Issue 48

F. V. Antunes et alii, Frattura ed Integrità Strutturale, 48 (2019) 676-692; DOI: 10.3221/IGF-ESIS.48.64 686 The P-criterion  20  considers the accumulated elastic strain energy (P) within a circular core with radius r 0 around the crack tip as the driving parameter. P-factor is given by: 2 2 P λ K λ K 1 I 3 II   (11) being  1 =0.0000191419 and  3 =0.0000300746, as indicated by Pavlou et al.  20  . The crack is assumed to propagate along direction of minimum P-factor. Another two criteria were used here: the maximum value of K I (K I -criterion) and the minimum value of energy release rate (G-criterion), being G obtained from effective stress intensity factor defined in Eqn. 8. Fig. 10a presents the results obtained for  =60º considering different criteria and crack propagation increments of 0.5 mm. Loading direction is also presented. It can be seen that all criteria, except J-criterion, predict crack slopes lower than experimentally observed. Best predictions were obtained with P-criterion and G criterion, which gave similar results. Finally, Fig. 10b presents the variation of crack tip slope (  ) with crack propagation. It can be seen that  reduces with crack propagation. The rate of variation of  with crack growth predicted numerically is similar to that measured experimentally. C ONCLUSIONS he main conclusions of the present work are: - K I , K II stress intensity factor solutions were obtained numerically for CTS (Compact Tension Shear) specimen. These solutions are valid for a wide range of x, y,  (load direction) and  (crack tip angle):  0, 60º  ; x/W   0.4, 0.75 mm  ; y/W   0, 0.167  . - The average accuracy of K V is expected to be 1.01 %; - The solution developed was applied to crack profiles obtained experimentally in 6082-T6 aluminium alloy. As expected, significant differences were found between present solution and Richard’s solution when  is different from zero. The differences reduce significantly when the whole crack length is used in Richard’s solution; - Experimental work was developed to study fatigue crack growth in CTS specimens. The cracks always adopted a direction approximately normal to loading direction, i.e., tend to propagate under mode I loading; - The solution developed here was used to predict crack growth direction considering different criteria. Best predictions were obtained with P-criterion and G-criterion. By request the authors will send by e-mail the solution developed here, implemented in an Excel file. A KNOWLEDGEMENTS his research is sponsored by FEDER funds through the program COMPETE (under project T449508144- 00019113) and by national funds through FCT – Portuguese Foundation for Science and Technology, under the project PTDC/EMS-PRO/1356/2014. R EFERENCES [1] Richard, H.A. (1981). A new compact shear specimen, International Journal of Fracture, 17, pp. R105-R107. [2] Biner, S.B. (2001). Fatigue Crack Growth Studies Under Mixed-mode Loading, International Journal of Fatigue, 23, pp. S259-S263. [3] Borrego, L.P., Antunes, F.V., Ferreira, J.M. and Costa, J.D. (2004). Mixed-mode fatigue crack growth and closure in aluminium alloys, Proc. 7th ICBMFF- Seventh International Conference on Biaxial/Multiaxial Fatigue  Fracture, Berlin, Germany, pp.1483-488. [4] Rikards, R. et al. (1998). Investigation of mixed Mode I/II Interlaminar Fracture Toughness of Laminated Composites by Using a CTS Type Specimen, Engineering Fracture Mechanics, 61, pp. 325-342. [5] Madhusudhana, K.S. and Narasimhan, R. (2002). Experimental and numerical investigations of mixed mode crack growth resistance of a ductile adhesive joint, Engineering Fracture Mechanics, 69, pp. 865-883. T T