PSI - Issue 2_A

Alberto Sapora et al. / Procedia Structural Integrity 2 (2016) 1975–1982

1981

Sapora et al. / Structural Integrity Procedia 00 (2016) 000–000

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3. Conclusions

It was shown that T -stress effects reveal to be more significant for i) sufficiently high T -magnitudes; ii) prevailing mode II conditions; iii) less brittle materials (i.e., higher l ch ). Indeed, for a specific test, since all the parameters K I , K II and T generally vary as the mode mixity ψ varies, the real impact of T -stress on predictions should be discussed from case to case, after evaluating these three parameters. Whereas for mode I loading conditions the crack propagation reveals to be unstable for τ ≥ 0 . 42, for mode II loading conditions a singular behavior was observed for τ ≤ − 0 . 325.

Acknowledgements

The financial support of V Plan Propio de Investigacio´n de la Universidad de Sevilla (Modalidad I.6C), the Spanish Ministry of Economy and Competitiveness and European Regional Development Fund (Project MAT2012-37387), the Junta de Andaluca and the European Social Fund (Project TEP-04051) are also gratefully acknowledged. Eventually, Dr. Alberto Sapora acknowledges the hospitality of Universidad de Sevilla, where this work was mostly accomplished.

Appendix A. Angular functions

The following equations hold for what concerns the angular functions related to the stress field:

f I θθ ( θ ) = cos

3 ( θ / 2 ) ,

f II θθ ( θ ) = − 3sin ( θ / 2 ) cos

2 ( θ / 2 )

(A.1)

whereas the approximating expressions for the functions β in Eq. (4) and (5) can be found in Amestoy and Leblond (1992), with m = θ / π :

β 11 = 4 . 1 m 20 + 1 . 63 m 18 − 4 . 059 m 16 + 2 . 996 m 14 − 0 . 0925 m 12 − 2 . 88312 m 10 + 5 . 0779 m 8 + +( π 2 / 9 − 11 π 4 / 72 + 119 π 6 / 15360 ) m 6 +( π 2 − 5 π 4 / 128 ) m 4 − 3 π 2 m 2 / 8 + 1 ,

(A.2)

19 + 4 . 21 m 17 − 6 . 915 m 15 + 4 . 0216 m 13 + 1 . 5793 m 11 − 7 . 32433 m 9 + 12 . 313906 m 7 +

β 12 = 4 . 56 m

(A.3)

+( − 2 π − 133 π 3 / 180 + 59 π 5 / 1280 ) m 5 +( 10 π / 3 + π 3 / 16 ) m 3 − 1 . 5 π m ,

19 − 3 . 95 m 17 + 4 . 684 m 15 − 2 . 07 m 13 − 1 . 534 m 11 + 4 . 44112 m 9 − 6 . 176023 m 7 +

β 21 = − 1 . 32 m

(A.4)

+( − 2 π / 3 + 13 π 3 / 30 − 59 π 5 / 3840 ) m 5 − ( 4 π / 3 + π 3 / 48 ) m 3 + π / 2 m ,

β 22 = 12 . 5 m 20 + 0 . 25 m 18 − 7 . 591 m 16 + 7 . 28 m 14 − 1 . 8804 m 12 − 4 . 78511 m 10 + 10 . 58254 m 8 + +( − 32 / 15 − 4 π 2 / 9 − 1159 π 4 / 7200 + 119 π 6 / 15360 ) m 6 +( 8 / 3 + 29 π 2 / 18 − 5 π 4 / 128 ) m 4 − ( 4 + 3 π 2 / 8 ) m 2 + 1 , (A.5)

20 − 2 . 85 m 18 + 10 . 947 m 16 − 7 . 314 m 14 − 6 . 0205 m 12 + 26 . 66807 m 10 − 50 . 70880 m 8 +

β 1 = − 13 . 7 m

(A.6)

+ 63 . 665987 m 6 − 47 . 93339 m 4 +( 2 π ) 3 / 2 m 2 ,