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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Γ = ∫ ( 22 − ) Γ and A =∫ ( − 1 ) A ,

(13) (14)

where is the strain energy density function (SED), defined by = ∫ : 0 , (15) is the Cauchy stress tensor, is the strain tensor, T is the traction vector ( = ), p is the outward normal vector, u is the displacement vector that can be obtained using DIC, 1 is the Kronecker delta, q -function represents the virtual crack extension function, linearly ranging from 0 on the outer boundary up to 1 on inner boundary edge, is a small increment of arc length along a closed counterclockwise contour defined by Γ and is an infinitesimal increment of area. Integrated path and domain J -Integrals have also been implemented in the MatchID post-processing module, allowing the extraction of the energy release rate of cracked specimens. It is important to note that the path or domain should be selected in a region positioned far enough from the crack-tip where the behaviour is linear elastic. The given module also gives the possibility of carrying out a convergence analysis considering different paths or domains. 6. Verification tests and discussion Considering a linear elastic material with = 2500 and =0.35 subjected to plane stress conditions, the MatchID FEDEF module was used to numerically deform a speckled image by imposing an analytical solution based on the Williams’s series expansion under mixed -mode loading (see Fig. 2). Predefined SIFs and crack-tip position were used in the image deformation. These images were processed using stereo DIC (using a subset size of 25×25 pixels 2 and step of 5 pixels) to reconstruct the full-field displacements used to deform the images. A set of verification tests were performed to validate the implementations and illustrate the importance of evaluating the uncertainties that can be present in the digital twin. The Williams’ series expansion module inside MatchID was used to reconstruct the SIFs and crack -tip position considering the imposed analytical full-field displacements and the results obtained by DIC. First, in order to illustrate the difference between the crack- tip estimated by opening displacements and Williams’ series expansion , Fig. 3 shows the measured crack-tip position per generated image using the imposed analytical full-field displacements. The region used in the full-field-fitting is illustrated by Fig. 3(a) and Fig. 3(c) exhibits the residuals measured by taking the difference between the reconstructed and imposed crack-tip positions. The reference crack-tip value is illustrated by the red curve, while the blue and red cross symbols depict the results estimated by crack opening displacements and Williams’ series expansion, respectively. It is important to highlight that the crack-tip can be identified by the opening displacement at the front of the crack. By defining a displacement limit, it can be used to indicate whether a material point is cracked or not. If the measured opening displacement is bigger than the selected limit, the material will be considered as cracked. Therefore, it is subjective to the user selection and can be detrimental for the crack-tip measurements. As can be seen, the crack opening displacement is not an appropriate metric to evaluate the position of the crack- tip. The Williams’s series expansion, on the other hand, can better estimate the position of the crack -tip.