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. Results and Discussion 4.1. Determination of strain energy release rate (SERR)

The SERR in the present work was determined by two different methods namely J-integral and ECLM. Based on the angular rotation of the load introduction points in DCB and MMB tests (with different mixed-mode ratios), SERR was determined. The determined angular rotations recorded by inclinometers installed on the load introduction points were employed in Equations (6) and (7) respectively to determine the SERR for DCB and MMB tests for any adhesive layer thickness. The repetitions of load-displacement of all the specimens showed a good agreement. The data reduction method J-integral used in the present work needs also the recorded load data during the tests. The J-integral used is not dependant on the elastic properties of the adhesive, adherents, crack measurements, compliance of the system, etc. which can hugely reduce the accuracy of the measured fracture energies. As previously discussed, a closed-form relation (namely ECLM) based on the equivalent flexural modulus and the equivalent crack length was developed for MMB test and used in the present work. Apart from the developed closed form formulae for MMB tests, for DCB tests carried out in the present work another closed-form formula previously developed by de Moura et al. (Moura et al., 2008) was used for determination of SERR of the adhesive used. In ECLM, crack growth is measured using experimental compliance data targeting to consider the fracture process zone formed ahead of the crack tip. Therefore, ECLM evades complications existing in the classical methods for measuring crack propagation length which always brings error in the measurements. However, the ECLM in comparison with J-integral approach needs more workaround such as determination of crack length correction, etc. Fig. 10 and Fig. 11 represent the comparative crack resistance curve (R-curve) based on ECLM and J-integral for different mixed-mode ratios for the adhesive thickness of t=0.35 and 1.0 mm respectively. As it is shown, the two methods for determination of fracture energy show a very good agreement with each other.

Fig. 10. Comparative of J-Integral vs ECLM for SERR-t=0.35 mm (top left) DCB, (top right),(bottom left), and (bottom right) MMB tests with 25, 50 and 75% MMR respectively.