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Strain Rate Dependent Compressive Response of Open Cell Polyurethane Foam

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Abstract

Polymeric foams are used for impact protection due to their ability to absorb large amounts of strain energy. In this work, the compressive response of an open cell polyurethane foam currently used as liner in the advanced combat helmet is examined across strain rates. A traditional load frame is used to investigate the quasi-static behavior, and two different modifications of a conventional Kolsky (split-Hopkinson) bar configuration are used to probe the dynamic response. A unique, independent method not relying on strain gage signals is presented that leverages high-speed full-field imaging to track the velocity on each side of the sample-bar interface and used to extract the dynamic stress-strain response; the results are compared against traditional strain gage measurements. X-ray tomography is used to examine the global morphological characteristics of the foam. The foam is found to be strongly rate dependent, where the characteristic properties vary logarithmically with strain rate. An analytical expression is presented to describe the rate dependency that collapses all stress-strain curves on a master curve. Full-field kinematic data from digital image correlation taken during loading is used to extract a nonlinear Poisson’s ratio as a function of strain, which is found to be strain rate insensitive. A tangent Poisson function is used to explore the foam’s auxetic behavior. These findings provide insight on physically-based constitutive modeling of foams, crucial to predictive brain injury simulations, as well as motivate the need to probe local heterogenous behavior across strain rates moving forward.

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References

  1. Ashby MF (1983) The mechanical properties of cellular solids. Metall Trans A 14(9):1755–1769

    Google Scholar 

  2. Gibson LJ, Ashby MF (1999) Cellular solids: structure and properties. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  3. Lakes R (2009) Viscoelastic materials. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  4. Siviour C, Jordan JL (2016) High strain rate mechanics of polymers: a review. J Dyn Behav Mater 2 (1):15–32

    Google Scholar 

  5. Moss WC, King MJ, Blackman EG (2014) Towards reducing impact-induced brain injury: lessons from a computational study of army and football helmet pads. Comput Methods Biomech Biomed Eng 17(11):1173–1184

    Google Scholar 

  6. Zhang L, Makwana R, Sharma S (2013) Brain response to primary blast wave using validated finite element models of human head and advanced combat helmet. Front Neurol 4:88

    Google Scholar 

  7. Li Y, Li X, Gao X-L (2015) Modeling of advanced combat helmet under ballistic impact, vol 82

  8. Li X, Gao X-L, Kleiven S (2016) Behind helmet blunt trauma induced by ballistic impact: a computational model. Int J Impact Eng 91:56–67

    Google Scholar 

  9. Nagy A, Ko W, Lindholm US (1974) Mechanical behavior of foamed materials under dynamic compression. J Cell Plast 10(3):127–134

    Google Scholar 

  10. Sun Y, Li Q (2017) Dynamic compressive behaviour of cellular materials: a review of phenomenon, mechanism and modelling. International Journal of Impact Engineering

  11. Avalle M, Belingardi G, Ibba A (2007) Mechanical models of cellular solids: parameters identification from experimental tests. Int J Impact Eng 34(1):3–27

    Google Scholar 

  12. Chen W, Song B (2010) Split Hopkinson (Kolsky) bar: design, testing and applications. Springer Science & Business Media

  13. Gray G, Blumenthal W (2000) Split-hopkinson pressure bar testing of soft materials. ASM International, Materials Park, pp 488–496

    Google Scholar 

  14. Kolsky H (1949) An investigation of the mechanical properties of materials at very high rates of loading. Proc Phys Soc, Sect B 62(11):676

    Google Scholar 

  15. 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

    Google Scholar 

  16. Yang L, Shim V (2005) An analysis of stress uniformity in split hopkinson bar test specimens. Int J Impact Eng 31(2):129–150

    Google Scholar 

  17. Song B, Chen W (2004) Dynamic stress equilibration in split hopkinson pressure bar tests on soft materials. Exp Mech 44(3):300–312

    Google Scholar 

  18. Daniel IM, Cho J-M, Werner BT (2013) Characterization and modeling of stain-rate-dependent behavior of polymeric foams. Compos A: Appl Sci Manuf 45:70–78

    Google Scholar 

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

    Google Scholar 

  20. Chen W, Lu F, Zhou B (2000) A quartz-crystal-embedded split hopkinson pressure bar for soft materials. Exp Mech 40(1):1–6

    Google Scholar 

  21. Song B, Chen W, Jiang X (2005) Split hopkinson pressure bar experiments on polymeric foams. Int J Veh Des 37(2-3):185–198

    Google Scholar 

  22. Chen W, Lu F, Winfree N (2002) High-strain-rate compressive behavior of a rigid polyurethane foam with various densities. Exp Mech 42(1):65–73

    Google Scholar 

  23. Zhao H, Gary G (1997) A new method for the separation of waves. application to the shpb technique for an unlimited duration of measurement. J Mech Phys Solids 45(7):1185–1202

    Google Scholar 

  24. Shim J, Mohr D (2009) Using split hopkinson pressure bars to perform large strain compression tests on polyurea at low, intermediate and high strain rates. Int J Impact Eng 36(9):1116–1127

    Google Scholar 

  25. Casem D, Fourney WL, Chang P (2003) A polymeric split hopkinson pressure bar instrumented with velocity gages. Exp Mech 43(4):420–427

    Google Scholar 

  26. Whisler D, Kim H (2015) Experimental and simulated high strain dynamic loading of polyurethane foam. Polym Test 41:219–230

    Google Scholar 

  27. Liu J, Saletti D, Pattofatto S, Zhao H (2014) Impact testing of polymeric foam using hopkinson bars and digital image analysis. Polym Test 36:101–109

    Google Scholar 

  28. Song B, Lu W-Y, Syn CJ, Chen W (2009) The effects of strain rate, density, and temperature on the mechanical properties of polymethylene diisocyanate (pmdi)-based rigid polyurethane foams during compression. J Mater Sci 44(2):351–357

    Google Scholar 

  29. Song B, Chen W, Dou S, Winfree NA, Kang JH (2005) Strain-rate effects on elastic and early cell-collapse responses of a polystyrene foam. Int J Impact Eng 31(5):509–521

    Google Scholar 

  30. Zhao H (1997) Testing of polymeric foams at high and medium strain rates. Polym Test 16(5):507–516

    Google Scholar 

  31. Lee YS, Park NH, Yoon HS (2010) Dynamic mechanical characteristics of expanded polypropylene foams. J Cell Plast 46(1):43–55

    Google Scholar 

  32. Saha M, Mahfuz H, Chakravarty U, Uddin M, Kabir ME, Jeelani S (2005) Effect of density, microstructure, and strain rate on compression behavior of polymeric foams. Mater Sci Eng: A 406(1-2):328–336

    Google Scholar 

  33. Bouix R, Viot P, Lataillade J-L (2009) Polypropylene foam behaviour under dynamic loadings: Strain rate, density and microstructure effects. Int J Impact Eng 36(2):329–342

    Google Scholar 

  34. Ouellet S, Cronin D, Worswick M (2006) Compressive response of polymeric foams under quasi-static, medium and high strain rate conditions. Polym Test 25(6):731–743

    Google Scholar 

  35. Cronin D, Ouellet S (2016) Low density polyethylene, expanded polystyrene and expanded polypropylene: Strain rate and size effects on mechanical properties. Polym Test 53:40–50

    Google Scholar 

  36. Bhagavathula KB, Azar A, Ouellet S, Satapathy S, Dennison CR, Hogan JD (2018) High rate compressive behaviour of a dilatant polymeric foam. Journal of Dynamic Behavior of Materials 4:573–585

  37. Subhash G, Liu Q, Gao X-L (2006) Quasistatic and high strain rate uniaxial compressive response of polymeric structural foams. Int J Impact Eng 32(7):1113–1126

    Google Scholar 

  38. Barnes A, Ravi-Chandar K, Kyriakides S, Gaitanaros S (2014) Dynamic crushing of aluminum foams: Part i–experiments. Int J Solids Struct 51(9):1631–1645

    Google Scholar 

  39. Maire E, Withers P (2014) Quantitative x-ray tomography. Int Mater Rev 59(1):1–43

    Google Scholar 

  40. Dillard T, N’guyen F, Maire E, Salvo L, Forest* S., Bienvenu Y, Bartout J-D, Croset M, Dendievel R, Cloetens P (2005) 3D quantitative image analysis of open-cell nickel foams under tension and compression loading using x-ray microtomography. Phil Mag 85(19):2147–2175

    Google Scholar 

  41. Pierron F, McDonald S, Hollis D, Fu J, Withers P, Alderson A (2013) Comparison of the mechanical behaviour of standard and auxetic foams by x-ray computed tomography and digital volume correlation. Strain 49(6):467–482

    Google Scholar 

  42. Brun E, Vicente J, Topin F, Occelli R (2008) Imorph: A 3d morphological tool to fully analyse all kind of cellular materials. Cellular Metals for Structural and Functional Applications

  43. Casem D, Weerasooriya T, Moy P (2005) Inertial effects of quartz force transducers embedded in a split hopkinson pressure bar. Exp Mech 45(4):368

    Google Scholar 

  44. Tagarielli V, Deshpande V, Fleck N (2008) The high strain rate response of pvc foams and end-grain balsa wood. Compos Part B: Eng 39(1):83–91

    Google Scholar 

  45. Arezoo S, Tagarielli V, Siviour C, Petrinic N (2013) Compressive deformation of rohacell foams: effects of strain rate and temperature. Int J Impact Eng 51:50–57

    Google Scholar 

  46. Gray III G, Idar D, Blumenthal W, Cady C, Peterson P (1998) High-and low-strain rate compression properties of several energetic material composites as a function of strain rate and temperature. Technical report, Los Alamos National Lab., NM

  47. Song B, Chen W (2005) Split hopkinson pressure bar techniques for characterizing soft materials. Latin Amer J Solids Struct 2(2):113–152

    Google Scholar 

  48. Bacon C (1998) An experimental method for considering dispersion and attenuation in a viscoelastic hopkinson bar. Exp Mech 38(4):242–249

    Google Scholar 

  49. Sutton MA (2008) Digital image correlation for shape and deformation measurements. In: Springer handbook of experimental solid mechanics. Springer, pp 565–600

  50. Greaves GN, Greer A, Lakes R, Rouxel T (2011) Poisson’s ratio and modern materials. Nat Mater 10(11):823

    Google Scholar 

  51. Smith C, Wootton R, Evans K (1999) Interpretation of experimental data for poisson’s ratio of highly nonlinear materials. Exp Mech 39(4):356–362

    Google Scholar 

  52. Pierron F (2010) Identification of poisson’s ratios of standard and auxetic low-density polymeric foams from full-field measurements. J Strain Anal Eng Des 45(4):233–253

    Google Scholar 

  53. Vicente J, Topin F, Daurelle J-V (2006) Open celled material structural properties measurement: from morphology to transport properties. Mater Trans 47(9):2195–2202

    Google Scholar 

  54. Vicente J, Daurelle J-V, Rigollet F (2006) Thermal conductivity of metallic foam: simulation on real x-ray tomographied porous medium and photothermal experiments. In: International heat transfer conference 13, begel house inc.

  55. Avalle M, Belingardi G, Montanini R (2001) Characterization of polymeric structural foams under compressive impact loading by means of energy-absorption diagram. Int J Impact Eng 25(5):455–472

    Google Scholar 

  56. Ravindran S, Koohbor B, Malchow P, Kidane A (2018) Experimental characterization of compaction wave propagation in cellular polymers. Int J Solids Struct 139:270–282

    Google Scholar 

  57. Landauer A, Patel M, Henann D, Franck C (2018) A q-factor-based digital image correlation algorithm (qdic) for resolving finite deformations with degenerate speckle patterns. Exp Mech 58:815–830

  58. Sanborn B, Song B (2019) Poisson’s ratio of a hyperelastic foam under quasi-static and dynamic loading. Int J Impact Eng 123:48–55

    Google Scholar 

  59. Mitschke H, Schury F, Mecke K, Wein F, Stingl M, Schröder-Turk GE (2016) Geometry: The leading parameter for the poisson’s ratio of bending-dominated cellular solids. Int J Solids Struct 100:1–10

    Google Scholar 

  60. Pierron F, Zhu H, Siviour C (2014) Beyond hopkinson’s bar, vol 372

  61. Koohbor B, Kidane A, Lu W-Y, Sutton MA (2016) Investigation of the dynamic stress–strain response of compressible polymeric foam using a non-parametric analysis. Int J Impact Eng 91:170–182

    Google Scholar 

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Acknowledgements

This research is performed under grant N00014-18-1-2494 from the Office of Naval Research. The authors would like to thank Dr. Antonios Zavaliangos and his research group of the Department of Material Science and Engineering at Drexel University for allowing us to use the x-ray microtomograph. Special thanks for the fruitful discussions with the research teams of Dr. Christian Franck of the University of Wisconsin-Madison, Dr. Haneesh Kesari, Dr. Diane Hoffmann-Kim, and Dr. David Henann of Brown University, Mr. Ron Szalkowski of TeamWendy, Dr. Chad Hovey of Sandia National Laboratories. Additional thanks to Dr. Bo Song of Sandia National Laboratories for his discussion on properly utilizing the Kolsky method and Dr. Fabrice Pierron for his discussion on Poisson’s ratio quantification. Lastly, thank you to the Dynamic Multifunctional Materials Laboratory members at Drexel University for the direct and indirect support on this project.

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  1. Mechanical Engineering and Mechanics Department, Drexel University, 3141 Chestnut Street, Philadelphia, PA, 19104, USA

    S. Koumlis & L. Lamberson

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  1. S. Koumlis
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The authors gratefully acknowledge the support from the Office of Naval Research (Dr. Timothy Bentley) under grant N00014-18- 1-2494.

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Koumlis, S., Lamberson, L. Strain Rate Dependent Compressive Response of Open Cell Polyurethane Foam. Exp Mech 59, 1087–1103 (2019). https://doi.org/10.1007/s11340-019-00521-3

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