PSI - Issue 13

Lukas Loh et al. / Procedia Structural Integrity 13 (2018) 1318–1323 Author name / Structural Integrity Procedia 00 (2018) 000–000

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Fig. 2. Test-setup in loaded state of MC-DCB specimen.

Fig. 3. ERR plotted over α for di ff erent angular velocities.

3.1. Verification of artificial contributions to J-integral

In section 2, the unintended artificial contributions to J -integral has been found to result from support / loading conditions of the MC-DCB test. Since the test is controlled on terms of J I and J III , the artificial contributions need to be negligible. For verification, Fig. 4 quantifies J I ∗ / ( J I + J III ) and J I + II / ( J I + J III ) as functions of J / ( J max ) for di ff erent constant mode-mixities. Thereby, J max denotes the maximum value of J . At the beginning of experiments, ratios of J I ∗ / ( J I + J III ) and J I + II / ( J I + J III ) are above 10%. This is caused by marginal manufacturing imperfections and own weight of the specimen in combination with supporting conditions. The lateral moments M x and M z already occurs during clamping procedure prior to start of testing while J I and J III are nearly zero at this point. This yields high percentage of artificial contributions, which seems to be not of negligible order of magnitude. At the performed test-series for M x , and M z , magnitudes of approximately < ± 5 Nm has been observed at the beginning of experiment. In comparison, the amount on J I ∗ contribution in case of pure mode I loading ( χ = 0 ◦ ) is obviously higher and the J I + II contribution is lower as in other mode-mixities. Due to loading, substrates are getting separated and F y must be taken into account. Regarding mode I loading, no separation of substrates in out-of-plane-direction occurs. Resultingly, M x rests unchanged and J I ∗ yields high contributions during tests. In comparison to other mixed mode ratios, contributions of J I and J II are relatively low. The moment resulting from own weight and the moment arising due to F y acting around z-axis cancel each other out, while they strengthen themselves for several other mixed modes. Just for the case of mode I loading, amount of J I ∗ is negligible later in the course of the ongoing experiment. Regarding all other cases, amounts of J I ∗ are less than approximately 3% and are furthermore tending towards zero. Hence, contribution of J I ∗ as well as J I − II can be classified to be negligible and the mode-mixities, besides mode I, do not influence artificial contributions. 3.2. Dependency of critical ERR on mode-mixity This section deals with evaluation of critical ERR regarding mode-mixity I + III realized on MC-DCB tests. Sub sequently, results are compared to literature dealing with Mixed-Mode-Bending (MMB) tests, where mode-mixity is defined by combining mode I and II. 3.2.1. Results of MC-DCB tests As previously explained, critical ERR J c has been calculated by averaging over plateau-values of J (viz. Fig 3). Fig. 5 shows the behavior of J c with respect to performed tests on constant mixed-mode ratios χ as well as the results of variable mode-mixity χ I − III . For latter mentioned tests, variable mixed-mode has been achieved by introducing pure