PSI - Issue 75

J. Filho et al. / Procedia Structural Integrity 75 (2025) 353–362 J.Filho, L. Wittevrongel, F. Pieron, P. Lava / Structural Integrity Procedia (2025)

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Fig. 5. Relative error of the reconstructed fracture parameters using the (a) imposed FEA full-field displacements and (b) digital twin.

It should be remembered that the path and domain J -Integrals can be obtained using equations (13) and (14), respectively, and considering the imposed SIFs and equation (11), it is possible to obtain the equivalent reference J integral for the linear elastic material used in the verification tests. With this regard, Fig. 6 illustrates both path (blue) and domain (red) J -Integrals, depicted by cross and circular symbols, using the imposed FEA full-field displacements and digital twin, respectively. The relative errors are also displayed. Since the formulation to estimate the equivalent J -Integral based on SIFs (equation (11)) is different from the path and domain formulations to calculate the J -integral (equations (13) and (14)), the systematic errors (ranging from 0.16% to 1.01%) depicted in Fig. 7(a) are expected. Considering the digital twin, the measured relative errors present in Fig. 7(b) illustrate the errors that can be associated with the shape function mismatch, interpolation bias and pattern-induced bias. Also, it can be observed that the errors obtained from the domain J -Integral are smaller than the errors obtained from the path J -Integral. The domain formulation acts as a filter, reducing errors included in DIC analysis that can appear stochastic ( e.g. interpolation bias and pattern-induced bias) or errors in the image deformation process itself. It is important to highlight that the path or domain must be selected in a region far enough from the crack-tip. The singularity produced by the crack-tip is detrimental to J -Integral estimations using the given approaches. The path or domain should be selected where the remains linear elastic (Becker (2024)).

Fig. 6. Path and domain J -Integrals.