PSI - Issue 5

Jürgen Bär et al. / Procedia Structural Integrity 5 (2017) 793–800 Jürgen Bär et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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For the potential drop measurements in this work an amplifier of the control electronics with a sampling rate of 1 kHz was used. The maximum value of the potential drop of each load cycle was stored. Thus, a crack length and a crack propagation rate for each load cycle could be determined. In figure 1 the crack propagation rate, calculated with the secant method according to ASTM E647 for an experiment with constant force, is shown as blue symbols. The scatter of the potential values is retrieved in the crack propagation rate and even negative crack propagation rates are generated. Using a semi logarithmic scale, the negative values disappear, but the scatter is still in the order of one decade. The scatter of the measured potential values leads obviously to an overestimation of the crack propagation rates. As the crack length and consequently the crack propagation rate is increasing, the correspondent scatter is reduced. This means that in case of long cracks the pure crack propagation superposes the scatter.

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Fig. 1. Crack propagation rates determined with the secant method with and without LOESS smoothing. (a) linear scale; (b) logarithmic scale.

To get reliable data, especially in the early stages of crack propagation, a new method for data treatment is suggested. This method is based on the so-called LOESS (robust lo cally weighted regr ess ion) smoothing (Cleveland 1979). For a center point x i and all neighboring points within a defined span weights w i are calculated using a tri-cube weight function. Hereby, data points closer to the center point x i are weighted more than those which are further away. Then, a weighted least square regression using a second-order polynomial is performed resulting in smoothed values (x i , y i ). In figure 1 data smoothed by the LOESS method are shown as a red line. In the semi logarithmic diagram (figure 1b), after some initial effects, the expected increase of the crack propagation rate can be observed in case of the LOESS-smoothed data, whereas the unsmoothed values of the secant method are very noisy and no usable results are obtained. In figure 2 the potential values of a fatigue experiment undertaken with a stress amplitude of  a =80 MPa smoothed with the LOESS method are shown. The steep increase at the beginning of the experiment is followed by a decrease to a minimum value. These “starting - effects” are not effected by crack propagation (Ljustell 2013), but rather by the deformation and changes in the conductivity of the press-fitted potential grips. After the minimum a continuous increase of the potential until failure of the specimen can be observed. This indicates clearly that crack propagation starts early at the second minimum of the potential curve, as it is marked in figure 2. According to that, the smoothing of the potential data by the LOESS method enhances the resolution of the potential drop measurement, especially for short cracks, and offers the possibility to determine the real initiation of the crack propagation phase in fatigue experiments. Normally, a so-called technical crack length is defined to determine the start of crack propagation in fatigue experiments. If this definition is applied, the whole short crack propagation phase is included in the crack initiation phase. Taking the last minimum of the potential curve before continuous crack propagation into account, instead of a technical crack length of 250µm, significant changes in the crack initiation lifetime can be observed. In case of the