材料研究学报  2004, Vol. 18 Issue (5): 549-555

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无序材料微裂缝分形几何与尺寸效应的微观机理

张彤;孟庆元;王富耻

北京理工大学

Size effect and fractal geometry of micro--cracks for disordered materials

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北京理工大学

张彤; 孟庆元; 王富耻 . 无序材料微裂缝分形几何与尺寸效应的微观机理[J]. 材料研究学报, 2004, 18(5): 549-555.

摘要 参考文献 相关文章 Metrics 全文: PDF(1685 KB)   摘要: 针对一些含有相同的微裂缝随机分布概率密度但无序度不同的材料, 建立了模拟材料断裂力学行为的二维不连续位移法边界元数值计算模型, 实现了材料微裂缝的生长、扩展到最终破坏的全过程数值模拟. 从分形几何的新视角深入地揭示了脆性或准脆性无序材料产生尺寸效应的微观机理. 材料断裂力学行为的数值模拟结果与Bazant尺寸效应定律相符, 不仅与微缺陷的密度有关, 更与微缺陷大小随机分布的无序度相关, 无序度越大的材料其尺寸效应越明显. 得到了用初始分形维数$D_{\rm 0}$表示的关于材料断裂强度的分形维数 $D_{\sigma}$经验公式, 可以更深入地解释材料的微观尺寸效应机理和断裂过程. 关键词 ： 材料科学基础学科,  无序度,  分形几何,  微裂缝     Abstract：Two--dimensional displacement discontinuity boundary element method was applied to simulate the mechanical behavior of brittle disordered materials, assuming that the specimens contain identical micro--crack density but with different degrees of disorder of micro-crack size distributions. The micro--mechanism for the size effect of the brittle or quasi--brittle disordered materials is explained by a new point of view of fractal geometry. The numerical simulation results are in good agreement with the Bazant size effect law. The size effect, which is more significant as the degrees of disorder of micro--crack size distribution increases, is related to not only the micro--defects density, but also the degrees of disorder of micro--crack size distribution. In addition, an empirical expression relating the fractal dimension of fracture surface with initial fractal dimension was obtained, which can be used to explain the micro--mechanism of size effect and the micro--crack evolution processes more deeply. Key words： foundational discipline in materials science    degree of disorder    fractal geometry    micro-crack size di 收稿日期: 2004-11-05      ZTFLH:  TB301   服务 把本文推荐给朋友 加入引用管理器 E-mail Alert RSS 作者相关文章 张彤 孟庆元 王富耻 44.8K 链接本文: https://www.cjmr.org/CN/Y2004/V18/I5/549 1 Zdenek P. Bazant, International Journal of Solids and Structures, 37(1～2) , 69(2000) 2 Zdenek P. Bazant, Y. Zhou,G.. Zi, Isaac M. Daniel, International Journal of Solids and Structures, 40(25) , 7197(2003) 3 B.Mandelbrot, The Fractal Geometry of Nature (New York, M.H.Freeman and Co., 1982) p.1～17 4 M.Tanaka, Journal of Materials Science, 30, 3668(1995) 5 Mohsen A. Issa, Mahmoud A. Issa, Md. S. Islam, A.Chudnovsky, Engineering Fracture Mechanics, 70(1) , 125(2003) 6 H.P.Xie, David J. Sanderson, Engineering Fracture Mechanics, 50(4) , 529(1995) 7 H.P.Xie, David J. Sanderson,Chinese Science Abstracts Series A, 14(3) , 21(1995) 8 Giuseppe Pezzotti, Mototsugu Sakai, Yasunari Okamoto, Toshihiko Nishida, Materials Science and Engineering, A197, 109(1995) 9 G.P.Cherepanov, A.S.Balankin, V.S.Ivanova, Engineering Fracture Mechanics, 51(6) , 997(1995) 10 A.Carpinteri, A.Spagnoli, S.Vantadori, Fatigue Fract. Eng. Mater. Struc., 25, 619(2002) 11 M.Rybaczuk, P.Stoppel, Inter. Journal of Fracture, 103, 71(2000) 12 O.K.Panagouli, E.S.Mistakidis, P.D.Panagiotopoulos, Computer Methods in Applied Mechanics and Engineering, 147, 1(1997) 13 A.Carpinteri, G.P.Yang, Theoretical and Applied Fracture Mechanics, 25(1) , 73(1996) 14 R.J.Nuismer, Inter. J. of Fracture, 11, 245(1975) 15 S.L.Crouch, A.M.Starfield, Boundary Element Methods in Solid Mechanics (London, George Allen & Unwin (Publishers) Ltd, 1983) p.21～67 16 ZHANG Tong, Investigation on the Scale Effects of Disordered Materials and Associated Micro-Mechanisms, PhD Thesis, Harbin Institute of Technology(2000) (张彤,无序材料的尺寸效应和微观机理,博士学位论文,哈尔滨工业大学(2000) ) 17 M.Kachanov, Advanced Applied Mechanics, 30, 259～445(1993) 18 P.Bocca, A.Carpinteri, S.Valente, Engineering Fracture Mechanics, 35, 159(1990) [1] 杨栋天, 熊良银, 廖洪彬, 刘实. 基于热力学模拟计算的CLF-1钢改良设计[J]. 材料研究学报, 2023, 37(8): 590-602. [2] 姜水淼, 明开胜, 郑士建. 晶界偏析以及界面相和纳米晶材料力学性能的调控[J]. 材料研究学报, 2023, 37(5): 321-331. [3] 孙艺, 韩同伟, 操淑敏, 骆梦雨. 氟化五边形石墨烯的拉伸性能[J]. 材料研究学报, 2022, 36(2): 147-151. [4] 谢明玲, 张广安, 史鑫, 谭稀, 高晓平, 宋玉哲. Ti掺杂MoS2薄膜的抗氧化性和电学性能[J]. 材料研究学报, 2021, 35(1): 59-64. [5] 岳颗, 刘建荣, 杨锐, 王清江. Ti65合金的初级蠕变和稳态蠕变[J]. 材料研究学报, 2020, 34(2): 151-160. [6] 鲁效庆,张全德,魏淑贤. A-π-D-π-A型吲哚类染料敏化剂的光电特性[J]. 材料研究学报, 2020, 34(1): 50-56. [7] 李学雄,徐东生,杨锐. 钛合金双态组织高温拉伸行为的晶体塑性有限元研究[J]. 材料研究学报, 2019, 33(4): 241-253. [8] 刘庆生, 曾少军, 张丹城. 基于细观结构的阴极炭块钠膨胀应力数值分析及实验验证[J]. 材料研究学报, 2017, 31(9): 703-713. [9] 马志军, 莽昌烨, 王俊策, 翁兴媛, 司力玮, 关智浩. 三种金属离子掺杂对纳米镍锌铁氧体吸波性能的影响[J]. 材料研究学报, 2017, 31(12): 909-917. [10] 黄莉. 石蜡/水相变乳液的稳定性能和储能容量[J]. 材料研究学报, 2017, 31(10): 789-795. [11] 朱良,王晶,李晓慧,锁红波,张亦良. 基于堆焊成形钛合金高周疲劳实验数据的R-S-N模型[J]. 材料研究学报, 2015, 29(9): 714-720. [12] 陈杨,钱程,宋志棠,闵国全. 用AFM力曲线技术测定聚合物微球的压缩杨氏模量*[J]. 材料研究学报, 2014, 28(7): 509-514. [13] 于桂琴,刘建军,梁永民. 胍盐离子液体的合成及其对钢/钢摩擦副的摩擦性能研究*[J]. 材料研究学报, 2014, 28(6): 448-454. [14] 王效岗,李乐毅,王海澜,周存龙,黄庆学. 双金属复合板材辊式矫直的数值模型*[J]. 材料研究学报, 2014, 28(4): 308-313. [15] 姚武,吴梦雪,魏永起. 三元复合胶凝体系中硅灰和粉煤灰反应程度的确定*[J]. 材料研究学报, 2014, 28(3): 197-203. Viewed Full text Abstract Cited   Shared      Discussed