PSI - Issue 39

5

Hannes Panwitt et al. / Procedia Structural Integrity 39 (2022) 20–33 Author name / Struc ural Integrity Procedia 00 (2019) 000–0 0

24

a

b

path detection at last load cycle, no N information crack width calculation

th cw = 1% ≙ 0.01 mm

1 ≥ th

th ε 1 = 1% 7.35

c

e

0.01 mm crack width

7.20 7.30 first load cycle (×10 5 ) when ε 7.25

7.15

7.30 first load cycle (×10 5 ) when crack width ≥ th cw th cw = 1% ≙ 0.01 mm 0.11 mm crack width first load cycle (x10 5 ) when crack width ≥ th cw 0.01 mm 7.25

7.15

f th ε 1 = 1%

d

0.0247 mm

first load cycle (×10 5 ) when ε 1 ≥ th 0.0 1.48 2.96 4.44 5.92 7.40

7.35

7.20 7.15

Fig. 2: Detection of the crack tip for a mode I crack. a) Area of the SEN specimen with a mode I fatigue crack; b) Entirely detected crack path; c f) Detecting the crack tip: c) Crack width method at 7.15×10 5 cycles; d) Crack width method at 7.35×10 5 cycles ; c) ε1 -method at 7.35×10 5 cycles; d) ε1 -method at 7.35×10 5 cycles for the whole crack.

3.1.1. Crack width method After the crack path is detected as a whole, the crack width is calculated with the original ACDM-script for each picture. For the present study with a subset size of 15 pixels and a scale of 0.027 mm/pixel, a reasonable distance between the reference points is 1 mm (i.e., the length of the virtual extensometers is 1 mm as well). To measure the load cycle, at which the crack tip reaches a point on the crack path, a threshold value th cw of the crack width is introduced for this method. When the crack width reaches the crack width threshold value for the first time, the corresponding number of cycles is assigned to this point on the crack (Fig. 2c and d). In the present example the crack width has to reach 1 % of the length of the virtual extensometer (i.e., 0.01 mm). 3.1.2. Principal strain method (ε1 -method) In contrast to the crack width method, the ε1 -method does not use the virtual extensometers of the original ACDM script, but the ε 1 -field itself. During the original crack path detection, the HSA of each picture is extracted as a binary image by means of the principal strain threshold value th ε1 . The result of combining these is also a binary image. For the new ε1 -method, the number of cycles of the respective picture is stored at each point in the HSA instead of the original binary information, resulting in a N -scaled-HSA. The combination step is conducted by only assigning lowest number of cycles at each point to the final N -scaled-HSA. Fig. 2e shows the N -scaled-HSA at the end of the mode I crack. By normalizing the contained values of N the visible gray scale image is obtained, where the varying shades of gray correspond to the different number of cycles at the detection. The final N -scaled-HSA of the whole crack is shown in Fig. 2f with a color map for better distinction of the different numbers of cycles. To determine the crack growth with this method, for each point (i.e., pixel) of the detected crack path the corresponding value of the N -scaled-HSA is assigned to the crack and treated as the load cycle, at which the crack tip reaches this specific point.