Advertisement

Particulate Composites Under High Strain Rate and Shock Loading

  • J. L. JordanEmail author
  • E. B. Herbold
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 35)

Abstract

Polymer-matrix particulate composites consist of individual particles of more than one material dispersed throughout and held together by a polymer binder. The mechanical and physical properties of the composite depend on the mechanical and physical properties of the individual components, particularly the polymer binder; their loading density; the shape and size of the particles; the interfacial adhesion; residual stresses; and matrix porosity. Systematic studies of the effects of volume fraction and microstructure on the behavior of these polymer-based composites are critical. The behavior of polymer-matrix particulate composites at intermediate to high strain rates has not been investigated in detail in the literature. The testing strain rate can greatly affect the behavior of these composites due to the dependency on rate dependant phase changes in the polymer binder. The intermediate strain rate behavior (~103–104/s) is studied using a split Hopkinson pressure bar. Shock, or high strain rate, properties of these composite materials have been investigated using gas gun and explosive loading techniques. This chapter will review results from recent experimental studies on the properties of polymer-based particulate composites containing metal and metal oxide powders.

Keywords

Particulate composite High strain rate Shock loading Hugoniot 

Notes

Acknowledgments

The authors would like to thank both AFOSR and AFRL/RW for funding the work presented in this chapter and references. JLJ was employed by the Air Force Research Laboratory, Munitions Directorate and EBH was employed by the Georgia Institute of Technology when this work was performed and they gratefully acknowledge their support. Additionally, JLJ would like to thank her collaborators over the years—Mel Baer, John Borg, Eric Brown, Dana Dattelbaum, Richard Dick, Louis Ferranti, Andrew Fraser, Jason Foley, Wayne Richards, Stephen Sheffield, Clive Siviour, Jonathan Spowart, Gerrit Sutherland, Naresh Thadhani, Brad White. Opinions, interpretations, conclusions and recommendations are those of the authors and are not necessarily endorsed by the United States Air Force.

References

  1. 1.
    Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. Lond. A 241(1226), 376–396 (1957)CrossRefGoogle Scholar
  2. 2.
    Hashin, Z., Shtrikman, S.: A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11(2), 127–140 (1963)CrossRefGoogle Scholar
  3. 3.
    Mori, T., Tanaka, K.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21(5), 571–574 (1973)CrossRefGoogle Scholar
  4. 4.
    Ahmed, S., Jones, F.R.: A review of particulate reinforcement theories for polymer composites. J. Mater. Sci. 25(12), 4933–4942 (1990)CrossRefGoogle Scholar
  5. 5.
    Gray, G.T.: Classic Split Hopkinson Pressure Bar Testing. In: ASM Handbook Volume 8: Mechanical Testing and Evaluation, pp. 462–76. ASM International, Materials Park, OH (2000)Google Scholar
  6. 6.
    Jordan, J.L., Siviour, C.R., Foley, J.R., Brown, E.N.: Compressive properties of extruded polytetrafluoroethylene. Polymer 48(14), 4184–4195 (2007)CrossRefGoogle Scholar
  7. 7.
    Song, B., Chen, W., Montgomery, S.T., Forrestal, M.J.: Mechanical response of an alumina-filled epoxy at various strain rates. J. Compos. Mater. 43(14), 1519–1536 (2009)CrossRefGoogle Scholar
  8. 8.
    Taylor, G.I.: The use of flat-ended projectiles for determining dynamic yield stress. I. Theoretical considerations. Proc. R. Soc. Lond. A 194(1038), 289–299 (1948)CrossRefGoogle Scholar
  9. 9.
    Hutchings, I.M.: Estimation of yield stress in polymers at high strain-rates using GI Taylor’s impact technique. J. Mech. Phys. Solids 26(5-6), 289–301 (1978)CrossRefGoogle Scholar
  10. 10.
    Rae, P.J., Brown, E.N., Clements, B.E., Dattelbaum, D.M.: Pressure-induced phase change in poly(tetrafluoroethylene) at modest impact velocities. J. Appl. Phys. 98, 063521 (2005)CrossRefGoogle Scholar
  11. 11.
    Sarva, S., Mulliken, A.D., Boyce, M.C.: Mechanics of Taylor impact testing of polycarbonate. Int. J. Solids Struct. 44, 2381–2400 (2007)CrossRefGoogle Scholar
  12. 12.
    Ferranti, L., Thadhani, N.N.: Dynamic mechanical behavior characterization of epoxy-cast Al+ Fe2O3 thermite mixture composites. Meta. Mater. Trans. A 38A, 2697–2715 (2007)CrossRefGoogle Scholar
  13. 13.
    Martin, M., Hanagud, S., Thadhani, N.N.: Mechanical behavior of nickel + aluminum powder-reinforced epoxy composites. Mater. Sci. Eng. A 443, 209–218 (2007)CrossRefGoogle Scholar
  14. 14.
    White, B. W., Thadhani, N.N., Jordan, J.L., Spowart, J.E.: The effect of particle reinforcement on the dynamic deformation of epoxy-matrix composites. In: American Institute of Physics Conference Proceedings, vol. 1195, pp. 1245–1248 (2009)Google Scholar
  15. 15.
    Meyers, M.A.: Dynamic Behavior of Materials. Wiley, New York (1994)Google Scholar
  16. 16.
    Field, J.E., Walley, S.M., Proud, W.G., Goldrein, H.T., Siviour, C.R.: Review of experimental techniques for high rate deformation and shock studies. Int. J. Impact Eng. 30, 725–775 (2004)CrossRefGoogle Scholar
  17. 17.
    Jordan, J.L., Dattelbaum, D.M., Sutherland, G., Richards, D.W., Sheffield, S.A., Dick, R.D.: Shock equation of state of a multi-phase epoxy-based composite (Al–MnO2− epoxy). J. Appl. Phys. 107, 103528 (2010)CrossRefGoogle Scholar
  18. 18.
    Vogler, T.J., Alexander, C.S., Wise, J.L., Montgomery, S.T.: Dynamic behavior of tungsten carbide and alumina filled epoxy composites. J. Appl. Phys. 107, 043520 (2010)CrossRefGoogle Scholar
  19. 19.
    Jordan, J.L., Ferranti, L., Austin, R.A., Dick, R.D., Foley, J.R., Thadhani, N.N., McDowell, D.L.: Equation of state of aluminum–iron oxide-epoxy composite. J. Appl. Phys. 10(9), 093520 (2007)Google Scholar
  20. 20.
    Millett, J.C.F., Bourne, N.K., Deas, D.: The equation of state of two alumina-filled epoxy resins. J. Phys. D Appl. Phys. 38, 930–934 (2005)CrossRefGoogle Scholar
  21. 21.
    Sheffield, S.A., Gustavsen, R.L., Alcon, R.R.: In situ magnetic gauging technique used at LANL-method and shock information obtained. In: Shock Compression of Condensed Matter-1999, pp. 1043–1048. AIP Publishing, College Park, MD (2000)Google Scholar
  22. 22.
    Munson, D.E., May, R.P.: Dynamically determined high-pressure compressibilities of three epoxy resin systems. J. Appl. Phys. 43(3), 962–971 (1972)Google Scholar
  23. 23.
    Anderson, M.U., Setchell, R.E., Cox, D.E.: Shock and release behavior of filled and unfilled epoxies. In: Furnish, M.D., Chhabildas, L.C., Hixson, R.S. (eds.) Shock Compression of Condensed Matter-1999, pp. 551–554 AIP Publishing, College Park, MD (2000) Google Scholar
  24. 24.
    Setchell, R.E., Anderson, M.U.: Shock-compression response of an alumina-filled epoxy. J. Appl. Phys. 97, 083518 (2005)CrossRefGoogle Scholar
  25. 25.
    Siviour, C.R., Walley, S.M., Proud, W.G., Field, J.E.: The high strain rate compressive behaviour of polycarbonate and polyvinylidene diflouride. Polymer 46, 12546–12555 (2005)CrossRefGoogle Scholar
  26. 26.
    Jordan, J.L., Foley, J.R., Siviour, C.R.: Mechanical properties of Epon 826/DEA epoxy. Mech. Time Dependant Mater. 12, 249–272 (2008)CrossRefGoogle Scholar
  27. 27.
    Clements, B.E., Mas, E.M.: Dynamic mechanical behavior of filled polymers. I. Theoretical developments. J. Appl. Phys. 90(11), 5522–5534 (2001)CrossRefGoogle Scholar
  28. 28.
    Clements, B.E., Mas, E.M.: Dynamic mechanical behavior of filled polymers. II. Applications. J. Appl. Phys. 90(11), 5535–5541 (2001)CrossRefGoogle Scholar
  29. 29.
    Jordan, J.L., Spowart, J.E., Richards, D.W.: Constitutive characterization of multi-constituent particulate composites. In: Proceedings of the Society for Experimental Mechanics Annual Meeting 2010. Springer, Heidelberg (2010)Google Scholar
  30. 30.
    Owens, A.T., Tippur, H.V.: A tensile split Hopkinson bar for testing particulate polymer composites under elevated rates of loading. Exp. Mech. 49, 799–811 (2009)CrossRefGoogle Scholar
  31. 31.
    Predecki, P., Barrett, C.: Stress measurement in graphite/epoxy composites by X-Ray diffraction from fsillers. J. Compos. Mater. 13, 61–71 (1979)CrossRefGoogle Scholar
  32. 32.
    Benedikt, B., Lewis, M., Rangaswamy, P.: An analysis of internal strains in unidirectional and chopped graphite fibre composites based on x-ray diffraction and micro Raman spectroscopy measurements. In: International Conference on Computational Methods and Experiments in Materials Characterization, pp. 13–22. Elsevier, Amsterdam (2005)Google Scholar
  33. 33.
    Benedikt, B., Lewis, M., Rangaswamy, P.: Measurement and modeling of internal stresses at microscopic and mesoscopic levels using micro-Raman spectroscopy and X-ray diffraction. Powder Diffr. 21(2), 118–121 (2006)CrossRefGoogle Scholar
  34. 34.
    Benedikt, B., Lewis, M., Rangaswamy, P., Kumosa, M., Predecki, P., Kumosa, L., Gentz, M.: Residual stress analysis in aged graphite/PMR-15 composites using X-ray diffraction. Mater. Sci. Eng. A 421, 1–8 (2006)CrossRefGoogle Scholar
  35. 35.
    Quane, S.L., Russell, J.K.: Bulk and particle strain analysis in high-temperature deformation experiments. J. Volcanol. Geoth. Res. 154, 63–73 (2006)CrossRefGoogle Scholar
  36. 36.
    Segurado, J., Llorca, J.: Computational micromechanics of composites: The effect of particle spatial distribution. Mech. Mater. 38, 873–883 (2006)CrossRefGoogle Scholar
  37. 37.
    White, B.W., Spowart, J.E., Jordan, J.L., Thadhani, N.N.: Strain rate effects on the deformation behavior of particles in epoxy-based composites. Presentation at 2010 TMS Annual Meeting & Exhibition (2010)Google Scholar
  38. 38.
    Kirkpatrick, S.: Percolation and conduction. Rev. Mod. Phys. 45, 574–588 (1973)CrossRefGoogle Scholar
  39. 39.
    Lange, F.F., Atteraas, L., Zok, F., Porter, J.R.: Deformation consolidation of metal powders containing steel inclusions. Acta metallurgica et metallica 39(2), 209–219 (1991)CrossRefGoogle Scholar
  40. 40.
    Lekatou, A., Faidi, S.E., Lyon, S.B., Newman, R.C.: Elasticity and fracture in particulate composites with strong and degraded interfaces. J. Mater. Res. 11(5), 1293–1304 (1996)CrossRefGoogle Scholar
  41. 41.
    Novak, I., Krupa, I., Chodak, I.: Relation between electrical and mechanical properties in polyurethane/carbon black adhesives. J. Mater. Sci. Lett. 21, 1039–1041 (2002)CrossRefGoogle Scholar
  42. 42.
    Chodak, I., Krupa, I.: ‘Percolation effect’ and mechanical behavior of carbon black filled polyethylene. J. Mater. Sci. Lett. 18, 1457–1459 (1999)CrossRefGoogle Scholar
  43. 43.
    Verbeek, C.J.R.: Effect of percolation on the mechanical properties of sand-filled polyethylene composites. J. Thermoplast. Compos. Mater. 20, 137–149 (2007)CrossRefGoogle Scholar
  44. 44.
    Setchell, R.E., Anderson, M.U., Montgomery, S.T.: Compositional effects on the shock-compression response of alumina-filled epoxy. J. Appl. Phys. 101, 083527 (2007)CrossRefGoogle Scholar
  45. 45.
    Ferranti, L.: Ph.D dissertation, Georgia Institute of Technology (2007)Google Scholar
  46. 46.
    Jordan, J.L., Herbold, E.B., Sutherland, G., Fraser, A., Borg, J., Richards, D.W.: Shock equation of state of multi-constituent epoxy-metal particulate composites. J. Appl. Phys. (2011 in press)Google Scholar
  47. 47.
    Carter, W.J., Marsh, S.P.: Hugoniot equation of state of polymers. LA-13006-MS, Los Alamos National Laboratory (1999)Google Scholar
  48. 48.
    Millett, J.C.F., Bourne, N.K., Barnes, N.R.: The behavior of an epoxy resin under one-dimensional shock loading. J. Appl. Phys. 92, 6590 (2002)CrossRefGoogle Scholar
  49. 49.
    Anderson, M.U., Setchell, R.E., Cox, D.E.: Effects of initial temperature on the shock and release behavior of filled and unfilled epoxies. In: Furnish, M.D., Thadhani, N.N., Horie, Y. (eds.) Shock Compression of Condensed Matter-2001, pp. 669–672 (2002)Google Scholar
  50. 50.
    Munson, D.E., Boade, R.R., Schuler, K.W.: Stress-wave propagation in Al2O3—epoxy mixtures. J. Appl. Phys. 49, 4797–4807 (1978)CrossRefGoogle Scholar
  51. 51.
    Chhabildas, L.C., Swegle, J.W.: On the dynamical response of particulate-loaded materials. I. Pressure-shear loading of alumina particles in an epoxy matrix. J. Appl. Phys. 53(2), 954–956 (1982)CrossRefGoogle Scholar
  52. 52.
    Drumheller, D.S.: On the dynamical response of particulate-loaded materials. II. A theory with application to alumina particles in an epoxy matrix. J. Appl. Phys. 53(2), 957–969 (1982)CrossRefGoogle Scholar
  53. 53.
    Millett, J.C.F., Bourne, N.K., Deas, D., Montgomery, S.T.: The deviatoric response of an alumina filled epoxy composite during shock loading. J. Appl. Phys. 102, 063518 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Air Force Office of Scientific ResearchArlingtonUSA
  2. 2.Lawrence Livermore National LaboratoryLivermoreUSA

Personalised recommendations