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Technical Papers
Jan 28, 2020

Optimization of Fiber-Reinforced Polymer Patches for Repairing Fatigue Cracks in Steel Plates Using a Genetic Algorithm

Publication: Journal of Composites for Construction
Volume 24, Issue 2

Abstract

A practical design optimization of fiber-reinforced polymer (FRP) patches for repairing fatigue cracks in metallic structures is presented. The design procedure combines finite-element (FE), genetic programming (GP), and genetic algorithm (GA) approaches. An optimum patch design is defined as the combination of design parameters that simultaneously minimizes the patch volume and reduces the stress intensity factor (SIF) range below the fatigue threshold range. A patching correction factor, which accounts for the positive effects of material and geometric properties of the patch and adhesive layer on the SIF solution, is proposed. The correction factor is developed by performing symbolic regression via GP analyses on the SIF values obtained from the three-dimensional FE models. The closed-form SIF solution facilitates the visualization of the effects of design parameters, simplifies the calculation of fatigue life, and reduces the computation effort for design optimization. An example of the center-cracked steel plate subjected to constant amplitude fatigue loading and then repaired with double-sided adhesive-bonded FRP patches is used to illustrate the optimization procedure.

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Data Availability Statement

Some or all data, models, or code generated or used during the study are available from the corresponding author by request.

Acknowledgments

The authors would like to acknowledge the financial supports from the ASEAN University Network/Southeast Asia Engineering Education Development Network (AUN/SEED-Net) and Chulalongkorn University.

References

Akbar, I., D. J. Oehlers, and M. M. Ali. 2010. “Derivation of the bond–slip characteristics for FRP plated steel members.” J. Constr. Steel Res. 66 (8–9): 1047–1056. https://doi.org/10.1016/j.jcsr.2010.03.003.
Albedah, A., S. M. Khan, F. Benyahia, and B. B. Bouiadjra. 2015. “Experimental analysis of the fatigue life of repaired cracked plate in aluminum alloy 7075 with bonded composite patch.” Eng. Fract. Mech. 145 (Aug): 210–220. https://doi.org/10.1016/j.engfracmech.2015.04.008.
Aljabar, N. J., X. L. Zhao, R. Al-Mahaidi, E. Ghafoori, M. Motavalli, and Y. C. Koay. 2017. “Fatigue tests on UHM-CFRP strengthened steel plates with central inclined cracks under different damage levels.” Compos. Struct. 160 (Jan): 995–1006. https://doi.org/10.1016/j.compstruct.2016.10.122.
Ayatollahi, M., and R. Hashemi. 2007. “Computation of stress intensity factors (KI, KII) and T-stress for cracks reinforced by composite patching.” Compos. Struct. 78 (4): 602–609. https://doi.org/10.1016/j.compstruct.2005.11.024.
Bocciarelli, M., P. Colombi, G. Fava, and C. Poggi. 2007. “Interaction of interface delamination and plasticity in tensile steel members reinforced by CFRP plates.” Int. J. Fract. 146 (1–2): 79–92. https://doi.org/10.1007/s10704-007-9144-8.
Bocciarelli, M., P. Colombi, G. Fava, and C. Poggi. 2009. “Prediction of debonding strength of tensile steel/CFRP joints using fracture mechanics and stress based criteria.” Eng. Fract. Mech. 76 (2): 299–313. https://doi.org/10.1016/j.engfracmech.2008.10.005.
Brighenti, R. 2007. “Patch repair design optimisation for fracture and fatigue improvements of cracked plates.” Int. J. Solids Struct. 44 (3–4): 1115–1131. https://doi.org/10.1016/j.ijsolstr.2006.06.006.
Budhe, S., M. Banea, S. De Barros, and L. Da Silva. 2017. “An updated review of adhesively bonded joints in composite materials.” Int. J. Adhes. Adhes. 72 (Jan): 30–42. https://doi.org/10.1016/j.ijadhadh.2016.10.010.
Campilho, R. D., M. D. Banea, J. Neto, and L. F. da Silva. 2013. “Modelling adhesive joints with cohesive zone models: Effect of the cohesive law shape of the adhesive layer.” Int. J. Adhes. Adhes. 44 (Jul): 48–56. https://doi.org/10.1016/j.ijadhadh.2013.02.006.
Campilho, R. D., M. D. Banea, A. M. Pinto, L. F. da Silva, and A. De Jesus. 2011. “Strength prediction of single-and double-lap joints by standard and extended finite element modelling.” Int. J. Adhes. Adhes. 31 (5): 363–372. https://doi.org/10.1016/j.ijadhadh.2010.09.008.
Chaves, F. J., L. F. M. Da Silva, M. F. S. F. De Moura, D. A. Dillard, and V. H. C. Esteves. 2014. “Fracture mechanics tests in adhesively bonded joints: A literature review.” J. Adhes. 90 (12): 955–992. https://doi.org/10.1080/00218464.2013.859075.
Chen, F., and P. Qiao. 2009. “Debonding analysis of FRP–concrete interface between two balanced adjacent flexural cracks in plated beams.” Int. J. Solids Struct. 46 (13): 2618–2628. https://doi.org/10.1016/j.ijsolstr.2009.02.007.
Colombi, P., A. Bassetti, and A. Nussbaumer. 2003a. “Analysis of cracked steel members reinforced by pre-stress composite patch.” Mater. Struc. 26 (1): 59–66. https://doi.org/10.1046/j.1460-2695.2003.00598.x.
Colombi, P., A. Bassetti, and A. Nussbaumer. 2003b. “Delamination effects on cracked steel members reinforced by prestressed composite patch.” Theor. Appl. Fract. Mech. 39 (1): 61–71. https://doi.org/10.1016/S0167-8442(02)00138-6.
Colombi, P., G. Fava, and L. Sonzogni. 2015. “Fatigue crack growth in CFRP-strengthened steel plates.” Composites Part B. 72 (Apr): 87–96. https://doi.org/10.1016/j.compositesb.2014.11.036.
Da Silva, L. F., A. Öchsner, and R. D. Adams. 2011. Handbook of adhesion technology. New York: Springer.
Deng, J., J. Li, Y. Wang, and W. Xie. 2018. “Numerical study on notched steel beams strengthened by CFRP plates.” Constr. Build. Mater. 163 (Feb): 622–633. https://doi.org/10.1016/j.conbuildmat.2017.12.110.
Dexter, R. J., and J. M. Ocel. 2013. Manual for repair and retrofit of fatigue cracks in steel bridges. Rep. McLean, VA: Federal Highway Administration.
Do, B., and A. Lenwari. 2018. “Empirical stress intensity factor equations for cracked steel plates repaired with double-sided FRP patches.” In Vol. 371 of IOP Conf. Series: Materials Science and Engineering, 012056. Bristol, UK: IOP Publishing.
Duong, C. N., and C. H. Wang. 2010. Composite repair: Theory and design. Kidlington, UK: Elsevier.
Emdad, R., and R. Al-Mahaidi. 2015. “Effect of prestressed CFRP patches on crack growth of centre-notched steel plates.” Compos. Struct. 123 (May): 109–122. https://doi.org/10.1016/j.compstruct.2014.12.007.
Errouane, H., Z. Sereir, and A. Chateauneuf. 2014. “Numerical model for optimal design of composite patch repair of cracked aluminum plates under tension.” Int. J. Adhes. Adhes. 49 (Mar): 64–72. https://doi.org/10.1016/j.ijadhadh.2013.12.004.
Fitzpatrick, J. M., and J. J. Grefenstette. 1988. “Genetic algorithms in noisy environments.” Mach. Learn. 3 (2): 101–120. https://doi.org/10.1007/BF00113893.
Ghafoori, E., and M. Motavalli. 2015. “Lateral-torsional buckling of steel I-beams retrofitted by bonded and un-bonded CFRP laminates with different pre-stress levels: Experimental and numerical study.” Constr. Build. Mater. 76 (Feb): 194–206. https://doi.org/10.1016/j.conbuildmat.2014.11.070.
Gu, L., A. R. M. Kasavajhala, and S. Zhao. 2011. “Finite element analysis of cracks in aging aircraft structures with bonded composite-patch repairs.” Composites Part B. 42 (3): 505–510. https://doi.org/10.1016/j.compositesb.2010.11.014.
Hmidan, A., Y. J. Kim, and S. Yazdani. 2014. “Correction factors for stress intensity of CFRP-strengthened wide-flange steel beams with various crack configurations.” Constr. Build. Mater. 70 (Nov): 522–530. https://doi.org/10.1016/j.conbuildmat.2014.08.008.
Hmidan, A., Y. J. Kim, and S. Yazdani. 2015. “Stress intensity factors for cracked steel girders strengthened with CFRP sheets.” J. Compos. Constr. 19 (5): 04014085. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000552.
Jiao, H., F. Mashiri, and X.-L. Zhao. 2012. “A comparative study on fatigue behaviour of steel beams retrofitted with welding, pultruded CFRP plates and wet layup CFRP sheets.” Thin Walled Struct. 59 (Oct): 144–152. https://doi.org/10.1016/j.tws.2012.06.002.
Jones, S. C., and S. A. Civjan. 2003. “Application of fiber reinforced polymer overlays to extend steel fatigue life.” J. Compos. Constr. 7 (4): 331–338. https://doi.org/10.1061/(ASCE)1090-0268(2003)7:4(331).
Kabir, M., and A. Seif. 2011. “Lateral torsional buckling of steel I-beam retrofitted using FRP sheets: Analytical solution and optimization.” In Advances in FRP composites in civil engineering, 915–918. Berlin: Springer.
Karatzas, V. A., E. A. Kotsidis, and N. G. Tsouvalis. 2015. “Experimental fatigue study of composite patch repaired steel plates with cracks.” Appl. Compos. Mater. 22 (5): 507–523. https://doi.org/10.1007/s10443-014-9420-5.
Koza, J. R. 1992. Genetic programming: On the programming of computers by means of natural selection. Cambridge, MA: MIT Press.
Kumar, A. M., and S. Hakeem. 2000. “Optimum design of symmetric composite patch repair to centre cracked metallic sheet.” Compos. Struct. 49 (3): 285–292. https://doi.org/10.1016/S0263-8223(00)00005-2.
Lam, A. C. C., M. C. H. Yam, J. J. R. Cheng, and G. D. Kennedy. 2010. “Study of stress intensity factor of a cracked steel plate with a single-side CFRP composite patching.” J. Compos. Constr. 14 (6): 791–803. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000136.
Lee Rodgers, J., and W. A. Nicewander. 1988. “Thirteen ways to look at the correlation coefficient.” Am. Stat. 42 (1): 59–66. https://doi.org/10.1080/00031305.1988.10475524.
Lenwari, A., T. Thepchatri, and P. Albrecht. 2005. “Flexural response of steel beams strengthened with partial-length CFRP plates.” J. Compos. Constr. 9 (4): 296–303. https://doi.org/10.1061/(ASCE)1090-0268(2005)9:4(296).
Lenwari, A., T. Thepchatri, and P. Albrecht. 2006. “Debonding strength of steel beams strengthened with CFRP plates.” J. Compos. Constr. 10 (1): 69–78. https://doi.org/10.1061/(ASCE)1090-0268(2006)10:1(69).
Liu, H., R. Al-Mahaidi, and X.-L. Zhao. 2009a. “Experimental study of fatigue crack growth behaviour in adhesively reinforced steel structures.” Compos. Struct. 90 (1): 12–20. https://doi.org/10.1016/j.compstruct.2009.02.016.
Liu, H., Z. Xiao, X.-L. Zhao, and R. Al-Mahaidi. 2009b. “Prediction of fatigue life for CFRP-strengthened steel plates.” Thin Walled Struct. 47 (10): 1069–1077. https://doi.org/10.1016/j.tws.2008.10.011.
Maiti, S. K. 2015. Fracture mechanics. Cambridge, UK: Cambridge University Press.
MathWorks. 2018. “Global optimization toolbox user’s guide (r2018a).” Accessed August 15, 2018. https://www.mathworks.com/help/pdf_doc/gads/gads_tb.pdf.
Miller, T. C., M. J. Chajes, D. R. Mertz, and J. N. Hastings. 2001. “Strengthening of a steel bridge girder using CFRP plates.” J. Bridge Eng. 6 (6): 514–522. https://doi.org/10.1061/(ASCE)1084-0702(2001)6:6(514).
Mitchell, M. 1998. An introduction to genetic algorithms. Cambridge, MA: MIT Press.
Naboulsi, S., and S. Mall. 1996. “Modeling of a cracked metallic structure with bonded composite patch using the three layer technique.” Compos. Struct. 35 (3): 295–308. https://doi.org/10.1016/0263-8223(96)00043-8.
Nakamura, H., W. Jiang, H. Suzuki, K.-I. Maeda, and T. Irube. 2009. “Experimental study on repair of fatigue cracks at welded web gusset joint using CFRP strips.” Thin Walled Struct. 47 (10): 1059–1068. https://doi.org/10.1016/j.tws.2008.10.016.
Nozaka, K., C. K. Shield, and J. F. Hajjar. 2005. “Effective bond length of carbon-fiber-reinforced polymer strips bonded to fatigued steel bridge I-girders.” J. Bridge Eng. 10 (2): 195–205. https://doi.org/10.1061/(ASCE)1084-0702(2005)10:2(195).
Papanikos, P., K. Tserpes, G. Labeas, and S. Pantelakis. 2005. “Progressive damage modelling of bonded composite repairs.” Theor. Appl. Fract. Mech. 43 (2): 189–198. https://doi.org/10.1016/j.tafmec.2005.01.004.
Papanikos, P., K. Tserpes, and S. Pantelakis. 2007. “Initiation and progression of composite patch debonding in adhesively repaired cracked metallic sheets.” Compos. Struct. 81 (2): 303–311. https://doi.org/10.1016/j.compstruct.2006.08.022.
PerformanceComposites. 2009. “Mechanical properties of carbon fibre composite materials, fibre / epoxy resin (120°C cure).” Accessed March 30, 2018. http://www.performance-composites.com/carbonfibre/mechanicalproperties_2.asp.
Pook, L. 1975. “Analysis and application of fatigue crack growth data.” J. Strain Anal. 10 (4): 242–250. https://doi.org/10.1243/03093247V104242.
Rao, S. S., and S. S. Rao. 2009. Engineering optimization: Theory and practice. New York: Wiley.
Rasane, A., P. Kumar, and M. Khond. 2017. “Optimizing the size of a CFRP patch to repair a crack in a thin sheet.” J. Adhes. 93 (13): 1064–1080. https://doi.org/10.1080/00218464.2016.1204236.
Reddy, J. N. 1987. “A generalization of two-dimensional theories of laminated composite plates.” Commun. Appl. Numer. Methods. 3 (3): 173–180. https://doi.org/10.1002/cnm.1630030303.
Rose, L. R. F. 1981. “An application of the inclusion analogy for bonded reinforcements.” Int. J. Solids Struct. 17 (8): 827–838. https://doi.org/10.1016/0020-7683(81)90091-3.
Rose, L. R. F. 1988. “Theoretical analysis of crack patching.” In Bonded repair of aircraft structures, 77–105. Dordrecht, Netherlands: Springer.
Schnerch, D., and S. Rizkalla. 2008. “Flexural strengthening of steel bridges with high modulus CFRP strips.” J. Bridge Eng. 13 (2): 192–201. https://doi.org/10.1061/(ASCE)1084-0702(2008)13:2(192).
Sette, S., and L. Boullart. 2001. “Genetic programming: Principles and applications.” Eng. Appl. Artif. Intell. 14 (6): 727–736. https://doi.org/10.1016/S0952-1976(02)00013-1.
SikaAG. 2009. “Sika® CarboDur® Plates. Pultruded carbon fiber plates for structural strengthening.” Accessed October 12, 2017. https://irn.sika.com/dms/getdocument.get/2d1f35bc-066e-35ff-b45a-e8fc8099b43b/Carbodur.pdf.
Staab, G. H. 2015. “Introduction to composite materials.” In Laminar composites, 1–16. Woburn, MA: Butterworth-Heinemann.
Sun, C., J. Klug, and C. Arendt. 1996. “Analysis of cracked aluminum plates repaired with bonded composite patches.” AIAA J. 34 (2): 369–374. https://doi.org/10.2514/3.13073.
Tada, H., P. C. Paris, and G. R. Irwin. 2000. “Two-dimensional stress solutions for various configurations with cracks.” In The stress analysis of cracks handbook, edited by H. Tada, P. C. Paris, and G. R. Irwin. 3rd ed. New York: ASME.
Täljsten, B., C. S. Hansen, and J. W. Schmidt. 2009. “Strengthening of old metallic structures in fatigue with prestressed and non-prestressed CFRP laminates.” Constr. Build. Mater. 23 (4): 1665–1677. https://doi.org/10.1016/j.conbuildmat.2008.08.001.
Teng, J., T. Yu, and D. Fernando. 2012. “Strengthening of steel structures with fiber-reinforced polymer composites.” J. Constr. Steel Res. 78 (Nov): 131–143. https://doi.org/10.1016/j.jcsr.2012.06.011.
Wagner, S., et al. 2014. “Architecture and design of the HeuristicLab optimization environment.” In Advanced methods and applications in computational intelligence, edited by R. Klempous, J. Nikodem, W. Jacak, and Z. Chaczko, 197–261. Heidelberg, Germany: Springer.
Wang, H.-T., G. Wu, Y.-T. Dai, and X.-Y. He. 2016a. “Experimental study on bond behavior between CFRP plates and steel substrates using digital image correlation.” J. Compos. Constr. 20 (6): 04016054. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000701.
Wang, H.-T., G. Wu, and J.-B. Jiang. 2016b. “Fatigue behavior of cracked steel plates strengthened with different CFRP systems and configurations.” J. Compos. Constr. 20 (3): 04015078. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000647.
Wang, H.-T., G. Wu, and Z.-S. Wu. 2014. “Effect of FRP configurations on the fatigue repair effectiveness of cracked steel plates.” J. Compos. Constr. 18 (1): 04013023. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000422.
Wu, C., X. Zhao, W. H. Duan, and R. Al-Mahaidi. 2012. “Bond characteristics between ultra high modulus CFRP laminates and steel.” Thin Walled Struct. 51 (Feb): 147–157. https://doi.org/10.1016/j.tws.2011.10.010.
Wu, C., X. L. Zhao, W. K. Chiu, R. Al-Mahaidi, and W. H. Duan. 2013. “Effect of fatigue loading on the bond behaviour between UHM CFRP plates and steel plates.” Composites Part B. 50 (Jul): 344–353. https://doi.org/10.1016/j.compositesb.2013.02.040.
Yu, Q., T. Chen, X. Gu, X. Zhao, and Z. Xiao. 2013. “Fatigue behaviour of CFRP strengthened steel plates with different degrees of damage.” Thin Walled Struct. 69 (Aug): 10–17. https://doi.org/10.1016/j.tws.2013.03.012.
Yu, T., D. Fernando, J. Teng, and X. Zhao. 2012. “Experimental study on CFRP-to-steel bonded interfaces.” Composites Part B. 43 (5): 2279–2289. https://doi.org/10.1016/j.compositesb.2012.01.024.
Zhao, X.-L., and L. Zhang. 2007. “State-of-the-art review on FRP strengthened steel structures.” Eng. Struct. 29 (8): 1808–1823. https://doi.org/10.1016/j.engstruct.2006.10.006.
Zheng, B., and M. Dawood. 2016. “Debonding of carbon fiber–reinforced polymer patches from cracked steel elements under fatigue loading.” J. Compos. Constr. 20 (6): 04016038. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000694.
Zheng, B., and M. Dawood. 2017. “Fatigue strengthening of metallic structures with a thermally activated shape memory alloy fiber-reinforced polymer patch.” J. Compos. Constr. 21 (4): 04016113. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000776.

Information & Authors

Information

Published In

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Journal of Composites for Construction
Volume 24Issue 2April 2020

History

Received: Sep 23, 2018
Accepted: Aug 20, 2019
Published online: Jan 28, 2020
Published in print: Apr 1, 2020
Discussion open until: Jun 28, 2020

Authors

Affiliations

Graduate Student, Dept. of Civil Engineering, Faculty of Engineering, Chulalongkorn Univ., Phayathai Rd., Pathumwan, Bangkok 10330, Thailand. ORCID: https://orcid.org/0000-0002-7359-0668. Email: [email protected]
Akhrawat Lenwari [email protected]
Associate Professor, Composite Structures Research Unit, Faculty of Engineering, Dept. of Civil Engineering, Chulalongkorn Univ., Phayathai Rd., Pathumwan, Bangkok 10330, Thailand (corresponding author). Email: [email protected]

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