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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)
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.