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# A Study on the Nonlinear Behaviors of Polymer-Bonded Explosives Considering Stress Softening Effect(응력연화현상을 고려한 복합화약의 비선형 거동에 관한 연구)

2013.09.08 23:53

저자명 | 염기선 |
---|---|

년도 | 2013 |

Polymer-bonded
explosive(PBX) is an energetic material in which small explosive crystals are
bonded in a polymer matrix which occupies typically 5−10 % by weight. PBX is
used in a wide variety of weapon applications ranging from rocket propellants
to the main explosive charge in conventional munitions and weapon systems. It
is important to characterize the mechanical properties of PBX and to accurately
model their response behavior because unwanted external stimuli could cause
accidental detonation during manufacturing, transportation or handling. The
mechanical properties of PBX are similar to those of particle-filled elastomers
which are known to exhibit highly nonlinear behaviors such as the stress
softening phenomenon (known as the Mullins effect), hysteresis under cyclic
loading, residual strain after unloading, and frequency dependant responses. The
characterization of the Mullins effect and hysteresis under cyclic loading is
considered in this paper. It is well
known that the initial material properties of unstretched specimens of particle-filled
elastomers are varied after the
specimen has been subjected to loading. This phenomenon was observed by Mullins
and his coworkers and has become widely known as the "Mullins
effect".

Ogden and Roxburgh proposed a pseudo-elastic phenomenological model in
order to consider the Mullins effect observed in particle-filled elastomers. In
this model, a single continuous damage parameter is incorporated into the
theory in order to modify the strain energy function so that the material
response then differs in the loading from a point on the primary loading path. The model, however, is not adequate to PBX because the PBX exhibit highly
nonlinear behavior such as a stress softening, hysteresis, and residual strain
effects. The stress softening, residual strain and hysteresis are the most
important inelastic phenomena for PBX. This
paper introduces a new pseudo-elastic phenomenological
model for the Mullins effect based on the strain energy functions of isotropic,
incompressible hyperelastic, time-independent PBX simulant materials. The damage function is suggested by
modification of an existing model. To develop a new damage function, the error
function which is employed in the Ogden-Roxburgh model is replaced with
hyperbolic tangent function and ratio of current strain to prior maximum strain
is additionally introduced. As for hysteresis under cyclic loading, it
is observed that second loading stress is located between first loading curve
and first unloading curve. However Ogden-Roxburgh
model do not represent hysteresis under cyclic loading because this
model follow first unloading curve in case of unloading and reloading.
Therefore this paper introduces additional term that follows gradually first
reloading curve in case of reloading and first unloading curve in case of
unloading.

For
safety and cost reasons, two types of inert PBX simulants were adopted as the
mechanical simulant. Compressive
uniaxial loading-unloading and simple shear tests were conducted at
quasi-static states in order to evaluate
prediction accuracy of the proposed pseudo-elastic model. In the experiments,
stress-strain relations of two kinds of PBX simulants with different particle
sizes are observed at the strain rate of 10^{-3} /sec with various
maximum strains. In the results of the experiments, two PBX simulants show
different stress-strain relations however the amount of stress softening
consistently tends to increase with larger strain applied to the specimen.
Stress-strain relations obtained from the experiments are approximated with
Ogden-Roxburgh and proposed pseudo-elastic models and applicability is
evaluated. Proposed damage function provides stress-strain relation which shows
smoother change of slope than Ogden-Roxburgh model and Prediction with
the new model shows
a good correspondence to the experimental data demonstrating that the model
properly describes the Mullins effect and the hysteresis of PBX simulant. Moreover, the proposed pseudo-elastic model
only requires three material parameters to be determined and is constructed based on a theoretical framework of energy function.
Judging from the results, the proposed damage variable and pseudo-elastic model
are predicted to provide enhanced results in applications of PBX simulants.