Discrete Element Simulations of Dynamic Compression Failure of Inorganic Glass in SHPB Tests
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摘要: 利用离散元软件PFC2D（Particle Flow Code）建立了分离式霍普金森压杆（SHPB）系统，模拟了无机玻璃圆柱和圆盘试件在冲击压缩下的动态力学行为和失效破坏模式。结果表明：无机玻璃作为典型的脆性材料，其抗压强度具有明显的应变率效应，而杨氏模量则对应变率不敏感；无机玻璃圆柱的破坏过程受纵向压力、端面摩擦力以及横向惯性力的影响，初期微裂纹呈三角状分布，随着纵向应力水平的提高，出现明显的泊松效应，产生横向张应力，致使微裂纹沿纵向扩展，最终试件发生沿轴向的劈裂断裂；摩擦系数和泊松比对试件破坏模式及强度有一定影响。将建立的SHPB数值实验平台用于模拟无机玻璃巴西圆盘试验，揭示了圆盘发生中心开裂的拉伸特征及拉伸强度的应变率相关性。Abstract: Based on the discrete element algorithm (DEM), a numerical split Hopkinson pressure bar (SHPB) platform is established by the mean of particle flow code software (PFC2D), and the feasibility of the system has been verified. The failure mode and the dynamic compressive strength of an inorganic glass specimen at different strain rates are investigated. The numerical simulation shows that the inorganic glass exhibits typical brittle characteristics during dynamic compression, and its compressive strength is significantly affected by the strain rate. The Young’s modulus, however, is strain rate insensitive. The failure mode of the specimen is affected by the boundary friction as well as the Poisson ratio. In the case of frictional contact, the initial micro-cracks within the specimen are distributed in a triangular zone due to the combined effect of longitudinal pressure and frictional force. With the increase of the longitudinal stress, the transverse tensile stress creates the longitudinal cracks, resulting in the axial splitting. The failure mode in the case of frictionless contact differs from the frictional case, in which no triangular crack zone exists. Moreover, the value of Poisson ratio affects the failure mode as it results in the transverse tensile stress during dynamic loading. Numerical simulations of dynamic Brazilian compression are also conducted to support future experimental works. It shows that Brazilian disk starts failure at the center in the moderate strain rate and the macroscopic splitting tensile strength is strain rate dependent.
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图 3 锥形子弹撞击速度为18 m/s时入射和透射波形
Figure 3. Incident and transmitted waves created by the impact of the conical projectile at 18 m/s
图 7 试件两侧的应力时程曲线以及内部应力不均匀系数
Figure 7. Temporal profile of stress on the surfaces facing the incident bar and the transmitted bar and the stress inhomogeneity coefficient
图 8 试件内部应力时程曲线（
${\mu = 0.1}$ ，${\dot \varepsilon = 700\;{{\rm{s}}^{ - 1}}}$ ）Figure 8. Stress history curve of specimen （
${\mu = 0.1}$ ，${\dot \varepsilon = 700\;{{\rm{s}}^{ - 1}}}$ ）
图 9 不同时刻试件内部裂纹分布（a）和破碎形态（b）（
${\mu = 0.1}$ ，${\dot \varepsilon = 700\;{{\rm{s}}^{ - 1}}}$ ）Figure 9. Crack distributions (a) and fragmentation morphologies (b) of the specimen at different time （
${\mu = 0.1}$ ，${\dot \varepsilon = 700\;{{\rm{s}}^{ - 1}}}$ ）
图 10 不同应变率下无机玻璃的应力-应变曲线
Figure 10. Stress-strain curves of inorganic glass at different strain rates
图 11 无摩擦时试件内部的应力时程曲线
Figure 11. Temporal profile of stress inside a specimen without the boundary friction
图 12 无摩擦时试件内部的破坏模式
Figure 12. Evolution of internal damage process inside a specimen without the boundary friction
图 13
${\nu \approx 0}$ 时材料的失效破坏演化Figure 13. Evolution of material failure when
${\nu \approx 0}$ 
图 14 不同摩擦力和泊松比条件下试件的宏观应力时程曲线（
${\dot \varepsilon}$ ≈700 s–1）Figure 14. Macroscopic stress histories of the specimen with various boundary friction and Poisson’s ratio (
${\dot \varepsilon}$ ≈700 s–1)
图 16 v0=9 m/s时无机玻璃动态巴西圆盘劈裂破坏过程：（a）压力时程曲线，（b）试样在各个时刻的破坏形貌
Figure 16. Typical Brazilian disk splitting process under dynamic loading (v0=9 m/s): (a) the pressure history; (b) failure patterns of the disk at different time
图 17 不同冲击速度下巴西圆盘试件的加载压力时程曲线
Figure 17. Pressure histories of the specimens under different impact velocities
图 18 压缩与拉伸强度的动态增强因子与应变率的关系
Figure 18. DIF of compressive and tensile strengths as a function of strain rate
表 1 SHPB数值实验的离散元模型的主要微观参数
Table 1. Main microscopic parameters of discrete element model in numerical experiments of SHPB
Material Effective modulus
of linear contact/
GPaNormal-to-shear
stiffness ratio of
linear contactMinimum radius of
particles/mmSize ratio of maximum
and minimum
particlesPorosity Steel bar 190 4.0 0.100 1.5 0.15 Inorganic glass 63 2.1 0.026 1.5 0.10 Material Effective modulus of
flat-joint contact/
GPaNormal-to-shear
stiffness ratio of
flat-joint contactTensile strength of
flat-joint contact/
GPaShear strength of
flat-joint
contact/GPaDensity of
particles/
(kg·m–3)Steel bar 190 4.0 1000 1000 8800 Inorganic glass 63 2.1 0.073 0.35 2444 
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表 2 石英玻璃宏观参数的数值模拟结果与文献数据的对比
Table 2. Macroscopic parameters of quartz glass: comparison of simulation results with ones published in the literatures
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