18 J. C. A. D. Filho et al. Fig. 5 Vertical strain maps for the FE model (left) and the synthetically deformed images (right) window of 3. The three fracture metrics (K, Jpath and Jfrac) were then compared between the Abaqus and MatchID outputs. The results are provided in Fig. 6. Fig. 6 Verification of the calculation of K from the Williams series (left) and for the J-integrals, for different strain windows. No image deformation, pure FE results loaded into MatchID and strains calculated from displacements in MatchID. For both K and J-integrals, the differences between Abaqus and MatchID are lower than 1%. There is a limited impact of the strain window too. This result verifies that the MatchID implementation is correct. The second step is to process the deformed images and compare to the Abaqus results. The data are reported in Fig. 7. For the Williams series, the errors are very similar to that obtained from the pure FE data but there are some larger errors at small loads (small strains) on the path J-integrals. These are caused by edge outliers over the faces of the crack. It is worth noting that the surface integrals do not suffer from these effects as the spurious edge data average out. It is also worth noting that for higher loads, this effect becomes negligible. Finally, the effect of camera noise was simulated by polluting each image by a Gaussian distribution of noise of zero mean and 1.5 grey level standard deviation for the 8-bit images, a realistic noise level for modern CMOS sensors. The results are summarized in Fig. 8. K is not affected by the camera noise as it bears only on displacements and a large number of points are used for the fit. This is a clear advantage of it. The contour J-integral is the most sensitive to noise as it does not use a lot of (noisy) strain data points, while the surface J-integral is more robust to strain noise. One also sees a reduction of noise with the strain window, as expected. From these results, the advantage of the surface J-integral formulation vs the contour one is clear.
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