Skip to main content

Advertisement

SpringerLink
Log in

A Two-Stage Genetic Algorithm for Molding Parameters Optimization for Minimized Residual Stresses in Composite Laminates During Curing

  • Published:
Applied Composite Materials Aims and scope Submit manuscript

Abstract

The residual stress generated during the curing process of composite structures will seriously reduce the material performance. This paper presents a two-stage genetic algorithm (GA) procedure to inversely determine the optimal molding parameters that minimize residual stresses. In our proposed two-stage GA procedure, a finite element model for Multiphysics simulation is first created to compute the residual stresses of the composite laminated plate for a given temperature curve. The FEM model is then modulated by an improved GA with the residual stresses of the plate as the objective function. The improved GA is called in two-stages: the first stage determines a set of likelihoods of the modeling parameters around which the "optimal" parameters may reside. The 2nd stage zooms-in the areas centered by these likelihoods, which finds molding parameters that minimize the residual stresses. The results show that the proposed two-stage genetic algorithm is more efficient than the traditional genetic algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data Availability

The raw data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

References

  1. Duan, S., Tao, Y., Han, X., Yang, X., Hou, S., Hu, Z.: Investigation on structure optimization of crashworthiness of fiber reinforced polymers materials. Compos. Part B 60(2), 471–478 (2014)

    Article  CAS  Google Scholar 

  2. Duan, S., Mo, F., Yang, X., Tao, Y., Wu, D., Yong, P.: Experimental and numerical investigations of strain rate effects on mechanical properties of LGFRP composite. Compos. Part B Eng. 88, 101–107 (2016)

    Article  CAS  Google Scholar 

  3. Duan, S., Yang, X., Tao, Y., Mo, F., Zhi, X., Kai, W.: Experimental and numerical investigation of Long Glass Fiber Reinforced Polypropylene composite and application in automobile components. Transport. 1–9 (2017)

  4. Wei, K., Liang, D., Mei, M., Wang, D., Yang, X., Qu, Z.: Preforming behaviors of carbon fiber fabrics with different contents of binder and under various process parameters. Compos. Part B Eng. 166, 221–232 (2019)

  5. Wei, K., Liang, D., Mei, M., Yang, X., Chen, L.: A viscoelastic model of compression and relaxation behaviors in preforming process for carbon fiber fabrics with binder. Compos. Part B Eng. 158, 1–9 (2019)

  6. Wang, X., et al.: Thermal protection system integrating graded insulation materials and multilayer ceramic matrix composite cellular sandwich panels. Compos. Struct. 209, 523–534 (2019)

    Article  Google Scholar 

  7. Liu, G., Xi, Z., Horie, Y.: Elastic Waves in Anisotropic Laminates. Appl. Mech. Rev. 56(2), B23 (2003)

    Article  Google Scholar 

  8. Guiming, Z., Jihui, W., Aiqing, N., Shuxin, L.: Process-induced residual stress of variable-stiffness composite laminates during cure. Compos. Struct. (2018)

  9. Hashim, J., Looney, L., Hashmi, M.S.J.: Particle distribution in cast metal matrix composites—Part II. J. Mater. Proc. Technol. 123(2), 251–257 (2002)

    Article  CAS  Google Scholar 

  10. White, S.R., Hahn, H.T.: Mechanical property and residual stress development during cure of a graphite/BMI composite. Polym. Eng. Sci. 30(22), 1465–1473 (2010)

    Article  Google Scholar 

  11. Baran, I., Cinar, K., Ersoy, N., Akkerman, R., Hattel, J.H.: A Review on the Mechanical Modeling of Composite Manufacturing Processes. Arch. Comput. Methods Eng. 24(2), 365–395 (2017)

    Article  Google Scholar 

  12. Bogetti, T.A., Gillespie, J., John W.: Process-Induced Stress and Deformation in Thick-Section Thermoset Composite Laminates, J. Compos. Mater. 26(5), 68 (1992)

    Article  Google Scholar 

  13. Cowley, K.D., Beaumont, P.W.R.: The measurement and prediction of residual stresses in carbon-fibre/polymer composites. Compos. Sci. Technol. 57(11), 1445–1455 (1997)

    Article  CAS  Google Scholar 

  14. Hahn, H.T., Pagano, N.J.: Curing Stresses in Composite Laminates. J. Compos. Mater. 9(1), 91–106 (1975)

    Article  Google Scholar 

  15. Kaushik, V., Raghavan, J.: Experimental study of tool–part interaction during autoclave processing of thermoset polymer composite structures. Compos. Part A: Appl. Sci. Manuf. 41(9), 1210–1218 (2010)

  16. Seif, M.A., Khashaba, U.A., Rojas-Oviedo, R.: Residual stress measurements in CFRE and GFRE composite missile shells. Compos. Struct. 79(2), 261–269 (2007)

  17. Yuan, Z., Wang, Y., Peng, X., Wang, J., Wei, S.: An analytical model on through-thickness stresses and warpage of composite laminates due to tool–part interaction. Compos. Part B Eng. 91, 408–413 (2016)

  18. Zeng, X., Raghavan, J.:: Role of tool-part interaction in process-induced warpage of autoclave-manufactured composite structures. Compos. Part A Appl. Sci. Manuf. 41(9), 1174–1183 (2010)

    Article  Google Scholar 

  19. Baran, I., Tutum, C.C., Nielsen, M.W., Hattel, J.H.: Process induced residual stresses and distortions in pultrusion. Compos. Part B Eng. 51(4), 148–161 (2013)

    Article  CAS  Google Scholar 

  20. Kravchenko, O.G., Kravchenko, S.G., Pipes, R.B.: Cure History Dependence of Residual Deformation in a Thermosetting Laminate. Compos. Part A Appl. Sci. Manuf. 99, 186–197 (2017)

    Article  CAS  Google Scholar 

  21. Zhu, Q.I., Geubelle, P.H., Min, L.I., Iii, C.L.T.: Dimensional Accuracy of Thermoset Composites: Simulation of Process-Induced Residual Stresses. J. Compos. Mater. 35(24), 2171–2205 (2015)

    Article  Google Scholar 

  22. White, S.R., Hahn, H.T.: Cure Cycle Optimization for the Reduction of Processing-Induced Residual Stresses in Composite Materials. J. Compos. Mater. 27(14), 1352–1378 (1993)

    Article  CAS  Google Scholar 

  23. Gopal, A.K., Adali, S., Verijenko, V.E.: Optimal temperature profiles for minimum residual stress in the cure process of polymer composites. Compos. Struct. 48(1), 99–106 (2000)

    Article  Google Scholar 

  24. Hao, W.F., Tang, C.: Effect of Dwell Time and Heating Rate on Thermal Residual Stresses in Co-Cured Aluminum/Composite Hybrid Shaft. Appl. Mech. Mater. 723, 485–488 (2015)

    Article  Google Scholar 

  25. White, S.R., Hahn, H.T.: Process Modeling of Composite Materials: Residual Stress Development during Cure. Part II. Experimental Validation. J. Compos. Mater. 26(16), 2423–2453 (1992)

    Article  CAS  Google Scholar 

  26. Li, J., Yao, X., Liu, Y., Cen, Z., Kou, Z., Di, D.: A study of the integrated composite material structures under different fabrication processing. Compos. Part A Appl. Sci. Manuf. 40(4), 455–462 (2009)

    Article  CAS  Google Scholar 

  27. Kim, H.S., Sang, W.P., Hui, Y.H., Dai, G.L.: Effect of the smart cure cycle on the performance of the co-cured aluminum/composite hybrid shaft. Compos. Struct. 75(1), 276–288 (2006)

    Article  Google Scholar 

  28. Liu, G.R., Quek, S.S.: The Finite Element Method. (2013)

  29. Darling, T.: Computational Inverse Techniques in Nondestructive Evaluation - G.R. Liu. Well Log. Form. Eval. (2014)

  30. Coley, D.A.: An Introduction to Genetic Algorithms for Scientists and Engineers. Bull. Volcanol. Soc. Japan Sec. 12, 90–91 (2015)

    Google Scholar 

  31. Anderson-Cook, C.M.: Practical genetic algorithms. Pub. Ame. Statist. Assoc. 100(471), 1099–1099 (2004)

    Article  Google Scholar 

  32. Coit, D.: Genetic Algorithms and Engineering Design. Eng. Econ. 43(4), 379–381 (2007)

    Article  Google Scholar 

  33. Dai, J., Xi, S., Li, D.: Numerical Analysis of Curing Residual Stress and Deformation in Thermosetting Composite Laminates with Comparison between Different Constitutive Models. Materials 12(4), 572 (2019)

    Article  CAS  Google Scholar 

  34. Kim, Y., White, S.: Cure-Dependent Viscoelastic Residual Stress Analysis of Filament-Wound Composite Cylinders. Mech. Adv. Mater. Struct. 5(4), 327–354 (1998)

  35. Mather, P.T., White, S.R.: Viscoelastic Properties of an Epoxy Resin during Cure. J. Compos. Mater. 35(10), 121–123 (2015)

    Google Scholar 

  36. Lee, W.I., Loos, A., Springer, G.: Heat of Reaction, Degree of Cure, and Viscosity of Hercules 3501–6 Resin. J. Compos. Mater. 16(6), 510–520 (1982)

    Article  CAS  Google Scholar 

  37. White, S.R., Kim, Y.K.: Process-Induced Residual Stress Analysis of AS4/3501-6 Composite Material. Mech. Compos. Mater. Struct. 5(2), 153–186 (1998)

  38. Lee, S.-Y., Kang, J.-K.: Residual stresses in a laminated shell during cure. KSME Int. J. 13(8), 625–633 (1999)

    Article  Google Scholar 

  39. Kim, Y.K., White, S.R.: Process-induced stress relaxation analysis of AS4/3501-6 laminate. J. Reinf. Plast. Compos. 16(1), 2–16 (1997)

    Article  CAS  Google Scholar 

Download references

Acknowledgment

This work is financially supported by the youth program of National Natural Science of China (Grant No. 51805141), Hebei natural science foundation of Youth science foundation (Grant No. E2018202243), the Open Fund of State Key Laboratory of Advanced Design and Manufacture for Vehicle Body (No. 31715008).

Author information

Authors and Affiliations

  1. State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin City, 300401, China

    Xuerui Li, Xu Han & Shuyong Duan

  2. Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, Cincinnati, Ohio, 45221, USA

    Gui-Rong Liu

Authors
  1. Xuerui Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xu Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shuyong Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gui-Rong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xuerui Li.

Ethics declarations

Conflict of Interest

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, X., Han, X., Duan, S. et al. A Two-Stage Genetic Algorithm for Molding Parameters Optimization for Minimized Residual Stresses in Composite Laminates During Curing. Appl Compos Mater 28, 1315–1334 (2021). https://doi.org/10.1007/s10443-021-09912-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10443-021-09912-z

Keywords

Search

Navigation