Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Closed-form solution for the buckling behavior of the delaminated FRP plates with a rectangular hole using super-elastic SMA stitches

  • Soltanieh, Ghazaleh (Department of Building and Real Estate, The Hong Kong Polytechnic University) ;
  • Yam, Michael CH. (The Chinese National Engineering Research Center (CNERC)) ;
  • Zhang, Jing-Zhou (The Chinese National Engineering Research Center (CNERC)) ;
  • Ke, Ke (Key Laboratory of New Technology for Construction of Cities in Mountain Area, School of Civil Engineering, Chongqing University)
  • Received : 2020.07.07
  • Accepted : 2021.10.22
  • Published : 2022.01.10
⟨ Previous Next ⟩

Abstract

Layer separation (delamination) is an essential threat to fiber-reinforced polymer (FRP) plates under dynamic, static, and fatigue loads. Under compressive load, the growth of delamination will lead to structural instability. The aim of this paper is to present a method using shape memory alloy (SMA) stitches to suppress the delamination growth in a FRP plate and to improve the buckling behavior of the plate with a rectangular hole. The present paper is divided into two parts. Firstly, a closed-form (CF) formulation for evaluating the buckling load of the FRP plate is presented. Secondly, the finite element method (FEM) will be employed to calculate the buckling loads of the plates which serves to validate the results obtained from the closed-form method. The novelty of this work is the development of the closed-form solution using the p-Ritz energy approach regarding the stress-dependent phase transformation of SMA to trace the equilibrium path. For the FEM, the Lagoudas constitutive model of the SMA material is implemented in FORTRAN programming language using a user material subroutines (VUMAT). The model is simulated in ABAQUS/Explicit solver due to the nature of the loading type. The cohesive zone model (CZM) is applied to simulate the delamination growth.

Keywords

Acknowledgement

This research is funded by a grant from the Chinese National Engineering Research Centre for Steel Connection, The Hong Kong Polytechnic University (Project No. 1-BBV4).

References

  1. ABAQUS Benchmarks Manual (2007), Version 6.7, ABAQUS, Inc., Dassault Systemes.
  2. Abaqus, V.6.14 (2014), 6.14 Documentation, Dassault Systemes Simulia Corporation.
  3. Abot, J.L., Song, Y., Vatsavaya, M.S., Medikonda, S., Kier, Z., Jayasinghe, C., Rooy, N., Shanov, V.N. and Schulz, M.J. (2010), "Delamination detection with carbon nanotube thread in self-sensing composite materials", Compos. Sci. Technol., 70(7), 1113-1119. https://doi.org/10.1016/j.compscitech.2010.02.022.
  4. Aktas, M. and Balcioglu, H.E. (2013), "Buckling behavior of pultruded composite beams with circular cutouts", Steel Compos. Struct., 17(4), 359-370. http://doi.org/10.12989/scs.2014.17.4.359.
  5. Alfano, G. and Crisfield, M.A. (2001), "Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues", Int. J. Numer. Meth. Eng., 50, 1701-1736. https://doi.org/10.1002/nme.93.
  6. Alfano, G. and Crisfield, M.A. (2001), "Finite element interface models for the delamination analysis of laminated composites: Mechanical and computational issues", Int. J. Numer. Meth. Eng., 50(7), 1701-1736. https://doi.org/10.1002/nme.93.
  7. Alinia, M.M., Soltanieh, G. and Amani, M. (2012), "Inelastic buckling behavior of stocky plates under interactive shear and in-plane bending", Thin Wall Struct., 55, 76-84. https://doi.org/10.1016/j.tws.2012.03.007.
  8. Antonopoulou, S., McNally, C. and Byrne, G. (2016), "Developing braided FRP reinforcement for concrete structures", Civil Engineering Research in Ireland Conference (CERI 2016), Galway, Ireland, August.
  9. Bigaud, J., Aboura, Z., Martins, A.T. and Verger, S. (2018), "Analysis of the mechanical behavior of composite T-joints reinforced by one side stitching", Compos. Struct., 184, 249-255. https://doi.org/10.1016/j.compstruct.2017.06.041.
  10. Boon, Y.D., Joshi, S.C., Martins, A.T. and Verger, S. (2020), "A review of methods for improving interlaminar interfaces and fracture toughness of laminated composites", Mater. Today Commun., 22, 100830. https://doi.org/10.1016/j.mtcomm.2019.100830.
  11. Borrelli, R., Riccio, A., Sellitto, A., Caputo, F. and Ludwig, T. (2015), "On the use of global-local kinematic coupling approaches for delamination growth simulation in stiffened composite panels", Compos. Sci. Technol., 115, 43-51. https://doi.org/10.1016/j.compscitech.2015.04.010.
  12. Brinson, L.C. (1993), "One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable", J. Intel. Mater. Syst. Struct., 4(2), 229-242. https://doi.org/10.1177/1045389X9300400213.
  13. Bulson, P.S. (1970), The Stability of Flat Plates, Chatto & Windus Ltd., London, UK.
  14. Butterworth S. (1930), "On the theory of filter amplifiers", Wireless Eng., 7(6), 536-541.
  15. Cafarova, F.I., Akbarov, S.D. and Yahnioglu, N. (2017), "Buckling delamination of the PZT/Metal/PZT sandwich circular platedisc with penny-shaped interface cracks", Smart Struct. Syst., 19(2), 163-179. http://doi.org/10.12989/sss.2017.19.2.163.
  16. Cohades, A., Hostettler, N., Pauchard, M., Plummer, C.J.G. and Michaud, V. (2018), "Stitched shape memory alloy wires enhance damage recovery in selfhealing fibre-reinforced polymer composites", Compos. Sci. Technol., 161, 22-31. https://doi.org/10.1016/j.compscitech.2018.03.040.
  17. Cohades, A., Pauchard, M. and Michaud, V. (2010), "Impact resistance and recovery in SMA stitched E-glass reinforced Poly (ⲉ-caprolactone)/epoxy composites", ICCM21, Xian, China.
  18. Dickinson, S.M. and Blasio, A.D. (1986), "On the use of orthogonal polynomials in the Rayleigh-Ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates", J. Sound Vib., 108, 51-62. https://doi.org/10.1016/S0022-460X(86)80310-8.
  19. Gliesche, K., Hubner, T. and Orawetz, H. (2003), "Application of the tailored fibre placement (TFP) process for a local reinforcement on an "open-hole" tension plate from carbon/epoxy laminates", Compos. Sci. Technol., 63(1), 81-88. https://doi.org/10.1016/S0266-3538(02)00178-1.
  20. Guo, Z., Han, X. and Zhu, X. (2012), "Finite element analysis of interlaminar stresses for composite laminates stitched around a circular hole", Appl. Compos. Mater., 19(3-4), 561-571. https://doi.org/10.1007/s10443-011-9234-7
  21. Han, H., Taheri, F., Pegg, N. and Zhang, Z. (2007), "Local buckling mitigation and stress analysis of a shape memory alloy hybrid composite plate with and without a cutout", Smart Mater. Struct., 16(3), 589. https://doi.org/10.1088/0964-1726/16/3/006.
  22. Hart, K.R., Lankford, S.M., Freund, I.A., Patrick, J.F., Krull, B.P., Wetzel, E.D., Sottos, N.R. and White, S.R. (2017), "Repeated healing of delamination damage in vascular composites by pressurized delivery of reactive agents", Compos. Sci. Technol., 151, 1-9. https://doi.org/10.1016/j.compscitech.2017.07.027.
  23. Heidari-Rarani, M., Shokrieh, M.M. and Camanho, P.P. (2013), "Finite element modeling of mode i delamination growth in laminated DCB specimens with R-curve effects", Compos. B. Eng., 45(1), 897-903. https://doi.org/10.1016/j.compositesb.2012.09.051.
  24. Hillman, J.R. (2008), "Product application of a hybrid-composite beam system", IDEA Program Final Report 2008, HSR-43. Prepared for the IDEA Program, Transportation Research Board; National Research Council, Washington, D.C. Teng & Associates, Inc.
  25. 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., 48(1), 41-56. https://doi.org/10.12989/sem.2013.48.1.041.
  26. Katariya, P.V., Panda, S.K, Hirwani, C.K., Mehar, K. and Thakare, O. (2017), "Enhancement of thermal buckling strength of laminated sandwich composite panel structure embedded with shape memory alloy fibre", Smart Struct. Syst., 20(5), 595-605. https://doi.org/10.12989/sss.2017.20.5.595.
  27. Kessler, M.R. and White, S.R. (2001), "Self-activated healing of delamination damage in woven composites", Compos. Part A Appl. Sci. Manuf., 32(5), 638-699. https://doi.org/10.1016/S1359-835X(00)00149-4.
  28. Kharazan, M., Sadr, M.H. and Kiani, M. (2013), "Delamination growth analysis in composite laminates subjected to low velocity impact", Steel Compos. Struct., 17(4), 387-403. http://doi.org/10.12989/scs.2014.17.4.387.
  29. Lagoudas, D., Bo, Z., Qidwai, M. and Entchev, P. (2003), "SMA UM: User material subroutine for thermomechanical constitutive model of shape memory alloys", Texas A&M University, College Station, TX, USA.
  30. Lau, K.T., Ling, H.Y. and Zhou, L.M. (2004), "Low velocity impact on shape memory alloy stitched composite plates", Smart Mater. Struct., 13(2), 364-370. https://doi.org/10.1088/0964-1726/13/2/015.
  31. Li, Z. (2005), "Computational analyses and simulations of fluid-structure interactions applied to stented abdominal aortic aneurysms", North Carolina State University.
  32. Liew, K.M. and Feng, Z.C. (2001), "Three-dimensional free vibration analysis of perforated super elliptical plates via the p-Ritz method", Int. J. Mech. Sci., 43(11), 2613-2630. https://doi.org/10.1016/S0020-7403(01)00051-0.
  33. Liew, K.M., Xiang, Y., Kitipornchai, S. and Wang, C.M. (1998), Vibration of Mindlin Plates: Programming the P-Version Ritz Method, Elsevier Science, Oxford, UK.
  34. Mahieddinet, A., Ouali, M. and Mazouz, A. (2015), "Modeling and simulation of partially delaminated composite beams", Steel Compos. Struct., 18(5), 1119-1127. https://doi.org/10.12989/scs.2015.18.5.1119.
  35. Manfredi, E., Cohades, A., Richard, I. and Michaud, V. (2014), "Assessment of solvent capsule-based healing for woven E-glass fibre-reinforced polymers", Smart Mater. Struct., 24(1), 015019. https://doi.org/10.1088/0964-1726/24/1/015019.
  36. Mara, V., Haghani, R. and Harryson, P. (2014), "Bridge decks of fibre reinforced polymer (FRP): A sustainable solution", Constr. Build. Mater., 50, 190-199. https://doi.org/10.1016/j.conbuildmat.2013.09.036.
  37. Panda, S.K. and Singh, B.N. (2010), "Thermal post-buckling analysis of a laminated composite spherical shell panel embedded with shape memory alloy fibres using non-linear finite element method", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 224(4), 757-769. https://doi.org/10.1243/09544062JMES1809.
  38. Patel, A.J., Sottos, N.R., Wetzel, E.D. and White, S.R. (2010), "Autonomic healing of low-velocity impact damage in fiber-reinforced composites", Compos. Part A Appl. Sci. Manuf., 41(3), 360-368. https://doi.org/10.1016/j.compositesa.2009.11.002.
  39. Phoenix, S.L., Yavuz, A.K., Papoulia, K.D. and Hui, C.Y. (2006), "Buckling analysis of delaminated and stitched composite plate system under hygrothermal pressure", J. Eng. Mater.-T. ASME, 128, 117-122. https://doi.org/10.1115/1.2128428.
  40. Potluri, P., Kusak, E. and Reddy, T.Y. (2003), "Novel stitch-bonded sandwich composite structures", Compos. Struct., 59(2), 251-259. https://doi.org/10.1016/S0263-8223(02)00087-9.
  41. Riccio A., Russo, A., Sellitto, A., Toscano, C., Alfano, D. and Zarrelli, M. (2020), "Experimental and numerical assessment of fibre bridging toughening effects on the compressive behaviour of delaminated composite plates", Polym., 12(3), 1-20. http://doi.org/10.3390/polym12030554.
  42. Riccio, A., Linde, P., Raimondo, A., Buompane, A. and Sellitto, A. (2017), "On the use of selective stitching in stiffened composite panels to prevent skinstringer debonding", Compos. B. Eng., 124, 64-75. https://doi.org/10.1016/j.compositesb.2017.05.052.
  43. Riccio, A., Russo, A., Sellitto, A., Toscano, C., Alfano, D. and Zarrelli, M. (2020), "Experimental and numerical assessment of fibre bridging toughening effects on the compressive behaviour of delaminated composite plates", Polym., 12(3), 554. https://doi.org/10.3390/polym12030554.
  44. Robinson, P. and Song, D.Q. (1992), "A modiffied DCB specimen for mode I testing of multidirectional laminates", J. Compos. Mater., 26(11), 1554-1577. https://doi.org/10.1177/002199839202601101.
  45. Russo, A., Zarrelli, M., Sellitto, A. and Riccio, A. (2019), "Fiber bridging induced toughening effects on the delamination behavior of composite stiffened panels under bending loading: A numerical/experimental study", Mater., 12(15), 2407. http://doi.org/2407.10.3390/ma12152407.
  46. Sharma, S.K. and Sankar, B.V. (1997), "Sublaminate buckling and compression strength of stitched uniweave graphite/epoxy laminates", J. Reinf. Plast. Compos., 16(5), 425-434. https://doi.org/10.1177/073168449701600503.
  47. Shokrgozar, H.R., Akrami, V., Maaf, T.J. and Shahbazi, N. (2021), "The effect of different retrofitting techniques on the axial load carrying capacity of damaged cylindrical shells" Struct., 31, 590-601. https://doi.org/10.1016/j.istruc.2021.01.048.
  48. Simulia, D.S. (2014), Abaqus 6.14 Analysis User's Guide, Dassault Systems, Providence, RI, USA.
  49. Simulia, D.S. (2014), Abaqus 6.14 Benchmark Manual, Dassault Systems, Providence, RI, USA.
  50. Soltanieh, G. and Yam, M.CH. (2021), "An algorithm for quantifying dynamic buckling and post-buckling behavior of delaminated FRP plates with a rectangular hole stiffened by smart (SMA) stitches", Smart Struct. Syst., 28(6), 745-760. https://doi.org/10.12989/sss.2021.28.6.745.
  51. Soltanieh, G., Kabir, M.Z. and Shariyat, M. (2017), "Snap instability of shallow laminated cylindrical shells reinforced with functionally graded shape memory alloy wires", Compos. Struct., 180, 581-595. https://doi.org/10.1016/j.compstruct.2017.08.027.
  52. Soltanieh, G., Kabir, M.Z. and Shariyat, M. (2018), "A robust algorithm for behavior and effectiveness investigations of super-elastic SMA wires embedded in composite plates under impulse loading", Compos. Struct., 179, 355-367. https://doi.org/10.1016/j.compstruct.2017.07.065.
  53. Soltanieh, G., Kabir, M.Z. and Shariyat, M. (2019), "Improvement of the dynamic instability of shallow hybrid composite cylindrical shells under impulse loads using shape memory alloy wires", Compos. B. Eng., 167, 167-179. https://doi.org/10.1016/j.compositesb.2018.12.040.
  54. Soltanieh, G., Kabir, M.Z. and Shariyat, M. (2019), "Influence of the 3D material tailoring on snap-through and snap-back post-buckling behaviors of steel-wire-reinforced hybrid 3D graded orthotropic shallow cylindrical panels", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 233(2), 685-701. https://doi.org/10.1177/0954406218760062.
  55. Spearing, S.M. and Evans, A.G. (1992), "The role of fiber bridging in the delamination resistance of fiber-reinforced composites", Acta Metallurgica Et Materialia, 40(9), 2191-2199. https://doi.org/10.1016/0956-7151(92)90137-4.
  56. Stickler, P.B. and Ramulu, M. (2002), "Parametric analyses of stitched composite T-joints by the finite element method", Mater. Des., 23(8), 751-758. https://doi.org/10.1016/S0261-3069(02)00070-5.
  57. Thapa, M., Jony, B, Mulani, S.B. and Roy, S. (2017), "Experimental characterization of shape memory polymer enhanced thermoplastic self-healing carbon/epoxy composites", AIAA Scitech 2019 Forum, 1112. https://doi.org/10.2514/6.2019-1112.
  58. Tong, L., Mouritz, A.P. and Bannister, M.K. (2002), 3D Fibre Reinforced Polymer Composites, Elsevier Science, Oxford.
  59. Tounsi, A., Ait Atmane, H., Khiloun, M., Sekkal, M., Taleb, O. and Bousahla, A.A. (2019), "On buckling behavior of thick advanced composite sandwich plates", Compos. Mater. Eng., 1(1), 1-19. https://doi.org/10.12989/cme.2019.1.1.001.
  60. Tvergaard, V. and Hutchinson, J.W. (1996), "Effect of strain-dependent cohesive zone model on predictions of crack growth resistance", Int. J. Solid. Struct., 33, 3297-3308. https://doi.org/10.1016/0020-7683(95)00261-8.
  61. Velmurugan, R. and Solaimurugan, S. (2007), "Improvements in Mode I interlaminar fracture toughness and in-plane mechanical properties of stitched glass/polyester composites", Compos. Sci. Technol., 67(1), 61-69. https://doi.org/10.1016/j.compscitech.2006.03.032.
  62. Whitney, J. (2018), Structural Analysis of Laminated Anisotropic Plates, Technomic Publishing Corp.
  63. Wolfram, S. (1999), The MATHEMATICA Book, Cambridge University Press, Cambridge, UK.
  64. Wolfram, S. (2013), Programming with Mathematica: An Introduction, Cambridge University Press, Cambridge, UK.
  65. Wu, E. and Wang, J. (1995), "Behavior of stitched laminates under in-plane tensile and transverse impact loading", J. Compos. Mater., 29(17), 2254-2279. https://doi.org/10.1177/002199839502901702.
  66. Xiaoquan, C., Al-Mansour, A., Zhengneng, L. and Takeda, N. (2009), "Residual strength of stitched laminates after low velocity impact", J. Reinf. Plast. Compos., 28(14), 1679-1688. https://doi.org/10.1177/0731684408090368.
  67. Yavuz, A.K., Papoulia, K.D., Phoenix, S.L. and Hui C.Y. (2006), "Stability analysis of stitched composite plate system with delamination under hygrothermal pressure", AIAA J., 44(7), 1579-1585. https://doi.org/10.2514/1.17367.
  68. Ye, L. (1988), "Role of matrix resin in delamination onset and growth in composite laminates", Compos. Sci. Technol., 33(4), 257-277. https://doi.org/10.1016/0266-3538(88)90043-7.
  69. Yoshimura, A., Nakao, T., Yashiro, S. and Takeda, N. (2008), "Improvement on out-ofplane impact resistance of CFRP laminates due to through-the-thickness stitching", Compos. Part A Appl. Sci. Manuf., 39(9), 1370-1379. https://doi.org/10.1016/j.compositesa.2008.04.019.
  70. Yudhanto, A., Iwahori, Y., Watanabe, N. and Hoshi, H. (2012), "Open hole fatigue characteristics and damage growth of stitched plain weave carbon/epoxy laminates", Int. J. Fatig., 43, 12-22. https://doi.org/10.1016/j.ijfatigue.2012.02.002.
  71. Zhang, J. and Wei, Y. (2007), "A predictive approach to the in-plane mechanical properties of stitched composite laminates", Acta Mechanica Solida Sinica, 20(2), 130-140. https://doi.org/10.1007/s10338-007-0716-y.
  72. Zhang, J.Z., Yam, M.CH., Soltanieh, G. and Feng, R. (2021), "Collapse resistance of steel frames in two-side-column-removal scenario: Analytical method and design approach", Struct. Eng. Mech., 78(4), 485-496. https://doi.org/10.12989/sem.2021.78.4.485.
  73. Zoghi, M. (2013), The International Handbook of FRP Composites in Civil Engineering, CRC Press, Taylor & Francis Group, Boca Raton, FL.