Skip to main content
Top
Published in: Acta Mechanica 6/2020

12-03-2020 | Original Paper

Visco-hyperelastic constitutive modeling of the dynamic mechanical behavior of HTPB casting explosive and its polymer binder

Authors: Youcai Xiao, Chenyang Fan, Zhijun Wang, Yi Sun

Published in: Acta Mechanica | Issue 6/2020

Login to get access

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

A new visco-hyperelastic constitutive model is developed to describe the dynamic compressive behavior of polymer-bonded explosive (60 wt% RDX, 16 wt% aluminum, and 24 wt% HTPB) and its polymer binder. The constitutive relationship comprises two parts: a component with a strain-energy function to characterize large deformation and a viscoelastic model to describe dynamic viscoelastic behavior. The hyperelastic model parameters are curve-fitted using quasi-static compressive test data under a strain rate of \(0.0001\,\hbox {s}^{-1}\). The time–temperature superposition principle master modulus curves are studied using relaxation tests at different temperatures, and their compressive relaxation time and modules are obtained by fitting the master modulus curves. To obtain the rational dynamic compressive results, a modified split-Hopkinson compressive bar setup is designed such that the specimens are in dynamic stress equilibrium and deformed homogeneously at nearly constant strain rates. A comparison of the constitutive relationship with the experimental results revealed a good agreement and demonstrates its potential to describe the dynamic mechanical behavior of the PBX and its polymer binder.
Literature
1.
go back to reference Xiao, Y., Sun, Y., Zhen, Y., et al.: Characterization, modeling and simulation of the impact damage for polymer bonded explosives. Int. J. Impact Eng 103, 149–158 (2017) Xiao, Y., Sun, Y., Zhen, Y., et al.: Characterization, modeling and simulation of the impact damage for polymer bonded explosives. Int. J. Impact Eng 103, 149–158 (2017)
2.
go back to reference Barua, A., Zhou, M.: A Lagrangian framework for analyzing microstructural level response of polymer-bonded explosives. Model. Simul. Mater. Sci. Eng. 19(5), 55001–55024 (2011) Barua, A., Zhou, M.: A Lagrangian framework for analyzing microstructural level response of polymer-bonded explosives. Model. Simul. Mater. Sci. Eng. 19(5), 55001–55024 (2011)
3.
go back to reference 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(3), 407–421 (2004) 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(3), 407–421 (2004)
4.
go back to reference Asay, B.W.: Shock Wave Science and Technology Reference Library, vol. 5. Non-Shock Initiation of Explosives. Springer, Berlin (2010) Asay, B.W.: Shock Wave Science and Technology Reference Library, vol. 5. Non-Shock Initiation of Explosives. Springer, Berlin (2010)
5.
go back to reference 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. 28(2004), 55–65 (2004) 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. 28(2004), 55–65 (2004)
6.
go back to reference Cady, C., Blumenthal, W., Gray, G., et al.: Mechanical properties of plastic-bonded explosive binder materials as a function of strain-rate and temperature. Polym. Eng. Sci. 46(6), 812–819 (2006) Cady, C., Blumenthal, W., Gray, G., et al.: Mechanical properties of plastic-bonded explosive binder materials as a function of strain-rate and temperature. Polym. Eng. Sci. 46(6), 812–819 (2006)
7.
go back to reference Thompson, D.G., Deluca, R., Brown, G.W.: Time-temperature analysis, tension and compression in PBXs. J. Energ. Mater. 30(4), 299–323 (2012) Thompson, D.G., Deluca, R., Brown, G.W.: Time-temperature analysis, tension and compression in PBXs. J. Energ. Mater. 30(4), 299–323 (2012)
8.
go back to reference Swanson, S., Christensen, L.: A constitutive formulation for high-elongation propellants. J. Spacecr. Rockets 20(6), 559–566 (1983) Swanson, S., Christensen, L.: A constitutive formulation for high-elongation propellants. J. Spacecr. Rockets 20(6), 559–566 (1983)
9.
go back to reference Park, S., Schapery, R.: A viscoelastic constitutive model for particulate composites with growing damage. Int. J. Solids Struct. 34(8), 931–947 (1997)MATH Park, S., Schapery, R.: A viscoelastic constitutive model for particulate composites with growing damage. Int. J. Solids Struct. 34(8), 931–947 (1997)MATH
10.
go back to reference Mas, E.M., Clements, B.E., Blumenthal, W.R., et al.: A viscoelastic model for PBX binders. Furnish, M.D., Thadhani, N.N., Horie, Y. Shock Compression of Condensed Matter—2001, Pts 1 and 2, Proceedings, pp. 661–664 (2002) Mas, E.M., Clements, B.E., Blumenthal, W.R., et al.: A viscoelastic model for PBX binders. Furnish, M.D., Thadhani, N.N., Horie, Y. Shock Compression of Condensed Matter—2001, Pts 1 and 2, Proceedings, pp. 661–664 (2002)
11.
go back to reference Xiao, Y., Sun, Y., Yang, Z., et al.: Dynamic compressive properties of polymer bonded explosives under confining pressure. Propellants Explos. Pyrotech. 42, 1–11 (2017) Xiao, Y., Sun, Y., Yang, Z., et al.: Dynamic compressive properties of polymer bonded explosives under confining pressure. Propellants Explos. Pyrotech. 42, 1–11 (2017)
12.
go back to reference Burke, M., Woytowitz, P., Reggi, G.: Nonlinear viscoelastic constitutive model for solid propellant. J. Propul. Power 8(3), 586–591 (1992) Burke, M., Woytowitz, P., Reggi, G.: Nonlinear viscoelastic constitutive model for solid propellant. J. Propul. Power 8(3), 586–591 (1992)
13.
go back to reference Jung, G.-D., Youn, S.-K.: A nonlinear viscoelastic constitutive model of solid propellant. Int. J. Solids Struct. 36(15), 3755–3777 (1999)MATH Jung, G.-D., Youn, S.-K.: A nonlinear viscoelastic constitutive model of solid propellant. Int. J. Solids Struct. 36(15), 3755–3777 (1999)MATH
14.
go back to reference Tarver, C.M., Chidester, S.K., Nichols, A.L.I.: Critical conditions for impact- and shock-induced hot spots in solid explosives. J. Phys. Chem. 100(100), 5794–5799 (1996) Tarver, C.M., Chidester, S.K., Nichols, A.L.I.: Critical conditions for impact- and shock-induced hot spots in solid explosives. J. Phys. Chem. 100(100), 5794–5799 (1996)
15.
go back to reference Rai, N.K., Schmidt, M.J., Udaykumar, H.S.: Collapse of elongated voids in porous energetic materials: effects of void orientation and aspect ratio on initiation. Phys. Rev. Fluids 2(4), 043201 (2017) Rai, N.K., Schmidt, M.J., Udaykumar, H.S.: Collapse of elongated voids in porous energetic materials: effects of void orientation and aspect ratio on initiation. Phys. Rev. Fluids 2(4), 043201 (2017)
16.
go back to reference Chen, W., Song, B.: One-dimensional dynamic compressive behavior of EPDM rubber. J. Eng. Mater. Technol. 125(3), 294–301 (2003)MathSciNet Chen, W., Song, B.: One-dimensional dynamic compressive behavior of EPDM rubber. J. Eng. Mater. Technol. 125(3), 294–301 (2003)MathSciNet
17.
go back to reference Wang, L.L., Huang, D., Gan, S.: Nonlinear viscoelastic constitutive relations and nonlinear viscoelastic wave propagation for polymers at high strain rates. IUTAM Symposia (International Union of Theoretical and Applied Mechanics), pp 137–146 (1996) Wang, L.L., Huang, D., Gan, S.: Nonlinear viscoelastic constitutive relations and nonlinear viscoelastic wave propagation for polymers at high strain rates. IUTAM Symposia (International Union of Theoretical and Applied Mechanics), pp 137–146 (1996)
18.
19.
go back to reference Wang, Y., Chen, Y.: Application of piezoelectric PVDF film to the measurement of impulsive forces generated by cavitation bubble collapse near a solid boundary. Exp. Therm Fluid Sci. 32(2), 403–414 (2007) Wang, Y., Chen, Y.: Application of piezoelectric PVDF film to the measurement of impulsive forces generated by cavitation bubble collapse near a solid boundary. Exp. Therm Fluid Sci. 32(2), 403–414 (2007)
20.
go back to reference Zeng, F., Sun, Y., Zhou, Y., et al.: A molecular dynamics simulation study to investigate the elastic properties of PVDF and POSS nanocomposites. Modell. Simul. Mater. Sci. Eng. 19(2), 025005–25016 (2011) Zeng, F., Sun, Y., Zhou, Y., et al.: A molecular dynamics simulation study to investigate the elastic properties of PVDF and POSS nanocomposites. Modell. Simul. Mater. Sci. Eng. 19(2), 025005–25016 (2011)
21.
go back to reference Frew, D., Forrestal, M.J., Chen, W.: Pulse shaping techniques for testing brittle materials with a split Hopkinson pressure bar. Exp. Mech. 42(1), 93–106 (2002) Frew, D., Forrestal, M.J., Chen, W.: Pulse shaping techniques for testing brittle materials with a split Hopkinson pressure bar. Exp. Mech. 42(1), 93–106 (2002)
22.
go back to reference Yang, L., Shim, V.: An analysis of stress uniformity in split Hopkinson bar test specimens. Int. J. Impact Eng. 31(2), 129–150 (2005) Yang, L., Shim, V.: An analysis of stress uniformity in split Hopkinson bar test specimens. Int. J. Impact Eng. 31(2), 129–150 (2005)
23.
go back to reference Frew, D., Forrestal, M.J., Chen, W.: A split Hopkinson pressure bar technique to determine compressive stress–strain data for rock materials. Exp. Mech. 41(1), 40–46 (2001) Frew, D., Forrestal, M.J., Chen, W.: A split Hopkinson pressure bar technique to determine compressive stress–strain data for rock materials. Exp. Mech. 41(1), 40–46 (2001)
24.
go back to reference Ravichandran, G., Subhash, G.: 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 (1994) Ravichandran, G., Subhash, G.: 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 (1994)
25.
go back to reference Chen, W., Lu, F., Frew, D., et al.: Dynamic compression testing of soft materials. J. Appl. Mech. 69(3), 214–223 (2002)MATH Chen, W., Lu, F., Frew, D., et al.: Dynamic compression testing of soft materials. J. Appl. Mech. 69(3), 214–223 (2002)MATH
26.
go back to reference Parab, N.D., Roberts, Z.A., Harr, M.H., et al.: High speed X-ray phase contrast imaging of energetic composites under dynamic compression. Appl. Phys. Lett. 109(13), 3725–3744 (2016) Parab, N.D., Roberts, Z.A., Harr, M.H., et al.: High speed X-ray phase contrast imaging of energetic composites under dynamic compression. Appl. Phys. Lett. 109(13), 3725–3744 (2016)
27.
go back to reference 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(14), 3701–3707 (1955) 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(14), 3701–3707 (1955)
28.
go back to reference Rivlin, R.S.: Proceedings of the first symposium on naval structural mechanics (1960) Rivlin, R.S.: Proceedings of the first symposium on naval structural mechanics (1960)
29.
go back to reference Han, C.D.: Mechanical properties of solid polymers. J. Polym. Sci. Polym. Lett. Ed. 23(2), 119–119 (1985)MathSciNet Han, C.D.: Mechanical properties of solid polymers. J. Polym. Sci. Polym. Lett. Ed. 23(2), 119–119 (1985)MathSciNet
30.
go back to reference Arruda, E.M., Boyce, M.C.: A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 41(2), 389–412 (1993)MATH Arruda, E.M., Boyce, M.C.: A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 41(2), 389–412 (1993)MATH
31.
go back to reference Mooney, M.: A theory of large elastic deformation. J. Appl. Phys. 11(9), 582–592 (1940)MATH Mooney, M.: A theory of large elastic deformation. J. Appl. Phys. 11(9), 582–592 (1940)MATH
32.
go back to reference Treloar, L.R.G.: Stresses and birefringence in rubber subjected to general homogeneous strain. Proc. Phys. Soc. 60(2), 135 (1949) Treloar, L.R.G.: Stresses and birefringence in rubber subjected to general homogeneous strain. Proc. Phys. Soc. 60(2), 135 (1949)
33.
go back to reference Ogden, R.W.: Large deformation isotropic elasticity—on the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc. London 326(1567), 565–584 (1972)MATH Ogden, R.W.: Large deformation isotropic elasticity—on the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc. London 326(1567), 565–584 (1972)MATH
34.
go back to reference Brown, R.: Physical Testing of Rubber. Springer, Boston, MA (2006) Brown, R.: Physical Testing of Rubber. Springer, Boston, MA (2006)
35.
go back to reference Li, C., Lua, J.: A hyper-viscoelastic constitutive model for polyurea. Mater. Lett. 63(7), 877–880 (2009) Li, C., Lua, J.: A hyper-viscoelastic constitutive model for polyurea. Mater. Lett. 63(7), 877–880 (2009)
36.
go back to reference Pouriayevali, H., Guo, Y., Shim, V.: A visco-hyperelastic constitutive description of elastomer behaviour at high strain rates. Procedia Eng. 10, 2274–2279 (2011) Pouriayevali, H., Guo, Y., Shim, V.: A visco-hyperelastic constitutive description of elastomer behaviour at high strain rates. Procedia Eng. 10, 2274–2279 (2011)
37.
go back to reference Blumenthal, W., Thompson, D., Cady, C., et al.: Compressive properties of PBXN-110 and its HTPB-based binder as a function of temperature and strain rate. In: Proceedings of the 12th International Detonation Symposium, F. (2002) Blumenthal, W., Thompson, D., Cady, C., et al.: Compressive properties of PBXN-110 and its HTPB-based binder as a function of temperature and strain rate. In: Proceedings of the 12th International Detonation Symposium, F. (2002)
38.
go back to reference Clements, B.E., Mas, E.M.: Dynamic mechanical behavior of filled polymers. I. Theoretical developments. J. Appl. Phys. 90(7), 5522–5534 (2001) Clements, B.E., Mas, E.M.: Dynamic mechanical behavior of filled polymers. I. Theoretical developments. J. Appl. Phys. 90(7), 5522–5534 (2001)
Metadata
Title
Visco-hyperelastic constitutive modeling of the dynamic mechanical behavior of HTPB casting explosive and its polymer binder
Authors
Youcai Xiao
Chenyang Fan
Zhijun Wang
Yi Sun
Publication date
12-03-2020
Publisher
Springer Vienna
Published in
Acta Mechanica / Issue 6/2020
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-020-02655-1

Other articles of this Issue 6/2020

Acta Mechanica 6/2020 Go to the issue

Premium Partners