PSI - Issue 39

Hannes Panwitt et al. / Procedia Structural Integrity 39 (2022) 20–33 Author name / Structural Integrity Procedia 00 (2019) 000–000

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3.2. Crack length measurement From the original ACDM-script, the coordinates of the crack branches are known. To calculate the length of a single path in a crack pattern, the growth direction must be determined for each branch on the one hand, and the connection to a continuous crack must be established on the other hand. The growth direction can be obtained by analyzing the number of cycles of the branches, while the end point with the lowest number of cycles can be considered as the respective start point of the branch. To account for noisy data, not only one point, but the average of multiple points at each end is considered to determine the starting point. To deal with a branching crack (Fig. 3a) continuous crack paths have to be found by connecting branches from the notch tip to the ends of the crack pattern. Therefore, each end of the crack pattern is considered as a separate crack with the initiation point at the notch tip. For example, the final crack pattern of the test shown in Fig. 3a is visible in Fig. 3b and Fig. 3c and results in four separated cracks, one for each end of the pattern. To find each individual crack path a loop is executed until each branch has been assigned to at least one crack number (parameter c ). Fig. 3b exemplarily shows the crack path of the longest crack, which comprises of four branches. To start the loop, the first branch of all cracks is determined by calculating the closest distance of all branches to a pre-defined global initiation point. This point is obtained by the pixel coordinates of the notch tip in the specimen before the test starts. Beginning with this branch number (parameter b ), the following instructions are executed to find all ends of the crack pattern: 1. Assign all data (coordinates, orientation, N ) of the branch b to the current crack c . 2. Find the next branch to be added to the current crack. Therefore, check the nodes connected to the branch. Either: branch has no nodes i.e., crack has not branched Increase branch number b +1 and crack number c +1. Or: branch has an end node i.e., the end of crack is not reached (an example with b = b5, c = c2 and end node n3 as labelled in Fig. 3b is described in brackets) i. Find branches without a crack number (b6 and b7) connected to the end node (n3). ii. Find the branch with the highest number of cycles (b7). iii. Create increasing crack numbers c + x (c3) for all other branches (b6). Add these and all previous branches (b1, b3, b5, b6) of the current crack (c2) to the new cracks (c3). iv. Continue with the current crack number (c2) and branch with highest number of cycles (b7). Or: branch has a start node and no end node i.e., the end of the crack is reached Increase the current crack number c +1. If existing, choose the last branch of this new crack, or increase the branch number b +1. 3. Repeat until the data of all branches have been assigned to at least one crack. After the assembly of the crack from the branches, the crack length a can be calculated from the coordinates of the pixels. The crack length at a certain point is the sum of all distances between subsequent points beginning from the notch tip until the current point. As a result of this process, the a - N -curves for the four cracks in Fig. 3c are identical up to the respective branching points. Furthermore, the described way of adding branches consecutively may lead to a decrease of the number of cycles with increasing crack length as can be seen at the indicated point in Fig. 3b. However, for this test this behavior is a result of branches initiating on the surface at a distance to the main crack. These branches connect to the main crack at a higher number of cycles (Fig. 3a).