PSI - Issue 72

A.F.L. Macedo et al. / Procedia Structural Integrity 72 (2025) 61–68

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Table 3. Average and standard deviation of G I and G II [N/mm] for all data reduction methods and t A =0.2 mm. Method Average G I Standard deviation ( G I ) Average G II

Standard deviation ( G II )

Model 1 Model 2 Model 3 Model 4 Model 5 CBBM

0.897 0.904 0.953 0.875 0.952 0.950

0.086 0.110 0.083 0.107 0.115 0.101

0.669 0.656 0.681 0.875 0.688 0.726

0.064 0.081 0.079 0.107 0.084 0.101

Fig. 5 summarizes the mean and deviation data for G I and G II and all t A (CBBM method) and the average of  . The trend of the G I - t A and G II - t A graphs is consistent, with a linear rise to t A =1 mm and a reduction in slope thereafter. For CBBM and t A =0.1 mm, the mean for G I and G II was 0.682 and 0.510 N/mm, correspondingly. The relative gains up to t A =1 mm was 390.4% ( G I ) and 382.6% ( G II ). Above t A =1 mm, the rate of improvement decreases because the increase in t A is no longer totally followed by the dimensions of the FPZ and the respective measurements of G I and G II , showing that the ductility of the adhesive has reached its limit. Therefore, for t A =2 mm, the increase in G I and G II in comparison to t A =0.1 mm was 543.1% ( G I ) and 535.6% ( G II ), cancelling out the proportion found for 0.1≤ t A ≤1.0 mm. The average  was practically constant regardless of t A , varying between 40.3º ( t A =2 mm) and 41.1º ( t A =0.2 mm). These values are in line with literature data (section 2.3).

6

48

G II

fi

G I

5

40

4

32

2 G I or G II [N/mm] 3

24

 [º]

16

1

8

0

0

0

0.5

1

1.5

2

t A [mm]

Fig. 5. G I , G II and  as a function of t A .

4. CZM modelling 4.1. Data fitting In the data fitting procedure, the parameters t n

0 and t s

0 are adjusted due to their unknown values. The values for G IC

and G IIC were taken from Table 3. A numerical fitting approach was conducted, to adjust the numerical P -  curves with the experimental ones by iteratively modifying t n 0 and t s 0 to accurately depict the experimental findings. The first step is the construction of numerical models for each specimen, incorporating their actual measurements. The iterations involve fine-tuning t n 0 and t s 0 on the numerical P -  curves to better emulate the experimental ones. Fig. 6 shows two instances of curve fitting: t A =0.2 mm (a), and t A =2.0 mm (b). Post-fitting, the numerical P -  curves closely mirror the experimental ones. However, for t A =2 mm, despite the maximum load ( P m ) and corresponding displacement ( δP m ) being nearly identical between the curves, discrepancies in initial stiffness are observed, due to the triangular CZM law’s limitations in adapting to t A =2 mm. Throughout the fitting process, the distinct impact of each CZM parameter on the numerical outcomes became apparent, with each parameter uniquely influencing the P -  curve. Parameters like G IC and G IIC exert significant control over P m and subsequent P values, without affecting initial stiffness, particularly with G IC ’s pronounced effect. Modifying t n 0 and t s 0 not only impacts the initial stiffness and P m but also sha rpens the curve’s transition from the ascending to the descending phase, especially at higher values.