Experimental study and numerical simulation of dynamic fracture behavior of biomimetic spiral structured composite
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摘要: 通过三点弯动态冲击实验和数值模拟，研究了仿生螺旋结构复合材料的动态断裂韧性，该结构是基于Bouligand结构设计的仿生复合结构。首先使用软硬两种基体通过3D打印技术制备了8组不同角度的试样，使用改进的分离式Hopkinson杆完成了动态三点弯冲击实验，得到了试样的位移-载荷曲线、起裂时间和起裂功，并对试样最终断裂形态进行分析。随后在ABAQUS软件中完成了试样断裂全过程的数值模拟，对裂纹的萌生和扩展过程进行了分析。实验和数值模拟结果都表明螺旋角对试样的断裂韧性有很大的影响，在螺旋角度0°~75°的范围内，随着角度的增加试样的断裂韧性增强，而螺旋角度为90°时试样的断裂韧性急剧下降。实验过程中观察到试样在动态断裂过程中存在裂纹偏转现象。最后考察了裂纹偏转对动态断裂的影响机制，结果显示裂纹偏转改变了复合材料的局部断裂模式，增加了断裂面积，从而提升了材料的断裂韧性。Abstract: The dynamic fracture toughness of the bionic spiral structured composite material was studied through three-point bending dynamic impact experiment and numerical simulation. The structure is a bionic composite structure based on the Bouligand structure design. Firstly, 8 groups of specimens with different angles were prepared by 3D printing technology using two kinds of substrates, soft and stiff, and the dynamic three-point bending impact tests were completed by using an improved split Hopkinson bar. The displacement-load curve, fracture time and fracture energy were obtained, and the final fracture morphology of the sample was analyzed. Then, the numerical simulation of the whole process of specimen fracture was completed in ABAQUS software, and the crack initiation and propagation process were analyzed. Both the experimental and numerical simulation results show that the helix angle has a great influence on the fracture toughness of the specimen, in the range of the helix angle of 0°-75°, the fracture toughness of the specimen increases with the increase of the angle, while when the helix angle is 90°, the fracture toughness of the sample drops sharply. In the process of experiment, it is observed that there is a crack deflection phenomenon during the dynamic fracture process of the sample. Finally, the influence mechanism of the crack deflection on the dynamic fracture was investigated. The results show that the crack deflection changes the local fracture mode of the composite material, increases the fracture area, and therefore improves the fracture toughness of the material.
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图 1 仿生螺旋结构复合材料试样的结构和尺寸
Figure 1. Structure and size of bionic spiral structure composite material sample
L—Length; S—Length of span; H—Height; W—Width; γ—Helical angle; h—Length of notch; d—Interlayer spacing
图 2 改进的分离式Hopkinson杆系统原理图
Figure 2. Schematic diagram of the improved split Hopkinson rod system
1—Bullet; 2—Incident rod; 3—Group I strain gauge; 4—Sample; 5—Group II strain gauge; 6—Fixture; 7—Strain gauge; 8—Oscilloscope; 9—Beam laser speedometer; v—Velocity
图 3 II组应变片信号
Figure 3. Strain gauge signal of group II
t1, t2—The moment when the two strain gauges respectively receive the stress wave
图 4 起裂功
Figure 4. Crack initiation work
U—Crack initiation work; P—Load; δ—Displacement; δt—Displacement at time t
图 5 不同角度仿生螺旋结构复合材料试样的载荷-位移曲线
Figure 5. Load-displacement curves of sample of bionic spiral structure composite with different angles
图 6 不同角度仿生螺旋结构复合材料试样的断裂功和起裂时间
Figure 6. Fracture work and initiation time of sample of bionic spiral structure composite with different angles
图 7 不同角度仿生螺旋结构复合材料试样的裂纹扩展：(a) γ=0°；(b) γ=45°；(c) γ=60°；(d) γ=75°
Figure 7. Crack growth of sample of bionic spiral structure composite with different angles: (a) γ=0°; (b) γ=45°; (c) γ=60°; (d) γ=75°
图 8 仿生螺旋结构复合材料有限元模型
Figure 8. Finite element model of bionic spiral structure composite
图 9 仿生螺旋结构复合材料拉伸应力-应变曲线
Figure 9. Tensile stress-strain curves of bionic spiral structure composite
图 10 仿生螺旋结构复合材料压缩应力-应变曲线
Figure 10. Compressive stress-strain curves of bionic spiral structure composite
图 11 仿生螺旋结构复合材料和硬质基体纯材料的实验和数值模拟的时间-载荷对比
Figure 11. Time-load comparison of experimental and numerical simulation of bionic spiral structure composite and hard matrix pure material
图 12 螺旋角75°仿生复合材料试样的实验和模拟裂纹扩展对比
Figure 12. Comparison of experimental and simulated crack growth of biomimetic composite samples with a helix angle of 75°
图 13 数值模拟中不同角度仿生螺旋结构复合材料试样的时间-载荷曲线
Figure 13. Numerical simulation of time-load curves of sample of bionic spiral structure composite with different angles
图 14 不同角度仿生螺旋结构复合材料试样的裂纹扩展过程
Figure 14. Crack growth process of sample of bionic spiral structure composite with different angles
Δ—Displacement
图 15 不同角度仿生螺旋结构复合材料试样的起裂时间(T)
Figure 15. Crack initiation time (T) of sample of bionic spiral structure composite with different angles
图 16 螺旋角75°仿生螺旋结构复合材料试样的裂纹扩展
Figure 16. Crack growth of sample of bionic spiral structure composite with a helix angle of 75°
图 17 不同角度仿生螺旋结构复合材料试样的断裂失效体积和断裂能
Figure 17. Fracture failure volume and fracture energy of sample of bionic spiral structure composite with different angles
图 18 螺旋角75°仿生螺旋结构复合材料的应力分布：(a) 拉伸应力；(b) 剪应力
Figure 18. Stress distribution of sample of bionic spiral structure composite with a helix angle of 75°: (a) Tensile stress; (b) Shear stress
图 19 螺旋角90°仿生螺旋结构复合材料的应力分布：(a) 拉伸应力；(b) 剪应力
Figure 19. Stress distribution of sample of bionic spiral structure composite with a helix angle of 90°: (a) Tensile stress; (b) Shear stress
图 20 螺旋角75°仿生螺旋结构复合材料的层间裂纹扩展
Figure 20. Interlaminar crack growth of sample of bionic spiral structure composite with a helix angle of 75°
图 21 螺旋角75°仿生螺旋结构复合材料各层层间的时间-剪应力曲线
Figure 21. Time-shear stress curves between each layer of the bionic spiral structure composite with a helix angle of 75°
图 22 螺旋角75°仿生螺旋结构复合材料各层层间的时间-拉伸应力曲线
Figure 22. Time-tensile stress curves between each layer of the bionic spiral structure composite with a helix angle of 75°
表 1 软质基体Tango Plus和硬质基体VeroWhite Plus材料参数
Table 1. Material parameters of soft Tango Plus and stiff VeroWhite Plus
Material VeroWhite Plus Tango Plus Density/(g·cm−3) 1.18 1.13 Energy dissipation ratio/% 33.4±2.4 99.5±3.7 Flexural stiffness/(kN·mm−1) 1.08±0.11 0.0167±0.0064 Response time/ms 0.48±0.12 ~2000 Maximum force at break/kN 1.76±0.78 0.109±0.059 Maximum displacement/mm 1.57±0.31 27.3±3.1 Maximum velocity without failure/(m·s−1) 3.45 3.40 Maximum energy without failure $ m{V}_{\mathrm{i}\mathrm{n}\mathrm{i}}^{2}/2 $/J 1.99 1.95 Minimum velocity with failure/(m·s−1) 3.50 3.62 Energy absorption with failure $\left(\dfrac{m{V}_{\mathrm{i}\mathrm{n}\mathrm{i} }^{2} }{2}-\dfrac{m{V}_{\mathrm{r}\mathrm{e}\mathrm{s} }^{2} }{2}\right)$/J 1.95 2.19 Notes: Vini—Initial velocity; Vres—Speed of fracture. 
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表 2 硬质基体和软质基体力学性能
Table 2. Mechanical parameters of stiff matrix and soft matrix
Material Stiff Soft Density/(g·mm3) 1.2 1.1 Young’s modulus/MPa 3000 300 Poisson’s ratio 0.3 0.3 Failure stress/MPa 100 0 Failure strain/MPa 0 1.4
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