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Triaxial Characterization of Foams at High Strain Rate Using Split-Hopkinson Pressure Bar

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Abstract

Background

For constitutive modeling of foams at high strain rates, it is necessary to dynamically probe their yield surface under triaxial conditions.

Objective

To demonstrate dynamic triaxial characterization of foams, using a split-Hopkinson pressure bar (SHPB), in which the yield surface can be probed in various directions in the effective versus mean stress space.

Methods

A conventional SHPB is augmented with a triaxial cell, using which one can dynamically apply both axial and lateral loads. The methodology is described in detail, analyzed using a one-dimensional analytical model and demonstrated using experiments.

Results

We show using analysis, and experiments on polyurethane (PU) closed-cell foams that the yield surface in the effective versus hydrostatic stress space can be probed dynamically in more than one direction by varying the cross-sectional area of the specimen used.

Conclusions

A methodology is presented to probe the yield surface of foams at high strain rates using the split-Hopkinson pressure bar. It was found that the uniaxial strength of PU foams increased with the loading rates. However, there was no significant enhancement of the hydrostatic strength with respect to the loading rates.

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Notes

  1. It is important to ensure that no air bubbles are trapped in the cell while filling the confining fluid. A video demonstration is included as a supplementary material.

References

  1. Miller RE (2000) A continuum plasticity model for the constitutive and indentation behaviour of foamed metals. Int J Mech Sci 42:729–754

    Article  MATH  Google Scholar 

  2. Gibson LJ, Ashby MF, Zhang J, Triantafillou TC (1989) Failure surfaces for cellular materials under multiaxial loads-i.modelling. Int J Mech Sci 31(9):635–663

    Article  Google Scholar 

  3. Deshpande VS, Fleck NA (2000) Isotropic constitutive models for metallic foams. J Mech Phys Solids 48(6–7):1253–1283

    Article  MATH  Google Scholar 

  4. Doyoyo M, Wierzbicki T (2003) Experimental studies on the yield behavior of ductile and brittle aluminum foams. Int J Plast 19(8):1195–1214

    Article  MATH  Google Scholar 

  5. Huang WM (2003) A simple approach to estimate failure surface of polymer and aluminum foams under multiaxial loads. Int J Mech Sci 45(9):1531–1540

    Article  MATH  Google Scholar 

  6. Blazy JS, Marie-Louise A, Forest S, Chastel Y, Pineau A, Awade A, Grolleron C, Moussy F (2004) Deformation and fracture of aluminium foams under proportional and non proportional multi-axial loading: Statistical analysis and size effect. Int J Mech Sci 46(2):217–244

    Article  Google Scholar 

  7. Gioux G, McCormack TM, Gibson LJ (2000) Failure of aluminum foams under multiaxial loads. Int J Mech Sci 42(6):1097–1117

    Article  MATH  Google Scholar 

  8. Hanssen AG, Hopperstad OS, Langseth M, Ilstad H (2002) Validation of constitutive models applicable to aluminium foams. Int J Mech Sci 44(2):359–406

    Article  Google Scholar 

  9. Triantafillou TC, Zhang J, Shercliff TL, Gibson LJ, Ashby MF (1989) Failure surfaces for cellular materials under multiaxial loads-ii. comparison of models with experiment. Int J Mech Sci 31(9):665–678

    Article  Google Scholar 

  10. Sridhar I, Fleck NA (2005) The multiaxial yield behaviour of an aluminium alloy foam. J Mater Sci 40(15):4005–4008

    Article  Google Scholar 

  11. Huo X, Jiang Z, Luo Q, Li Q, Sun G (2022) Mechanical characterization and numerical modeling on the yield and fracture behaviors of polymethacrylimide (pmi) foam materials. Int J Mech Sci 218:107033

  12. Vengatachalam B, Huang R, Poh LH, Liu Z, Qin Q, Swaddiwudhipong S (2021) Initial yield behaviour of closed-cell aluminium foams in biaxial loading. Int J Mech Sci 191:106063

  13. Wang E, Sun G, Zheng G, Li Q (2020) Characterization of initial and subsequent yield behaviors of closed-cell aluminum foams under multiaxial loadings. Compos B Eng 202:108247

  14. Felten M, Diebels S, Jung A (2020) Experimental investigation of initial yield surfaces of solid foams and their evolution under subsequent loading. Mater Sci Eng, A 791:139762

  15. Ruan D, Lu G, Ong LS, Wang B (2007) Triaxial compression of aluminium foams. Compos Sci Technol 67(6):1218–1234

    Article  Google Scholar 

  16. Li P, Guo YB, Shim VPW (2020) A rate-sensitive constitutive model for anisotropic cellular materials - application to a transversely isotropic polyurethane foam. Int J Solids Struct 206:43–58

    Article  Google Scholar 

  17. Luo G, Xue P, Li Y (2021) Experimental investigation on the yield behavior of metal foam under shear-compression combined loading. SCIENCE CHINA Technol Sci 64(7):1412–1422

    Article  Google Scholar 

  18. Kuhn H, Medlin D (2000) ASM Handbook Volume 8: Mechanical Testing and Evaluation. American Society of Materials

  19. Xia K, Yao W (2015) Dynamic rock tests using split hopkinson (kolsky) bar system-a review. J Rock Mech Geotech Eng 7(1):27–59

    Article  Google Scholar 

  20. Chen W, Ravichandran G (2000) Failure mode transition in ceramics under dynamic multiaxial compression. Int J Fract 101(1):141–159

    Article  Google Scholar 

  21. Bailly P, Delvare F, Vial J, Hanus JL, Biessy M, Picart D (2011) Dynamic behavior of an aggregate material at simultaneous high pressure and strain rate: Shpb triaxial tests. Int J Impact Eng 38(2–3):73–84

    Article  Google Scholar 

  22. Chen W, Lu F (2000) A technique for dynamic proportional multiaxial compression on soft materials. Exp Mech 40(2):226–230

    Article  Google Scholar 

  23. Kabir ME, Chen WW (2009) Measurement of specimen dimensions and dynamic pressure in dynamic triaxial experiments. Rev Sci Instrum 80(12):125111

  24. Rome J, Isaacs J, Nemat-Nasser S (2002) Hopkinson Techniques for Dynamic Triaxial Compression Tests, pages 3–12. Springer Netherlands, Dordrecht

  25. Senol K, Shukla A (2019) Dynamic response of closed cell pvc foams subjected to underwater shock loading. Int J Impact Eng 130:214–225

    Article  Google Scholar 

  26. Sadd MH (2009) Elasticity: Theory, applications, and numerics. Academic Press

    Google Scholar 

  27. Chen W, Zhang B, Forrestal MJ (1999) A split hopkinson bar technique for low-impedance materials. Exp Mech 39(2):81–85

    Article  Google Scholar 

  28. Peirce D, Shih CF, Needleman A (1984) A tangent modulus method for rate dependent solids. Comput Struct 18(5):875–887

    Article  MATH  Google Scholar 

  29. Needleman A, Tvergaard V, Van der Giessen E (2015) Indentation of elastically soft and plastically compressible solids. Acta Mech Sin 31(4):473–480

    Article  MathSciNet  MATH  Google Scholar 

  30. Fox C, Kishore S, Senol K, Shukla A (2021) Experiments in measuring dynamic hydrostatic constitutive properties of soft materials. Mech Mater 160:103948

  31. Viot P (2009) Hydrostatic compression on polypropylene foam. Int J Impact Eng 36(7):975–989

    Article  Google Scholar 

  32. Song B, Chen W (2005) Split hopkinson pressure bar techniques for characterizing soft materials. Latin American Journal of Solids and Structures 2(2):113–152

    Google Scholar 

  33. Kwon J, Subhash G (2010) Compressive strain rate sensitivity of ballistic gelatin. J Biomech 43(3):420–425

    Article  Google Scholar 

  34. Ravichandran G, Subhash G (1994) Critical appraisal of limiting strain rates for compression testing of ceramics in a split hopkinson pressure bar. J Am Ceram Soc 77(1):263–267

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Kandi, Telangana, 502285, India

    D. Kumar & S. N. Khaderi

  2. Department of Mechanical and Product Design Engineering, School of Engineering, Swinburne University of Technology, Hawthorn, VIC3122, Australia

    D. Ruan

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  1. D. Kumar
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  2. D. Ruan
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Correspondence to S. N. Khaderi.

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Kumar, D., Ruan, D. & Khaderi, S.N. Triaxial Characterization of Foams at High Strain Rate Using Split-Hopkinson Pressure Bar. Exp Mech 63, 1171–1192 (2023). https://doi.org/10.1007/s11340-023-00978-3

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  • DOI: https://doi.org/10.1007/s11340-023-00978-3

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