Initial Study on Constitutive Model of PBXs via Viscoelastic StatisticalCrack Mechanics Including Anisotropic Damage
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摘要: 建立含损伤本构模型是研究炸药动态力学响应规律的基础。基于PBX炸药材料的宏观黏弹性特征和细观上微裂纹面的方向性，建立了含各向异性损伤的黏弹性统计微裂纹(Aniso-Visco SCRAM)本构模型, 简化后得到单轴应力加载下的本构方程。利用数值计算程序，以PBX9501为例，分析了微裂纹扩展的各向异性、PBX炸药破坏强度及临界应变的拉压异性和应变率相关性，考察了微裂纹数密度、初始微裂纹尺寸、微裂纹面摩擦系数及断裂表面能4个主要参数的敏感性及影响规律。结果表明，它们对微裂纹的扩展演化有较大影响，进而导致材料表现出不同的力学响应。
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关键词:
- PBX炸药 /
- 各向异性损伤 /
- 黏弹性统计微裂纹本构模型 /
- 单轴加载
Abstract: Building constitutive models that include damage is the foundation for the research of dynamic mechanical responses of explosives.Based on the viscoelastic character on macroscale and the crack directions on mesoscale, we established a viscoelastic statistical crack mechanics including anisotropic damage, and then obtained the simplified constitutive model under uniaxial loading.By using a numerical program, and taking PBX9501 as an example, we analyzed the extension rules of cracks with various directions, and the strength-difference and strain-rate dependence of failure strength and critical strain of explosives.Furthermore, we discussed the sensitivity of 4 main parameters, the crack number density, the initial crack size, the friction coefficient between crack surfaces and the fracture surface energy.The result demonstrates that the 4 parameters greatly affect the extension and evolvement of cracks, which causes the different mechanical responses of explosives.-
Key words:
- PBX explosive /
- anisotropic damage /
- visco statistical crack mechanics /
- uniaxial loading
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图 1 Aniso-Visco SCRAM模型示意图(E为弹性模量)
Figure 1. Schematic of Aniso-Visco SCRAM(E is the elasticity modulus)
图 2 具有不同法向的微裂纹尺寸扩展曲线
Figure 2. Calculated crack extension curves of different orientations
图 4 单轴拉伸和压缩作用下应力-应变曲线
Figure 4. Calculated stress-stain curves under uniaxial tension and compression
图 5 不同应变率条件下单轴压缩应力-应变曲线
Figure 5. Calculated stress-strain curves under uniaxial compression at different strain rates
图 6 不同应变率条件下单轴拉伸应力-应变曲线
Figure 6. Calculated stress-strain curves under uniaxial tension at different strain rates
图 7 不同微裂纹数密度取值的计算结果
Figure 7. Calculated results under uniaxialcompression with different number densities
图 8 不同初始裂纹尺寸的计算结果
Figure 8. Calculated results under uniaxialcompression with different initial crack sizes
图 9 不同微裂纹面摩擦系数的计算结果
Figure 9. Calculated results under uniaxial compressionwith different frictional coefficients
图 10 不同断裂表面能的计算结果
Figure 10. Calculated results under uniaxialcompression with different surface energies
表 1 Aniso-Visco SCRAM模型输入参数
Table 1. Constitutive model parameters for Aniso-Visco SCRAM
Density/(g/cm3) G/(GPa) μ ν c0/(μm) cR/(m/s) N0/(cm-3) m γ/(J/m2) 1.86 3.235 0.5 0.3 30 300 45* 10 0.5* G(1)/(GPa) G(2)/(GPa) G(3)/(GPa) G(4)/(GPa) G(5)/(GPa) 0.9440 0.1738 0.5212 0.9085 0.6875 [1/τ(1)]/(μs-1) [1/τ(2)]/(μs-1) [1/τ(3)]/(μs-1) [1/τ(4)]/(μs-1) [1/τ(5)]/(μs-1) 0 0.00732 0.0732 0.732 2.0 Note：(1)c0 is the initial crack size；(2)Values with subscript “*” are dedicated to this study. 
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