DOI QR코드

DOI QR Code

Modified DEBA for determining size dependent shear fracture energy of laminates

  • Goodarzi, M. Saeed (Department of Industrial, Mechanical and Aerospace Engineering, Buein Zahra Technical University) ;
  • Hosseini-Toudeshky, Hossein (Department of Aerospace Engineering, Amirkabir University of Technology)
  • 투고 : 2017.04.21
  • 심사 : 2018.05.25
  • 발행 : 2018.07.10

초록

It has been argued that fracture energy of composite laminates depends on their thickness and number of layers. In this paper a modified direct energy balance approach (DEBA) has been developed to evaluate the mode-II shear fracture energy for E-glass/Epoxy laminates from finite element model at an arbitrary thickness. This approach considers friction and damage/plasticity deformations using cohesive zone modeling (CZM) and nonlinear finite element modeling. The presence of compressive stress and resulting friction was argued to be a possible cause for the thickness dependency of fracture energy. In the finite element modeling, CZM formulation has been developed with bilinear cohesive constitutive law combined with friction consideration. Also ply element have been developed with shear plastic damage model. Modified direct energy balance approach has been proposed for estimation of mode-II shear fracture energy. Experiments were performed on laminates of glass epoxy specimens for characterization of material parameters and determination of mode-II fracture energies for different thicknesses. Effect of laminate thickness on fracture energy of transverse crack tension (TCT) and end notched flexure (ENF) specimens has been numerically studied and comparison with experimental results has been made. It is shown that the developed numerical approach is capable of estimating increase in fracture energy due to size effect.

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참고문헌

  1. Achillopoulou, D.V., Kiziridou, A.N., Papachatzakis, G.A. and Karabinis, A.I. (2016), "Investigation of interface response of reinforced concrete columns retrofitted with composites", Steel Compos. Struct., Int. J., 22(6), 1337-1358. https://doi.org/10.12989/scs.2016.22.6.1337
  2. Alfano, G. and Sacco, E. (2006), "Combining interface damage and friction in a cohesive zone model", Int. J. Numer. Methods Eng., 68(5), 542-582. https://doi.org/10.1002/nme.1728
  3. ASTM D7905/D7905M-14(2014), Standard Test Method for Determination of the Mode II Interlaminar Fracture Toughness of Unidirectional Fiber-Reinforced Polymer Matrix Composites; American Society for Testing and Materials International, West Conshohocken, PA, USA
  4. Barenblatt, G. (1959), "The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axiallysymmetric cracks", J. Appl. Math. Mech., 23(3), 622-636. https://doi.org/10.1016/0021-8928(59)90157-1
  5. Barenblatt, G.I. (1962), "The mathematical theory of equilibrium cracks in brittle fracture", Adv. Appl. Mech., 7(1), 55-129.
  6. Bocciarelli, M., Colombi, P., Fava, G. and Sonzogni, L. (2016), "Energy-based analytical formulation for the prediction of end debonding in strengthened steel beams", Compos. Struct., 153, 212-221. https://doi.org/10.1016/j.compstruct.2016.05.084
  7. Camanho, P.P., Davila, C.G. and De Moura, M.F. (2003), "Numerical simulation of mixed-mode progressive delamination in composite materials", J. Compos. Mater., 37(16), 1415-1438. https://doi.org/10.1177/0021998303034505
  8. Chaboche, J.L., Girard, R. and Schaff, A. (1997), "Numerical analysis of composite systems by using interphase/interface models", Comput. Mech., 20(1), 3-11. https://doi.org/10.1007/s004660050209
  9. Cui, W., Wisnom, M.R. and Jones, M. (1994), "An experimental and analytical study of delamination of unidirectional specimens with cut central plies", J. Reinf. Plast. Compos., 13(8), 722-739. https://doi.org/10.1177/073168449401300804
  10. Davidson, B.D., Sun, X. and Vinciquerra, A.J. (2007), "Influences of friction, geometric nonlinearities, and fixture compliance on experimentally observed toughnesses from three and four-point bend end-notched flexure tests", J. Compos. Mater., 41(10), 1177-1196. https://doi.org/10.1177/0021998306067304
  11. Girot, F., Dau, F. and Gutierrez-Orrantia, M.E. (2017), "New analytical model for delamination of CFRP during drilling", J. Mater. Process. Technol., 240, 332-343. https://doi.org/10.1016/j.jmatprotec.2016.10.007
  12. Hosseini-Toudeshky, H., Goodarzi, M.S. and Mohammadi, B. (2013), "Prediction of through the width delamination growth in post-buckled laminates under fatigue loading using de-cohesive law", Struct. Eng. Mech., Int. J., 48(1), 41-56. https://doi.org/10.12989/sem.2013.48.1.041
  13. Hosseini-Toudeshky, H., Jahanmardi, M. and Goodarzi, M.S. (2015), "Progressive debonding analysis of composite blade root joint of wind turbines under fatigue loading", Compos. Struct., 120, 417-427. https://doi.org/10.1016/j.compstruct.2014.10.025
  14. Kharazan, M., Sadr, M.H. and Kiani, M. (2014), "Delamination growth analysis in composite laminates subjected to low velocity impact", Steel Compos. Struct., Int. J., 17(4), 387-403. https://doi.org/10.12989/scs.2014.17.4.387
  15. Kim, N., Kim, Y.H. and Kim, H.S. (2015), "Experimental and analytical investigations for behaviors of RC beams strengthened with tapered CFRPs", Struct. Eng. Mech., Int. J., 53(6), 1067-1081. https://doi.org/10.12989/sem.2015.53.6.1067
  16. Krueger, R. (2004), "Virtual crack closure technique: history, approach, and applications", Appl. Mech. Rev., 57(2), 109-143. https://doi.org/10.1115/1.1595677
  17. Lin, G., Geubelle, P.H. and Sottos, N.R. (2001), "Simulation of fiber debonding with friction in a model composite pushout test", Int. J. Solids Struct., 38(46), 8547-8562. https://doi.org/10.1016/S0020-7683(01)00085-3
  18. van der Meer, F.P.P. and Sluys, L.J.J. (2013), "A numerical investigation into the size effect in the transverse crack tension test for mode II delamination", Compos. Part A Appl. Sci. Manuf., 54, 145-152. https://doi.org/10.1016/j.compositesa.2013.07.013
  19. Van Paepegem, W., De Baere, I. and Degrieck, J. (2006), "Modelling the nonlinear shear stress-strain response of glass fibre-reinforced composites. Part I: Experimental results", Compos. Sci. Technol., 66(10), 1455-1464. https://doi.org/10.1016/j.compscitech.2005.04.014
  20. Rybicki, E.F. and Kanninen, M.F. (1977), "A finite element calculation of stress intensity factors by a modified crack closure integral", Eng. Fract. Mech., 9(4), 931-938. https://doi.org/10.1016/0013-7944(77)90013-3
  21. Shi, Y. and Soutis, C. (2016), "Modelling transverse matrix cracking and splitting of cross-ply composite laminates under four point bending", Theor. Appl. Fract. Mech., 83, 73-81. https://doi.org/10.1016/j.tafmec.2015.11.006
  22. Shiming, C. and Huifen, Z. (2012), "Numerical analysis of the axially loaded concrete filled steel tube columns with debonding separation at the steel-concrete interface", Steel Compos. Struct., Int. J., 13(3), 277-293. https://doi.org/10.12989/scs.2012.13.3.277
  23. Sun, X. and Davidson, B.D. (2005), "A direct energy balance approach for determining energy release rates in three and four point bend end notched flexure tests", Int. J. Fract., 135(1), 51-72. https://doi.org/10.1007/s10704-005-3746-9
  24. Sun, X. and Davidson, B.D. (2006), "Numerical evaluation of the effects of friction and geometric nonlinearities on the energy release rate in three-and four-point bend end-notched flexure tests", Eng. Fract. Mech., 73(10), 1343-1361. https://doi.org/10.1016/j.engfracmech.2005.11.007
  25. Turon, A., Costa, J., Camanho, P.P. and Davila, C.G. (2007), "Simulation of delamination in composites under high-cycle fatigue", Compos. Part A Appl. Sci. Manuf., 38(11), 2270-2282. https://doi.org/10.1016/j.compositesa.2006.11.009
  26. Tvergaard, V. (1990), "Effect of fibre debonding in a whiskerreinforced metal", Mater. Sci. Eng. A., 125(2), 203-213. https://doi.org/10.1016/0921-5093(90)90170-8
  27. Wisnom, M.R. (1992), "On the increase in fracture energy with thickness in delamination of unidirectional glass fibre-epoxy with cut central plies", J. Reinf. Plast. Compos., 11(8), 897-909. https://doi.org/10.1177/073168449201100802