含预制裂纹陶瓷圆盘劈裂破坏的离散元模拟

杨玲; 任会兰; 赵涵

doi:10.11858/gywlxb.20230625

含预制裂纹陶瓷圆盘劈裂破坏的离散元模拟

doi: 10.11858/gywlxb.20230625

北京理工大学爆炸科学与技术国家重点实验室, 北京　100081

基金项目: 国家自然科学基金（12072028）

详细信息

作者简介:
杨　玲（1998－），女，硕士研究生，主要从事冲击动力学研究. E-mail：18810520109@163.com

通讯作者:
任会兰（1973－），女，教授，主要从事冲击动力学研究. E-mail：huilanren@bit.edu.cn

中图分类号: O347; O346.1
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出版历程
- 收稿日期: 2023-03-13
- 修回日期: 2023-04-15
- 录用日期: 2023-05-02
- 刊出日期: 2023-11-07

Discrete Element Simulation of Splitting Failure of Ceramic Disk with Prefabricated Crack

State Key Laboratory of Explosive Science and Technology, Beijing Institute of Technology, Beijing 100081, China

摘要

摘要: 为研究氧化铝陶瓷在冲击载荷作用下的裂纹演化过程，对平台圆盘陶瓷开展动态巴西劈裂的离散元数值计算研究。利用离散元颗粒流软件建立陶瓷试件冲击加载实验的数值计算模型，分析了不同倾角（预制裂纹与加载方向的夹角）的试件在冲击载荷下的裂纹演化过程和破坏形式，并结合复合型裂纹尖端的应力场分布分析了翼型裂纹起裂和扩展规律。研究结果表明：平台圆盘试件的裂纹首先产生于中心部位，之后次生裂纹从圆盘边缘处萌生扩展，试件最终呈现拉伸破坏模式；离散元模拟结果与基于分离式霍普金森压杆装置的动态巴西劈裂的实验现象吻合；预制裂纹倾角为0°～60°时，改变倾角可以产生介于Ⅰ型与Ⅱ型裂纹之间的复合型裂纹，试件上主裂纹从预制裂纹尖端处成核扩展，表现为翼型裂纹扩展类型（扩展的曲率逐渐趋于零）；试件裂纹的起裂角度随着预制裂纹倾角的增加而增大，起裂应力呈现先降低后升高的趋势；当预制裂纹倾角为30°时，试件最易发生开裂。
- 氧化铝陶瓷 /
- 动态响应 /
- 预制裂纹 /
- 离散元 /
- 翼型裂纹
Abstract: To investigate the alumina ceramics’ crack evolution process under impact loading, a numerical simulation of dynamic Brazilian splitting for platform disc ceramics was carried out by the discrete element method. The discrete element particle flow software was adopted to establish the numerical simulation model of ceramic specimens in impact loading experiments. The crack evolution process and failure mode of specimens with different inclination angles (the angle between the prefabricated crack and the loading direction) under impact loading were analyzed. Combined with the stress field distribution at the tip of mixed mode crack, the initiation and propagation laws of wing crack were analyzed. The results show that the cracks in the platform disc specimen are produced in the center firstly, then the secondary cracks sprouted and expanded from the disc edge. The specimen finally shows a tensile damage pattern. The results of the discrete element simulations are consistent with the experimental phenomena of dynamic Brazilian splitting based on the SHPB device. When the inclination angle of the prefabricated crack is 0°～60°, changing the inclination angle can produce a mixed crack mode between type Ⅰ crack and type Ⅱ crack. And the main crack on the specimen is nucleated from the tip of the prefabricated crack and exhibits a winged crack extension type (the curvature of the extension tapers to zero). With the increase of the inclination angle of the prefabricated crack, the crack initiation angle increases, and the crack initiation stress shows a trend of decreasing firstly and then increasing. The specimens are most susceptible to cracking when the prefabricated crack inclination is 30°.
- alumina ceramics /
- dynamic response /
- prefabricated crack /
- discrete element /
- wing crack

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图 1 SHPB二维计算模型

Figure 1. Two-dimensional simulation model of SHPB

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图 2 无试件状态下的波形信号

Figure 2. Waveform signal without specimen

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图 3 平台圆盘试件动态破坏计算结果

Figure 3. Dynamic failure results of platform disk specimen by simulation

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图 4 实验波形

Figure 4. Experimental waveform

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图 5 陶瓷试件巴西劈裂的破坏过程

Figure 5. Failure process of the ceramic specimen in Brazilian splitting test

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图 6 β=30°时含预制裂纹陶瓷不同时刻的受力云图

Figure 6. Stress distribution of the ceramic specimens at different moment with prefabricated cracks at β =30°

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图 7 不同β下陶瓷的裂纹演化过程

Figure 7. Crack evolution process of the ceramic specimens with different β

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图 8 翼型裂纹示意图

Figure 8. Schematic diagram of wing crack

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图 9 翼型裂纹模型

Figure 9. Model of wing cracks

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图 10 不同倾角β下的起裂角

Figure 10. Crack initiation angle at different β

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图 11 β=60°时裂纹的演化

Figure 11. Evolution of cracks at β=60°

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图 12 不同倾角β下的起裂应力

Figure 12. Crack initiation stress at different β

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表 1 材料Flat-joint模型的细观参数

Table 1. Micro parameters of the Flat-joint model for materials

Material	Minimum particle diameter/mm	Maximum particle diameter/mm	Effective modulus of linear contact/GPa	Normal shear stiffness ratio of linear contact	Porosity
Steel bar	0.20	0.300	218.0	6.0	0.1
Ceramics	0.05	0.075	346.5	1.9	0.1

Material	Effective modulus of Flat-joint contact/GPa	Shear strength of Flat-joint contact/GPa	Tensile strength of Flat-joint contact/GPa	Normal shear stiffness ratio of Flat-joint contact
Steel bar	218.0	100	100	6.0
Ceramics	346.5	390	1760	1.9

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表 2 陶瓷力学性能的数值模拟与实验结果

Table 2. Numerical simulation and experimental results of mechanical properties of the ceramics

Method	Modulus of elasticity/GPa	Compressive strength/MPa	Tensile strength/MPa	Bending strength/MPa	Fracture toughness/ （MPa·m^1/2）
Experimental results	360	2942		343.0	4
Simulation results	360	2940	200	337.5	4

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表 3 理论和数值计算的起裂角对比

Table 3. Comparison of the crack initiation angles between theoretical and simulation results

β/(°)	θ/(°)
β/(°)	Simulation results	Theoretical results
0	0	0
5	39	39.8
10	55	55.1
15	63	62.8
20	68	68.0
25	112	111.1
30	112	114.7
45	114
60	118

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