Numerical simulation of stress wave attenuation in brittle material and spalling experiment design
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摘要: 对混凝土、岩石类脆性材料的层裂实验进行了有限元模拟，研究了应力波在此类材料中传播的衰减规律，包括两类机制：弹性波因大尺寸试样的几何弥散产生的小幅度线性衰减、与应变率相关的黏塑性波因本构关系导致的指数衰减。在此基础上，提出了包含常数项的指数型应力波峰值拟合公式。建议采用可以忽略应力波衰减影响的细长形试样进行层裂实验。混凝土类脆性材料层裂破坏模拟结果显示，有限元模拟得到的层裂片厚度与一维应力波理论得到的结果非常吻合，验证了按一维应力波理论确定层裂强度的实验方法的有效性。通过对比3种不同入射波形下层裂片的形状和净拉应力波形，发现不对称的入射波形状更有利于实验获得平直的层裂断面和较准确的层裂强度。Abstract: Using finite element simulation, we investigated the spalling of such brittle materials as concrete and rock, studied the attenuation mechanism governing the stress wave propagation through the specimen of brittle materials, and found two kinds of mechanisms: the small amplitude linear attenuation of the elastic wave due to the geometric dispersion of the large size specimen, and the exponential decay of the viscoplastic wave associated with the strain rate due to the constitutive relation. Based on this, we proposed a peak fitting formula of exponential type stress wave with a constant term. It is suggested that we should choose a slender specimen in the spalling test in which the attenuation of the stress wave can be ignored. In addition, we studied the spalling damage of concrete and rock. The scab thickness obtained from the finite element method agrees well with one-dimensional stress wave theory, verifying that the method for determining the spalling strength by one-dimensional stress wave theory is effective. By comparing the scab shape and the tensile stress wave of the brittle material loading by three kinds of the incident wave, we proved that it is more feasible to obtain a flatter spalling cross-section and more precise strength by using an asymmetric incident wave.
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Key words:
- brittle material /
- stress wave /
- attenuation law /
- spalling
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图 5 短历时应力波在线弹性材料中的衰减规律
Figure 5. Attenuation of short duration stress wave in linear elastic material
图 6 短历时应力波在HJC模型材料中的衰减规律
Figure 6. Attenuation of short duration stress wave in HJC material
图 7 应力波在细长混凝土试样中的衰减规律
Figure 7. Attenuation of stress wave in slender concrete specimen
表 1 HJC模型参数
Table 1. Parameters of HJC constitutive model
ρ/(kg·m-3) G/GPa f′c/MPa A B C N Smax D1 D2 2 400 14.86 48 0.79 1.6 0.007 0.61 7.0 0.04 1.0 ˙ε0/s-1 εf, min T/MPa pc/MPa pl/GPa μc μl k1/GPa k2/GPa k3/GPa 1×10-6 0.01 30 16.0 0.81 0.001 0.1 85 -171 208 
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[1] 王礼立.应力波基础[M].第2版.北京:国防工业出版社, 2005. [2] Rinehart J S. Some quantitative data bearing on the scabbing of metals under explosive attack[J]. Journal of Applied Physics, 1951, 22(5):555-560. doi: 10.1063/1.1700005 [3] Klepaczko J R, Brara A. An experimental method for dynamic tensile testing of concrete by spalling[J]. International Journal of Impact Engineering, 2001, 25(4):387-409. doi: 10.1016/S0734-743X(00)00050-6 [4] Díaz-Rubio F G, Pérez J R, Gálvez V S. The spalling of long bars as a reliable method of measuring the dynamic tensile strength of ceramics[J]. International Journal of Impact Engineering, 2002, 27(2):161-177. doi: 10.1016/S0734-743X(01)00039-2 [5] 胡时胜, 张磊, 武海军, 等.混凝土材料层裂强度的实验研究[J].工程力学, 2004, 21(4):128-132. doi: 10.3969/j.issn.1000-4750.2004.04.023Hu Shisheng, Zhang Lei, Wu Haijun, et al. Experimental study on spalling strength of concrete[J]. Engineering Mechanics, 2004, 21(4):128-132. doi: 10.3969/j.issn.1000-4750.2004.04.023 [6] Zhu J, Sun C, Qian Z, et al. The spalling strength of ultra-fiber reinforced cement mortar[J]. Engineering Failure Analysis, 2011, 18(7):1808-1817. doi: 10.1016/j.engfailanal.2011.05.001 [7] Rong Z, Sun W. Experimental and numerical investigation on the dynamic tensile behavior of ultra-high performance cement based composites[J]. Construction & Building Materials, 2012, 31(6):168-173. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=7229a4cff4af75ed8bc9dc2039905eae [8] 陈柏生, 肖岩, 黄政宇, 等.钢纤维活性粉末混凝土动态层裂强度试验研究[J].湖南大学学报(自然科学版), 2009, 36(7):12-16. http://d.old.wanfangdata.com.cn/Periodical/hndxxb200907003Chen Baisheng, Xiao Yan, Huang Zhengyu, et al. Experimental study on the spalling strength of fiber reactive powder concrete[J]. Journal of Hunan University(Natural Sciences), 2009, 36(7):12-16. http://d.old.wanfangdata.com.cn/Periodical/hndxxb200907003 [9] Holmquist T J, Johnson G R, Cook W H. A computational constitutive model for concrete subjected to large strains high strain rates, and high pressure[C]// Jackson N, Dickert S. The 14th International Symposium on Ballistics. USA: American Defense Prepareness Association, 1993: 591-600. -
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