PSI - Issue 39

9

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

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Fig. 5: Calibration of the a - N -measurement methods on a K I -controlled test with constant block loads. a) C rack width method; b) ε1 method c) Smoothing of the crack path, crack width method.

The calibration procedure was continued with a force-controlled mode I test, where the maximum force ( F max = 30 kN) was kept constant. Fig. 6a shows the cali bration results for the ε1 -method. With the previously calibrated parameter of th ε1 = 0.4 % the a-N- curve is in good agreement with the results of the potential drop technique up to a crack length of approx. a = 10 mm. For long cracks though, the crack length is overestimated, as shown in the detail in Fig. 6a. This is a result of an increasing stress intensity factor (SIF) at the crack tip and therefore higher strains around the crack tip with increasing crack length. This may lead to a very large HSA and subsequently to a frayed detected crack pattern (Fig. 6c). To account for this, a threshold value of th ε1 = 1.0 % leads to a plausible detected crack pattern, where the a-N- curve is in good agreement with the results of the potential drop method for large crack lengths. However, this threshold leads to an underestimation of the crack length for short cracks (Fig. 6a). Thus, a variable threshold value th ε1 ( N ) depending on the number of cycles is introduced th ε1 ( N ) = th ε1 ,start + � th ε1 ,end - th ε1 ,start � � N N end � n th (1) where th ε1,start and th ε1,end are the strain threshold values at the first and last picture, respectively. With the exponent n th different interpolations between the start and end value can be chosen. Whereas values of n th > 1 can be used to resemble an exponentially increasing crack growth and therefore HSA size, equal values of th ε1,start and th ε1,end lead to a constant factor. For the values th ε1,start = 0.4 % and th ε1,end = 1.0 % the previously obtained values for low and high crack lengths, are used, respectively. An exponent of n th = 2 was found to be suitable for interpolating the threshold between start and end values, so that the whole a - N -curve is in good agreement with the curve of the potential drop technique. Fig. 6b shows that the crack width method with the previously calibrated constant threshold of 0.3 % is suitable for the detection of long cracks as well. Nevertheless, the results for the crack width method are noisier than the results of the ε1 -method, with several outliers. These outliers can be detected by evaluating the moving median absolute deviation and can be removed to obtain less noisy data with this method as well. It should be noted that the crack width method is less sensitive to different experimental procedures ( F max = const. vs. K I = const.) than the ε1 -method, but it relies on an accurate crack path detection as well. This means that the two crack patterns shown in Fig. 6 lead to the same a-N- curves up to the point, where the detected crack path exceeds the true crack path (due to the large HSA in the crack pattern with th ε 1 = 0.4%). Therefore, for the crack width method a more conservative (i.e., higher) strain threshold for the crack path detection is recommended, when investigating high crack lengths under constant force-controlled loading.