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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Table 2. Stress intensity factors ˆ K m ( m = 1 , 2) and phase angles ˆ ψ for each C-ELS NPC specimen, calculated by means of VCCT with ˆ L = 100 µ m. ˆ K 1 (MPa √ m) ˆ K 2 (MPa √ m) ˆ ψ (rad) CELS-2-2 0.36 2.86 1.44 CELS-2-3 0.37 2.98 1.45 CELS-2-4 0.38 3.02 1.45 CELS-2-5 0.35 3.18 1.46 CELS-2-6 0.35 2.79 1.45 CELS-2-7 0.32 2.55 1.44 and at the deflection point the degree of freedom in the x 1 -direction was fixed. The area J -integral was calculated in each analysis and presented in the fourth, eighth and twelfth columns of Table 1 for the NL, visual, and 5% o ff set or maximum initiation loads, respectively. Di ff erences in the results obtained by means of the BT and the J -integral methods with respect to the J -integral were calculated as %di ff = G BT ic − G J ic G J ic × 100% . (9) The di ff erences are presented in the fifth, ninth and thirteenth columns of Table 1 and were found to be approximately 24.5%. The FEA results were also used to calculate the stress intensity factors, defined in eq. (7), by means of DE [16] and VCCT [22]. Maximum di ff erences of 7% and 1% were observed for ˆ K 1 and ˆ K 2 , respectively, between the results obtained by the two methods with ˆ L = 100 µ m. Since VCCT is considered to be more accurate, the normalized ˆ K m ( m = 1 , 2) values obtained using this method are presented in Table 2. From the results, by means of eq. (6), the in-plane phase angle ˆ ψ was calculated and found to be between 1.44 rad and 1.46 rad for all specimens. It may be observed, as expected, that ˆ K 2 is dominant for the C-ELS NPC tests of this material and interface. In a previous investigation [16], the same material and interface were tested under various mixed mode deforma tions using the BD specimen. Two and three-dimensional failure criteria were proposed for this material in [17]. One of these is the two-dimensional ’5 branch’ criterion, presented in Fig. 3 as the solid curve. Note that this criterion was obtained by means of three-dimensional FEAs with all results throughout the specimen thickness projected onto the plane for which K III = 0. Also in [17], a statistical analysis was carried out for the ’5 branch’ criterion to obtain

Fig. 3. Averaged initiation energy release rate values obtained from C-ELS NPC tests by means of the J -integral and eq. (8), as well as results from BD tests [16] plotted versus the ’5-branch’ failure criterion and statistical criterion which were proposed in [17] as a function of ˆ ψ for ˆ L = 100 µ m.