Skip to main content
SpringerLink
Log in

Investigations on the influence of the triaxial state of stress on the failure of polyurethane rigid foams

  • Original Article
  • Published:
Continuum Mechanics and Thermodynamics Aims and scope Submit manuscript

Abstract

This paper investigates the failure strain as a dependence of the stress triaxiality and the Lode angle parameter for polyurethane rigid foams (PUR) of two densities (100 and \(300\,\hbox {kg/m}^{3})\). Tests were carried out in tension for various configurations, resulting in different states of stress triaxiality at various Lode angles in the critical areas. The failure strain was determined for each setup using finite element analysis, as the tests were replicated with numerical models. The displacement at failure recorded in the experiments was imposed for the models, determining the failure strain as a function of stress triaxiality and the Lode angle parameter. The results were validated through the analysis of the failure of sandwich structures with aluminium faces and PUR cores.

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
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Abbreviations

d :

Plastic displacement

D :

Damage evolution parameter

\(e^{\mathrm{c}}\) :

Logarithmic compressive strain

\(e^{\mathrm{t}}\) :

Logarithmic tensile strain

\(I_{1}\) :

First invariant of the stress tensor

\(J_{2}\) :

Second invariant of the deviatoric stress tensor

\(J_{3}\) :

Third invariant of the deviatoric stress tensor

p :

Hydrostatic pressure

\(p^{\mathrm{c}}\) :

Yield stress in hydrostatic compression

\(p^{\mathrm{t}}\) :

Yield stress in hydrostatic tension

q :

von Mises equivalent stress

r :

Normalized third invariant

\(s^{\mathrm{c}}\) :

True compressive stress

\(s^{\mathrm{t}}\) :

True tensile stress

\(\gamma \) :

Bai–Wierzbicki Lode angle-dependent parameter

\(\varepsilon ^{\mathrm{c}}\) :

Engineering compressive strain

\(\varepsilon ^{\mathrm{t}}\) :

Engineering tensile strain

\(\bar{\varepsilon }_{\mathrm{D}}^{\mathrm{pl}}\) :

Critical plastic strain

\(\bar{\varepsilon }^{\mathrm{pl}}\) :

Equivalent plastic strain

\(\dot{\bar{\varepsilon }}^{\mathrm{pl}}\) :

Equivalent plastic strain rate

\(\eta \) :

Stress triaxiality

\(\bar{\theta }\) :

Lode angle

\(\nu \) :

Poisson’s ratio

\(\xi \) :

Lode angle parameter

\({{\varvec{\sigma }}}\) :

Stress tensor

\(\bar{{\varvec{\sigma }}}\) :

Effective stress tensor

\(\sigma ^{\mathrm{c}}\) :

Engineering compressive stress

\(\sigma ^{\mathrm{t}}\) :

Engineering tensile stress

\(\sigma _{ij}\) :

Stress tensor components

\(\sigma _{i}\) :

Principal stresses

\({{\varvec{\sigma }}}^{\prime }\) :

Deviatoric stress tensor

\(\sigma _{ij}^{\prime }\) :

Deviatoric stress tensor components

\(\sigma _{\mathrm{y}}\) :

Equivalent yield stress

\(\Phi \) :

Yield function

\(\psi \) :

Dissipated plastic energy

\(\omega \) :

Damage initiation parameter

References

  1. Gibson, L., Ashby, M.: Cellular Solids: Structure and Properties. Cambridge University Press, Cambridge (1997)

    Book  MATH  Google Scholar 

  2. Şerban, D., Linul, E., Voiconi, T., Marsavina, L., Modler, N.: Numerical evaluation of two-dimensional micromechanical structures of anisotropic cellular materials: case study for polyurethane rigid foams. Iran. Polym. J. 24, 515–529 (2015)

    Article  Google Scholar 

  3. Şerban, D., Voiconi, T., Linul, E., Marşavina, L., Modler, N.: Viscoelastic properties of PUR foams: impact excitation and dynamic mechanical analysis. Materiale Plastice 52, 537–541 (2015)

    Google Scholar 

  4. Marşavina, L., Şerban, D., Pop, C., Negru, R.: Experimental investigation of failure modes for sandwich beams. In: 16th International Conference on Fracture and Damage Mechanics. Key Engineering Materials, vol. 754, pp. 115–118 (2017)

  5. Negru, R., Marşavina, L., Filipescu, H.: Evaluation of generalized MTS criterion for mixed-mode fracture of polyurethane materials. In: Advances in Fracture and Damage Mechanics XII, Key Engineering Materials, vol. 557–558, pp. 117–120 (2014)

  6. Negru, R., Marşavina, L., Voiconi, T., Linul, E., Filipescu, H., Belgiu, G.: Application of TCD for brittle fracture of notched PUR materials. Theor. Appl. Fract. Mech. 80, 87–95 (2015)

    Article  Google Scholar 

  7. Marşavina, L., Berto, F., Negru, R., şerban, D., Linul, E.: An engineering approach to predict mixed mode fracture of PUR foams based on ASED and micromechanical modelling. Theor. Appl. Fract. Mech. 91, 148–154 (2017)

    Article  Google Scholar 

  8. Zapara, M.A., Tutyshkin, N.D., Müller, W.H., Weinberg, K., Wille, R.: A physico-mechanical approach to modeling of metal forming processes—part I: theoretical framework. Contin. Mech. Thermodyn. 20, 231–254 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Hosford, W.: A generalized isotropic yield criterion. J. Appl. Mech. 39(2), 607–609 (1972)

    Article  ADS  Google Scholar 

  10. Bai, Y., Wierzbicki, T.: A new model of metal plasticity and fracture with pressure and Lode dependence. Int. J. Plast. 24, 1071–1096 (2008)

    Article  MATH  Google Scholar 

  11. Deshpande, V., Fleck, N.: Multi-axial yield behaviour of polymer foams. Acta Materialia 49, 1859–1866 (2001)

    Article  ADS  Google Scholar 

  12. Tutyshkin, N.D., Lofink, P., Müller, W.H., Wille, R., Stahn, O.: Constitutive equations of a tensorial model for strain-induced damage of metals based on three invariants. Contin. Mech. Thermodyn. 29, 251–269 (2017)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Abaqus, “User’s Manual,” vol. Analysis (2017)

  14. Şerban, D., Marşavina, L., Modler, N.: Finite element modelling of the progressive damage and failure of thermoplastic polymers in puncture impact. In: Proceedings of the XXIII Italian Group of Fracture Meeting, Procedia Engineering, vol. 109, pp. 97–104 (2015)

  15. ISO 527, Plastics—Determination of Tensile Properties, International Standard Organization (1996)

  16. Bleistein, T., Jung, A., Diebels, S.: A microsphere-based material model for open cell metal foams. Contin. Mech. Thermodyn. 32, 255–267 (2020)

    Article  MathSciNet  ADS  Google Scholar 

  17. Şerban, D., Weber, G., Marşavina, L., Silberschmidt, V., Hufenbach, W.: Tensile properties of semi-crystalline thermoplastic polymers: effects of temperature and strain rates. Polym. Test. 32, 413–425 (2013)

    Article  Google Scholar 

  18. Şerban, D., Marşavina, L., Rusu, L., Negru, R.: Numerical study of the behavior of magnesium alloy AM50 in tensile and torsional loadings. Arch. Appl. Mech. 89(5), 911–917 (2019)

    Article  ADS  Google Scholar 

  19. ISO 6892-1, Metallic materials—tensile testing—part 1: method of test at room temperature. International Standard Organization (2019)

  20. Murugesan, M., Jung, D.W.: Johnson Cook material and failure model parameters estimation of AISI-1045 medium carbon steel for metal forming applications. Materials 12, 609 (2009)

    Article  ADS  Google Scholar 

  21. Bao, Y., Wierzbicki, T.: On the cut-off value of negative triaxiality for fracture. Eng. Fract. Mech. 72, 1049–1069 (2005)

    Article  Google Scholar 

  22. Pineau, A., Benzerga, A., Pardeon, T.: Failure of metals I: Brittle and ductile fracture. Acta Materialia 107, 424–483 (2016)

    Article  ADS  Google Scholar 

  23. Bridgman, P.: Studies in Large Plastic Flow and Fracture—with Special Emphasis on the Effects of Hydrostatic Pressure. McGraw-Hill, New York (1952)

    MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the Romanian National Authority for Scientific Research and Innovation, CCCDI—UEFISCDI, projects number PD 13/2018 and CCCDI—UEFISCDI, project number PN-III-P1-1.2-PCCDI-2017-0391/CIA_CLIM.

Author information

Authors and Affiliations

  1. Department of Mechanics and Strength of Materials, Politehnica University Timişoara, Timisoara, Romania

    Dan-Andrei Şerban, Radu Negru & Liviu Marşavina

  2. Department of Mechatronics, Politehnica University Timişoara, Timisoara, Romania

    Hannelore Filipescu

Authors
  1. Dan-Andrei Şerban
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Radu Negru
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hannelore Filipescu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Liviu Marşavina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dan-Andrei Şerban.

Additional information

Communicated by Luca Placidi and Emilio Barchiesi.

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

Şerban, DA., Negru, R., Filipescu, H. et al. Investigations on the influence of the triaxial state of stress on the failure of polyurethane rigid foams. Continuum Mech. Thermodyn. 35, 905–918 (2023). https://doi.org/10.1007/s00161-020-00924-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00161-020-00924-x

Keywords

Search

Navigation