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Study of the dynamic mechanical behavior of PBX by Eshelby theory

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Abstract

The dynamic mechanical behavior of PBX1314 is examined by means of a micromechanical model. The basis for this work is Eshelby theory. The effective moduli derived by Weng and Tandon are used for the randomly oriented two-phase composites. The dynamic mechanical behavior of the PBX1314 is described as a function of aspect ratio and inclusion concentration. The viscoelastic behavior of the polymer binder is modeled using a generalized Maxwell model with a Prony series representation for the stress relaxation functions. Numerical inverse Laplace transform required by the model can be performed analytically. To demonstrate the utility and validity of the theory, we compare its predictions to several dynamic compressive experiments on the PBX1314. We also compare the predictions of the present model to the theoretical results derived by Mas and Clements. Their studies can be used to assess the properties of energetic composites, and this method is a useful tool for the design of energetic composites.

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References

  1. Meyer, R., Köhler, J., Homburg, A.: Explosives. Explosives (2007)

  2. Asay, B.W.: Shock Wave Science and Technology Reference Library. Non-shock Initiation of Explosives, vol. 5. Springer, Berlin (2010)

    Book  Google Scholar 

  3. Banerjee, B., Cady, C.M., Adams, D.O.: Micromechanics simulations of glass-estane mock polymer bonded explosives. Model. Simul. Mater. Sci. Eng. 11, 457–475 (2003)

    Article  Google Scholar 

  4. Banerjee, B., Adams, D.O.: Micromechanics-based determination of effective elastic properties of polymer bonded explosives. Phys. B 338, 8–15 (2003)

    Article  Google Scholar 

  5. Banerjee, B., Adams, D.O.: On predicting the effective elastic properties of polymer bonded explosives using the recursive cell method. Int. J. Solids Struct. 41, 481–509 (2004)

    Article  MATH  Google Scholar 

  6. Bardenhagen, S.G., Brackbill, J.U.: Dynamic stress bridging in granular material. J. Appl. Phys. 83, 5732–5740 (1998)

    Article  Google Scholar 

  7. Bardenhagen, S.G., Brackbill, J.U., Sulsky, D.: The material-point method for granular materials. Comput. Methods Appl. Mech. Eng. 187, 529–541 (2000)

    Article  MATH  Google Scholar 

  8. Brinson, L., Lin, W.: Comparison of micromechanics methods for effective properties of multiphase viscoelastic composites. Compos. Struct. 41, 353–367 (1998)

    Article  Google Scholar 

  9. Lévesque, M., Derrien, K., Mishnaevski Jr., L., Baptiste, D., Gilchrist, M.D.: A micromechanical model for nonlinear viscoelastic particle reinforced polymeric composite materials-undamaged state. Compos. A: Appl. Sci. Manuf. 35, 905–913 (2004)

    Article  Google Scholar 

  10. Clements, B.E., Mas, E.M.: Dynamic mechanical behavior of filled polymers. I. Theoretical developments. J. Appl. Phys. 90, 5522–5534 (2001)

    Article  Google Scholar 

  11. Mas, E.M., Clements, B.E.: Dynamic mechanical behavior of filled polymers. II. Applications. J. Appl. Phys. 90, 5535–5541 (2001)

    Article  Google Scholar 

  12. Clements, B.E., Mas, E.M.: A theory for plastic-bonded materials with a bimodal size distribution of filler particles. Model. Simul. Mater. Sci. Eng. 12, 407–421 (2004)

    Article  Google Scholar 

  13. Li, J., Weng, G.: Effective creep behavior and complex moduli of fiber-and ribbon-reinforced polymer–matrix composites. Compos. Sci. Technol. 52, 615–629 (1994)

    Article  Google Scholar 

  14. Weng, G.: Some elastic properties of reinforced solids, with special reference to isotropic ones containing spherical inclusions. Int. J. Eng. Sci. 22, 845–856 (1984)

    Article  MATH  Google Scholar 

  15. Wang, Y., Weng, G.: The influence of inclusion shape on the overall viscoelastic behavior of composites. J. Appl. Mech. 59, 510–518 (1992)

    Article  MATH  Google Scholar 

  16. Li, J., Weng, G.: Strain-rate sensitivity, relaxation behavior, and complex moduli of a class of isotropic viscoelastic composites. J. Eng. Mater. Technol. 116, 495–504 (1994)

    Article  Google Scholar 

  17. Li, J., Weng, G.: Stress–strain relations of a viscoelastic composite reinforced with elliptic cylinders. J. Thermoplast. Compos. Mater. 10, 19–30 (1997)

    Article  Google Scholar 

  18. Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. Lond. Math. Phys. Eng. Sci. 241, 376–396 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  19. Eshelby, J.D.: The elastic field outside an ellipsoidal inclusion. Proc. R. Soc. Math. Phys. Eng. Sci. 252, 561–569 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  20. Tandon, G., Weng, G.: Average stress in the matrix and effective moduli of randomly oriented composites. Compos. Sci. Technol. 27, 111–132 (1986)

    Article  Google Scholar 

  21. Idar, D., Thompson, D., Gray, G., Blumenthal, W., Cady, C., Peterson, P., Roemer, E., Wright, W., Jacquez, B.: Influence of polymer molecular weight, temperature, and strain rate on the mechanical properties of PBX 9501 (2002)

  22. Blumenthal, W., Gray, G., 3rd, Idar, D., Holmes, M., Scott, P., Cady, C., Cannon, D.: Influence of temperature and strain rate on the mechanical behavior of PBX 9502 and Kel-F \(800^{{\rm TM}}\). Shock Compress. Condens. Matter 1999, 671–674 (2000)

  23. Colak, O.U.: Mechanical behavior of PBXW-128 and PBXN-110 under uniaxial and multiaxial compression at different strain rates and temperatures. Turk. J. Eng. Environ. Sci. 32, 390–395 (2004)

  24. Xiao, Y.C., Sun, Y., Li, X., Zhang, Q.H., Liu, S.W., Yang, H.: Dynamic mechanical behavior of PBX. Propellants Explos. Pyrotech. 41, 629–636 (2016)

    Article  Google Scholar 

  25. Tobolsky, A.V., Catsiff, E.: Elastoviscous properties of polyisobutylene (and other amorphous polymers) from stress–relaxation studies. J. Polym. Sci. 19, 111–121 (1956)

    Article  Google Scholar 

  26. Williams, M.L., Landel, R.F., Ferry, J.D.: The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J. Am. Chem. Soc. 77, 3701–3707 (1955)

    Article  Google Scholar 

  27. Mas, E.M., Clements, B.E., Blumenthal, W.R., Cady, C.M., Gray, G.T., Liu, C.: A viscoelastic model for PBX binders. In: Furnish, M.D., Thadhani, N.N., Horie Y. (Eds.) Shock Compression of Condensed Matter, pp. 661–664 . Office of Scientific & Technical Information Technical Reports (2001)

  28. Xue, L., Borodin, O., Smith, G.D., Nairn, J.: Micromechanics simulations of the viscoelastic properties of highly filled composites by the material point method (MPM). Model. Simul. Mater. Sci. Eng. 14, 703 (2006)

    Article  Google Scholar 

  29. Cost, T.L., Becker, E.B.: A multidata method of approximate Laplace transform inversion. Int. J. Numer. Methods Eng. 2, 207–219 (1970)

    Article  MATH  Google Scholar 

  30. Kwok, Y.-K., Barthez, D.: An algorithm for the numerical inversion of Laplace transforms. Inverse Prob. 5, 1089 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  31. De Hoog, F.R., Knight, J., Stokes, A.: An improved method for numerical inversion of Laplace transforms. SIAM J. Sci. Stat. Comput. 3, 357–366 (1982)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Astronautic Science and Mechanics, Harbin Institute of Technology, Harbin, 150001, China

    Youcai Xiao, Yi Sun, Zhiqiang Yang & Licheng Guo

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  1. Youcai Xiao
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  2. Yi Sun
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  3. Zhiqiang Yang
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  4. Licheng Guo
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Correspondence to Yi Sun.

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Xiao, Y., Sun, Y., Yang, Z. et al. Study of the dynamic mechanical behavior of PBX by Eshelby theory. Acta Mech 228, 1993–2003 (2017). https://doi.org/10.1007/s00707-017-1809-4

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  • DOI: https://doi.org/10.1007/s00707-017-1809-4

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