PSI - Issue 28

F. Conrad et al. / Procedia Structural Integrity 28 (2020) 2195–2205 Author name / Structural Integrity Procedia 00 (2019) 000–000

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yield a sufficient base length. For full-field calculation with a large number of ROIs, the correlation rate of the GPU of about 74 kHz becomes the limiting bottleneck. In this case, 40,000 ROIs are evaluated within 540 ms. The coordinates ( , ) and ( , ) of the camera- and machine systems are transformed by equation � � � √ � � � � � � �� � � � � � � � � � � . (1) Vector ( � , � ) describes the offset between the origins of both systems. Similarly, the displacements �⃗ are transformed from camera coordinates to those of the testing machine: � � � � � √ � � � � � � �� � � � � � � � . (2) In camera coordinates, the symmetrical local strain tensor ̿� � is calculated from local displacement �⃗� � using the derivative operators � � � and � � � along the axes of the system: ̿� � ≡ � � �� �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � . (3) To maximize spatial information according to Nyquist theorem in full-field mode, the spacing between neighbored ROIs is chosen as half ROI pitch, i.e. 21 x 21 pixel sized ROIs are spaced by 11 pixel resulting in an overlap of about 50 %. As cracks are discontinuities in local displacement, normalized 5 x 5 ROI Sobel-like operators � and � are used as derivative operators: � � ⎢ ⎢ ⎢ ⎡ ⎣ 0 0 0 0 0 �0.25 0 0 0 0.25 �0.5 0 0 0 0.5 �0.25 0 0 0 0.25 0 0 0 0 0 ⎦ ⎥ ⎥ ⎥ ⎤ , � � ⎢ ⎢ ⎢ ⎡ ⎣ 0 �0.25 �0.5 �0.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.25 0.5 0.25 0 ⎦ ⎥ ⎥ ⎥ ⎤ . (4) The strain tensor in equation (3) is calculated by the convolution of the displacement field �⃗� � with the derivative operators � � � ≡ � � � � , � � � ≡ � � � � (5) where � is the diameter of the convolution kernels � and � , i.e. four times the ROI spacing of 11 pixel or about 200 µm for an image resolution of 4.5 µm/pixel. The 5x5 shape of the operators makes the non-zero elements non overlapping. Therefore, a sufficient number of ROIs lie completely on either side of the crack, which makes simple median filtering sufficient to obtain the displacement fields shown in Fig. 3 and Fig. 5. The size of the discontinuity at the crack in the direction of strain is measured as � � . (6) Similarly, the crack opening can be calculated along any axis if the corresponding strain is known. However, for strain transformation from camera coordinates � � to biaxial coordinates � � the inner derivatives have to be considered. For a tilt angle of 45 degrees, the transformation of the components of the strain tensor ̿� � becomes � � � � � � � � � � �� ; � � � � � � � � � � �� ; �� � � � � � � � � . (7)