Skip to main content
SpringerLink
Log in

A multi-scale analysis of local stresses development during the cure of a composite tooling material

  • Original Research
  • Published:
International Journal of Material Forming Aims and scope Submit manuscript

Abstract

This paper is dedicated to the cure of an in-plane isotropic carbon-epoxy tooling material presenting a specific mesostructure. Eshelby-Kröner self-consistent model (EKSC) is used to achieve a two-steps scale transition procedure, allowing relating microscopic to macroscopic properties of the material, and estimating its multi-scale mechanical states. This procedure is used to predict the local residual stresses due to thermal and chemical shrinkage of the resin, depending on the manufacturing process conditions. An experimental investigation provides the BMI resin cure kinetics and mechanical properties as a function of the temperature and conversion degree. The consequences of these evolutions on the local mechanical states are investigated and discussed.

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
Fig. 10

Similar content being viewed by others

References

  1. Adolf DB, Chambers RS (1997) Verification of the capability for quantitative stress prediction during epoxy cure. Polymer 38(21):5481–5490

    Article  Google Scholar 

  2. Bailleul JL (1997) Optimisation du cycle de cuisson des pièces épaisses en matériau composite. Application à un préimprégné résine époxyde/fibres de verre. Doctoral Thesis, University of Nantes

  3. Berryman J, Berge P (1996) Critique of two explicit schemes for estimating elastic properties of multiphase composites. Mech Mater 22:149–164

    Article  Google Scholar 

  4. Bogetti TA, Gillespie JW (1992) Process-induced stress and deformation in thick-section thermo-set composite laminates. J Compos Mater 26:626–659

    Article  Google Scholar 

  5. Dillman SH, Seferis JC (1987) Kinetic viscoelasticity for the dynamic mechanical properties of polymer system. J Macromol Sci Pure Appl Chem 27:749–772

    Google Scholar 

  6. Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc Lond A241:376–396

    Article  MathSciNet  Google Scholar 

  7. Etienne S, Cavaillé JY, Perez J, Salvia M (1982) Automatic system for analysis of micromechanical properties. Rev Sci Instrum 53:1261–1266

    Article  Google Scholar 

  8. Feyel F, Chaboche JL (2000) FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials. Comput Meth Appl 183(3–4):309–330

    Article  MATH  Google Scholar 

  9. Fiedler B, Hojo M, Ochiai S, Schulte K, Ando M (2001) Failure behavior of an epoxy matrix under different kinds of static loading. Compos Sci Technol 61:1615–1624

    Article  Google Scholar 

  10. Fréour S, Gloaguen D, François M, Guillén R (2004) Thermal properties of polycrystals - X-ray diffraction and scale transition modelling. Phys Status Solidi 201:59–71

    Article  Google Scholar 

  11. Fréour S, Jacquemin F, Guillén R (2005) On an analytical self-consistent model for internal stress prediction in fiber-reinforced composites submitted to hygroelastic load. J Reinforc Plast Compos 24:1365–1377

    Article  Google Scholar 

  12. Fréour S, Jacquemin F, Guillén R (2006) Extension of Mori-Tanaka approach to hygroelastic loading of fiber-reinforced composites - Comparison with Eshelby-Kröner self-consistent model. J Reinf Plast Compos 25:1039–1053

    Article  Google Scholar 

  13. Fréour S, Jacquemin F, Guillén R (2007) On the use of the geometric mean approximation in estimating the effective hygro-elastic behaviour of fiber-reinforced composites. J Mater Sci 42:7537–7543

    Article  Google Scholar 

  14. Grandidier JC, Drapier S, Potier-Ferry M (2001) A structural approach of plastic microbuckling in long fibre composites: comparison with theoretical and experimental results. Int J Solid Struct 38:3877–3904

    Article  MATH  Google Scholar 

  15. Ha SK, Jin KK, Huang Y (2008) Effects of fiber arrangement on mechanical behavior of unidirectional composites. J Compos Mater 42:1851–1871

    Article  Google Scholar 

  16. Ha SK, Jin KK, Huang Y (2008) Micro-mechanics of failure (MMF) for continuous fiber reinforced composites. J Compos Mater 42:1873–1895

    Article  Google Scholar 

  17. Hashin Z, Shtrikman S (1963) A variational approach to the elastic behavior of multiphase materials. J Mech Phys Solid 11:127–140

    Article  MathSciNet  MATH  Google Scholar 

  18. Hexcel Composites France (2010) Hexply M61 Datasheet, Hextool User Guide and Hextool DataSheet (www.hexcel.com/); internal reports and exchanges with C. Dauphin and M. Bonnafoux (Hexcel Composites France), unpublished results

  19. Hill R (1967) The essential structure of constitutive laws for metals composites and polycrystals. J Mech Phys Solid 15:79–95

    Article  Google Scholar 

  20. Jacquemin F, Fréour S, Guillén R (2005) A hygroelastic self-consistent model for fiber-reinforced composites. J Reinf Plast Compos 24:485–502

    Article  Google Scholar 

  21. Jin KK, Huang Y, Lee YH, Ha SK (2008) Distribution of micro stresses and interfacial tractions in unidirectional composites. J Compos Mater 42:1825–1849

    Article  Google Scholar 

  22. Kamal MR, Sourour S (1973) Kinetics and thermal characterization of thermosets cure. Polym Eng Sci 13:59–64

    Article  Google Scholar 

  23. Kocks UF, Tomé CN, Wenk HR (1998) Texture and anisotropy. Cambridge University Press

  24. Kröner E (1958) Berechnung der elastischen Konstanten des Vielkristalls aus des Konstanten des Einkristalls. Z Phys 151:504–508

    Article  Google Scholar 

  25. Kugler D, Moon TJ (2002) Identification of the most significant processing parameters on the development of fiber waviness in thin laminates. J Compos Mater 36(12):1451–1479

    Article  Google Scholar 

  26. Lacoste E, Fréour S, Jacquemin F (2010) On the validity of the self-consistent scale transition model for inclusions with varying morphologies. Mech Mater 42:218–226

    Article  Google Scholar 

  27. Matsuoka M, Quan X, Bair HE, Boyle DJ (1989) A model for the curing reaction of epoxy resins. Macromolecules 22:4093–4098

    Article  Google Scholar 

  28. Menard KP (1999) Dynamic mechanical analysis: a practical introduction. CRC, Boca Raton

    Book  Google Scholar 

  29. Mori T, Tanaka K (1973) Average stress in the matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica 21:571–574

    Article  Google Scholar 

  30. Moulinec H, Suquet P (1998) A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput Meth Appl Mech Eng 157:69–94

    Article  MathSciNet  MATH  Google Scholar 

  31. Msallem YA (2008) Caractérisation thermique et mécanique d’un matériau composite aéronautique pendant le procédé d’élaboration – Contribution à l’estimation des contraintes résiduelles. Doctoral Thesis, Ecole Centrale de Nantes

  32. Msallem YA, Jacquemin F, Boyard N, Poitou A, Delaunay D, Chatel S (2010) Material characterization and residual stresses simulation during the manufacturing process of epoxy matrix composites. Compos Appl Sci Manuf 41(1):108–115

    Article  Google Scholar 

  33. Mura T (1982) Micromechanics of defects in solids. Martinus Nijhoff Publishers, The Hague

    Book  Google Scholar 

  34. Niu K, Talreja R (2000) Modeling of compressive failure in fiber reinforced composites. Int J Solid Struct 37:2405–2428

    Article  MATH  Google Scholar 

  35. Parlevliet PP, Bersee HEN, Beukers A (2006) Residual stresses in thermoplastic composites – a study of the literature. Part I: Formation of residual stresses. Compos Appl Sci Manuf 37:1847–1857

    Article  Google Scholar 

  36. Parlevliet PP, Bersee HEN, Beukers A (2007) Residual stresses in thermoplastic composites – a study of the literature. Part II: Experimental techniques. Compos Appl Sci Manuf 38:651–665

    Article  Google Scholar 

  37. Parlevliet PP, Bersee HEN, Beukers A (2007) Residual stresses in thermoplastic composites – a study of the literature. Part III: Effects of thermal residual stresses. Compos Appl Sci Manuf) 38:1581–1596

    Article  Google Scholar 

  38. Pascault JP, Sautereau H, Verdu J, Williams R (2002) Thermosetting polymers. Marcel Dekker Inc. p. 157–196

  39. Rabearison N, Jochum C, Grandidier JC (2009) A FEM coupling model for properties prediction during the curing of an epoxy matrix. Comput Mater Sci 45(3):715–724

    Article  Google Scholar 

  40. Rosen VW (1965) Mechanics of composite strengthening. In: Fiber Composite Materials. American Society of Metals, Metals Park, Ohio, pp 37–75

  41. Sanford WM, McCullough RL (1990) A free-volume-based approach to modeling thermoset cure behavior. J Polymer Sci, Part B: Polymer Phys 28:973–1000

    Article  Google Scholar 

  42. Sbirrazzuoli N, Vyazovkin S (2002) Learning about epoxy cure mechanisms from isoconversional analysis of DSC data. Thermochim Acta 388(1–2):289–298

    Article  Google Scholar 

  43. Schultheisz CR, Waas AM (1996) Compressive failure of composites, part I: testing and micromechanical theories. Prog Aerosp Sci 32(1):1–42

    Article  Google Scholar 

  44. Schultheisz CR, Waas AM (1996) Compressive failure of composites, part II: Experimental studies. Prog Aerosp Sci 32(1):43–78

    Article  Google Scholar 

  45. Terekhina S, Salvia M, Fouvry S (2011) Contact fatigue and wear behaviour of bismaleimide polymer subjected to fretting loading under various temperature conditions. Tribol Int 44(4):396–408

    Article  Google Scholar 

  46. Tsai SW, Hahn HT (1980) Introduction to composite materials. Technomic, Westport

    Google Scholar 

  47. Welzel U, Fréour S, Mittemeijer EJ (2005) Direction-Dependent Elastic Grain-Interaction Models – A Comparative Study. Philos Mag 85:2391–2414

    Article  Google Scholar 

  48. White SR, Kim KS (1998) Process-induced residual stress analysis of AS4/3501-6 composite material. Mech Compos Mater Struct 5:153–186

    Article  Google Scholar 

  49. Zhao LG, Warrior NA, Long AC (2007) A thermo-viscoelastic analysis of process-induced residual stress in fibre-reinforced polymer-matrix composites. Mater Sci Eng, A 452–453:483–498

    Article  Google Scholar 

Download references

Acknowledgments

The authors wish to acknowledge C. Dauphin and M. Bonnafoux (from Hexcel Composites France) for the valuable information provided on the Hextool, and for the supplied materials.

Author information

Authors and Affiliations

  1. Institut de Recherche en Génie Civil et Mécanique (UMR CNRS 6183), LUNAM Université - Université de Nantes - Ecole Centrale de Nantes, 37 Bd de l’Université, BP 406, 44602, Saint-Nazaire, France

    E. Lacoste, S. Fréour & F. Jacquemin

  2. Laboratoire de Tribologie et Dynamique des Systèmes (UMR CNRS 5513), Ecole Centrale de Lyon, 36 Avenue Guy de Collongue, 69134, Ecully Cedex, France

    K. Szymanska, S. Terekhina & M. Salvia

Authors
  1. E. Lacoste
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Szymanska
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Terekhina
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Fréour
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. F. Jacquemin
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. M. Salvia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. Jacquemin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lacoste, E., Szymanska, K., Terekhina, S. et al. A multi-scale analysis of local stresses development during the cure of a composite tooling material. Int J Mater Form 6, 467–482 (2013). https://doi.org/10.1007/s12289-012-1100-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12289-012-1100-0

Keywords

Search

Navigation