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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mode I loading until crack propagation took place. Afterwards, mode III loading was superimposed at this stage of mode I separation. It can be stated that in range of scatter within χ = 30 ◦ and χ = 75 ◦ , values of constant J c strongly coincide with those of variable mode-mixity. Near pure modes I and III, critical values of J c are slightly higher. This can be explained by evaluation method of constant mixed-mode where the entire range of plateau values has been averaged. In case of variable mixed-mode, actual value of J c has been plotted only. Within χ = 0 ◦ and χ = 60 ◦ , values of J c has been detected to be constant nearly between 3-5 kJ / m 2 . Nevertheless, it is obvious that the critical ERR for χ = 90 ◦ (pure mode III) is above those for χ = 0 ◦ (pure mode I). Hence, a factor of approximately 5 can be observed in between both. Furthermore, the calculation of critical ERR also holds for the particular contributions of J I and J III , denoted with J Ic and J IIIc . Therefore, in Fig. 6, J IIIc is plotted with respect to J Ic for several constant mode-mixities (depicted with black dots). This quantifies the particular contributions to J c and is therefore denoted fracture envelope.

Mode-mix ratio: 00°

Mode-mix ratio: 15°

0.1

0.1

J I* / (J I + J III ) J I-II / (J I + J III )

J I* / (J I + J III ) J I-II / (J I + J III )

0.05

0.05

0

0

0

0.1

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0.5

0.6

0

0.1

0.2

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0.6

Percentage (-)

Percentage (-)

J / J max (-)

J / J max (-)

Mode-mix ratio: 30°

Mode-mix ratio: 45°

0.1

0.1

J I* / (J I + J III ) J I-II / (J I + J III )

J I* / (J I + J III ) J I-II / (J I + J III )

0.05

0.05

0

0

0

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0.6

0

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Percentage (-)

Percentage (-)

J / J max (-)

J / J max (-)

Mode-mix ratio: 60°

Mode-mix ratio: 75°

0.1

0.1

J I* / (J I + J III ) J I-II / (J I + J III )

J I* / (J I + J III ) J I-II / (J I + J III )

0.05

0.05

0

0

0

0.1

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0.6

0

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Percentage (-)

Percentage (-)

J / J max (-)

J / J max (-)

Mode-mix ratio: 85°

Mode-mix ratio: 90°

0.1

0.1

J I* / (J I + J III ) J I-II / (J I + J III )

J I* / (J I + J III ) J I-II / (J I + J III )

0.05

0.05

0

0

0

0.1

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0

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Percentage (-)

Percentage (-)

J / J max (-)

J / J max (-)

Fig. 4. Artificial contributions to J -integral of tested constant mode-mixities.

3.2.2. Comparison to results of MMB-tests and discussion As previously mentioned, the MMB-test is used to investigate fracture behavior under mixed-mode I + II. A detailed description on test-conditions can be found in Stamoulis et al. (2014). Since both, the MMB- as well as the MC DCB test considers a combination of ”shear” (mode II respectively mode III) and ”peel” (mode I) mode-mixity, a comparison can be undertaken. Stamoulis et al. (2014) investigated the adhesive SikaPower R -498 as well, where mode-mixity has been applied using the MMB-test. Thereby, four ratios of mixed-mode has been investigated on MMB-tests while tests on pure mode I loading has been carried out by tapered DCB tests (viz. BS 7991:2001 (2009); ISO 25217 (2009)). The results are plotted colored in red in Fig. 6. In comparison, two observation can be stated: Stamoulis et al. (2014) have been determined a plateau value of approximately J IIc = 2 kJ / m 2 , which cannot be observed for results of MC-DCB test. This could be caused due to the test conditions, since the evaluation method of MMB tests is based on linear elastic fracture mechanics (LEFM). Furthermore, values of critical ERR on MMB-tests are distinctly higher than those of MC-DCB tests. The reasons for that may be found in di ff erences in the adhesive layer thickness. Stamoulis et al. (2014) has been applied a nominal layer thickness of 0.5 mm in contrast to 0.3 mm used in this work. Distinctive influence of layer thickness on fracture behavior has already been stated out in Marzi et al. (2011). Therefore, it cannot be decided at the moment if there is a coincidence of mode-mixity I + III and I + II.