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Damaged composite structural strength enhancement under elevated thermal environment using shape memory alloy fiber

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Abstract

The damaged laminated composite structural strength and repair action due to functional material reinforcement is investigated mathematically in this research using a higher-order displacement field model. The effect of a crack on the frequency responses is predicted numerically using the finite element (FE) approach. The reduction in total structural strength due to the crack and elevated temperatures are computed using the proposed model. Further, the enhancement of parent structural strength/stiffness is achieved by reinforcing the shape memory alloy (SMA). Moreover, the damage repair and improved frequency are achieved through activated SMA under a temperature range. The numerical model efficacy is established by conducting the convergence and adequate comparison studies. The study of the cracked laminate is verified for different temperature ranges, with and without SMA fiber. Additionally, a few experimental frequencies of intact and damaged composite panels have been carried out for comparison to gain confidence in the proposed model. Finally, several numerical examples are solved by varying the important structural input parameters (material and geometry) and their influences discussed in detail.

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References

  1. Leissa, A.W.: The free vibration of rectangular plates. J. Sound Vib. 31, 257–293 (1973). https://doi.org/10.1016/S0022-460X(73)80371-2

    Article  MATH  Google Scholar 

  2. Liew, K.M., Hung, K.C., Lim, M.K.: A solution method for analysis of cracked plates under vibration. Eng. Fract. Mech. 48, 393–404 (1994). https://doi.org/10.1016/0013-7944(94)90130-9

    Article  Google Scholar 

  3. Lee, H.P., Lim, S.P.: Vibration of cracked rectangular plates including transverse shear deformation and rotary inertia. Comput. Struct. 49, 715–718 (1993). https://doi.org/10.1016/0045-7949(93)90074-N

    Article  MATH  Google Scholar 

  4. Brethee, K.F.: Free vibration analysis of clamped laminated composite plates with centeral crack. Anbar J. Eng. Sci. 9, 108–115 (2021)

    Google Scholar 

  5. Fujimoto, T., Wakata, K., Cao, F., Nisitani, H.: Vibration analysis of a cracked plate subjected to tension using a hybrid method of FEM and BFM. Mater. Sci. Forum. 440–441, 407–414 (2003). https://doi.org/10.4028/www.scientific.net/msf.440-441.407

    Article  Google Scholar 

  6. Guan-Liang, Q., Song-Nian, G., Jie-Sheng, J.: A finite element model of cracked plates and application to vibration problems. Comput. Struct. 39, 483–487 (1991). https://doi.org/10.1016/0045-7949(91)90056-R

    Article  Google Scholar 

  7. Huang, C.S., Leissa, A.W.: Vibration analysis of rectangular plates with side cracks via the Ritz method. J. Sound Vib. 323, 974–988 (2009). https://doi.org/10.1016/j.jsv.2009.01.018

    Article  Google Scholar 

  8. Huang, C.S., Chan, C.W.: Vibration analyses of cracked plates by the ritz method with moving least-squares interpolation functions. Int. J. Struct. Stab. Dyn. (2014). https://doi.org/10.1142/S0219455413500600

    Article  MathSciNet  MATH  Google Scholar 

  9. Asadigorji, H., Dardel, M.: Natural vibration analysis of rectangular plates with multiple all-over part- through cracks natural vibration analysis of rectangular plates with multiple all-over part through cracks. (2012)

  10. Huang, C.S., Leissa, A.W., Chan, C.W.: Vibrations of rectangular plates with internal cracks or slits. Int. J. Mech. Sci. 53, 436–445 (2011). https://doi.org/10.1016/j.ijmecsci.2011.03.006

    Article  Google Scholar 

  11. Rath, M.K., Sahu, S.K.: Vibration of woven fiber laminated composite plates in hygrothermal environment. JVC/Journal Vib. Control. 18, 1957–1970 (2012). https://doi.org/10.1177/1077546311428638

    Article  Google Scholar 

  12. Joshi, P.V., Jain, N.K., Ramtekkar, G.D.: Effect of thermal environment on free vibration of cracked rectangular plate: an analytical approach. Thin-Walled Struct. 91, 38–49 (2015). https://doi.org/10.1016/j.tws.2015.02.004

    Article  Google Scholar 

  13. Xue, J., Wang, Y.: Free vibration analysis of a flat stiffened plate with side crack through the Ritz method. Arch. Appl. Mech. 89, 2089–2102 (2019). https://doi.org/10.1007/s00419-019-01565-6

    Article  Google Scholar 

  14. Pushparaj, P., Suresha, B.: Free vibration analysis of laminated composite plates using finite element method. Polym. Polym. Compos. 24, 529–538 (2016). https://doi.org/10.1177/096739111602400712

    Article  Google Scholar 

  15. Qu, G.M., Li, Y.Y., Cheng, L., Wang, B.: Vibration analysis of a piezoelectric composite plate with cracks. Compos. Struct. 72, 111–118 (2006). https://doi.org/10.1016/j.compstruct.2004.11.001

    Article  Google Scholar 

  16. Damnjanović, E., Marjanović, M., Nefovska-Danilović, M.: Free vibration analysis of stiffened and cracked laminated composite plate assemblies using shear-deformable dynamic stiffness elements. Compos. Struct. 180, 723–740 (2017). https://doi.org/10.1016/j.compstruct.2017.08.038

    Article  Google Scholar 

  17. Verma, A.K., Kumhar, V., Verma, M., Rastogi, V.: Vibration analysis of partially cracked symmetric laminated composite plates using Grey-Taguchi. Biointerface Res. Appl. Chem. 12, 4529–4543 (2021)

    Article  Google Scholar 

  18. Imran, M., Badshah, S., Khan, R.K.: Vibration analysis of cracked composite laminated plate: a review. Mehran Univ. Res. J. Eng. Technol. 38, 687–704 (2019)

    Article  Google Scholar 

  19. Li, D.: Layerwise theories of laminated composite structures and their applications: a review. Arch. Comput. Methods Eng. 28, 577–600 (2021). https://doi.org/10.1007/s11831-019-09392-2

    Article  MathSciNet  Google Scholar 

  20. Gayen, D., Tiwari, R., Chakraborty, D.: Static and dynamic analyses of cracked functionally graded structural components: a review. Compos. Part B Eng. 173, 106982 (2019). https://doi.org/10.1016/j.compositesb.2019.106982

    Article  Google Scholar 

  21. Ostachowicz, W., Krawczuk, M., Zak, A.: Natural frequencies of a multilayer composite plate with shape memory alloy wires. Finite Elem. Anal. Des. 32, 71–83 (1999). https://doi.org/10.1016/S0168-874X(98)00076-6

    Article  MATH  Google Scholar 

  22. Lau, K., Zhou, L., Tao, X.: Control of natural frequencies of a clamped–clamped composite beam with embedded shape memory alloy wires. Compos. Struct. 58, 39–47 (2002). https://doi.org/10.1016/S0263-8223(02)00042-9

    Article  Google Scholar 

  23. Lau, K.: Vibration characteristics of SMA composite beams with different boundary conditions. Mater. Des. 23, 741–749 (2002). https://doi.org/10.1016/S0261-3069(02)00069-9

    Article  Google Scholar 

  24. Barzegari, M.M., Dardel, M., Fathi, A., Pashaei, M.H.: Effect of shape memory alloy wires on natural frequency of plates. J. Mech. Eng. Autom. 2, 23–28 (2012). https://doi.org/10.5923/j.jmea.20120201.05

    Article  Google Scholar 

  25. Barzegari, M.M., Dardel, M., Fathi, A.: Vibration analysis of a beam with embedded shape memory alloy wires. Acta Mech. Solida Sin. 26, 536–550 (2013). https://doi.org/10.1016/S0894-9166(13)60048-8

    Article  Google Scholar 

  26. Kheirikhah, M.M., Khosravi, P.: Buckling and free vibration analyses of composite sandwich plates reinforced by shape-memory alloy wires. J. Brazilian Soc. Mech. Sci. Eng. 40, 515 (2018). https://doi.org/10.1007/s40430-018-1438-4

    Article  Google Scholar 

  27. Zhang, R., Ni, Q.-Q., Masuda, A., Yamamura, T., Iwamoto, M.: Vibration characteristics of laminated composite plates with embedded shape memory alloys. Compos. Struct. 74, 389–398 (2006). https://doi.org/10.1016/j.compstruct.2005.04.019

    Article  Google Scholar 

  28. Zhao, S., Teng, J., Wang, Z., Sun, X., Yang, B.: Investigation on the mechanical properties of SMA/GF/Epoxy hybrid composite laminates: flexural, impact, and interfacial shear performance. Materials (2018). https://doi.org/10.3390/ma11020246

    Article  Google Scholar 

  29. Amabili, M.: A comparison of shell theories for large-amplitude vibrations of circular cylindrical shells: Lagrangian approach. J. Sound Vib. 264, 1091–1125 (2003). https://doi.org/10.1016/S0022-460X(02)01385-8

    Article  Google Scholar 

  30. Panda, S.K., Singh, B.N.: Nonlinear finite element analysis of thermal post-buckling vibration of laminated composite shell panel embedded with SMA fibre. Aerosp. Sci. Technol. 29, 47–57 (2013). https://doi.org/10.1016/j.ast.2013.01.007

    Article  Google Scholar 

  31. Civalek, Ö.: Free vibration analysis of symmetrically laminated composite plates with first-order shear deformation theory (FSDT) by discrete singular convolution method. Finite Elem. Anal. Des. 44, 725–731 (2008). https://doi.org/10.1016/j.finel.2008.04.001

    Article  Google Scholar 

  32. Kamarian, S., Shakeri, M.: Natural Frequency Analysis of Composite Skew Plates with Embedded Shape Memory Alloys in Thermal Environment. AUT J. Mech. Eng. 1, 179–190 (2017)

    Google Scholar 

  33. Saeedi, A., Shokrieh, M.M.: Effect of shape memory alloy wires on the enhancement of fracture behavior of epoxy polymer. Polym. Test. 64, 221–228 (2017). https://doi.org/10.1016/j.polymertesting.2017.10.009

    Article  Google Scholar 

  34. Wang, E., Tian, Y., Wang, Z., Jiao, F., Guo, C., Jiang, F.: A study of shape memory alloy NiTi fiber/plate reinforced (SMAFR/SMAPR) Ti-Al laminated composites. J. Alloys Compd. 696, 1059–1066 (2017). https://doi.org/10.1016/j.jallcom.2016.12.062

    Article  Google Scholar 

  35. Ali, O.M.M., Al-Kalali, R.H.M., Mubarak, E.M.M.: Vibrational analysis of composite beam embedded with Nitinol shape memory alloy wires. Int. J. Eng. Technol. 7, 143 (2018)

    Google Scholar 

  36. John, S., Hariri, M.: Effect of shape memory alloy actuation on the dynamic response of polymeric composite plates. Compos. Part A Appl. Sci. Manuf. 39, 769–776 (2008). https://doi.org/10.1016/j.compositesa.2008.02.005

    Article  Google Scholar 

  37. Balasubramanian, M., Srimath, R., Vignesh, L., Rajesh, S.: Application of shape memory alloys in engineering - a review. J. Phys. Conf. Ser. (2021). https://doi.org/10.1088/1742-6596/2054/1/012078

    Article  Google Scholar 

  38. Behera, A., Rajak, D.K., Kolahchi, R., Scutaru, M.-L., Pruncu, C.I.: Current global scenario of Sputter deposited NiTi smart systems. J. Mater. Res. Technol. 9, 14582–14598 (2020). https://doi.org/10.1016/j.jmrt.2020.10.032

    Article  Google Scholar 

  39. Taheri, M.N., Sabet, S.A., Kolahchi, R.: Experimental investigation of self-healing concrete after crack using nano-capsules including polymeric shell and nanoparticles core. Smart Struct. Syst. 25, 337–343 (2020)

    Google Scholar 

  40. Taherifar, R., Zareei, S.A., Bidgoli, M.R., Kolahchi, R.: Seismic analysis in pad concrete foundation reinforced by nanoparticles covered by smart layer utilizing plate higher order theory. Steel Compos. Struct. 37, 99–115 (2020)

    Google Scholar 

  41. Arbabi, A., Kolahchi, R., Bidgoli, M.R.: Experimental study for ZnO nanofibers effect on the smart and mechanical properties of concrete. Smart Struct. Syst. 25, 97–104 (2020). https://doi.org/10.12989/SSS.2020.25.1.097

  42. Ghorbanpour Arani, A., Mortazavi, S.A., Kolahchi, R., Ghorbanpour Arani, A.H.: Vibration response of an elastically connected double-smart nanobeam-system based nano-electro-mechanical sensor. J. Solid Mech. 7, 121–130 (2015)

    Google Scholar 

  43. Xue, L., Dui, G., Liu, B., Zhang, J.: Theoretical analysis of a functionally graded shape memory alloy plate under graded temperature loading. Mech. Adv. Mater. Struct. 23, 1181–1187 (2016). https://doi.org/10.1080/15376494.2015.1068398

    Article  Google Scholar 

  44. Tobushi, H., Pieczyska, E., Ejiri, Y., Sakuragi, T.: Thermomechanical properties of shape-memory alloy and polymer and their composites. Mech. Adv. Mater. Struct. 16, 236–247 (2009). https://doi.org/10.1080/15376490902746954

    Article  Google Scholar 

  45. Panda, S.K., Singh, B.N.: Thermal post-buckling behaviour of laminated composite cylindrical/hyperboloid shallow shell panel using nonlinear finite element method. Compos. Struct. 91, 366–374 (2009). https://doi.org/10.1016/j.compstruct.2009.06.004

    Article  Google Scholar 

  46. Mehar, K., Panda, S.K., Dehengia, A., Kar, V.R.: Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment. J. Sandw. Struct. Mater. 18, 151–173 (2016). https://doi.org/10.1177/1099636215613324

    Article  Google Scholar 

  47. Mehar, K., Mishra, P.K., Panda, S.K.: Numerical investigation of thermal frequency responses of graded hybrid smart nanocomposite (CNT-SMA-Epoxy) structure. Mech. Adv. Mater. Struct. 28, 2242–2254 (2021). https://doi.org/10.1080/15376494.2020.1725193

    Article  Google Scholar 

  48. Cook RD, Malkus DS, Plesha ME, W.R.: Concepts and Applications of Finite Element Analysis. John Willy and Sons Pvt-Singapore (2003)

  49. Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells. CRC Press (2003)

  50. Dewangan, H.C., Panda, S.K.: Numerical transient responses of cut-out borne composite panel and experimental validity. Proc. Inst Mech. Eng. Part G J. Aerosp. Eng. 235, 1521–1536 (2021). https://doi.org/10.1177/0954410020977344

    Article  Google Scholar 

  51. Dewangan, H.C., Sharma, N., Panda, S.K.: Numerical nonlinear static analysis of Cutout-Borne multilayered structures and experimental validation. AIAA J. 60, 985–997 (2022). https://doi.org/10.2514/1.J060643

    Article  Google Scholar 

  52. Bachene, M., Tiberkak, R., Rechak, S.: Vibration analysis of cracked plates using the extended finite element method. Arch. Appl. Mech. 79, 249–262 (2009). https://doi.org/10.1007/s00419-008-0224-7

    Article  MATH  Google Scholar 

  53. Duan, B., Tawfik, M., Goek, S.N., Ro, J.-J., Mei, C.: Vibration of laminated composite plates embedded with shape memory alloy at elevated temperatures. Smart Struct. Mater. 2000 Ind. Commer. Appl. Smart Struct. Technol. 3991, 366–376 (2000). https://doi.org/10.1117/12.388179

  54. Cross, W.B., Anthony, H.K., Frederick, J.S.: Nitinol characterization study. NASA, Langley Research Center (1969)

  55. Mahabadi, R.K., Shakeri, M., Daneshpazhooh, M.: Free vibration of laminated composite plate with shape memory alloy fibers. Lat. Am. J. Solids Struct. 13, 314–330 (2016). https://doi.org/10.1590/1679-78252162

    Article  Google Scholar 

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Acknowledgements

SERB India supports this research work under Teachers Associateship for Research Excellence (TARE) scheme. The authors are thankful to TARE (SERB India) for their constant support. File no TAR/2020/000168 dated 19th Dec 2020.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology, Rourkela, 769008, India

    Kalyan Kumar Erukala, Hukum Chand Dewangan & Subrata Kumar Panda

  2. Department of Mechanical Engineering, CAPGS, BPUT, Rourkela, 769015, India

    Pradeep Kumar Mishra

  3. Department of Food Process Engineering, National Institute of Technology, Rourkela, 769008, India

    Madhuresh Dwivedi

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  1. Kalyan Kumar Erukala
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Correspondence to Subrata Kumar Panda.

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Appendix

Appendix

Individual terms of matrix [B]:

[B]1,1 = \(\partial /\partial x\), [B]1,3 = \(1/R_{x}\), [B]2,2 = \(\partial /\partial y\), [B]2,3 = \(1/R_{y}\), [B]3,1 = \(\partial /\partial y\), [B]3,2 = \(\partial /\partial x\), [B]3,3 = \(2/R_{xy}\), [B]4,1 = \(- 1/R_{x}\), [B]4,3 = \(\partial /\partial x\), [B]4,4 = 1, [B]5,2 = \(- 1/R_{y}\), [B]5,3 = \(\partial /\partial x\), [B]5,5 = 1, [B]6,4 = \(\partial /\partial x\), [B]7,5 = \(\partial /\partial y\), [B]8,4 = \(\partial /\partial y\), [B]8,5 = \(\partial /\partial x\), [B]9,4 = \(- 1/R_{x}\), [B]9,6 = 2, [B]10,5 = \(- 1/R_{y}\), [B]10,7 = 2, [B]11,6 = \(\partial /\partial x\), [B]12,7 = \(\partial /\partial y\), [B]13,6 = \(\partial /\partial y\), [B]13,7 = \(\partial /\partial x\), [B]14,6 = \(- 1/R_{x}\), [B]14,8 = 2, [B]15,7 = \(- 1/R_{y}\), [B]15,9 = 2, [B]16,8 = \(\partial /\partial x\), [B]17,9 = \(\partial /\partial y\), [B]18,8 = \(\partial /\partial y\), [B]18,9 = \(\partial /\partial x\),[B]19,8 = \(- 1/R_{x}\), [B]20,9 = \(- 1/R_{y}\).

Individual terms of matrix [BG]:

[BG]1,1 = \(\partial /\partial x\), [BG]1,3 = \(1/R_{x}\), [BG]2,1 = \(\partial /\partial y\), [BG]3,2 = \(\partial /\partial x\), [BG]4,2 = \(\partial /\partial y\), [BG]4,3 = \(1/R_{y}\), [BG]5,1 = \(- 1/R_{x}\), [BG]5,3 = \(\partial /\partial x\), [BG]6,2 = \(- 1/R_{y}\), [BG]6,3 = \(\partial /\partial y\), [BG]7,4 = \(\partial /\partial x\), [BG]8,4 = \(\partial /\partial y\), [BG]9,5 = \(\partial /\partial x\), [BG]10,5 = \(\partial /\partial y\), [BG]11,4 = \(- 1/R_{x}\), [BG]12,5 = \(- 1/R_{y}\), [BG]13,6 = \(\partial /\partial x\), [BG]14,6 = \(\partial /\partial y\), [BG]15,7 = \(\partial /\partial x\), [BG]16,7 = \(\partial /\partial y\), [BG]17,6 = \(- 1/R_{x}\), [BG]18,7 = \(- 1/R_{y}\), [BG]19,8 = \(\partial /\partial x\), [BG]20,8 = \(\partial /\partial y\), [BG]21,9 = \(\partial /\partial x\), [BG]22,9 = \(\partial /\partial y\), [BG]23,8 = \(- 1/R_{x}\), [BG]24,9 = \(- 1/R_{y}\).

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Erukala, K.K., Mishra, P.K., Dewangan, H.C. et al. Damaged composite structural strength enhancement under elevated thermal environment using shape memory alloy fiber. Acta Mech 233, 3133–3155 (2022). https://doi.org/10.1007/s00707-022-03272-w

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