PSI - Issue 41

T.F.C. Pereira et al. / Procedia Structural Integrity 41 (2022) 14–23 Pereira et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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3.2.4. Damage propagation criterion The power law (PW) criterion, given by Equation (5), establishes that the failure under mixed-mode conditions is determined by the interaction of the required energies to cause damage in both individual modes (tensile and shear) Eq. (5) where G I and G II are the current fracture energies in tension and shear, respectively. The power law exponent ( α ) parameter was varied to the values of 0.5, 1, 1.5 and 2, while in the literature α =1 is the most common choice. The Benzeggagh-Kenane (BK) criterion is also tested, whose three-dimensional implementation is commonly used when G IIC = G IIIC ( G IIIC represents the out-of-plane shear fracture toughness). This criterion is presented in Equation (6) ( ) S C IC IIC IC T , G G G G G G    = + −     Eq. (6) where G S = G II + G III , G T = G I + G S and η is a material parameter (in this work, η =0.5, 1 and 2.5 were tested). In this Section, the QUADS damage initiation criterion was always considered, as the benchmark criterion. Comparison with the PW criterion (  =1) results is also given. Fig. 8 presents the P m vs. L O curves for the different PW exponents. Compared against  =1 (benchmark), smaller  greatly underpredict P m , up to 23.7% for L O =25 mm. This result could be expected, since the mixed-mode G I and G II are greatly diminished by the respective PW function, when compared to a straight line. Oppositely, increasing  , although increasing P m for all L O , does not result in a major difference. Moreover,  =1.5 and 2 provides almost identical results (highest difference of 5.9% for L O =37.5 mm –  =1.5, and 7.6% also for L O =37.5 mm –  =2). Thus, it is concluded that errors by excess of this parameter do not affect the predictions by a significant amount. I G G G G  + II IC    IIC 1,           =

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P m [kN]

4

0

0

12.5

25

37.5

50

L O [mm]

PW 0.5

PW 1

PW 1.5

PW 2

Fig. 8 – Numerical P m vs. L O curves as a function of the PW exponent.

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P m [kN]

4

0

0

12.5

25

37.5

50

L O [mm]

PW 1

BK 0.5

BK 1

BK 2.5

Fig. 9 – Numerical P m vs. L O curves as a function of the BK exponent.

Fig. 9 shows the P m comparison between  =1 (benchmark) and the different η (BK criterion), as a function of L O . In this analysis, no major variations were found between the curves, and compared against the reference curve, showing a relatively small influence of η for the range of typical values for this parameter (in opposition to  ).