PSI - Issue 33

10

Derouiche Sami et al. / Procedia Structural Integrity 33 (2021) 996–1006 Author name / Structural Integrity Procedia 00 (2019) 000–000

1005

It is clear that the results shown in the table 2 and fig. 5 displays the approximation between the proposed method and the results provided from literature. From the 0° to 90° the ERR calculated with the stiffness derivative procedure with RMQ7 coincides with the different analytical results for all the angles of the same range respectfully. The error gap varies between 3,4% to 1,3% demonstrating the efficiency of the proposed method.

Table 2. ERR comparison between the SDP and the Analytical results. Angle (°) SDP(Nm/m²) Analytic (Nm/m²) (Maiti 1986)

0

79,7948

76,2940

30

69,1043

66,6276

45

56,4234

54,0661

60

39,8973

38,6244

75

20,6524

20,9613

90

6,9546

7,0000

4. Conclusion A two dimensional mixed finite element named Reissner’s Modified Quadrilateral with 7 nodes (5 displacement nodes and 2 stress nodes) is used to model a crack kinking in an orthotropic media. The RMQ7 does illustrate accurately the fracture problems related to the kinking crack with the consideration of the orthotropic nature of materials. The stiffness derivative procedure is a technique used with the RMQ7 to obtain the energy release rates and provides results with a high accuracy regarding the domain size of the application. Acknowledgements This work was supported by the Laboratory of Civil Engineering and Hydraulic (LGCH) of the University of May 8, 1945, Guelma, Algeria. References Afshar, Arman, Saeed Hatefi Ardakani, and Soheil Mohammadi. 2016. “Transient Analysis of Stationary Interface Cracks in Orthotropic Bi-Materials Using Oscillatory Crack Tip Enrichments.” Composite Structures 142:200–214. Bouzerd, Hamoudi. 1992. “Elémént Fini Mixte Pour Interface Cohérente Ou Fissurée.” Université de Claude Bernard, Lyon I, France. Bouziane, Salah, Hamoudi Bouzerd, Noureddine Boulares, and Mohamed Guenfoud. 2014. “Energy Release Rate for Kinking Crack Using Mixed Finite Element.” Structural Engineering and Mechanics 50(5):665–77. Bouziane, Salah, Hamoudi Bouzerd, and Mohamed Guenfoud. 2009. “Mixed Finite Element for Modelling Interfaces.” European Journal of Computational Mechanics 18(2):155–75. Dag, Serkan, Bora Yildirim, and Duygu Sarikaya. 2007. “Mixed-Mode Fracture Analysis of Orthotropic Functionally Graded Materials under Mechanical and Thermal Loads.” International Journal of Solids and Structures 44(24):7816–40. Derouiche, Sami, Bouziane Salah, and Bouzerd Hamoudi. 2021. “Mixed Finite Element Method for Crack Analysis in Anisotropic Materials.” Fallah, N. and N. Nikraftar. 2018. “Meshless Finite Volume Method for the Analysis of Fracture Problems in Orthotropic Media.” Engineering Fracture Mechanics 204(May):46–62.