Advertisement

Mechanics of Time-Dependent Materials

, Volume 22, Issue 3, pp 351–371 | Cite as

Time dependent voiding mechanisms in polyamide 6 submitted to high stress triaxiality: experimental characterisation and finite element modelling

  • Nathan SellesEmail author
  • Andrew King
  • Henry Proudhon
  • Nicolas Saintier
  • Lucien Laiarinandrasana
Article

Abstract

Double notched round bars made of semi-crystalline polymer polyamide 6 (PA6) were submitted to monotonic tensile and creep tests. The two notches had a root radius of 0.45 mm, which imposes a multiaxial stress state and a state of high triaxiality in the net (minimal) section of the specimens. Tests were carried out until the failure occurred from one of the notches. The other one, unbroken but deformed under steady strain rate or steady load, was inspected using the Synchrotron Radiation Computed Tomography (SRCT) technique. These 3D through thickness inspections allowed the study of microstructural evolution at the peak stress for the monotonic tensile test and at the beginning of the tertiary creep for the creep tests. Cavitation features were assessed with a micrometre resolution within the notched region. Spatial distributions of void volume fraction (\(\mathit{Vf}\)) and void morphology were studied. Voiding mechanisms were similar under steady strain rates and steady loads. The maximum values of \(\mathit{Vf}\) were located between the axis of revolution of the specimens and the notch surface and voids were considered as flat cylinders with a circular basis perpendicular to the loading direction. A model, based on porous plasticity, was used to simulate the mechanical response of this PA6 material under high stress triaxiality. Both macroscopic behaviour (loading curves) and voiding micro-mechanisms (radial distributions of void volume fraction) were accurately predicted using finite element simulations.

Keywords

Semi-crystalline polymer Voiding Synchrotron radiation computed tomography Tensile test Creep test Finite elements 

Notes

Acknowledgements

The authors should thank Anthony Bunsell for scientific and technical discussions and Nicolas Lenoir (UMS 3626 Placamat, CNRS Université de Bordeaux) for tomographic observations of the undeformed notch.

References

  1. Beremin, F.M.: Elastoplastic calculation of circumferentially notched specimens using the finite element method. J. Mech. 4(3), 307–325 (1980) Google Scholar
  2. Besson, J., Foerch, R.: Large scale object-oriented finite element code design. Comput. Methods Appl. Mech. Eng. 142, 165–187 (1997) CrossRefzbMATHGoogle Scholar
  3. Besson, J., Guillemer-Neel, C.: An extension of the Green and Gurson models to kinematic hardening. Mech. Mater. 35, 1–18 (2003) CrossRefGoogle Scholar
  4. Besson, J.: Damage of ductile materials deforming under multiple plastic or viscoplastic mechanisms. Int. J. Plast. 25, 2204–2221 (2009) CrossRefGoogle Scholar
  5. Boisot, G., Laiarinandrasana, L., Besson, J., Fond, C., Hochstetter, G.: Experimental investigations and modeling of volume change induced by void growth in polyamide 11. Int. J. Solids Struct. 48, 2642–2654 (2011) CrossRefGoogle Scholar
  6. Bridgman, P.: The stress distribution at the neck of a tension specimen. Trans. Am. Soc. Mech. Eng. 32, 553–574 (1944) Google Scholar
  7. Cao, T.S., Mazière, M., Danas, K., Besson, J.: A model for ductile damage prediction at low stress triaxialities incorporating void shape change and void rotation. Int. J. Solids Struct. 63, 240–263 (2015) CrossRefGoogle Scholar
  8. Cayzac, C., Saï, K., Laiarinandrasana, L.: Damage based constitutive relationships in semi-crystalline polymer by using multi-mechanisms model. Int. J. Plast. 51, 47–64 (2013) CrossRefGoogle Scholar
  9. Challier, M., Besson, J., Laiarinandrasana, L., Piques, R.: Damaged and fracture of polyvinylidene fluoride (PVDF) at 20 °C: experiments and modelling. Eng. Fract. Mech. 73, 79–90 (2006) CrossRefGoogle Scholar
  10. Cheng, Y., Laiarinandrasana, L., Helfen, L., Proudhon, H., Klinkova, O., Baumbach, T., Morgeneyer, T.F.: 3D damage micromechanisms in polyamide 6 ahead of a severe notch studied by in situ synchrotron laminography. Macromol. Chem. Phys. 217, 701–715 (2016) CrossRefGoogle Scholar
  11. Cloetens, P., Pateyron-Salome, M., Buffiere, J.Y., Peix, G., Baruchel, J., Peyrin, F., Schlenker, M.: Observation of microstructure and damage in materials by phase sensitive radiography and tomography. J. Appl. Phys. 81, 5878–5886 (1997) CrossRefGoogle Scholar
  12. Feret, L.: La grosseur des grains de matières pulvérulentes. Premières communications de la nouvelle Association Internationale pour l’essai des matériaux. groupe D, pp. 428–436 (1930) Google Scholar
  13. Gologanu, M., Leblond, J.B., Devaux, J.: Approximate models for ductile metals containing spherical voids—case of axisymmetric prolate ellipsoidal cavities. J. Mech. Phys. Solids 41, 1723–1754 (1993) CrossRefzbMATHGoogle Scholar
  14. Gologanu, M., Leblond, J.B., Devaux, J.: Theoretical models for void coalescence in porous ductile solids, II: coalescence “in columns”. Int. J. Solids Struct. 38, 5595–5604 (2001) CrossRefzbMATHGoogle Scholar
  15. Gurson, A.: Continuum theory of ductile rupture by void nucleation and growth, part 1: yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. 99, 2–15 (1977) CrossRefGoogle Scholar
  16. Lafarge, M.: Modélisation couplée comportement-endommagement et critères de rupture dans le domaine de la transition du PVDF. PhD thesis, École des Mines de Paris (2007) (in French) Google Scholar
  17. Laiarinandrasana, L., Morgeneyer, T., Proudhon, H., Regrain, C.: Damage of semicrystalline polyamide 6 assessed by 3D X-ray tomography: from microstructural evolution to constitutive modelling. J. Polym. Sci., Part B, Polym. Phys. 48, 1516–1525 (2010) CrossRefGoogle Scholar
  18. Laiarinandrasana, L., Morgeneyer, T., Proudhon, H., N’Guyen, F., Maire, E.: Effect of multiaxial stress state on morphology and spatial distribution of voids in deformed semicrystalline polymer assessed by X-ray tomography. Macromolecules 45, 4658–4668 (2012) CrossRefGoogle Scholar
  19. Laiarinandrasana, L., Klinkova, O., Nguyen, F., Proudhon, H., Morgeneyer, T.F., Ludwig, W.: Three dimensional quantification of anisotropic void evolution in deformed semi-crystalline polyamide 6. Int. J. Plast. 83, 19–36 (2016a) CrossRefGoogle Scholar
  20. Laiarinandrasana, L., Selles, N., Klinkova, F., Morgeneyer, T.F., Proudhon, H., Helfen, L.: Structural versus microstructural evolution of semi-crystalline polymers during necking under tension: influence of the skin-core effects, the relative humidity and the strain rate. Polym. Test. 55, 297–309 (2016b) CrossRefGoogle Scholar
  21. Pawlak, A., Galeski, A.: Cavitation during tensile deformation of polypropylene. Macromolecules 41, 2839–2851 (2008) CrossRefGoogle Scholar
  22. Pawlak, A., Galeski, A.: Cavitation and morphological changes in polypropylene deformed at elevated temperatures. J. Polym. Sci., Part B, Polym. Phys. 48, 1271–1280 (2010) CrossRefGoogle Scholar
  23. Ponçot, M., Addiego, F., Dahoun, A.: True intrinsic mechanical behaviour of semi-crystalline and amorphous polymers: influences of volume deformation and cavities shape. Int. J. Plast. 40, 126–139 (2013) CrossRefGoogle Scholar
  24. Poulet, P.A., Hochstetter, G., King, A., Proudhon, H., Joannès, S., Laiarinandrasana, L.: Observations by in-situ X-ray synchrotron computed tomography of the microstructural evolution of semi-crystalline polyamide 11 during deformation. Polym. Test. 56, 245–260 (2016) CrossRefGoogle Scholar
  25. Regrain, C., Laiarinandrasana, L., Toillon, S.: Experimental and numerical study of creep rupture behavior of PA6. Eng. Fract. Mech. 76, 2656–2665 (2009a) CrossRefGoogle Scholar
  26. Regrain, C., Laiarinandrasana, L., Toillon, S., Saï, K.: Multi-mechanism models for semi-crystalline polymer: constitutive relations and finite element implementation. Int. J. Plast. 25, 1253–1279 (2009b) CrossRefzbMATHGoogle Scholar
  27. Saï, K., Laiarinandrasana, L., Naceur, I.B., Besson, J., Jeridi, J., Cailletaud, G.: Multi-mechanism damage-plasticity model for semi-crystalline polymer: creep damage of notched specimen of PA6. Mater. Sci. Eng. A 528, 1087–1093 (2011) CrossRefGoogle Scholar
  28. Selles, N., Nguyen, F., Morgeneyer, T.F., Proudhon, H., Ludwig, W., Laiarinandrasana, L.: Comparison of voiding mechanisms in semi-crystalline polyamide 6 during tensile and creep tests. Polym. Test. 49, 137–146 (2016a) CrossRefGoogle Scholar
  29. Selles, N., Saintier, N., Laiarinandrasana, L.: Voiding mechanisms in semi-crystalline polyamide 6 during creep tests assessed by damage based constitutive relationships and finite elements calculations. Int. J. Plast. 86, 112–127 (2016b) CrossRefGoogle Scholar
  30. Stoer, J.: Principles of sequential quadratic programming methods for solving nonlinear programs. In: Computational Mathematical Programming, pp. 165–207. Springer, Berlin (1985) CrossRefGoogle Scholar
  31. Tvergaard, V.: On localization in ductile materials containing spherical voids. Int. J. Fract. 18, 237–252 (1982) Google Scholar
  32. Tvergaard, V., Needleman, A.: Analysis of the cupcone fracture in a round tensile bar. Acta Mater. 32, 157–169 (1984) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Nathan Selles
    • 1
    Email author
  • Andrew King
    • 2
  • Henry Proudhon
    • 1
  • Nicolas Saintier
    • 3
  • Lucien Laiarinandrasana
    • 1
  1. 1.MINES ParisTech, CNRS UMR7633PSL Research University MAT-Centre des MatériauxEvry CedexFrance
  2. 2.SOLEIL SynchrotronSaint-AubinFrance
  3. 3.Arts et Métiers ParisTech, I2M-DuMAS, CNRS UMR5295Esplanade des Arts et MétiersTalenceFrance

Personalised recommendations