PSI - Issue 72

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

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movement of the loading cylinder while allowing vertical displacement, and restraining a discrete point horizontally to prevent rigid body motion. Surface-to-surface frictionless contact was established between the cylinders and the specimen. Each experimental test was represented by a distinct model, incorporating specific measured dimensions, t A , and a 0 values for maximum accuracy. The adhesive layer’s cohesive properties, including E , G , t n 0 , t s 0 , G IC , and G IIC , were directly derived from a previous work (Faneco et al. 2017). t n 0 and t s 0 were approximated using σ f and τ f , respectively. To numerically capture the adhesive's mixed-mode behavior, the power-law exponent (  ), critical for defining the fracture envelopes for each t A , was calculated based on experimental data. The value of  varied with t A , and was applied accordingly in the respective numerical models. 3. Experimental results The pure mode (DCB and ENF) and mixed mode (SLB) specimens showed cohesive rupture of the adhesive, The results of the pure mode tests are used to construct the failure envelopes. Therefore, only the average values of G IC and G IIC and the deviations have been presented (Table 2). The highest coefficient of variation was 12.7% for G IC and t A =0.2 mm. The average values were used to construct the fracture envelopes for each t A .

Table 2. Average and standard deviation of G IC and G IIC [N/mm] for all t A .

t A [mm]

Average G IC

Standard deviation ( G IC )

Average G IIC

Standard deviation ( G IIC )

0.1 0.2 0.5 1.0 2.0

1.094 1.402 2.350 3.768 5.425

0.06 0.09 0.11 0.42 0.53

1.620 2.062 3.461 5.552 7.989

0.13 0.26 0.19 0.11 0.34

The P -  curves made it possible to draw the R curves and estimate G I and G II . The R -curves selected for t A =0.1 mm are illustrated in Fig. 4. The R -curves for the CBBM method, both in tension and shear, produce higher a eq than the real a . This is explained by a eq being a calculated quantity, taking into account the FPZ (Santos and Campilho 2017). Variations in G I and G II were identified for all specimens/ t A values, due to experimental defects. However, crack growth occurs with approximately constant G I and G II and, correspondingly, with a constant mode mix.

1

1

Model 1 Model 2 Model 3 Model 4 Model 5 CBBM

Model 1 Model 2 Model 3 Model 4 Model 5 CBBM

0.8

0.8

0.6

0.6

0.4 G II [N/mm]

0.4 G I [N/mm]

0.2

0.2

0

0

40

80

120

160

200

40

80

120

160

200

a [mm]

a [mm]

a)

b)

Fig. 4. G I - a (a) and G II - a (b) R -curves for a specimen with t A =0.1 mm.

Table 3 illustrates an extract of the data recorded for t A =0.2 mm using the data reduction methods. However, the qualitative conclusions are transversal to all values of t A . The relative variations are obtained as an average for the CBBM, due to its robustness. The variation in the values obtained for one of the data reduction methods was low and, for t A =0.2 mm, the highest coefficient of variation was found to be 13.9% ( G II as calculated using the CBBM). The methods compared led to close results. For G I , the highest deviation from CBBM was -7.9% (model 4). Not considering model 4, the highest deviation was -9.6% (model 2).