PSI - Issue 28

F. Conrad et al. / Procedia Structural Integrity 28 (2020) 2195–2205 Author name / Structural Integrity Procedia 00 (2019) 000–000 7 To verify these two methods for crack tip localization with DIC, the progression of the crack length a measured at maximum tension-loads of the fatigue crack-growth experiment are compared to crack-length measurements derived with an ACPD probe. The left of Fig. 4 shows the cross section of the sample with the crack profiles at Cycle 0 (brown Heat-Tint) and End of Test (EOT, golden Heat-Tint). The cross section reveals, that boundary effects are prevalent in near-surface areas ( < 5°) leading to a shorter crack length as in the middle of the specimen. As the camera measures crack-growth at the surface of the specimen only, the potential drop signal was calibrated with measured surface crack length (white arrows) for a more accurate comparability. Fig. 4b shows the resulting progression of the crack length a as a function of load cycles. The black line represents the crack length measured by ACPD, the open diamonds give the DIC values measured by thresholding the divergence in Fig. 3b with a value of ∆ = 3 µm, and the blue dots are the maximum gradients corresponding to the green arrows in Fig. 3c. Both DIC values agree well with the ACPD values. However, maximum gradient has the advantage of uniqueness whereas the threshold ∆ε is load dependent. It is also plausible from the point of view of physics that maximum rotation occurs at crack tip near the surface. 2201

Fig. 4: (a) Cross section where dark area shows initial crack shape at cycle 0 and lighter area at end-of-test (EOT). The white arrows mark the surface crack length at the camera side. (b) Comparison of crack depth between DIC system by threshold in divergence (see Fig. 3b) and by maximum gradient in the rotation of the displacement field (Fig. 3c). 5. Consistency of DIC and FEM on biaxially loaded specimens Fig. 5 shows full-field results with 173 x 52 ROIs of a biaxial crack growth experiment, with a cruciform specimen (26NiCrMoV14-5). The results were obtained under a maximum load of 35.0 kN along axis A and 17.5 kN in direction of axis B (see table 1). Evaluation time was 121 ms corresponding to a 74 kHz ROI correlation rate. Before the start of the experiment, the specimen was pre-fatigued with equal forces on each axis, to create a fine initial crack parallel to the crack-starter notch in the center of the specimen. Fig. 5a shows the displacement � � � in strained coordinates. The crack appears as discontinuity in the displacement field. Towards the crack tip, this discontinuity decreases continuously to zero. Fig. 5b displays the divergence �⃗ according to equation (8). Within the rotation rot �u⃗ given in Fig. 5c, the gradients indicated by the green arrows are clearly visible at the crack tip, similar to Fig. 3c. To measure crack contour, a polynomial is fitted to a thresholded image of the divergence in Fig. 5b. The result is plotted to the rotation in Fig. 5c, where the crack tip is located by the gradients perpendicular to the contour. Polynomials of 7 th degree were best suited as they fitted the contour well and were still usable for extrapolation outside the thresholded area. However, no automated version was implemented yet.