Skip to main content
SpringerLink
Log in

A thermovisco-hyperelastic constitutive model of HTPB propellant with damage at intermediate strain rates

  • Published:
Mechanics of Time-Dependent Materials Aims and scope Submit manuscript

Abstract

The uniaxial compressive tests at different temperatures (223–298 K) and strain rates (\(0.40\mbox{--}63~\mbox{s}^{-1}\)) are reported to study the properties of hydroxyl-terminated polybutadiene (HTPB) propellant at intermediate strain rates, using a new INSTRON testing machine. The experimental results indicate that the compressive properties (mechanical properties and damage) of HTPB propellant are remarkably affected by temperature and strain rate and display significant nonlinear material behaviors at large strains under all the test conditions. Continuously decreasing temperature and increasing strain rate, the characteristics of stress-strain curves and damage for HTPB propellant are more complex and are significantly different from that at room temperature or at lower strain rates. A new constitutive model was developed to describe the compressive behaviors of HTPB propellant at room temperature and intermediate strain rates by simply coupling the effect of strain rate into the conventional hyperelastic model. Based on the compressive behaviors of HTPB propellant and the nonlinear viscoelastic constitutive theories, a new thermovisco-hyperelastic constitutive model with damage was proposed to predict the stress responses of the propellant at low temperatures and intermediate strain rates. In this new model, the damage is related to the viscoelastic properties of the propellant. Meanwhile, the effect of temperature on the hyperelastic properties, viscoelastic properties and damage are all considered by the macroscopical method. The constitutive parameters in the proposed constitutive models were identified by the genetic algorithm (GA)-based optimization method. By comparing the predicted and experimental results, it can be found that the developed constitutive models can correctly describe the uniaxial compressive behaviors of HTPB propellant at intermediate strain rates and different temperatures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Bencher, C.D.: Microstructural damage and fracture processes in a composite solid rocket propellant. J. Spacecr. Rockets 32, 328–334 (1995)

    Article  Google Scholar 

  • Canga, M.E., Becker, W.B., Özüpek, S.: Constitutive modeling of viscoelastic materials with damage-computational aspects. Comput. Methods Appl. Math. 190(15–17), 2207–2226 (2001)

    MATH  Google Scholar 

  • Chang, X., Lai, J., Zhang, X., Hu, K., Qi, W.: High strain-rate viscoelastic constitutive model for HTPB propellant. J. Propuls. Technol. 35(1), 123–127 (2014)

    Google Scholar 

  • Chen, W.W.: Experimental methods for characterizing dynamic response of soft materials. J. Dyn. Behav. Mater. 2, 2–14 (2016)

    Article  Google Scholar 

  • Chu, H.T., Chou, J.H.: Effect of cooling load on the safety factor of propellant grains. J. Propuls. Power 29, 27–33 (2013)

    Article  Google Scholar 

  • Duncan, E.J.S.: Characterization of a glycidylazide polymer composite propellant: strain rate effects and relaxation response. J. Appl. Polym. Sci. 56, 365–375 (1995)

    Article  Google Scholar 

  • Duncan, E.J.S., Margetson, J.: A nonlinear viscoelastic theory for solid rocket propellants based on a cumulative damage approach. Propellants Explos. Pyrotech. 23(2), 94–104 (1998)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Furmanski, J., Cady, C.M., Brown, E.N.: Time-temperature equivalence and adiabatic heating at large strains in high density polyethylene and ultrahigh molecular weight polyethylene. Polymer 54(1), 381–390 (2013)

    Article  Google Scholar 

  • Gent, A.N.: A new constitutive relation for rubber. Rubber Chem. Technol. 69(1), 59–61 (1996)

    Article  MathSciNet  Google Scholar 

  • Gligorijević, N., Živković, S., Subotić, S., Rodić, V., Gligorijević, I.: Effect of cumulative damage on rocket motor service life. J. Energ. Mater. 33(4), 229–259 (2015)

    Article  Google Scholar 

  • Gray, G.T. III, Blumenthal, W.R.: Split-Hopkinson pressure bar testing of soft materials. In: Kuhn, H., Medlin, D. (eds.) ASM Handbook: Mechanical Testing and Evaluation, pp. 488–496. ASM International, Materials Park (2000)

    Google Scholar 

  • Han, L., Chen, X., Xu, J., Zhou, C., Yu, J.: Research on the time-temperature-damage superposition principle of NEPE propellant. Mech. Time-Depend. Mater. 19(4), 581–599 (2015)

    Article  Google Scholar 

  • Hinterhoelzl, R.M., Schapery, R.A.: FEM implementation of a three-dimensional viscoelastic constitutive model for particulate composites with damage growth. Mech. Time-Depend. Mater. 8(1), 65–94 (2004)

    Article  Google Scholar 

  • Ho, S.Y.: High strain-rate constitutive models for solid rocket propellants. J. Propuls. Power 18, 1106–1111 (2002)

    Article  Google Scholar 

  • Ho, S.Y., Fong, C.W.: Temperature dependence of high strain-rate impact fracture behaviour in highly filled polymeric composite and plasticized thermoplastic propellants. J. Mater. Sci. 22, 3023–3031 (1987)

    Article  Google Scholar 

  • Hsiao, R.C.: Structural analyses of solid propellant grains under ignition pressurization using explicit dynamics method. In: AIAA 2013-3959, (2013)

    Google Scholar 

  • Iwamoto, T., Yokoyama, T.: Effects of radial inertia and end friction in specimen geometry in split Hopkinson pressure bar test: a computational study. Mech. Mater. 51, 97–109 (2012)

    Article  Google Scholar 

  • Jeremic, R.: Some aspects of time-temperature superposition principle applied for predicting mechanical properties of solid rocket propellants. Propellants Explos. Pyrotech. 24, 221–223 (1999)

    Article  Google Scholar 

  • Jiang, S., Rui, X., Hong, J., Wang, G., Rong, B., Wang, Y.: Numerical simulation of impact breakage of gun propellant charge. Granul. Matter 13, 611–622 (2011)

    Article  Google Scholar 

  • Jordan, J.L., Montaigne, D., Gould, P., Neel, C., Sunny, G., Molek, C.: High strain rate and shock properties of hydroxyl-terminated polybutadiene (HTPB) with varying amounts of plasticizer. J. Dyn. Behav. Mater. 2, 91–100 (2016)

    Article  Google Scholar 

  • Judge, M.D.: An investigation of composite propellant accelerated ageing mechanisms and kinetics. Propellants Explos. Pyrotech. 28(3), 114–119 (2003)

    Article  Google Scholar 

  • Kakavas, P.A.: Mechanical properties of propellant composite materials reinforced with ammonium perchlorate particles. Int. J. Solids Struct. 51, 2019–2026 (2014)

    Article  Google Scholar 

  • Kunz, R.K.: Characterization of solid propellant for linear cumulative damage modeling. In: AIAA-2009-5257 (2009)

    Google Scholar 

  • Long, B., Chang, X., Hu, K., Zhang, Y.: Effects of temperature and strain rate on the dynamic fracture properties of HTPB propellant. Propellants Explos. Pyrotech. 40(4), 479–483 (2015)

    Article  Google Scholar 

  • Matheson, E.R., Nguyen, D.Q.: A rate-dependent viscoelastic damage model for simulation of solid propellant impacts. In: Furnish, E., Rusell, W. (eds.) Shock Compression of Condensed Matter, pp. 913–916. American Institute of Physics, New York (2005)

    Google Scholar 

  • Ogden, R.W.: Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 326, 565–584 (1972)

    Article  MATH  Google Scholar 

  • Özüpek, Ş., Becker, E.B.: Constitutive modeling of high-elongation solid propellants. J. Eng. Mater. Technol. 114, 111–115 (1992)

    Article  Google Scholar 

  • Park, S.W., Schapery, R.A.: A viscoelastic constitutive model for particulate composites with growing damage. Int. J. Solids Struct. 34(8), 931–947 (1997)

    Article  MATH  Google Scholar 

  • Pouriayevalia, H., Guoa, Y.B., Shim, V.P.W.: A visco-hyperelastic constitutive description of elastomer behaviour at high strain rates. Proc. Eng. 10, 2274–2279 (2011)

    Article  Google Scholar 

  • Ren, P., Hou, X., He, G., Gao, J., He, T.: Comparative research of tensile and compressive modulus of composite solid propellant for solid rocket motor. J. Astronaut. 31, 2354–2359 (2010)

    Google Scholar 

  • Rivlin, R.S.: Large elastic deformations of isotropic materials. IV. Further developments of the general theory. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 241(835), 379–397 (1948)

    MathSciNet  MATH  Google Scholar 

  • Rivlin, R.S.: Proceedings of First Symposium on Naval Structural Mechanics. Pergamon, New York (1960)

    Google Scholar 

  • Shim, V.P.W., Yang, L.M., Lim, C.T., Law, P.H.: A viscohyperelastic constitutive model to characterize both tensile and compressive behavior of rubber. J. Appl. Polym. Sci. 92(1), 523–531 (2004)

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Siviour, C.R., Walley, S.M., Proud, W.G., Field, J.E.: The high strain rate compressive behaviour of polycarbonate and polyvinylidene difluoride. Polymer 46(26), 12546–12555 (2005)

    Article  Google Scholar 

  • Song, B., Chen, W.W., Lu, W.Y.: Mechanical characterization at intermediate strain rates for rate effects on an epoxy syntactic foam. Int. J. Mech. Sci. 49, 1336–1343 (2007)

    Article  Google Scholar 

  • Sounik, D.F., Gansen, P., Clemons, J.L., Liddle, J.W.: Head-impact testing of polyurethane energy-absorbing (EA) foams. SAE Trans. J. Mater. Manuf. 106, 211–220 (1997)

    Google Scholar 

  • Sun, C., Xu, J., Chen, X., Zheng, J., Zheng, Y., Wang, W.: Strain rate and temperature dependence of the compressive behavior of a composite modified double-base propellant. Mech. Mater. 89, 35–46 (2015)

    Article  Google Scholar 

  • Swanson, S.R., Christensen, L.W.: A constitutive formulation for high-elongation propellants. J. Spacecr. Rockets 20, 559–566 (1983)

    Article  Google Scholar 

  • Wang, P., Wang, Z., Ju, Y., Sun, C., Xu, J.: Experimental research on rate dependent constitutive relation of double-basepropellant under impact load. J. Solid Rocket Technol. 35(1), 69–72 (2012)

    Google Scholar 

  • Wang, Z., Qiang, H., Wang, G.: Experimental investigation on high strain rate tensile behaviors of HTPB propellant at low temperatures. Propellants Explos. Pyrotech. 40, 814–820 (2015a)

    Article  Google Scholar 

  • Wang, Z., Qiang, H., Wang, G., Huang, Q.: Tensile mechanical properties and constitutive model for HTPB propellant at low temperature and high strain rate. J. Appl. Polym. Sci. 132, 42104 (2015b)

    Google Scholar 

  • Xu, F., Aravas, N., Sofronis, P.: Constitutive modeling of solid propellant materials with evolving microstructural damage. J. Mech. Phys. Solids 56, 2050–2073 (2008)

    Article  MATH  Google Scholar 

  • Xu, J., Ju, Y., Han, Bo., Zhou, C., Zheng, J.: Research on relaxation modulus of viscoelastic materials under unsteady temperature states based on TTSP. Mech. Time-Depend. Mater. 17(4), 543–556 (2013)

    Article  Google Scholar 

  • Xu, J., Chen, X., Wang, H., Zheng, J., Zhou, C.: Thermo-damage-viscoelastic constitutive model of HTPB composite propellant. Int. J. Solids Struct. 51, 3209–3217 (2015)

    Article  Google Scholar 

  • Yang, L.M., Shim, V.P.W., Lim, C.T.: A visco-hyperelastic approach to modelling the constitutive behaviour of rubber. Int. J. Impact Eng. 24(6–7), 545–560 (2000)

    Article  Google Scholar 

  • Yang, L., Wang, N., Xie, K., Sui, X., Li, S.: Influence of strain rate on the compressive yield stress of CMDB propellant at low, intermediate and high strain rates. Polym. Test. 51, 49–57 (2016)

    Article  Google Scholar 

  • Yeoh, O.H.: Some forms of the strain energy function for rubber. Rubber Chem. Technol. 66(5), 754–771 (1993)

    Article  Google Scholar 

  • Yıldırım, H.C., Özüpek, Ş.: Structural assessment of a solid propellant rocket motor: effects of aging and damage. Aerosp. Sci. Technol. 15(8), 635–641 (2011)

    Article  Google Scholar 

  • Zalewski, R., Wolszakiewicz, T.: Analysis of uniaxial tensile tests for homogeneous solid propellants under various loading conditions. Central Eur. J. Energ. Mater. 8, 223–231 (2011)

    Google Scholar 

  • Zalewski, R., Pyrz, M., Wolszakiewicz, T.: Modeling of solid propellants viscoplastic behavior using evolutionary algorithms. Central Eur. J. Energ. Mater. 7, 289–300 (2010)

    Google Scholar 

  • Zhang, X., Chang, X., Lai, J., Hu, K.: Comparative research of tensile and compressive mechanical properties of HTPB propellant at low temperature. J. Solid Rocket Technol. 36(6), 771–774 (2013)

    Google Scholar 

  • Zhang, J., Zheng, J., Chen, X., Sun, C., Xu, J.: A thermovisco-hyperelastic constitutive model of NEPE propellant over a large range of strain rates. J. Eng. Mater. Technol. Trans. ASME 136(3), 1–8 (2014)

    Article  Google Scholar 

Download references

Acknowledgements

This research was funded by the National 973 Program in China through Grant Nos. 61338 and 613142 and the National Funds in China through Grant 51328050101.

Author information

Authors and Affiliations

  1. Xi’an Hi-Tech Institute, 601 Staff room, Xi’an, 710025, P.R. China

    Zhejun Wang, Hongfu Qiang & Guang Wang

  2. MOE Key Laboratory for Strength and Vibration, Department of Engineering Mechanics, Xi’an Jiaotong University, Xi’an, 710049, P.R. China

    Tiejun Wang

  3. The Fourth Institute of China Aerospace Science and Technology Corporation, Xi’an, 710025, P.R. China

    Xiao Hou

Authors
  1. Zhejun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hongfu Qiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tiejun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xiao Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhejun Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Z., Qiang, H., Wang, T. et al. A thermovisco-hyperelastic constitutive model of HTPB propellant with damage at intermediate strain rates. Mech Time-Depend Mater 22, 291–314 (2018). https://doi.org/10.1007/s11043-017-9357-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11043-017-9357-9

Keywords

Search

Navigation