PSI - Issue 2_B

Moslem Shahverdi et al. / Procedia Structural Integrity 2 (2016) 1886–1893 Shahverdi et al./ Structural Integrity Procedia 00 (2016) 000–000

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lengths ranging from 227 to 60 mm. Nominal G I / G II ratios for crack propagation corresponding to c =227-60 mm were 3.70, 2.20, 1.08, and 0.28 respectively, and are higher than the corresponding nominal values, 2.21, 1.02, 0.31, and 0.00, calculated according to ASTM D 6671-01 by considering a symmetric joint configuration. The mode partitioning results according to the EGM and the non-linear FE analyses are shown in Figure 6 right. Similar mode partition was achieved using these two methods. The EGM is more practical because it provides the fracture mode partition under mixed-mode loading conditions based on closed form equations with their parameters obtained directly from the experiments. In contrast, the use of the FE method requires the establishment of complex models containing parameters that must be estimated via iterative trial and error procedures.

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Experimental compliance method

G tot

Extended global method Finite element method

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G I

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G (J/m 2 )

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G II

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Figure 5. Right: Load and crack length vs. load-point displacement for a MMB specimen with c=227 mm, Left: G versus crack length from same specimen determined by extended global and experimental compliance methods and finite element modeling

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G II-EGM G II-tip G II-br G II-FE

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G I-EGM G I-tip G I-br G I-FE

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G II (J/m 2 )

G I (J/m 2 )

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Crack length (mm)

Crack length (mm)

Figure 6. Separation of G into G tip and G br , c=227 mm, (a) G I and (b) G II The G I and G II curves shown in Figure 6 are expressed as the sum of the energy release rate at the crack tip, G tip , and the contribution of the fiber bridging, G br . Fiber bridging results in an increase of G with increasing crack length. This phenomenon is expressed by the R-curve that follows an initially increasing trend before reaching a plateau as from which the bridging length remains constant. Using the presented FE models, it was possible to compute the G tip and G br for the representative specimens. The summation of these two values, shown as “ G I-FE and G II-FE ” in Figure 6, was in good agreement with the experimentally derived values according to the “extended global method”. The contribution of the fiber bridging was not constant, depended on the G I / G II and decreased as the G I / G II decreased. The G br / G ratio was around 60%, 55%, 52%, and 45% for c equal to, 227, 150, 100, and 60 mm respectively. 5. Conclusions A new approach, designated as the “extended global method”, was introduced and used for mode partitioning of asymmetric crack propagation and the analysis of the experimental data. The introduced “extended global method” is able to accurately determine the energy release rate and mode-mixity ratios from a set of closed form equations.