Ubiquitiform Crack of Quasi-Brittle Materials under Dynamic Loading
-
摘要: 为建立动态拉伸载荷作用下准脆性材料裂纹扩展路径的泛形表征，提出了一种非均匀准脆性材料动态裂纹扩展的泛形模型，计算得到的泛形裂面复杂度与已有实验数据吻合较好。结果表明：动态拉伸载荷作用下的裂纹扩展路径是泛形的，其复杂度随加载应变率的增大而减小，并与材料动态拉伸承载能力的空间随机分布无关，且随Weibull分布形状参数m的增加而减小。研究结果为分析动态拉伸载荷作用下准脆性材料的裂纹扩展机理即泛形表征提供了依据。Abstract: To investigate the ubiquitiformal characteristic of the crack extension path in a heterogeneous quasi-brittle material under the dynamic tensile loadings, a ubiquitiformal model is developed in this paper, and the calculated numerical results for the ubiquitiform complexity are in agreement with the previous experiments. It is found that such a crack extension path is indeed of a ubiquitiform, and its complexity decreases with the increase of the loading strain-rate. Moreover, it is also found that the complexity is independent of the randomness of the spatial distribution of the dynamic tensile load-carrying capacity of the material under consideration, and the complexity decreases with increasing shape parameter m of the Weibull distribution. Thus, this work can be taken as a basis for analyzing further the mechanism as well as the ubiquitiformal characteristic of the crack profile in a quasi-brittle material under the dynamic tensile loadings.
-
Key words:
- quasi-brittle materials /
- ubiquitiform crack /
- strain-rate /
- complexity
-
图 1 由Weibull分布表征的强度分布直方图
Figure 1. Histogram of the strength distribution characterized by Weibull distribution
图 2 动态拉伸承载能力分布
Figure 2. Typical distribution of the dynamic tensile load-carrying capacity
图 5 计盒维数法计算泛形复杂度
Figure 5. Box-counting dimension method is used to compute the ubiquitiformal complexity
图 6 局部应变率为103 s–1的泛形裂纹轮廓线
Figure 6. Profile of ubiquitiform cracks under the local strain rate of 103 s–1
表 1 复杂度的数值计算结果
Table 1. Numerical results of the complexity C
Strain rate/s−1 C S1 S2 S3 S4 S5 Avg. 10–6 1.381 1.382 1.379 1.381 1.383 1.381 10 1.215 1.213 1.210 1.212 1.208 1.212 102 1.182 1.182 1.180 1.178 1.179 1.180 103 1.127 1.132 1.134 1.131 1.142 1.133 
下载: 导出CSV
表 2 不同形状参数下的泛形复杂度
Table 2. Ubiquitiform complexity under different shape parameters
m C m C 5 1.142 8 1.086 6 1.126 9 1.057 7 1.108 10 1.033
下载: 导出CSV
-
[1] MANDELBROT B B, PASSOJA D E, PAULLAY A J. Fractal character of fracture surfaces of metals [J]. Nature, 1984, 308(5961): 721–722. doi: 10.1038/308721a0 [2] 王金安, 谢和平. 岩石断裂表面分形测量的尺度效应 [J]. 岩石力学与工程学报, 2000, 19(1): 11–17. doi: 10.3321/j.issn:1000-6915.2000.01.003WANG J A, XIE H P. Scale effect on fractal measurement of rock fracture surfaces [J]. Chinese Journal of Rock Mechanics and Engineering, 2000, 19(1): 11–17. doi: 10.3321/j.issn:1000-6915.2000.01.003 [3] 裴建良, 苏立, 刘建锋, 等. 层状大理岩间接拉伸试验及断口形貌和断裂机理分析 [J]. 四川大学学报(工程科学版), 2014, 46(4): 39–45.PEI J L, SU L, LIU J F, et al. Indirect tensile test of layered marble and analysis of fracture morphology and mechanism [J]. Journal of Sichuan University (Engineering Science Edition), 2014, 46(4): 39–45. [4] SAGAR R V, PRASAD B K R. Fracture analysis of concrete using singular fractal functions with lattice beam network and confirmation with acoustic emission study [J]. Theoretical and Applied Fracture Mechanics, 2011, 55(3): 192–205. doi: 10.1016/j.tafmec.2011.07.003 [5] 党发宁, 方建银, 丁卫华. 基于CT的混凝土试样静动力单轴拉伸破坏裂纹分形特征比较研究 [J]. 岩石力学与工程学报, 2015, 34(Suppl 1): 2922–2928.DANG F N, FANG J Y, DING W H. Fractal comparison research of fracture of concrete samples under static and dynamic uniaxial tensile using CT [J]. Chinese Journal of Rock Mechanics and Engineering, 2015, 34(Suppl 1): 2922–2928. [6] LIANG H, PAN F S, CHEN Y M, et al. Influence of the strain rates on tensile properties and fracture interfaces for Mg-Al alloys containing Y [J]. Advanced Materials Research, 2011, 284/286: 1671–1677. doi: 10.4028/www.scientific.net/AMR.284-286.1671 [7] OU Z C, LI G Y, DUAN Z P, et al. Ubiquitiform in applied mechanics [J]. Journal of Theoretical and Applied Mechanics, 2014, 52: 37–46. [8] CARPINTERI A. Fractal nature of material microstructure and size effects on apparent mechanical properties [J]. Mechanics of Materials, 1994, 18(2): 89–101. doi: 10.1016/0167-6636(94)00008-5 [9] CARPINTERI A, PUZZI S. Self-similarity in concrete fracture: size-scale effects and transition between different collapse mechanisms [J]. International Journal of Fracture, 2008, 154(1/2): 167–175. [10] BORODICH F M. Some fractal models of fracture [J]. Journal of the Mechanics and Physics of Solids, 1997, 45(2): 239–259. doi: 10.1016/S0022-5096(96)00080-4 [11] LI G Y, OU Z C, XIE R, et al. A ubiquitiformal one-dimensional steady-state conduction model for a cellular material rod [J]. International Journal of Thermophysics, 2016, 37(4): 1–13. [12] OU Z C, YANG M, LI G Y, et al. Ubiquitiformal fracture energy [J]. Journal of Theoretical and Applied Mechanics, 2017, 55(3): 1101–1108. [13] LI J Y, OU Z C, TONG Y, et al. A statistical model for ubiquitiformal crack extension in quasi-brittle materials [J]. Acta Mechanica, 2017, 228(7): 1–8. [14] WEIBULL W. A statistical distribution of wide applicability [J]. Journal of Applied Mechanics, 1951, 18(2): 293–297. [15] OU Z C, DUAN Z P, HUANG F L. Analytical approach to the strain rate effect on the dynamic tensile strength of brittle materials [J]. International Journal of Impact Engineering, 2010, 37(8): 942–945. doi: 10.1016/j.ijimpeng.2010.02.003 [16] WANG Y D, DAN W J, XU Y F, et al. Fractal and morphological characteristics of single marble particle crushing in uniaxial compression tests [J]. Advances in Materials Science and Engineering, 2015, 2015(1): 1–10. [17] ISA K, ABU A R K, SOUSA R L. Computational modelling of fracture propagation in rocks using a coupled elastic-plasticity-damage model [J]. Mathematical Problems in Engineering, 2016, 2016: 3231092. [18] GRANGE S, FORQUIN P, MENCACCI S, et al. On the dynamic fragmentation of two limestones using edge-on impact tests [J]. International Journal of Impact Engineering, 2008, 35(9): 977–991. doi: 10.1016/j.ijimpeng.2007.07.006 [19] ZHU W C, TANG C A. Numerical simulation on shear fracture process of concrete using mesoscopic mechanical model [J]. Construction and Building Materials, 2002, 16(8): 453–463. doi: 10.1016/S0950-0618(02)00096-X [20] PETROV Y, KAZARINOV N, BRATOV V. Dynamic crack propagation: quasistatic and impact loading [J]. Procedia Structural Integrity, 2016, 2: 389–394. doi: 10.1016/j.prostr.2016.06.050 [21] LIU L G, OU Z C, DUAN Z P, et al. Strain-rate effects on deflection/penetration of crack terminating perpendicular to bimaterial interface under dynamic loadings [J]. International Journal of Fracture, 2011, 167(2): 135–145. doi: 10.1007/s10704-010-9533-2 [22] PEI C W, YAO Y, CHEN D G, et al. Experimental study of the tensile bond strength in concrete aggregate-paste interfacial transition zone [J]. Applied Mechanics and Materials, 2012, 193/194: 1384–1388. doi: 10.4028/www.scientific.net/AMM.193-194.1384 [23] WONG T F, WONG R H C, CHAU K T, et al. Microcrack statistics, Weibull distribution and micromechanical modeling of compressive failure in rock [J]. Mechanics of Materials, 2006, 38(7): 664–681. doi: 10.1016/j.mechmat.2005.12.002 [24] SMIRNOV I, KONSTANTINOV A, BRAGOV A, et al. The structural temporal approach to dynamic and quasi-static strength of rocks and concrete [J]. Procedia Structural Integrity, 2017, 6: 34–39. doi: 10.1016/j.prostr.2017.11.006 [25] 谢和平, 高峰, 周宏伟, 等. 岩石断裂和破碎的分形研究 [J]. 防灾减灾工程学报, 2003, 23(4): 1–9.XIE H P, GAO F, ZHOU H W, et al. Fractal fracture and fragmentation in rocks [J]. Journal of Disaster Prevention and Mitigation Engineering, 2003, 23(4): 1–9. [26] SAKELLARIOU M. On the fractal character of rock surfaces [J]. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 1991, 28(6): 527–533. [27] YAN D, LIN G. Dynamic properties of concrete in direct tension [J]. Cement and Concrete Research, 2006, 36(7): 1371–1378. doi: 10.1016/j.cemconres.2006.03.003 -
下载:
点击查看大图
图(6) / 表(2)
计量
- 文章访问数: 8599
- HTML全文浏览量: 3047
- PDF下载量: 30
