PSI - Issue 68

Giovanni Chianese et al. / Procedia Structural Integrity 68 (2025) 1245–1251 Chianese et al. / Structural Integrity Procedia 00 (2025) 000–000

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geometries with increasing severity of the crack tunnelling conditions. The value of R width = 80 mm was chosen to simulate a crack front with a negligible curvature, that is equivalent to a straight crack front. Given the dimensions of the considered C(T) specimen (B = 6.2 mm), to simulate crack tunnelling conditions greater than 5%, which in agreement with the standard ASTM E647 would require corrective factors, the length of R width was limited to 5 mm. Finally, the normalized crack length α = a/W was varied between 0.34 and 0.84 to simulate different configurations, with a total of 170 simulations which were computed to generate the dataset encompassing values of β reported in Tab. 1. It is worth noting that the crack length was computed on the lateral surface of the specimen as this is in compliance with the laboratory practice.

Table 1. Details about the geometry of the crack front.

β , aspect ratio of the crack front [mm/mm]

R width [mm]

R depth [mm]

0.05

80

4 4 4 6

0.8

5 4 4

1

1.5

With reference to Fig. 2 (c), selected output from simulations are: (i) the average strain in the Y direction over the 1 mm-long path SG1 in the middle of the back-face of the specimen, (ii) the average strain in the Y direction over a 1 mm-long path SG2 on the lateral face of the specimen, and (iii) the strain field in X and Y direction on the lateral face of the C(T)-specimen. Note that outputs (i) and (ii) simulate typical signals collected with electrical strain gauges having length equal to 1.0 mm, whereas (iii) represents measurements acquired with full field experimental techniques, such as the digital image correlation (DIC). 2.3. Approach 1: local strain measurements with fitting functions Solution of problem stated in (1) involves deriving two scalar unknowns, therefore, at least two measurements, ε 1 and ε 2 , were needed. For this reason, the two local strains ε 1 and ε 2 were computed during the simulation campaign. In this way, fitting of two functions was perform to map α and β based on ε 1 and ε 2 . Inversion of these functions enabled solution of the problem stated in (1), as shown in (2). , ) = ) ( , ) * = * ( , ) ⇒ ( , ) = +) ( ) , * ) (2) In compliance with works by Newman Jr et al. (2011), and Riddel and Piascik (1998), position of SG1 was kept at the back face of the specimen, whereas SG2 adopted for the investigation presented herein was placed on the lateral surface, with different positions investigated. The choice of locating on the lateral surface local strain measurements to gather additional information was motivated with results reported by Saeed et al. (2023) for short crack quantification. 2.4. Approach 2: full field strain measurements processed with CNNs The second approach involved the use of the strain field in Y and X directions, respectively ε X and ε Y . They were concatenated in one instance for each of the simulated scenario, and were used as input to train and validate CNNs that estimated the crack front geometry and the crack length. Simulated stain fields were imported and processed in MATLAB environment (MATLAB R2023b and Deep Learning Toolbox). A region of interest (ROI), whose dimensions are 17 mm x 15 mm, was cropped by considering nodes with X coordinate ranging between -17.5 mm and -0.5 mm and Y coordinate ranging between -7.5 mm and 7.5 mm. The nodal strains in X and Y directions were linearly interpolated, and values of the two functions interpolating ε X and ε Y were calculated at points of a grid that covers the ROI with a resolution of 0.15 mm, which