertical gradient of the vertical displacement \(s^{\prime}y\) is introduced in order to highlight local changes in vertical displacement and simultaneously exclude possible global movement. The corresponding result of the displacement gradient is depicted in Figure 8b explicitly indicating the present cracks only. Figure 8: Result of image correlation at N = 84,000: (**a**) Displacement field \(s_{y}\) in vertical (y)-direction; (**b**) vertical gradient of vertical displacement field \(s^{\prime}y\).