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Rate-Dependent Hardening Model for Polymer-Bonded Explosives Considering a Wide Range of Strain Rates (광범위한 변형률속도를 고려한 복합화약의 변형률속도 의존 경화모델)
This study is concerned with the effect of the strain rate on the strain hardening behavior of polymer-bonded explosives (PBXs) at a wide range of strain rates. When PBXs are applied in a warhead system that undergoes severe dynamic loading conditions, it is very important to investigate the deformation behavior of PBXs subjected to dynamic loads in order to guarantee the safety of the warhead system before explosion. PBXs in the warhead system undergo not only localized large deformation with high strain rates induced by direct dynamic loads but also small deformation with low and intermediate strain rates due to stress wave propagation. The strain hardening behavior of PBXs at quasi-static states, intermediate and high strain rates should be thoroughly investigated to perform the design of the warhead system because PBXs undergo deformation at a wide range of strain rates irregularly distributed in PBXs from quasi-static states to high strain rates. It is noticed that the strain hardening behavior of PBXs varies significantly as a function of the strain rate. It is, hence, essential to incorporate the effect of the strain rate on the strain hardening behavior of PBXs in the numerical simulation of the warhead to predict the deformation behavior of PBXs accurately.
In previous research works, it was demonstrated that the flow stresses generally increase as the strain rate increases in various PBXs. The effect of the strain rate can be explained by the intrinsic characteristics of the polymer matrix. It is noticed that the elastic modulus and flow stress of polymers increase significantly as the strain rate increases. The effect of the strain rate on the strain hardening behavior of PBXs is highly influenced by the mechanism of failure in accordance with the strain rate as well as the intrinsic characteristics of the polymer matrix. It was reported that the debonding stresses between the particles and the polymer matrix increase as the elastic modulus of the polymer matrix increases. The debonding stresses between the particles and the polymer matrix increase as the strain rate increases since the elastic modulus of the polymer matrix increases with increasing strain rates. It corresponds to the previous research work reporting that the crystal fracture of particles became the dominant failure mechanism in uniaxial compressive tests at high strain rates while the debonding, which can also be expressed as the interfacial failure, was the dominant failure mechanism in uniaxial compressive tests at low strain rates.
In this study, uniaxial compressive tests of two kinds of PBX simulants classified into particulate composites were conducted at a wide range of strain rates ranging from 10-4 s-1 to 3,870 s-1 to investigate the effect of the strain rate on the strain hardening behavior of PBXs. The dynamic material testing machine (Instron 8801) was utilized for uniaxial compressive tests from quasi-static states to low strain rates ranging from 10-4 s-1 to 100 s-1 and the developed high speed material testing machine (HSMTM) was used for uniaxial compressive tests at intermediate strain rates ranging from 101 s-1 to 102 s-1. A new jig system was designed and utilized for uniaxial compressive tests at intermediate strain rates using the HSMTM so that uniaxial compressive tests can be conducted within the designated strain. The split Hopkinson pressure bar (SHPB) was used for uniaxial compressive tests at high strain rates ranging from 1,250 s-1 to 3,870 s-1. For SHPB tests, preceding researches such as determination of the bar material of the SHPB system, pulse shaping techniques and consideration of the variation of the true strain rate were conducted to acquire accurate stress--strain relationships of soft materials including PBXs at high strain rates. The significant effect of the strain rate on the strain hardening behavior during uniaxial compressive deformation is quantitatively investigated from the experimental data at various strain rates.
A new rate-dependent hardening model based on the DSGZ model was proposed from the investigated result to model the effect of the strain rate on the strain hardening behavior of PBXs. The model gives a concise expression of the stress dependence on the strain and strain rate with a second-order exponentially-increasing strain rate sensitivity function. The model is capable of representing the non-linear viscoelasticity, yielding and subsequent strain softening behavior. It can also describe the steady-state behavior at large strain. The proposed model was implemented in the commercial finite element analysis (FEA) software, LS-DYNA, with the user defined material models (UMAT). Finite element analyses of uniaxial compressive tests at various strain rates were conducted with the implemented UMAT to validate the proposed model. The comparisons of FEA results with the experimental data show that the proposed model was successfully able to describe the significant effect of the strain rate on the strain hardening behavior of PBXs.
Keywords: Polymer-Bonded Explosive (PBX), PBX Simulant, Split Hopkinson Pressure Bar Test, Rate-Dependent Hardening Model, Strain Rate Sensitivity