Structural Engineering and Mechanics

  • 제72권6호
  • /
  • Pages.713-722
  • /
  • 2019
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A 3D RVE model with periodic boundary conditions to estimate mechanical properties of composites

  • 투고 : 2019.05.10
  • 심사 : 2019.08.03
  • 발행 : 2019.12.25
⟨ 이전 논문 다음 논문 ⟩

초록

Micromechanics is a technique for the analysis of composites or heterogeneous materials which focuses on the components of the intended structure. Each one of the components can exhibit isotropic behavior, but the microstructure characteristics of the heterogeneous material result in the anisotropic behavior of the structure. In this research, the general mechanical properties of a 3D anisotropic and heterogeneous Representative Volume Element (RVE), have been determined by applying periodic boundary conditions (PBCs), using the Asymptotic Homogenization Theory (AHT) and strain energy. In order to use the homogenization theory and apply the periodic boundary conditions, the ABAQUS scripting interface (ASI) has been used along with the Python programming language. The results have been compared with those of the Homogeneous Boundary Conditions method, which leads to an overestimation of the effective mechanical properties. According to the results, applying homogenous boundary conditions results in a 33% and 13% increase in the shear moduli G23 and G12, respectively. In polymeric composites, the fibers have linear and brittle behavior, while the resin exhibits a non-linear behavior. Therefore, the nonlinear effects of resin on the mechanical properties of the composite material is studied using a user-defined subroutine in Fortran (USDFLD). The non-linear shear stress-strain behavior of unidirectional composite laminates has been obtained. Results indicate that at arbitrary constant stress as 80 MPa in-plane shear modulus, G12, experienced a 47%, 41% and 31% reduction at the fiber volume fraction of 30%, 50% and 70%, compared to the linear assumption. The results of this study are in good agreement with the analytical and experimental results available in the literature.

키워드

참고문헌

  1. Aboudi, J. (1990), "Micromechanical prediction of initial and subsequent yield surfaces of metal matrix composites", J. Plasticity, 6(4), 471-484. https://doi.org/10.1016/0749-6419(90)90014-6.
  2. Aboudi, J. (2013), Mechanics of Composite Materials: A Unified Micromechanical Approach, Elsevier, The Netherlands.
  3. Adams, D.F. and Crane, D.A. (1984), "Finite element micromechanical analysis of a unidirectional composite including longitudinal shear loading", Comput. Struct., 18(6), 1153-1165. https://doi.org/10.1016/0045-7949(84)90160-3.
  4. Ahmadi, I. (2017), "Micromechanical failure analysis of composite materials subjected to biaxial and off-axis loading", Struct. Eng. Mech., 62(1), 43-54. https://doi.org/10.12989/sem.2017.62.1.043
  5. Aliabadi, M.H. (2015), Woven Composites, Imperial College Press, London, United Kingdom.
  6. Allen, D.H. and Boyd, J.G. (1993), "Convergence rates for computational predictions of stiffness loss in metal matrix composites", Composite Materials and Structures, AMD 179/AD 37, ASME, New York, USA. 31-45.
  7. Bakhvalov, N.S. and Panasenko, G.P. (1984), Homogenization in Periodic Media, Mathematical Problems of the Mechanics of Composite Materials, Nauka, Moscow, Russia.
  8. Belkacem, A., Tahar, H.D., Abderrezak, R., Amine, B.M., Mohamed, Z. and Boussad, A. (2018), "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions", Struct. Eng. Mech., 66(6), 761-769. https://doi.org/10.12989/sem.2018.66.6.761.
  9. Bensoussan, A., Lions, J.L. and Papanicolaou, G. (2011), Asymptotic Analysis for Periodic Structures, American Mathematical Society, Providence, Rhode Island, USA.
  10. Bigelow, C.A. (1993), "Thermal residual stresses in a siliconcarbide/titanium [0/90] laminate", J. Compos. Technol. Res., 15(4), 304-310. https://doi.org/10.1520/CTR10383J.
  11. Bonora, N., Costanzi, M., Newaz, G. and Marchetti, M. (1994), "Microdamage effects on the overall response of long fibre/metal-matrix composites", Compos., 25(7), 575-582. https://doi.org/10.1016/0010-4361(94)90187-2.
  12. Chamis, C.C. (1983), "Simplified composite micromechanics for hygral, thermal and mechanical properties", SAMPE Quarterly, 14-23. https://ntrs.nasa.gov/search.jsp?R=19830011546.
  13. Chen, Y., Xia, Z. and Ellyin, F. (2001), "Evolution of Residual Stresses Induced during Curing Processing Using a Viscoelastic Micromechanical Model", J. Compos. Mater., 35(6), 522-542. https://doi.org/10.1177%2F002199801772662145. https://doi.org/10.1177/002199801772662145
  14. Chu, X., Yu, C., Xiu, C. and Xu, Y. (2015), "Two scale modeling of behaviors of granular structure: size effects and displacement fluctuations of discrete particle assembly", Struct. Eng. Mech., 55(2), 315-334. https://doi.org/10.12989/sem.2015.55.2.315.
  15. Ebrahimi, F. and Habibi, S. (2018), "Thermal effects on nonlinear dynamic characteristics of polymer-CNT-fiber multiscale nanocomposite structures", Struct. Eng. Mech., 67(4), 403-415. https://doi.org/10.12989/sem.2018.67.4.403.
  16. Ellyin, F., Xia, Z. and Chen, Y. (2002), "Viscoelastic micromechanical modeling of free edge and time effects in glass fiber/epoxy cross-ply laminates", Composites Part A Appl. Sci. Manufact., 33(3), 399-409. https://doi.org/10.1016/S1359-835X(01)00112-9.
  17. Gilat, A., Goldberg, R.K. and Roberts, G.D. (2007), "Strain Rate Sensitivity of Epoxy Resin in Tensile and Shear Loading", J. Aerosp. Eng., 20(2), 75-89. https://doi.org/10.1061/(ASCE)0893-1321(2007)20:2(75).
  18. Guedes, M. and Kikuchi, N. (1990), "Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods", Comput. Methods Appl. Mech. Eng., 83, 143-198. https://doi.org/10.1016/0045-7825(90)90148-F.
  19. Hamedi, M., Golestanian, H., Tadi Beni, Y. and Alasvand Zarasvand, K. (2018), "Evaluation of fracture energy for nanocomposites reinforced with carbon nanotubes using numerical and micromechanical methods", Mech. Adv. Mater. Struct., 1-9. https://doi.org/10.1080/15376494.2018.1432787.
  20. Hashin, Z. and Rosen, B.W. (1964), "The Elastic Moduli of Fiber-Reinforced Materials", J. Appl. Mech., 31, 223-232. https://doi.org/10.1115/1.3629590
  21. Hashin, Z. and Shtrikman, S. (1963), "A variational approach to the theory of the elastic behaviour of multiphase materials", J. Mech. Phys. Solids, 11, 127-140. https://doi.org/10.1016/0022-5096(63)90060-7.
  22. Hollister, S.J. and Kikuchi, N. (1992), "A comparison of homogenization and standard mechanics analyses for periodic porous composites", Comput. Mech., 10(2), 73-95. https://doi.org/10.1007/BF00369853.
  23. Hori, M. and Nemat-Nasser, S. (1999), "On two micromechanics theories for determining micro-macro relations in heterogeneous solids", Mech. Mater., 31(10), 667-682. https://doi.org/10.1016/S0167-6636(99)00020-4.
  24. Kenaga, D., Doyle, J.F. and Sun, C.T. (1987), "The characterization of boron/aluminum composite in the nonlinear range as an orthotropic elastic-plastic material", J. Compos. Mater., 21(6), 516-531. https://doi.org/10.1177/002199838702100603.
  25. Khodjet-Kesba, M., Benkhedda, A., Adda Bedia, E. and Boukert, B. (2018), "On transverse matrix cracking in composite laminates loaded in flexure under transient hygrothermal conditions", Struct. Eng. Mech., 67(2), 165-173. https://doi.org/10.12989/sem.2018.67.2.165.
  26. Liao, B., Tan, H., Zhou, J. and Jia, L. (2018), "Multi-scale modelling of dynamic progressive failure in composite laminates subjected to low velocity impact", Thin-Walled Struct., 131, 695-707. https://doi.org/10.1016/j.tws.2018.07.047.
  27. Lubineau, G. and Ladeveze, P. (2008), "Construction of a micromechanics-based intralaminar mesomodel, and illustrations in ABAQUS/Standard", Comput. Mater. Sci., 43(1), 137-145. https://doi.org/10.1016/j.commatsci.2007.07.050.
  28. Ma, J., Wriggers, P. and Li, L. (2016), "Homogenized thermal properties of 3D composites with full uncertainty in the microstructure", Struct. Eng. Mech., 57(2), 369-387. https://doi.org/10.12989/sem.2016.57.2.369.
  29. Moorthy, S. and Ghosh, S. (1998), "Particle cracking in discretely reinforced materials with the voronoi cell finite element model", J. Plasticity, 14(8), 805-827. https://doi.org/10.1016/S0749-6419(98)00024-2.
  30. Naghdinasab, M., Farrokhabadi, A. and Madadi, H. (2018), "A numerical method to evaluate the material properties degradation in composite RVEs due to fiber-matrix debonding and induced matrix cracking", Finite Elements Analysis Design, 146, 84-95. https://doi.org/10.1016/j.finel.2018.04.008.
  31. Needleman, A. and Tvergaard, V. (1993), "Comparison of Crystal Plasticity and Isotropic Hardening Predictions for Metal-Matrix Composites", J. Appl. Mech., 60, 70-76. https://doi.org/10.1115/1.2900781
  32. Nemat-Nasser, S. and Hori, M. (2013), Micromechanics: Overall Properties of Heterogeneous Materials, Elsevier, The Netherlands.
  33. Pindera, M.J. and Aboudi, J. (1988), "Micromechanical analysis of yielding of metal matrix composites", J. Plasticity, 4(3), 195-214. https://doi.org/10.1016/0749-6419(88)90010-1.
  34. Raghavan, P., Moorthy, S., Ghosh, S. and Pagano, N.J. (2001), "Revisiting the composite laminate problem with an adaptive multi-level computational model", Compos. Sci. Technol., 61, 1017-1040. https://doi.org/10.1016/S0266-3538(00)00230-X.
  35. Riley, M.B. and Whitney, J.M. (1966), "Elastic properties of fiber reinforced composite materials", AIAA J., 4(9), 1537-1542. https://doi.org/10.2514/3.3732.
  36. Sanchez-Palencia, E. (1980), Non-homogeneous Media and Vibration Theory, Lecture Notes in Physics Series Volume 127, Springer, Berlin, Germany.
  37. Shahzamanian, M.M., Tadepalli, T., Rajendran, A.M., Hodo, W.D., Mohan, R., Valisetty, R., Chung, P.W. and Ramsey, J.J. (2014), "Representative volume element based modeling of cementitious materials", J. Eng. Mater. Technol., 136(1), https://doi.org/10.1115/1.4025916.
  38. Shokrieh, M., Nasir, V. and Karimipour, H. (2012), "A micromechanical study on longitudinal strength of fibrous composites exposed to acidic environment", Mater. Design, 35, 394-403. https://doi.org/10.1016/j.matdes.2011.08.044.
  39. Simulia, A.V. (2013), "6.13 Documentation", Dassault System, Velizy-Villacoublay, France.
  40. Sun, C.T. and Chen, J.L. (1991), "A micromechanical model for plastic behavior of fibrous composites", Compos. Sci. Technol., 40(2), 115-129. https://doi.org/10.1016/0266-3538(91)90092-4.
  41. Sun, C.T. and Vaidya, R.S. (1996), "Prediction of composite properties from a representative volume element", Compos. Sci. Technol., 56, 171-179. https://doi.org/10.1016/0266-3538(95)00141-7.
  42. Suquet, P. (1987), Elements of Homogenization Theory for Inelastic Solid Mechanics, Homogenization Techniques for Composite Media, Springer-Verlag, Berlin, Germany.
  43. Tchalla, A., Belouettar, S., Makradi, A. and Zahrouni, H. (2013), "An ABAQUS toolbox for multiscale finite element computation", Compos. Part B Eng., 52, 323-333. https://doi.org/10.1016/j.compositesb.2013.04.028.
  44. Wu, W., Owino, J., Al-Ostaz, A. and Cai, L. (2014), "Applying periodic boundary conditions in finite element analysis", Simulia Community Conference, 707-719.
  45. Xia, Z., Chen, Y. and Ellyin, F. (2000), "A meso/micro-mechanical model for damage progression in glass-fiber/epoxy cross-ply laminates by finite-element analysis", Compos. Sci. Technol., 60, 1171-1179. https://doi.org/10.1016/S0266-3538(00)00022-1.
  46. Xia, Z., Ju, F. and Sasaki, K. (2007), "A general finite element analysis method for balloon expandable stents based on repeated unit cell (RUC) model", Finite Elements Anal. Design, 43(8), 649-658. https://doi.org/10.1016/j.finel.2007.01.001.
  47. Xia, Z., Zhang, Y. and Ellyin, F. (2003), "A unified periodical boundary conditions for representative volume elements of composites and applications", J. Solids Struct., 40(8), 1907-1921. https://doi.org/10.1016/S0020-7683(03)00024-6.
  48. Xia, Z., Zhou, C., Yong, Q. and Wang, X. (2006), "On selection of repeated unit cell model and application of unified periodic boundary conditions in micro-mechanical analysis of composites", J. Solids Struct., 43(2), 266-278. https://doi.org/10.1016/j.ijsolstr.2005.03.055.
  49. Xu, K. and Xu, X.W. (2008), "Finite element analysis of mechanical properties of 3D five-directional braided composites", Mater. Sci. Eng. A, 487(1-2), 499-509. https://doi.org/10.1016/j.msea.2007.10.030.
  50. Yahia, S.A., Amar, L.H.H., Belabed, Z. and Tounsi, A. (2018), "Effect of homogenization models on stress analysis of functionally graded plates", Struct. Eng. Mech., 67(5), 527-544. https://doi.org/10.12989/sem.2018.67.5.527.
  51. Yuan, Z. and Fish, J. (2008), "Toward realization of computational homogenization in practice", J. Numerical Methods Eng., 73(3), 361-380. https://doi.org/10.1002/nme.2074.
  52. Zhang, Y., Xia, Z. and Ellyin, F. (2005), "Nonlinear viscoelastic micromechanical analysis of fibre-reinforced polymer laminates with damage evolution", J. Solids Struct., 42(2), 591-604. https://doi.org/10.1016/j.ijsolstr.2004.06.021.
  53. Zuo, Z.H. and Xie, Y.M. (2015), "A simple and compact Python code for complex 3D topology optimization", Adv. Eng. Software, 85, 1-11. https://doi.org/10.1016/j.advengsoft.2015.02.006.