不同长径比煤样动力学特征及本构模型

解北京; 栾铮; 陈冬新; 钟诗晴

doi:10.19606/j.cnki.jmst.2023.02.006

不同长径比煤样动力学特征及本构模型

doi: 10.19606/j.cnki.jmst.2023.02.006

中国矿业大学(北京)应急管理与安全工程学院，北京 100083

基金项目:

国家重点研发计划 2019YFC0810800

国家自然科学基金青年基金 51404277

中央高校基本科研业务费专项资金 2022YJSAQ15

详细信息

作者简介:
解北京(1984—)，男，安徽滁州人，博士，副教授，主要从事矿井瓦斯灾害防治、煤岩动力灾害防治等方面的研究工作。Tel：15201290493，E-mail：bjxie1984@cumtb.edu.cn

中图分类号: TD315
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- 被引次数: 0
出版历程
- 收稿日期: 2022-05-31
- 修回日期: 2022-09-09
- 刊出日期: 2023-03-30

Dynamic characteristics and constitutive model of coal samples with different length diameter ratio

School of Emergency Management and Safety Engineering, China University of Mining and Technology-Beijing, Beijing 100083, China

摘要

摘要: 为研究冲击荷载下不同长径比煤样的动力学性能，借助改进的霍普金森压杆实验装置(ϕ75 mm)，开展6个冲击等级(4.18~8.03 m/s)、4种长径比(0.33~1.33)下的冲击压缩实验，并结合灰色关联理论分析动力学参数与长径比之间的关联性，建立基于力学机制、Weibull分布、D-P准则的4参数单轴煤岩强度型统计损伤模型。研究表明：①煤样长径比与应变率、动抗压强度、耗散能均呈二次函数关系，且耗散能随长径比增加而降低; 与电磁能呈一次函数关系，且保持正相关。②煤样长径比对动力学参数的影响排序为：电磁能(0.88)>动抗压强度(0.84)>耗散能(0.81)>应变率(0.78)。③基于Weibull分布、D-P准则构建初始本构模型，并借助动抗压强度σ_max与应变率、长径比n的关系修正，进而对比实验应力-应变曲线，验证模型可靠性(R²>0.91)。
- 长径比 /
- 应变率 /
- 霍普金森压杆 /
- 灰色关联 /
- 损伤本构模型
Abstract: In order to study the dynamic performance of coal samples with different length diameter ratio under impact load, this paper used an improved Hopkinson compression bar experimental device (ϕ75 mm), and carried out the impact compression experiments under 6 impact grades (4.18~8.03 m/s)and 4 aspect ratios(0.33~1.33).It analyzed the correlation between the dynamic parameters and the aspect ratio in combination with the gray correlation theory, and this study then established a 4-parameter uniaxial strength type statistical damage model of coal and rock based on the mechanical mechanism, Weibull distribution and D-P failure criterion.Results show that: ① The length diameter ratio of coal samples has a quadratic function relationship with the strain rate and dynamic compressive strength; The relationship between the dissipation energy and the aspect ratio is a quadratic function, and the dissipation energy decreases with the increase of the aspect ratio; The relationship between the electromagnetic energy and the aspect ratio is a linear function and keeps a positive correlation. ② According to the grey correlation theory, this study obtained the influence order of length diameter ratio of coal sample on dynamic parameters: electromagnetic energy(0.88)>dynamic compressive strength(0.84)>dissipation energy(0.81)>strain rate(0.78).③ The initial constitutive model is constructed based on Weibull distribution and D-P criterion, and the dynamic compressive strength σ_max and strain rate、the relationship between length to diameter ratio n was corrected, and then the experimental stress-strain curves were compared to verify the reliability of the model(R²>0.91).
- aspect ratio /
- strain rate /
- SHPB /
- grey correlation /
- damage constitutive model

HTML全文

图 1 原煤试样加工及成品

Figure 1. Raw coal sample processing and finished products

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图 2 SHPB实验系统

Figure 2. SHPB experimental system

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图 3 煤样应力平衡曲线

Figure 3. Stress balance curve of coal sample

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图 4 典型应变率时程曲线

Figure 4. Typical strain rate time history curve

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图 5 应变率与煤样长径比关系

Figure 5. Relationship between strain rate and length diameter ratio of coal sample

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图 6 应力-应变曲线

Figure 6. Curve of stress and strain

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图 7 煤样动抗压强度与应变率关系

Figure 7. Relationship between compressive strength and strain rate of coal sample

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图 8 动抗压强度与煤样长径比关系

Figure 8. Relationship between compressive strength and length diameter ratio of coal sample

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图 9 CM1煤样破坏电磁信号降噪前后对比

Figure 9. Comparison of electromagnetic signal of CM1 coal

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图 10 应变率-耗散能关系曲线

Figure 10. Relationship curve between strain rate and dissipation energy

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图 11 长径比-耗散能关系曲线

Figure 11. Relationship curve between length diameter ratio and dissipated energy

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图 12 应变率-电磁辐射能关系曲线

Figure 12. Strain rate electromagnetic radiation energy relation curve

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图 13 长径比-电磁辐射能关系曲线

Figure 13. Relationship curve between length diameter ratio and electromagnetic radiation energy

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图 14 煤样动抗压强度的3D曲面

Figure 14. 3D curved surface of dynamic compressive strength of coal sample

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图 15 煤样实验和理论应力-应变曲线

Figure 15. Coal sample test and theoretical stress-strain curve

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表 1 煤样基础物理力学参数

Table 1. Fundamental physical and mechanical parameters of coal sample

密度/ (kg·m^-3)	静态抗压强度/ MPa	弹性模量/ GPa	泊松比	孔隙率/%
1 307.10	18.39	0.89	0.43	2.54

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表 2 SHPB冲击破坏实验数据统计

Table 2. Data of SHPB impact damage experiment

直径×高度/ (mm×mm)	编号	速度/ (m·s^-1)	应变率$ \overline{\dot{\varepsilon}}$ /s^-1	动抗压强度σ_max/MPa	耗散能/J	辐射能/J	直径×高度/ (mm×mm)	编号	速度/ (m·s^-1)	应变率$ \overline{\dot{\varepsilon}}$/s^-1	动抗压强度σ_max/MPa	耗散能/J	辐射能/J
75×25	CM1	5.06	120.04	22.45	3.65	0.08	75×75	MM1	4.63	103.62	7.06	2.21	0.46
	CM2	5.64	136.51	12.62	7.45	0.19		MM2	5.58	123.86	11.35	3.29	0.63
	CM3	6.32	146.01	35.82	9.19	0.15		MM3	6.00	139.03	12.97	5.55	0.97
	CM4	6.86	159.39	34.38	12.57	0.31		MM4	6.54	149.244	13.97	6.61	0.93
	CM5	7.47	177.79	32.92	13.36	0.56		MM5	7.40	169.07	15.27	7.16	1.18
	CM6	7.78	182.29	43.14	14.08	0.63		MM6	8.03	176.79	20.37	9.34	1.65
75×50	ZM1	4.18	98.26	6.18	1.44	0.23	75×100	LM1	4.71	109.26	9.42	0.49	0.70
	ZM2	5.25	122.50	11.00	2.04	0.43		LM2	5.69	125.68	11.82	2.59	0.78
	ZM3	6.18	145.31	13.93	2.71	0.61		LM3	6.26	140.35	13.57	4.26	1.01
	ZM4	6.76	155.58	16.89	5.95	0.87		LM4	6.84	152.81	14.12	4.37	1.08
	ZM5	7.22	173.40	23.41	9.34	1.07		LM5	7.50	172.44	16.41	6.44	1.27
	ZM6	7.61	180.04	26.32	9.42	1.24		LM6	7.90	180.98	18.07	8.25	1.38

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表 3 动抗压强度拟合结果

Table 3. Fitting results of dynamic compressive strength

长径比	应变率拟合		R²	应变率/s^-1	长径比拟合			R²
长径比	a	-b	R²	应变率/s^-1	a	-b	c	R²
0.33	0.42	34.73	0.88	100	9.12	13.65	10.89	0.91
0.67	0.24	18.44	0.95	120	15.52	30.36	24.12	0.84
1.00	0.15	8.40	0.91	140	21.91	47.07	37.35	0.99
1.33	0.11	2.61	0.98	160	28.31	63.78	50.57	0.99
—	—	—	—	180	34.71	80.50	63.80	0.98
—	—	—	—	200	41.11	97.22	77.03	0.98

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表 4 应变率-耗散能拟合结果

Table 4. Fitting results of strain rate and dissipation energy

长径比	应变率拟合		R²
长径比	a	b	R²
0.33	0.16	-15.02	0.95
0.67	0.11	-10.53	0.85
1.00	0.10	-9.72	0.97
1.33	0.09	-7.60	0.95

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表 5 长径比-耗散能拟合结果

Table 5. Fitting results of length diameter ratio and dissipation energy

应变率/s^-1	长径比拟合			R²
应变率/s^-1	a	b	c	R²
100	-1.12	0.37	1.45	0.72
120	1.54	-5.17	6.14	0.98
140	4.21	-10.71	10.84	0.99
160	6.87	-16.25	15.53	0.96
180	9.53	-21.79	20.22	0.94
200	12.19	-27.33	24.92	0.92

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表 6 应变率-电磁辐射能拟合结果

Table 6. Fitting results of strain rate and electromagnetic radiation energy

长径比	应变率拟合		R²
长径比	a	b	R²
0.33	0.009	-1.06	0.92
0.67	0.012	-1.04	0.96
1.00	0.011	-0.73	0.97
1.33	0.010	-0.38	0.99

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表 7 长径比-电磁辐射能拟合结果

Table 7. Fitting results of length diameter ratio and electromagnetic radiation energy

应变率/s^-1	长径比拟合		R²
应变率/s^-1	a	b	R²
100	0.56	-0.16	0.99
120	0.53	0.08	0.99
140	0.51	0.33	0.98
160	0.48	0.57	0.95
180	0.45	0.85	0.91
200	0.42	1.06	0.84

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表 8 灰色综合关联结果

Table 8. Grey comprehensive correlation results

比较序列	综合关联度
应变率	0.78
动抗压强度	0.84
耗散能	0.81
电磁能	0.88

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表 9 本构模型拟合参数

Table 9. Fitting parameters of constitutive model

编号	n	$ \dot{\varepsilon}$/s^-1	E/GPa	ε_m/‰	R²
CM6	0.33	182.29	37.11	7.05	0.95
ZM6	0.67	180.04	6.20	13.01	0.93
MM6	1.00	176.79	25.00	5.40	0.91
LM6	1.33	180.98	9.50	5.63	0.99

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不同长径比煤样动力学特征及本构模型

doi: 10.19606/j.cnki.jmst.2023.02.006

作者简介:
解北京(1984—)，男，安徽滁州人，博士，副教授，主要从事矿井瓦斯灾害防治、煤岩动力灾害防治等方面的研究工作。Tel：15201290493，E-mail：bjxie1984@cumtb.edu.cn

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Dynamic characteristics and constitutive model of coal samples with different length diameter ratio

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不同长径比煤样动力学特征及本构模型

doi: 10.19606/j.cnki.jmst.2023.02.006

作者简介: 解北京(1984—)，男，安徽滁州人，博士，副教授，主要从事矿井瓦斯灾害防治、煤岩动力灾害防治等方面的研究工作。Tel：15201290493，E-mail：bjxie1984@cumtb.edu.cn

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Dynamic characteristics and constitutive model of coal samples with different length diameter ratio

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出版历程

目录

作者简介:
解北京(1984—)，男，安徽滁州人，博士，副教授，主要从事矿井瓦斯灾害防治、煤岩动力灾害防治等方面的研究工作。Tel：15201290493，E-mail：bjxie1984@cumtb.edu.cn