PSI - Issue 28

Mor Mega et al. / Procedia Structural Integrity 28 (2020) 917–924 M. Mega and L. Banks-Sills / Structural Integrity Procedia 00 (2019) 000–000

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a failure curve with a 10% probability of unexpected failure and a 95% confidence. The statistical two-dimensional criterion is also plotted in Fig. 3 as a dashed curve. Also in that figure, from BD tests described in [16], which resulted with ˆ ψ ≈ 1 . 44 rad, an average G ic value with error bars representing the standard deviation (SD), are plotted in green. The average values and SDs of the results obtained here by means of BT and the J -integral for the C-ELS NPC spec imens with the visually observed load in Table 1, are also presented in Fig. 3 in red and blue, respectively. Note that both values were plotted for the same ˆ ψ which was obtained based on the two-dimensional FEA results by means of VCCT. It may be observed in Fig. 3 that the average G ic value obtained by means of the BT method is similar to the average obtained from the BD tests [17]. It may be noted that it was previously shown in [24] for a UD material that the BT method results in an upper bound for the energy release rate value. From Fig. 3, it may also be observed that the average G ic value obtained by means of the J -integral is similar to the value obtained using the statistical failure curve. It is important to note that the numerical analysis takes into account the two dissimilar ply properties above and below the considered interface, whereas the BT method does not. Hence, a more accurate result is expected for the J -integral. However, since a two-dimensional analysis was carried out here, whereas the statistical analysis is based on an average through the thickness of three-dimensional results, the value obtained by the J -integral may provide a lower bound for G ic . 4. Conclusions In this investigation, results from six C-ELS NPC tests were reported. Two-dimensional FEAs were carried out and the stress intensity factors ˆ K 1 and ˆ K 2 , defined in eq. (7), were obtained for each test by means of DE and VCCT. The in-plane phase angles ˆ ψ were calculated by means of eq. (6) to be approximately 1.45 rad which demonstrates that the C-ELS tests result in a dominant ˆ K 2 value. The critical initiation interface energy release rate G ic was calculated by means of one numerical and two analytical methods, namely, J -integral, ECM and BT, respectively. For the ECMmethod in eqs. (1) and (3), since a small number of propagation data points are obtained from the C-ELS NPC test, inaccurate results for G ic were obtained. It was concluded that this method is not suitable for determining G ic for such tests. The results from the BT method in eqs. (4) and the area J -integral were compared with those from previously tested BD specimens [16], as well as with a ’5 branch’ two-dimensional deterministic and statistical criterion [17]. It was observed from this comparison that the average G ic value obtained by means of the BT method was similar to the average result obtained from the BD tests and to the value calculated by means of the ’5 branch’ criterion for ˆ ψ ≈ 1 . 44 ( ˆ L = 100 µ m). It may be concluded that this method provides an upper bound for G ic with ˆ K 2 dominant. The average G ic value obtained by means of the J -integral was similar to the value calculated by means of the statistical criterion. Note that the statistical criterion is based on data from three-dimensional analyses, whereas here, the J -integral was calculated from two-dimensional FEAs. It appears that this method provides a lower bound for G ic with ˆ K 2 dominant. In [18], the same material and interface was tested using DCB specimens to obtain nearly mode I fracture toughness values. It was observed from a comparison of these results with those from the BD tests with ˆ K 1 dominant that higher G Ic values are obtained for the DCB specimens which are much thinner than the BD specimens [16]. Note that the C ELS NPC specimens used here were made from same batch of material tested in [18] for the DCB specimens. Hence, both specimen types had a similar thickness of approximately 5 mm; whereas, the thickness of the BD specimens was approximately 15 mm. From the comparison shown here for dominant ˆ K 2 , it may be observed that the thickness of the specimens did not influence G ic . The average G ic values which were calculated by means of BT or the J -integral methods were found to be in the range between the statistical and the deterministic criterion which are based upon the BD test results. It may be concluded that the critical initiation G ic value is dependent on specimen thickness for the case of dominant ˆ K 1 ; but no influence was observed for the case of dominant ˆ K 2 . In the future, fracture resistance curves or R -curves which relate the energy required for a delamination to propagate G iR to the delamination extension ∆ a will be determined from C-ELS propagation tests for the NPC specimens presented here.

5. Acknowledgment

We would like to express our gratitude to Dr. Victor Fourman for his assistance during the tests. This project was supported by the Israel Ministry of Science, Technology and Space, Grant No. 0605405591.