PSI - Issue 28

M.Z. Sadeghi et al. / Procedia Structural Integrity 28 (2020) 1601–1620 M.Z. Sadeghi et al./ Structural Integrity Procedia 00 (2019) 000–000

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4.2. Fracture envelope: Based on the values of G c obtained for different mode mix ratios and different adhesive thickness (Table 2 and Table 3), the fracture envelope was developed through curve fitting using MATLAB to assess their applicability for Power-law and BK law. For a mode mixity up to 25%, the trend is in line with the estimated Gc value for SLB (Mode mix – 41%) (Santos and Campilho, 2017). This study, however, examines the effect of higher mode mixities > 50% where G c monotonically increases with the mode mix ratio as shown in Fig. 12. This trend in G c versus mode mix ratio is similar to the findings in (Balzani et al., 2011; Khoo and Kim, 2011; Sadeghi et al., 2019). However, the same argument cannot be extended to pure Mode -I and Mode -II values where a relationship exists between the plastic zone size’s dependence on adherents constraining effect. Based on the values of G I and G II , for the range of mode mixity tested in the present work, determination of power-law index based on Equation (1), (assuming  =  ) yielded unrealistic exponents and considering an index of (  =  =1 and 2) yielded large error at high mode mix ratios and thus not presented in this work. It is possible that a curve fit based on Equation (2), would yield a better fit. However, no such attempt was made since this failure envelope model could not be incorporated in Abaqus. Hence a curve fit with B-K law was attempted and was found adequate to characterise the fracture for the range of mode mix ratios tested and have been outlined in the below Fig. 12 and values are outlined in Table 4. The same results were incorporated in the commercial Abaqus FE package.

Fracture Toughness [N/mm]

Fracture Toughness [N/mm]

Fig. 12. Fracture envelopes based on the B-K Law (left) adhesive thickness (t a = 0.35 mm), (right) adhesive thickness (t a = 1.0 mm).

Table 4. Extrapolated values of G IIC and exponent  . J – integral

ECLM

Thickness (mm)

G IIC

G IIC





0.35

6.10

2.13

4.80

1.80

1.00

6.10

2.63

5.58

2.55

For same adhesive – Araldite 2015, the extrapolated values of G IIC (Table 4) is in good agreement with the few previously published results G IIC = 4.70 N/mm (Nunes et al., 2019), (Campilho et al., 2009) and deviate from G IIC = 2.958 N/mm (Santos and Campilho, 2017) and G IIC = 2.96 N/mm (Azevedo et al., 2015). However, in the latter work, it has been stated that the value of G IIC = 2.96 N/mm is inaccurate with a negative deviation from the actual value. A possibility of such a discrepancy can be attributed to the data reduction scheme that is considered while estimation of G II component. From the below Fig. 13, it is evident that fracture toughness in Mode – I, G IC would not represent the absolute maximum. This is attributed to the presence of mode-II component at higher mode mix ratios. This alters the nature of crack propagation by mode-I component in terms of surface energy and energy dissipation – as the plastic regime extends over a wide region. Hence a non-linearity with mode-interaction could be expected. (Bui, 2011).