应变率对含裂隙红砂岩裂纹扩展模式及破碎特征的影响

闻磊; 冯文杰; 李明烨; 寇子龙; 王亮; 于俊红

doi:10.11883/bzycj-2023-0061

应变率对含裂隙红砂岩裂纹扩展模式及破碎特征的影响

doi: 10.11883/bzycj-2023-0061

闻磊^1,,
冯文杰¹,
李明烨²,
寇子龙^{1, 3},
王亮¹,
于俊红¹

1.
石家庄铁道大学工程力学系，河北石家庄 050043
2.
河北工程技术学院，河北石家庄 050091
3.
中铁大桥科学研究院有限公司，湖北武汉 430034

基金项目: 国家自然科学基金（11872257）；河北省自然科学基金（A2020210008）

详细信息

作者简介:
闻　磊（1983－　），男，博士，副教授，wl0921@126.com

中图分类号: O383
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出版历程
- 收稿日期: 2023-02-27
- 修回日期: 2023-08-25
- 网络出版日期: 2023-08-25
- 刊出日期: 2023-11-17

Strain rate effect on crack propagation and fragmentation characteristics of red sandstone containing pre-cracks

1.
Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, Hebei, China
2.
Hebei Polytechnic Institute, Shijiazhuang 050091, Hebei, China
3.
China Railway Bridge Science Research Institute Co. Ltd., Wuhan 430034, Hubei, China

摘要

摘要: 以含不同倾角预制裂纹的长方形板状红砂岩为研究对象，采用分离式霍普金森压杆沿试样宽度方向施加冲击荷载，使用高速摄像机记录裂纹扩展过程，获得试样的裂纹路径特征以及动态压缩强度和动态弹性模量，利用筛分统计法分析试样碎块分布特征，结合分形理论定量描述试样破碎程度及特点，探讨中应变率条件下含裂隙试样裂纹扩展模式与动态力学性质和破碎程度的相互关系。研究结果表明，应变率较高时试样会更多地出现远场裂纹和离层裂纹，并且相比相关低应变率实验结果，中应变率范围内试样破坏模式及裂纹分布情况随应变率的变化规律是不同的。随着应变率的提高，试样大体上从1条拉伸裂纹的临界破坏演变成X形剪切裂纹为主的复杂裂隙网络，并且不同角度预制裂隙对于这种裂纹扩展模式的演变有重要影响。在预制裂纹倾角一定的情况下，岩样动态压缩强度和动态弹性模量表现出明显的应变率效应，不同角度预制裂纹对于试样的应变率敏感性有显著影响。随裂纹倾角的增大，试样的动态强度、动态弹性模量和分形维数表现出的变化趋势具有一定的相似性，大体呈现先减小后增大的趋势，裂纹倾角为45°的试样的动态压缩强度、动态弹性模量和分形维数均为最小。随应变率的升高，不同预制裂纹倾角的试样碎块分布更加分散，应变率越高，预制裂纹倾角对于岩石冲击破碎程度、分形维数的影响越显著。
- 应变率 /
- 裂纹扩展 /
- 红砂岩 /
- 分离式霍普金森压杆 /
- 裂纹倾角 /
- 破碎
Abstract: In this experiment, finite size red sandstone containing pre-existing single crack was taken as the research object. The ratio of length to width of the samples was set about 0.65. The inclination angle of the pre-crack includes 0°, 30°, 45°, 60° and 90°. A split Hopkinson pressure bar was used for impact test, and a high-speed camera was used to record the crack propagation. The dynamic loads were applied along the width of the samples. Velocities of striker in impact tests were set as 6, 8 and 10 m/s by adjusting the pressure of the air gun. Acquisition frequency of the high-speed camera was set as 75000 s⁻¹. The characteristics of crack propagation, dynamic compressive strength and dynamic elastic modulus of the samples were obtained. The fractal theory was used to describe the fragmentation characteristics of the samples. The relationship between dynamic mechanical properties, fragmentation characteristics and crack propagation under medium strain rate was discussed. The findings show that when the strain rate is high, more far-field cracks and separation cracks appear in the sample. In the range of medium strain rate, the failure mode and the number of cracks change differently with strain rate compared with the experimental results of low strain rate. The strain rate and the angle of pre-existing crack have a great influence on the crack propagation and failure mode of the samples. The crack propagation of the samples with different pre-existing crack is different. With the increase of strain rate, the failure mode of the sample becomes more complex, gradually evolving from critical failure with a tensile crack to complex failure mainly with X-shaped shear crack. When the angle of the pre-existing crack is fixed, the dynamic compressive strength and dynamic elastic modulus of the samples show obvious strain rate effect, and the pre-existing crack with different angles have significant influence on the strain rate sensitivity of the samples. With the increase of pre-existing crack angle, the variation of dynamic compressive strength, dynamic elastic modulus and fractal dimension of the samples show a certain similarity. In all types of samples, the dynamic compressive strength, dynamic elastic modulus and fractal dimension of the sample containing cracks with the inclination angle at 45° are the smallest. With the increase of strain rate, distribution of fragments becomes more dispersed. The higher the strain rate, the more significant the effect of the pre-existing crack on the fracture degree and fractal dimension of the samples.
- strain rate /
- crack propagation /
- red sandstone /
- split Hopkinson pressure bar /
- crack inclination angle /
- fracture

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图 1 部分试样照片

Figure 1. Photo of some samples

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图 2 试样形态及加载方向

Figure 2. Sample morphology and loading directions

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图 3 霍布金森压杆系统

Figure 3. An SHPB system

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图 4 高速摄像机记录裂纹扩展过程

Figure 4. The crack propagation recorded by a high-speed camera

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图 5 裂纹宏观扩展模式种类

Figure 5. Types of crack propagation modes

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图 6 裂纹扩展过程与应力的对应关系

Figure 6. Relationship between crack propagation and stress

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图 7 采用SHPB系统得到的典型波形

Figure 7. Typical waves obtained by an SHPB system

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图 8 60 s⁻¹左右应变率下不同倾角裂隙试样的动态应力-应变曲线

Figure 8. Dynamic stress-strain curves of samples containing cracks with different inclination angles at the strain rate of about 60 s⁻¹

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图 9 不同应变率下60°倾角裂隙试样的应力-应变曲线

Figure 9. Dynamic stress-strain curves of samples containing cracks with the inclination angle of 60° at different strain rates

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图 10 动态压缩强度与应变率的关系

Figure 10. Relationship between dynamic compressivestrength and strain rate

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图 11 动态压缩强度与裂纹倾角的关系

Figure 11. Relationship between dynamic compressivestrength and crack inclination angle

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图 12 含有不同倾角裂纹试样的动态弹性模量随应变率的变化

Figure 12. Dynamic elasticity moduli of samples containing cracks with different inclination angles varied with strain rate

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图 13 不同应变率下试样动态弹性模量随裂纹倾角的变化

Figure 13. Dynamic elasticity moduli of samples varied with crack inclination angle at different strain rates

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图 14 平均破碎块度与裂纹倾角关系

Figure 14. Relationship between average granularity and crack inclination angle

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图 15 分形维数与裂纹倾角的关系

Figure 15. Relationship between fractal dimensionand crack dip angle

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图 16 不同裂纹倾角试样分形维数随应变率的变化

Figure 16. Variations of fractal dimensions of samples with different crack inclination angles with strain rate

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表 1 各类型裂纹扩展模式的特点

Table 1. Characteristics of each type of crack propagation

裂纹类型	裂纹扩展模式特点
Ⅰ型	从预制裂纹端部垂直方向起裂，随后逐步向加载方向扩展
Ⅱ型	从预制裂纹端部，沿预制裂纹方向起裂，随后逐步沿加载方向扩展
Ⅲ型	从预制裂纹端部沿加载方向起裂，或在裂纹中部起裂（预制裂纹90°布设时），随后沿荷载方向扩展
Ⅳ型	与加载方向呈一定角度起裂，产生剪切裂纹，之后沿加载方向发展为拉伸裂纹。与Ⅱ型裂纹相比该型裂纹在预制裂纹端部附近可能表现出局部的压碎区
Ⅴ型	与加载方向呈一定角度起裂，之后与加载方向呈一定角度继续扩展，一般情况下裂纹扩展路径不平滑，可形成沿裂纹扩展路径的岩屑覆盖剪切带
Ⅵ型	在预制裂隙端部沿预制裂隙方向起裂，并沿预制裂隙方向扩展
Ⅶ型	远场剪切型裂纹普遍从试样受荷面起裂，一般不会早于预制裂隙端部裂纹的形成，并且最终将发展为剪切带
Ⅷ型	远场拉伸型裂纹普遍比预制裂隙端部裂纹形成晚，通常将发展为沿荷载方向贯通试样的拉伸裂纹

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表 2 应变率为40 s⁻¹左右和60 s⁻¹左右时试样的裂纹形态

Table 2. Crack shapes of the samples at the strain rates of about 40 s⁻¹and about 60 s⁻¹

β/(°)	应变率40 s⁻¹左右		应变率60 s⁻¹左右
β/(°)	裂纹形态	裂纹类型	裂纹形态	裂纹类型
0		Ⅱ型 Ⅳ型		Ⅱ型 Ⅴ型 Ⅶ型
30		Ⅲ型 Ⅴ型		Ⅴ型 Ⅶ型
45		Ⅲ型 Ⅴ型		Ⅱ型 Ⅴ型 Ⅶ型
60		Ⅴ型		Ⅴ型 Ⅶ型
90		Ⅲ型		Ⅰ型 Ⅴ型 Ⅶ型 Ⅷ型

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表 3 含不同倾角预制裂隙试样裂纹扩展过程

Table 3. Crack propagation processes in samples containing precracks with different inclination angles

β/(°)	裂纹扩展过程			裂纹最终形态
0	119.7 μs	172.9 μs	232.2 μs	678.3 μs
0	预制裂纹端部Ⅳ型裂纹剪切段开始萌生，出现远场Ⅶ型、Ⅷ型裂纹	预制裂纹端部Ⅳ型裂纹继续发展，远场Ⅶ型、Ⅷ型裂纹继续萌生和发展	预制裂纹端部Ⅳ型裂纹剪切段继续扩展，出现向拉伸裂纹转变的趋势，远场Ⅶ型裂纹贯通试件	最初产生的预制裂纹端部Ⅳ型裂纹贯通试样，同时产生Ⅴ型剪切裂纹以及1条Ⅱ型拉伸裂纹，远场Ⅶ型、Ⅷ型裂纹相互贯通，靠近入射杆侧出现垂直向离层裂纹
30	133.0 μs	186.2 μs	252.7 μs	611.8 μs
30	预制裂纹两端各产生1条Ⅲ型、Ⅴ型裂纹，并开始萌生远场Ⅷ型裂纹	预制裂纹两端的Ⅲ型、Ⅴ型裂纹贯通试样，同时预制裂纹两端各产生1条Ⅵ型剪切裂纹	远场Ⅶ型、Ⅷ型裂纹大量出现、扩展并相互贯通，靠近入射杆侧出现垂直向离层裂纹	远场Ⅷ型裂纹迅速发展并贯通试样
45	133.4 μs	146.3 μs	199.5 μs	438.9 μs
45	预制裂纹端部产生Ⅲ型拉伸裂纹，出现远场Ⅶ型、 Ⅷ型裂纹	预制裂纹端部Ⅲ型拉伸裂纹贯通试样，另一端产生Ⅱ型拉伸裂纹并贯通，远场Ⅶ型、 Ⅷ型裂纹继续扩展	远场裂纹继续扩展贯通试样，预制裂纹端部出现1条Ⅲ型拉伸裂纹	新出现的Ⅲ型拉伸裂纹贯通试样，产生新的远场Ⅶ型裂纹，部分远场裂纹相互贯通，出现离层裂纹
60	146.3 μs	172.9 μs	212.8 μs	452.2 μs
60	预制裂纹两端萌生Ⅴ型剪切裂纹，出现远场Ⅶ型裂纹	预制裂纹两端Ⅴ型剪切裂纹继续扩展，出现大量远场 Ⅶ型裂纹	预制裂纹两端Ⅴ型剪切裂纹扩展至试样两端，远场Ⅶ型裂纹继续扩展	远场Ⅶ型裂纹扩展至试样两端， Ⅴ型裂纹、远场Ⅶ型裂纹相互贯通，靠近入射杆侧出现垂直向离层裂纹
90	134.0 μs	172.9 μs	272.6 μs	399.0 μs
90	预制裂纹两端出现Ⅴ型剪切裂纹，并开始萌生远场Ⅶ型裂纹	Ⅴ型剪切裂纹扩展至试样一端，远场Ⅶ型裂纹迅速扩展、贯通试样，并出现Ⅷ型裂纹	Ⅴ型剪切裂纹扩展至试样另一端，远场Ⅶ型、Ⅷ型裂纹迅速扩展	Ⅴ型剪切裂纹、远场Ⅶ型裂纹相互贯通

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表 4 含不同倾角裂隙试样的动态力学参数

Table 4. Dynamic mechanical parameters for samples containing precracks with different inclination angles

试样	应变率/s⁻¹	动态压缩强度/MPa	弹性模量/GPa	试样	应变率/s⁻¹	动态压缩强度/MPa	弹性模量/GPa
D-0-1	16.7	35.8	6.3	D-45-7	55.3	45.3	10.9
D-0-2	23.5	40.2	7.2	D-45-8	59.7	50.8	12.0
D-0-3	19.8	37.6	5.9	D-45-9	62.5	52.8	12.0
D-0-4	41.3	48.7	10.3	D-45-10	80.2	60.1	14.6
D-0-5	38.7	45.2	9.7	D-45-11	83.7	65.8	15.2
D-0-6	40.9	44.8	10.7	D-45-12	78.9	63.2	14.1
D-0-7	65.8	64.9	16.8	D-60-1	19.8	42.1	5.7
D-0-8	60.4	61.9	15.2	D-60-2	23.5	41.9	5.2
D-0-9	57.2	57.3	15.9	D-60-3	17.6	39.7	5.0
D-0-10	76.8	79.8	20.8	D-60-4	38.8	48.8	7.5
D-0-11	82.3	81.1	21.0	D-60-5	43.5	50.2	8.0
D-0-12	83.2	83.5	20.4	D-60-6	41.3	53.8	7.8
D-30-1	17.8	31.8	6.4	D-60-7	59.7	55.7	13.3
D-30-2	19.2	33.2	5.7	D-60-8	63.2	59.8	13.3
D-30-3	21.9	34.3	5.8	D-60-9	58.6	55.7	13.7
D-30-4	37.8	39.8	8.8	D-60-10	75.3	62.7	18.8
D-30-5	42.3	43.5	9.3	D-60-11	79.4	66.8	17.0
D-30-6	39.8	41.7	9.0	D-60-12	83.2	67.8	18.6
D-30-7	55.6	55.2	14.6	D-90-1	17.9	41.8	5.7
D-30-8	59.7	58.8	15.2	D-90-2	19.6	37.6	5.9
D-30-9	62.1	54.3	13.9	D-90-3	21.8	45.7	6.3
D-30-10	76.5	76.2	16.5	D-90-4	39.7	50.1	8.9
D-30-11	79.8	79.3	17.3	D-90-5	45.8	53.2	9.5
D-30-12	83.2	78.5	16.9	D-90-6	42.1	47.8	8.7
D-45-1	18.7	32.9	4.4	D-90-7	62.1	52.1	14.3
D-45-2	23.5	35.3	4.2	D-90-8	60.7	54.9	15.0
D-45-3	20.1	31.8	3.7	D-90-9	65.2	59.8	15.2
D-45-4	40.8	39.7	7.0	D-90-10	77.9	69.4	19.4
D-45-5	39.7	41.2	7.6	D-90-11	83.9	72.8	20.2
D-45-6	43.2	42.8	7.0	D-90-12	79.8	70.1	19.8

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表 5 指数函数系数值

Table 5. The coefficient values of the exponential function

β/(°)	0	30	45	60	90
a/MPa	28.01	23.87	26.49	36.14	34.3
b/s	0.01308	0.01467	0.01070	0.00761	0.00867

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表 6 不同应变率下含裂隙试样筛分情况

Table 6. The sieving of samples containing cracks at different strain rates

β/(°)	应变率/s⁻¹
β/(°)	～40	～60	～80
0
30
45
60
90

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表 7 含裂隙试样破碎块度

Table 7. The granularity of samples containing cracks after impact

试样	d_a/mm	试样	d_a/mm	试样	d_a/mm	试样	d_a/mm	试样	d_a/mm
D-0-4	29.96	D-30-4	29.56	D-45-4	29.33	D-60-4	28.06	D-90-4	29.33
D-0-5	29.52	D-30-5	29.82	D-45-5	29.53	D-60-5	27.63	D-90-5	29.14
D-0-6	29.21	D-30-6	29.69	D-45-6	29.14	D-60-6	28.03	D-90-6	29.51
D-0-7	18.42	D-30-7	19.56	D-45-7	21.83	D-60-7	15.94	D-90-7	15.94
D-0-8	17.68	D-30-8	19.26	D-45-8	21.12	D-60-8	17.51	D-90-8	15.44
D-0-9	17.94	D-30-9	19.31	D-45-9	21.90	D-60-9	17.59	D-90-9	15.59
D-0-10	12.29	D-30-10	13.34	D-45-10	12.73	D-60-10	8.79	D-90-10	11.42
D-0-11	11.96	D-30-11	12.64	D-45-11	13.01	D-60-11	8.77	D-90-11	10.35
D-0-12	10.77	D-30-12	13.00	D-45-12	13.44	D-60-12	8.98	D-90-12	11.32

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表 8 不同工况下试样的分形维数

Table 8. Fractal dimensions of samples under different cases

试样	D_b	试样	D_b	试样	D_b	试样	D_b	试样	D_b
D-0-4	1.28	D-30-4	1.29	D-45-4	1.25	D-60-4	1.31	D-90-4	1.25
D-0-5	1.40	D-30-5	1.33	D-45-5	1.29	D-60-5	1.22	D-90-5	1.33
D-0-6	1.28	D-30-6	1.25	D-45-6	1.26	D-60-6	1.40	D-90-6	1.33
D-0-7	2.07	D-30-7	1.78	D-45-7	1.63	D-60-7	2.05	D-90-7	2.05
D-0-8	1.89	D-30-8	1.85	D-45-8	1.57	D-60-8	2.06	D-90-8	2.04
D-0-9	1.89	D-30-9	1.87	D-45-9	1.62	D-60-9	2.16	D-90-9	2.01
D-0-10	2.54	D-30-10	2.20	D-45-10	2.14	D-60-10	2.42	D-90-10	2.22
D-0-11	2.50	D-30-11	2.14	D-45-11	2.17	D-60-11	2.46	D-90-11	2.14
D-0-12	2.56	D-30-12	2.22	D-45-12	2.15	D-60-12	2.35	D-90-12	2.25

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表 9 拟合直线系数值

Table 9. The coefficient values of the fitting straight lines

β/(°)	0	30	45	60	90
p₁/s	0.02946	0.02212	0.02200	0.02793	0.02857
p₂	0.1454	0.4509	0.3461	0.2513	0.1679

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参考文献(37)

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