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

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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.

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Abbreviations

\(\varepsilon \) :

Strain (–)

\(\dot{\varepsilon }\) :

Strain rate (1/s)

\(\sigma \) :

Stress (MPa)

\(\beta \) :

Ratio of the wave impedances of the specimen and bar (–)

\(\alpha _{k} \) :

Degree of stress uniformity in a specimen (–)

\(\tau _{i} \) :

Relaxation time (s)

\(\lambda =l/{l_{0}}\) :

Stretch, where \(l_0\) and l the original and current thickness, respectively, of the specimen during deformation (–)

\(\dot{\lambda }\) :

Stretch rate (1/s)

\({\varvec{\upsigma }}\) :

Cauchy stress tensor (MPa)

\(\sigma _{ij} \) :

Components of \({\varvec{\upsigma }}\) (MPa)

\(\varOmega \) :

Constitutive functional (–)

A :

Cross-sectional area (\({\text {mm}}^{{2}}\))

\(a_{T} \) :

Shift factor (–)

\({\mathbf{B}}\) :

Left Cauchy–Green deformation tensor (–)

\(B_{ij} \) :

Components of \({\mathbf{B}}\) (–)

\({\mathbf{C}}\) :

Right Cauchy–Green deformation tensor (–)

\(C_{{1}}\) :

Constant value (–)

\(C_{{2}}\) :

Constant value (–)

c :

Elastic wave velocity (m/s)

\({\mathbf{E}}\) :

Green–Lagrange strain tensor (–)

\({\dot{\mathbf{E}}}\) :

Strain rate tensor (–)

\(E_{ij} \) :

Components of \({\mathbf{E}}\) (–)

E :

Young’s modulus (GPa)

\({\mathbf{F}}\) :

Deformation gradient tensor (–)

\(F_{ij} \) :

Components of \({\mathbf{F}}\) (–)

\({\mathbf{I}}\) :

Unit tensor (–)

\(I_{1} \) :

First strain invariant (–)

\(I_{2} \) :

Second strain invariant (–)

l :

Length (mm)

k :

Incident wave travel times (–)

\(M_{i}\) :

Compressive relaxation modulus (MPa)

n :

Number of wave transit from one end of specimen to the other (–)

p :

Pressure (MPa)

t :

Time (s)

T :

Temperature (\({^\circ }\hbox {C}\))

\({T}_0\) :

Reference temperature (\({^\circ }\hbox {C}\))

\(\Delta t\) :

Time for elastic wave to transit between ends of a specimen (s)

U :

Stress-energy function (–)

b:

The incident/transmitted bar

s:

Specimen

i:

Incident

r:

Reflected

t:

Transmitted

e:

Elastic

v:

Viscoelastic

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Acknowledgements

The present work is supported by the National Natural Science Foundation of China (NSFC 11802273), the opening project of Science and Technology on Electromechanical Dynamic Control Laboratory (6142601180404), Shanxi Province Science Foundation for Youths (201901D211279) and Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (2019L0586).

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Authors and Affiliations

  1. College of Mechatronic Engineering, North University of China, Taiyuan, 030051, China

    Youcai Xiao & Zhijun Wang

  2. Science and Technology on Electromechanical Dynamic Control Laboratory, Xi’an, 710000, China

    Youcai Xiao & Chenyang Fan

  3. Departments of Astronautic Science and Mechanics, Harbin Institute of Technology, Harbin, 150001, China

    Yi Sun

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  1. Youcai Xiao
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Xiao, Y., Fan, C., Wang, Z. et al. Visco-hyperelastic constitutive modeling of the dynamic mechanical behavior of HTPB casting explosive and its polymer binder. Acta Mech 231, 2257–2272 (2020). https://doi.org/10.1007/s00707-020-02655-1

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  • DOI: https://doi.org/10.1007/s00707-020-02655-1

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