混凝土类材料SHPB实验中确定应变率的方法

胡亮亮; 黄瑞源; 高光发; 蒋东; 李永池

doi:10.11883/bzycj-2018-0142

混凝土类材料SHPB实验中确定应变率的方法

doi: 10.11883/bzycj-2018-0142

胡亮亮^1,,
黄瑞源^{1, 2, ,},
高光发¹,
蒋东^{2, 3},
李永池²

1.
南京理工大学瞬态物理国家重点实验室，江苏南京 210094
2.
中国科学技术大学近代力学系，安徽合肥 230027
3.
北京航天长征飞行器研究所，北京 100076

基金项目: 国家自然科学基金（11402266, 11502099, 11672138, 11772160）；装备预研基金（61426040403162604005）；中央高校基本科研业务费专项（30916011348）；中国空气动力研究与发展中心超高速碰撞研究中心开放基金（20181203）

详细信息

作者简介:
胡亮亮（1995－　），男，硕士研究生，18362906302@163.com

通讯作者:
黄瑞源（1984－　），男，博士，讲师，ryhuang@njust.edu.cn

中图分类号: O347
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- 被引次数: 0
出版历程
- 收稿日期: 2018-04-26
- 修回日期: 2018-06-22
- 网络出版日期: 2019-07-25
- 刊出日期: 2019-06-01

A novel method for determining strain rate of concrete-like materials in SHPB experiment

HU Liangliang^1
,,
HUANG Ruiyuan^{1, 2
, ,},
GAO Guangfa¹,
JIANG Dong^{2, 3},
LI Yongchi²

1.
National Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China
2.
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, Anhui, China
3.
Beijing Institute of Space Long March Vehicle, Beijing 100076, China

摘要

摘要: 由于混凝土类材料在SHPB实验中很难实现恒应变率加载，为了确定非恒应变率加载下的实验数据所对应的应变率，本文中针对不同强度（C20，C45，C70）和不同钢纤维含量（0%，0.75%，1.50%，4.50%）的混凝土进行了SHPB实验。对实验得到的30组恒应变率加载下的数据进行了分析总结，结果表明：实验数据所对应的恒应变率与全段平均应变率之间存在一定的比值关系，从而混凝土类材料SHPB实验数据所对应的应变率可以采用全段平均应变率的1.38倍来表征。通过对比非恒应变率加载和恒应变率加载下得到的应力应变曲线，验证了该确定应变率方法的合理性，并指出较短恒应变率加载下实验数据对应的应变率直接采用短平台段对应的应变率来表征是不合理的。
- 混凝土 /
- SHPB /
- 应变率效应 /
- 动态力学行为
Abstract: In this paper, we performed SHPB experiments on concrete-like materials with different strengths (C20, C45, C70) and different steel fiber contents (0%, 0.75%, 1.50%, 4.50%) and analyzed the data drawn. The results showed that the constant strain rate corresponding to the experimental data was co-related with the whole-stage average strain rate to a certain degree and therefore the former could be determined by the 1.38 times of the latter. This method was verified as rational by the comparative analysis of the experimental data of non-constant strain rate with the experimental data of constant strain rate. It was also found that, at the constant strain rate in a relatively short loading time, it is unreasonable to characterize the strain rate corresponding to the experimental data using the constant strain rate corresponding to the short platform stage. In this case, the method proposed in this paper offers a good choice.
- concrete /
- SHPB /
- strain rate effect /
- dynamic mechanical behavior

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图 1 实验装置

Figure 1. Experimental device

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图 2 不同强度和不同钢纤维含量的混凝土材料的典型波形

Figure 2. Typical waveforms for concrete-like materials with different strengths and different fiber contents

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图 3 典型的应力曲线与应变率曲线

Figure 3. Typical stress curves and strain rate curves

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图 4 相近恒应变率加载下的应力应变曲线对比

Figure 4. Comparison of stress-strain curves under similar constant strain rate loading

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图 5 确定应变率的不同方法

Figure 5. Ways for determining strain rate

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图 6 恒应变率与半段（全段）平均应变率之比

Figure 6. Constant strain rate versus average strain rate of half and whole-stage

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图 7 非恒应变率加载与相近恒应变率加载下的应力应变曲线对比

Figure 7. Comparison of stress-strain curves under non-constant strain rate loading (NCSRL) and similar constant strain rate loading (CSRL)

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图 8 较短平台段的原始波形

Figure 8. Original waveform of short time constant strain rate loading

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图 9 C45混凝土在不同加载情况下的应力应变曲线对比

Figure 9. Comparison of stress-strain curves of C45 concrete under different loading conditions

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表 1 不同强度混凝土试件配合比

Table 1. Mixture ratio of concrete specimen with different strengths

混凝土	石子/(kg·m⁻³)	砂/(kg·m⁻³)	水/(kg·m⁻³)	水泥/(kg·m⁻³)	水灰比	外加剂/(kg·m⁻³)	28 d 抗压强度/MPa
C20	1 100	725	205	350	0.586	7.5	23.05
C45	950	900	173	500	0.346	12.5	46.20
C70	1 150	600	150	600	0.250	16.0	70.06

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表 2 不同钢纤维含量混凝土试件配合比

Table 2. Mixture ratio of steel fiber reinforced concrete specimen

混凝土	钢纤维体积含量/%	钢纤维/(kg·m⁻³)	石子/(kg·m⁻³)	砂/(kg·m⁻³)	水/(kg·m⁻³)	水泥/(kg·m⁻³)	水胶比	外加剂/(kg·m⁻³)
C40	0	0	1 090	698	158	391	0.38	8.1
	0.75	58.5	1 056	676	182	450	0.38	8.1
	1.50	117.0	1 004	645	204	505	0.38	8.1
	4.50	351.0	726	470	280	693	0.38	8.1

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表 3 恒应变率加载下的实验数据

Table 3. Experimental data at constant strain rate loading

实验	试件	恒应变率/s⁻¹	半段平均应变率/s⁻¹	全段平均应变率/s⁻¹	η₁	η₂
1	C20	32.6	24.6	24.5	1.325	1.331
2	C20	44.2	34.4	31.9	1.285	1.386
3	C20	50.4	31.0	37.9	1.613	1.319
4	C20	51.2	28.6	45.1	2.182	1.384
5	C20	65.3	41.0	46.8	1.593	1.395
6	C20	77.2	55.1	54.9	1.401	1.406
7	C20	81.2	57.1	57.0	1.422	1.424
8	C45	37.3	23.9	25.8	1.561	1.446
9	C45	62.5	39.5	45.2	1.582	1.383
10	C45	70.3	51.4	51.5	1.368	1.365
11	C45	77.3	42.2	56.2	1.832	1.375
12	C45	80.7	60.1	62.5	1.343	1.291
13	C70	45.4	32.8	33.3	1.384	1.363
14	C70	53.6	38.7	41.8	1.385	1.282
15	C70	57.7	42.7	42.4	1.328	1.337
16	C70	69.4	56.1	50.2	1.237	1.382
17	C70	77.4	55.4	51.7	1.397	1.503
18	C70	87.1	60.1	65.6	1.449	1.328
19	C40	59.2	43.0	40.8	1.377	1.451
20	C40	66.8	33.0	49.5	2.024	1.349
21	C40	82.1	54.3	55.6	1.512	1.477
22	C40 (0.75%)	62.0	31.3	45.0	1.981	1.378
23	C40 (0.75%)	80.7	64.8	59.2	1.245	1.363
24	C40 (0.75%)	81.2	51.3	59.4	1.583	1.367
25	C40 (1.50%)	59.1	43.4	44.6	1.362	1.325
26	C40 (1.50%)	65.4	51.8	48.2	1.262	1.357
27	C40 (1.50%)	81.2	46.0	58.6	1.765	1.386
28	C40 (4.50%)	34.5	26.2	24.6	1.317	1.402
29	C40 (4.50%)	82.3	62.1	60.1	1.325	1.369
30	C40 (4.50%)	105.3	62.6	78.9	1.682	1.334

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参考文献(28)

[1]	江见鲸, 冯乃谦. 混凝土力学 [M]. 北京: 中国铁道出版社, 1991.
[2]	郑全平, 周早生, 钱七虎, 等. 防护结构中的震塌问题 [J]. 岩石力学与工程学报, 2003, 28(8): 1393–1398. DOI: 10.3321/j.issn:1000-6915.2003.08.031. ZHENG Quanping, ZHOU Zaosheng, QIAN Qihu, et al. Spallation in protective structures [J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 28(8): 1393–1398. DOI: 10.3321/j.issn:1000-6915.2003.08.031.
[3]	王礼立, 王永刚. 应力波在用SHPB研究材料动态本构特性中的重要作用 [J]. 爆炸与冲击, 2005, 25(1): 17–25. DOI: 10.11883/1001-1455(2005)01-0017-09. WANG Lili, WANG Yonggang. The important role of stress waves in the study on dynamic constitutive behaviour of materials by SHPB [J]. Explosion and Shock Waves, 2005, 25(1): 17–25. DOI: 10.11883/1001-1455(2005)01-0017-09.
[4]	胡时胜, 王道荣. 冲击载荷下混凝土材料的动态本构关系 [J]. 爆炸与冲击, 2002, 22(3): 242–246. HU Shisheng, WANG Daorong. Dynamic constitutive relation of concrete under impact [J]. Explosion and Shock Waves, 2002, 22(3): 242–246.
[5]	XIAO J, LI L, SHEN L, et al. Compressive behaviour of recycled aggregate concrete under impact loading [J]. Cement and Concrete Research, 2015, 71: 46–55. DOI: 10.1016/j.cemconres.2015.01.014.
[6]	李世超, 黄瑞源, 唐奎, 等. 一种基于围压和应变率效应的动态本构模型在钢纤维混凝土中的应用 [J]. 兵工学报, 2017, 10(S1): 66–72. LI Shichao, HUANG Ruiyuan, TANG Kui, et al. Application of a dynamic constitutive model with confining pressure and strain rate effects in steel fiber reinforced concrete [J]. Acta Armamcntarii, 2017, 10(S1): 66–72.
[7]	胡时胜, 王礼立, 宋力, 等. Hopkinson压杆技术在中国的发展回顾 [J]. 爆炸与冲击, 2014, 34(6): 641–657. DOI: 10.11883/1001-1455(2014)06-0641-17. HU Shisheng, WANG Lili, SONG Li, et al. Review of the development of Hopkinson bar technique in China [J]. Explosion and Shock Waves, 2014, 34(6): 641–657. DOI: 10.11883/1001-1455(2014)06-0641-17.
[8]	AL-SALLOUM Y, ALMUSALLAM T, IBRAHIM S M, et al. Rate dependent behavior and modeling of concrete based on SHPB experiments [J]. Cement and Concrete Composites, 2015, 55: 34–44. DOI: 10.1016/j.cemconcomp.2014.07.011.
[9]	DONG J K, SIRIJAROONCHAI K, El-Tawil S, et al. Numerical simulation of the split Hopkinson pressure bar test technique for concrete under compression [J]. International Journal of Impact Engineering, 2010, 37(2): 141–149. DOI: 10.1016/j.ijimpeng.2009.06.012.
[10]	孟益平, 胡时胜. 混凝土材料冲击压缩试验中的一些问题 [J]. 实验力学, 2003, 18(1): 108–112. doi: 10.3969/j.issn.1001-4888.2003.01.020 MENG Yiping, HU Shisheng. Some problems in the test of concrete under impact compressive loading [J]. Journal of Experimental Mechanics, 2003, 18(1): 108–112. doi: 10.3969/j.issn.1001-4888.2003.01.020
[11]	方秦, 洪建, 张锦华, 等. 混凝土类材料SHPB实验若干问题探讨 [J]. 工程力学, 2014, 31(5): 1–14. DOI: 10.6052/j.issn.1000-4750.2013.05.ST07. FANG Qin, HONG Jian, ZHANG Jinhua, et al. Issues of SHPB test on concrete-like material [J]. Enginccring Mechanics, 2014, 31(5): 1–14. DOI: 10.6052/j.issn.1000-4750.2013.05.ST07.
[12]	朱珏, 胡时胜, 王礼立. 率相关混凝土类材料SHPB试验的若干问题 [J]. 工程力学, 2007, 24(1): 78–87. DOI: 10.3969/j.issn.1000-4750.2007.01.014. ZHU Jue, HU Shisheng, WANG Lili. Problems of SHPB technique used for rate-dependent concrete-sort materials [J]. Engineering Mechanics, 2007, 24(1): 78–87. DOI: 10.3969/j.issn.1000-4750.2007.01.014.
[13]	FREW D J, FORRESTAL M J, CHEN W. Pulse shaping techniques for testing brittle materials with a split hopkinson pressure bar [J]. Experimental Mechanics, 2002, 42(1): 93–106. DOI: 10.1007/BF02411056.
[14]	卢玉斌, 武海军, 李庆明, 等. 脆性材料SHPB实验中脉冲整形技术实现近似恒应变率加载功能的进一步研究 [J]. 爆炸与冲击, 2013, 33(S1): 47–53. LU Yubin, WU Haijun, LI Qingming, et al. Further investigation on nearly constant strairrrate loading in SHPB tests for brittle materials using a pulse-shaping technique [J]. Explosion and Shock Waves, 2013, 33(S1): 47–53.
[15]	陶俊林, 田常津, 陈裕泽, 等. SHPB系统试件恒应变率加载实验方法研究 [J]. 爆炸与冲击, 2004, 24(5): 413–418. TAO Junlin, TIAN Changjin, CHEN Yuze, et al. Investigation of experimental method to obtain constant strain rate of specimen in SHPB [J]. Explosion and Shock Waves, 2004, 24(5): 413–418.
[16]	周子龙, 李夕兵, 岩小明. 岩石SHPB测试中试样恒应变率变形的加载条件 [J]. 岩石力学与工程学报, 2009, 28(12): 2443–2452. ZHOU Zilong, LI Xibing, YAN Xiaoming. Loading condition for specimen deformation at constant strain rate in SHPB test of rocks [J]. Chinese Journal of Rock Mechanics and Engineering, 2009, 28(12): 2443–2452.
[17]	宋力, 胡时胜. SHPB测试中的均匀性问题及恒应变率 [J]. 爆炸与冲击, 2005, 25(3): 207–216. DOI: 10.11883/1001-1455(2005)03-0207-10. SONG Li, HU Shisheng. Stress uniformity and constant strain rate in SHPB test [J]. Explosion and Shock Waves, 2005, 25(3): 207–216. DOI: 10.11883/1001-1455(2005)03-0207-10.
[18]	张书, 卢玉斌. 混凝土SHPB实验中惯性效应的机理及其影响因素研究 [J]. 兵工学报, 2014, 35(S2): 281–287. ZHANG Shu, LU Yubing. Research on the mechanism of inertial effect and its influencing factors in SHPB tests of concrete [J]. Acta Armamentarii, 2014, 35(S2): 281–287.
[19]	李玉龙, 索涛, 郭伟国, 等. 确定材料在高温高应变率下动态性能的Hopkinson杆系统 [J]. 爆炸与冲击, 2005, 25(6): 487–492. DOI: 10.11883/1001-1455(2005)06-0487-06. LI Yulong, SUO Tao, GUO Weiguo, et al. Determination of dynamic behavior of materials at elevated tempera-tures and high strain rates using Hopkinson bar [J]. Explosion and Shock Waves, 2005, 25(6): 487–492. DOI: 10.11883/1001-1455(2005)06-0487-06.
[20]	刘孝敏, 胡时胜. 应力脉冲在变截面SHPB锥杆中的传播特性 [J]. 爆炸与冲击, 2000, 20(2): 110–114. LIU Xiaomin, HU Shisheng. Wave propagation characteristics in cone bars used for variable cross-section SHPB [J]. Explosion and Shock Waves, 2000, 20(2): 110–114.
[21]	李为民, 许金余. 大直径分离式霍普金森压杆试验中的波形整形技术研究 [J]. 兵工学报, 2009, 30(3): 350–355. DOI: 10.3321/j.issn:1000-1093.2009.03.019. LI Weimin, XU Jinyu. Pulse shaping techniques for large-diameter split Hopkinson pressure bar test [J]. Acta Armamcntarii, 2009, 30(3): 350–355. DOI: 10.3321/j.issn:1000-1093.2009.03.019.
[22]	NEMAT N S. Hopkinson techniques for dynamic recovery experiments [J]. Proceedings of the Royal Society A, 1991, 435(1894): 371–391. DOI: 10.1098/rspa.1991.0150.
[23]	牛雷雷, 朱万成, 李少华, 等. 摆锤冲击加载下砂岩中应变率动力特性的试验研究 [J]. 岩石力学与工程学报, 2014, 33(12): 2443–2450. DOI: 10.13722/j.cnki.jrme.2014.12.009. NIU Leilei, ZHU Wancheng, LI Shaohua, et al. Experimental study of dynamic haracteristic of sandstone under intermediate strain rate by using pendulum hammer driven " SHPB” apparatus [J]. Chinese Journal of Rock Mechanics and Engineering, 2014, 33(12): 2443–2450. DOI: 10.13722/j.cnki.jrme.2014.12.009.
[24]	于水生, 卢玉斌, 蔡勇. 一种确定岩石类材料真实应变率效应的数值方法 [J]. 岩石力学与工程学报, 2013, 32(S2): 3283–3290. YU Shuisheng, LU Yubin, CAI Yong. A numerical method to detemine real strain-rate effect for rock-like materials [J]. Chinese Journal of Rock Mechanics and Engineering, 2013, 32(S2): 3283–3290.
[25]	RAVICHANDRAN G, SUBHASH G. Critical appraisal of limiting strain rates for compression testing of ceramics in a split hopkinson pressure bar [J]. Journal of the American Ceramic Society, 1994, 77(1): 263–267. DOI: 10.1111/j.1151-2916.1994.tb06987.x.
[26]	陶俊林, 陈裕泽, 田常津, 等. 应变率历史对应力应变曲线的影响 [J]. 爆炸与冲击, 2005, 25(1): 80–84. DOI: 10.11883/1001-1455(2005)01-0080-05. TAO Junlin, CHEN Yuze, TIAN Changjin, et al. Investigation of the effect of strain rate history on the stress-strain curves [J]. Explosion and Shock Waves, 2005, 25(1): 80–84. DOI: 10.11883/1001-1455(2005)01-0080-05.
[27]	李为民, 许金余, 沈刘军, 等. Φ100 mm SHPB应力均匀及恒应变率加载试验技术研究 [J]. 振动与冲击, 2008, 27(2): 129–132. doi: 10.3969/j.issn.1000-3835.2008.02.030 LI Weimin, XU Jinyu, SHEN Liujun, et al. Study on 100 mm-diameter SHPB techniques of dynamic stress equilibrium and nearly constant strain rate loading [J]. Journal of Vibration and Shock, 2008, 27(2): 129–132. doi: 10.3969/j.issn.1000-3835.2008.02.030
[28]	WANG S, ZHANG M H, QUEK S T. Mechanical behavior of fiber-reinforced high-strength concrete subjected to high strain-rate compressive loading [J]. Construction and Building Materials, 2012, 31(6): 1–11. DOI: 10.1016/j.conbuildmat.2011.12.083.