岩石材料动载下泛形裂纹扩展数值模拟

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (22) : 88-91.

论文

岩石材料动载下泛形裂纹扩展数值模拟

李竟艳，高文学，宋肖龙

作者信息 +

Numerical simulation on the extension of a ubiquitiformal crack of rock materials under dynamic loading

LI Jingyan, GAO Wenxue, SONG Xiaolong

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文章历史 +

摘要

岩石材料性能的非均匀性导致断裂面呈现不规则的泛形特性，基于此应用ABAQUS软件建立细观有限元模型，由Weibull分布表征岩石材料性能的非均匀性，对动态拉伸载荷下岩石材料泛形裂纹扩展进行研究。计盒维数计算得到的泛形断裂面的复杂度与实验结果吻合。不同应变率下的泛形裂纹扩展路径及复杂度的计算结果表明，断裂面的复杂度随应变率的增加而减小。进一步分析不同应变率下裂纹扩展的泛形断裂能，发现裂纹扩展的能量释放率随应变率增大而增大。低加载率下，裂纹向断裂韧性较小的单元扩展，但随着加载率的提高，裂纹瞬间穿过断裂韧性相对较高的单元，沿自相似方向扩展。上述结果揭示了应变率对泛形裂纹扩展路径的影响与材料性能的细观非均匀性有关，加深了对岩石材料泛形断裂机制的理解。

Abstract

Considering that an irregular ubiquitiformal fracture surface is resulted from the heterogeneity of rock material, a numerical simulation on the extension of a ubiquitiformal crack in rock material was carried out by using the ABAQUS software, together with the Weibull distribution characterization of the heterogeneity of material properties.The ubiquitiformal crack extension of rock material under dynamic tensile loading was analysed and the complexity of the fractured profile was calculated by using the box counting dimension.The numerical results were in good agreement with previous experimental data.The results of the crack extension path and the complexity of the fracture surface under different strain rate show that the complexity decreases with the increase of strain rate.Furthermore, from the analysis of ubiquitiformal fracture energy, it is found that the energy release rate increases with the increase of strain rate.Under lower strain rate,the crack propagates in the direction of minimum energy dissipation, while, with the increase of strain rate, the crack penetrates through the higher fracture energy element and propagates along the self-similar extension direction.These results imply that the strain rate effect on the extension of the ubiquitiformal crack can be induced by the heterogeneity of rock material, which could help to understand the mechanism of ubiquitiformal fracture.

导出引用

李竟艳，高文学，宋肖龙. 岩石材料动载下泛形裂纹扩展数值模拟[J]. 振动与冲击, 2018, 37(22): 88-91

LI Jingyan, GAO Wenxue, SONG Xiaolong. Numerical simulation on the extension of a ubiquitiformal crack of rock materials under dynamic loading[J]. Journal of Vibration and Shock, 2018, 37(22): 88-91

参考文献

[1] Mandelbrot B B. Fractals: Form, Chance, and ance, and Dimension[M]. San Francisco: Freeman，1977.
[2] Mandelbrot B B. How long is the coast of Britain? Statistical self-similarity and fractional dimension[J]. Science, 1967, 156(3775): 636-638. 
[3] Mandelbrot B B. The Fractal Geometry of Nature[M]. San Francisco: Freeman，1982.
[4] Saouma V E, Barton C C, Gamaleldin N A. Fractal characterization of fracture surfaces in concrete[J]. Engineering Fracture Mechanics, 1990, 35(1-3): 47-53. 
[5] Carpinteri A. Fractal nature of material microstructure and size effects on apparent mechanical properties [J]. Mechanics of Materials, 1994, 18(2): 89-101.  
[6] Borodich M F. Some fractal models of fracture [J]. Journal of the Mechanics and Physics of Solids, 1997, 45(2): 239-259. 
[7] Mandelbrot B B, Passoja D E, Paullay A J. Fractal character of fracture surfaces of metals [J]. Nature, 1984, 308: 721-722.
[8] Brandt A M, Prokopski G. On the fractal dimension of fracture surfaces of concrete elements. Journal of Materials Science, 1993, 28(17): 4762–4766.
[9] Sakellariou M, Nakos B, Mitsakaki C. On the fractal character of rock surfaces [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1991, 28:527-533.
[10] Xie H. Fractal in Rock Mechanics[M]. Netherlands: A A Balkema Publishers, 1993.
[11] Ou Z C, Li G Y, Duan Z P, et al. Ubiquitiform in applied mechanics [J]. Journal of Theoretical and Applied Mechanics, 2014, 52(1): 37-46.
[12] Li J Y, Ou Z C, Tong Y et al. A statistical model for ubiquitiformal crack extension in brittle materials[J]. Acta Machenica, DOI: 10.1007/S00707-017-1859-7.
[13] Ou Z C, Yang M, Li G Y, et al. Ubiquitiformal fracture energy[J]. Journal of Theoretical and Applied Mechanics, DOI: 10.15632/jtam-pl.55.3.xxx.
[14] Tedesco J W, Ross C A, Kuennen S T. Experimental and numerical analysis of high strain rate splitting tensile tests. ACI Mater J 1993;90:162–9.
[15] Ma G, Miyake A, Ogawa T, et al. Study on the tensile strength of brittle materials under high stress rate using the technique based on Hopkinson’s effect. J Jpn Explos Soc, 1998, 59(2):49–56 [in Japanese].
[16] 姜峰，李子沐，王宁昌，等. 高应变率条件下山西黑花岗岩的动态力学性能研究[J]. 振动与冲击，2016, 35(8): 177- 182.
Jiang Feng, Li Zi-mu, Wang Ning-chang, et al. Research on dynamic characteristics of Shanxi black granite under high strain rates [J]. Journal of Vibration and Shock. 2016, 35(8): 177- 182. (in Chinese)
[17] Van Mier J G M, Van V, Wang T K. Fracture mechanisms in particle composites: statistical aspects in lattice type analysis[J]. Mechanics of Materials, 2002, 34(11):705-724.
[18] 梁昌玉，李晓，李守定，等. 岩石静态和准动态加载应变率的界限值研究[J]. 岩石力学与工程学报，2012, 31(6): 1156- 1161.
Liang Chang-yu, Li Xiao, Li Shou-ding, et al. Study of strain rates threshold value between static and quasi-dynamic loading of rock[J]. Chinese Journal of Rock Mechanics and Engineering. 2012, 31(6): 1156- 1161. (in Chinese)