Finite Element Analyzing of the Effect of Crack on Mechanical Behavior of Honeycomb and Re-entrant Structures

Öz

Developments in technology require the new materials, lighter and more efficient structures and also new manufacturing methods. In this study, after doing researches about topology optimization, regular honeycomb and re-entrant structures; the regular honeycomb and re-entrant structures were designed, and then Ti-6Al-4V material was chosen for these structures in finite element (FE) analyzing. The three different rib thickness values (t) of 1 mm, 1.5 mm and 2 mm were assigned for honeycomb and re-entrant structures in FE analyses. Also, the crack was created on the models, and then 2-D FE analyses were done for both cracked and un-cracked honeycomb and re-entrant structures under tensile forces through y axis. Afterwards, the effect of crack on stress intensity factor, stresses, strains and displacement were obtained and characterized the auxetic behavior of the regular honeycomb and re-entrant structures. Furthermore, increase in rib thickness decreases stress and strains for each structure. Moreover, re-entrant structures have negative Poisson’s ratio due to their geometric properties and the notable effect of crack on the equivalent stress in re-entrant was emerged in comparison with honeycomb structure.  As a result, the only possible fracture in honeycomb for thickness of 1 mm might be observed owing to stress intensity factor obtained from analyses bigger than fracture toughness of honeycomb structure.    

Anahtar Kelimeler

• Auxetic behavior,crack,negative Poisson’s ratio,stress intensity factor

Kaynakça

1. [1] Lakes R., “Foam structures with a negative Poisson’s ratios”, Science, 235:1038–1040, (1987)
2. [2] Undershill R.S., “Defense applications of auxetic materials”, Advanced Materials, 1(1):7-12, (2014)
3. [3] Novak N., Vesenjak M., Ren Z, “Auxetic cellular materials - a review”, Journal of Mechanical Engineering, 62(9): 485-493, (2016)
4. [4] Scarpa F., Smith F.C., “Passive and MR fluid-coated auxetic PU foam –mechanical, acoustic, and electromagnetic properties”, Int. Journal Mater. Syst. Struct., 15: 973–979, (2004)
5. [5] Yang L., Harrysson O., West H., Cormier D., “Mechanical properties of 3D re-entrant honeycomb auxetic structures realized via additive manufacturing”, Int. Journal of Solids and Structures, 69–70: 475–490, (2015)
6. [6] Choy Y.S., Sun C.N., Leonga K.F., Weia J., “Compressive properties of Ti-6Al-4V lattice structures fabricated by selective laser melting: Design, orientation and density”, Additive Manufacturing, 16: 213–224, (2017)
7. [7] Yan C., Hao L., Hussein A., Young P., Raymont D., “Advanced lightweight 316Lstainless steel cellular lattice structures fabricated via selective laser melting”, Materials&Design, 55: 533–541, (2014)
8. [8] Prawota Y., “Solid Mechanics for Materials Engineers: Auxetic Materials Seen from the Mechanics Point of View, Chapter 15”, USA (2013).

9. [9] Alderson A., and Alderson K.L., “Auxetic materials”, Journal of Aerospace Engineering, 221 G: 565-575, (2007)
10. [10] Budarapu P.R., Sudhir Sastry Y.B., Natarajan R., “Design concepts of an aircraft wing: composite and morphing airfoil with auxetic structures”, Front. Struct. Civ. Eng., 10(4): 394–408, (2016)
11. [11] Critchley R., Corni I., Wharton J.A., Walsh F.C., Wood R.J.K., Stokes K.R., “The preparation of auxetic foams by three-dimensional printing and their characteristics”, Adv. Eng. Mat., 15 (10): 980–985, (2013)
12. [12] Maiti K., Ashby M.F., Gibson L.J., “Fracture toughness of brittle cellular solids”, Scripta Metallurgica, 18: 213-217, (1984)
13. [13] Green D., “Fabrication and mechanical properties of lightweight ceramics produced by sintering of hollow spheres”, Journal of Am. Ceram. Soc., 68: 403–409, (1985)
14. [14] Choi J., and Lakes R, “Fracture toughness of re-entrant foam materials with a negative Poisson’s ratio: Experiment and analysis”, Int. Journal of Fracture, 80: 73–83, (1986)
15. [15] Yang L., Harrysson O., West H., Cormier D., “Compressive properties of Ti–6Al–4V auxetic mesh structures made by electron beam melting”, Acta Materialia, 60: 3370–3379, (2012)
16. [16] Ingrole A., Hao A., Liang R., “Design and modeling of auxetic and hybrid honeycomb structures for in-plane property enhancement”, Materials & Design, 117: 72–83, (2017)
17. [17]http://www.mse.mtu.edu/~drjohn/my4150/honey/h1.html
18. [18] Vogiatzis P., Chen S., “Topology optimization of 3d auxetic meta materials using reconciled level-set method”, Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, USA (1986).
19. [19] Zhou Z., Zhou J., Fan H., “Plastic analyses of thin-walled steel honeycombs with re-entrant deformation style”, Materials Science & Engineering, A 688: 123–133, (2017)
20. [20] Bates S.R.G, Farrow I.R., Trask R.S, “3D printed polyurethane honeycombs for repeated tailored energy absorption”, Materials &Design, 112: 172–183, (2016)
21. [21] Carneıro V.H., Meıreles J., Puga H., “Auxetic materials – a review”, Materials Science-Poland, 31(4): 561-571, (2013)
22. [22] Argatov I.I., Diaz R.G., Sabina F.J., “On local indentation and impact compliance of isotropic auxetic materials from the continuum mechanics viewpoint”, Int. Journal of Engineering Science, 54: 42-57, (2012)
23. [23] Bianchi M., Scarpa F., Smith C.W., “Shape memory behaviour in auxetic foams: Mechanical properties”, Acta Materilia, 58: 858–865, (2010)
24. [24] Yalçın B., and Ergene B., “Analyzing the effect of crack in different hybrid composite materials on mechanical behaviors”, Pamukkale University Journal of Engineering Sciences, 24(4): 616-625, (2018)
25. [25] Akkuş H., Düzcükoğlu H., and Şahin Ö.S., “Experimental research and use of finite elements method on mechanical behaviors of honeycomb structures assembled with epoxy-based adhesives reinforced with nanoparticles”, Journal of Mechanical Science and Technology,31(1): 165-170, (2017)
26. [26] Usman Aslam M., Darwish S.M., “Development and analysis of different density auxetic cellular structures”, Int. Journal on Recent and Innovation Trends in Computing and Communication, 3(1): 27-32, (2015)
27. [27] Hertzberg R.W., “Deformation and Facture Mechanics of Engineering Materials”, 3. Edition, John Wiley, USA, (1989)
28. [28] Schmidt I., Fleck N.C., “Ductile fracture of two dimensional cellular structures”, International Journal of Fracture, 111: 324-342, (2001)
29. [29] Ravirala N., Alderson A, Alderson K, and Davies P., “Auxetic polypropylene films”, Polym. Eng. and Sci., 45: 517-528, (2005)
30. [30] Rehme O., Emmelmann C., “Selective laser melting of honeycombs with negative poisson’s ratio”, Journal of Laser Micro/Nanoengineering, 4(2): 128-134, (2009)
31. [31] Gibson L.J., Ashby M.F., Schajer G.S., Robertson C.I., Proc. R. Soc. Lond. A, 382, 25, (1982)
32. [32] Joseph N.G., Oliveri L., Attard D., Ellul B., Gatt R., Cicala G. and Recca G., “Hexagonal honeycombs with zero poisson’s ratios and enhanced stiffness”, Advanced Engıneerıng Materıals, 12(9): 855-862, (2010)
33. [33] Osama A.M.A, and Darwish S.M.H., “Analysis, fabrication and a biomedical application of auxetic cellular structures”, International Journal of Engineering and Innovative Technology, 2 (3), ( 2012)
34. [34] Lee J., Choi J.B., and Choi K., “Application of homogenization FEM analysis to regular and re-entrant honeycomb structures”, Journal of Materials Science, 31: 4105- 4110, (1996)
35. [35] Whitty J.P.M., Nazare F., and Alderson A., “Modelling the effects of density variations on the in-plane poisson's ratios and young's moduli of periodic conventional and re-entrant honeycombs - part 1: Rib thickness variations”, Cellular Polymers, 21(2): 69-98, (2005)
36. [36] Greaves G.N., Greer A.L., Lakes R.S., and Rouxel T., “Poisson’s ratio and modern materials”, Nature Materials, 10: 823-838, (2011)