一类非均布载荷下中心裂纹圆盘T应力分析

彭凡; 董世明

doi:10.21656/1000-0887.380136

一类非均布载荷下中心裂纹圆盘T应力分析

doi: 10.21656/1000-0887.380136

彭凡,
董世明

四川大学建筑与环境学院, 成都 610065

基金项目: 国家自然科学基金（11172186）;四川省科技计划（2018JY0024）

详细信息

作者简介:
彭凡(1995—)，男（E-mail: 1145747505@qq.com）；董世明（1963—），男，教授，博士（通讯作者. E-mail: smdong@126.com).

中图分类号: O346.1
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- 被引次数: 0
出版历程
- 收稿日期: 2017-05-12
- 修回日期: 2017-12-26
- 刊出日期: 2018-07-15

T-Stress in a Centrally Cracked Brazilian Disk Under Nonuniform Pressure Load

College of Architecture and Environment, Sichuan University, Chengdu 610065, P.R.China

Funds: The National Natural Science Foundation of China（11172186）

摘要

摘要: 实际结构中，岩石常承受非均布载荷作用；并且试验中，集中力作用下往往会存在微小的分布角，这一载荷分布也是非均匀分布的.基于此类情况提出一类非均布载荷，这种载荷为三角函数形式，在分布角的中间压力最大，然后向两边逐渐减小直至为0.运用径向集中压力下中心裂纹巴西圆盘T应力解析公式，在分布角范围内积分获得这类非均布载荷下试件的T应力解析解，并同时进行有限元分析获得数值解.通过比较这两种结果，发现二者非常吻合，相互验证了各自分析的正确性.此外，与均布力作用相比，同等条件下此类非均布载荷作用的无量纲T应力值更接近集中力作用的值，而且两者的数值误差相当小.进一步论证了实际试验中采用集中力加载的T应力公式是正确与合理的.
- 非均布压力 /
- 中心裂纹巴西圆盘 /
- T应力 /
- 有限元分析
Abstract: In an engineering structure, the rock is often subjected to nonuniform load; in addition, there is a small distribution angle under a concentrated force in actual experimental study, and the load distribution also should be nonuniform. Based on this case, a class of nonuniform loads were proposed in the trigonometric function form. Then the maximum loading pressure appeared in the middle of the distribution angle and gradually became small to both sides until 0. By means of the centrally cracked Brazilian disk (CCBD) T-stress formula under a radial concentrated load, the analytical T-stress solution under this kind of nonuniform load was acquired via the integral in the range of the distribution angle, meanwhile the finite element simulation was conducted to obtain the numerical solution. There is a very good consistency between the numerical results and the analytical results, which verifies the accuracy of each other. Compared with those under the uniform load, the dimensionless T-stress values under this nonuniform load are closer to the values under the concentrated load when the other condition is the same, and the discrepancy between the stresses under the nonuniform load and the concentrated load is very small. The further calculated results show that it is accurate and reasonable to use the T-stress formula for the CCBD subjected to the concentrated forces in actual testing.
- nonuniform load /
- centrally cracked Brazilian disk /
- T-stress /
- finite element analysis

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参考文献(15)

[1]	AYATOLLAHI M R, ALIHA M R M. On the use of Brazilian disc specimen for calculating mixed mode Ⅰ-Ⅱ fracture toughness of rock materials[J]. Engineering Fracture Mechanics,2008,75(16): 4631-4641.
[2]	AYATOLLAHI M R, ALIHA M R M. Mixed mode fracture analysis of polycrystalline graphite: a modified MTS criterion[J]. Carbon,2008,46(10): 1302-1308.
[3]	AYATOLLAHI M R, ALIHA M R M. Fracture analysis of some ceramics under mixed mode loading[J]. Journal of the American Ceramic Society,2011,94(2): 561-569.
[4]	WILLIAMS J G, EWING P D. Fracture under complex stress: the angled crack problem[J]. International Journal of Fracture,1972,8(4): 441-446.
[5]	唐世斌, 黄润秋, 唐春安. T应力对岩石裂纹扩展路径及起裂强度的影响研究[J]. 岩土力学, 2016,37(6): 1521-1529.(TANG Shibin, HUANG Runqiu, TANG Chunan. Effect of T-stress on crack growth path in rock and fracture strength[J]. Rock and Soil Mechanics,2016,37(6): 1521-1529.(in Chinese))
[6]	FETT T. T-stresses in rectangular plates and circular disks[J]. Engineering Fracture Mechanics,1998,60(5): 631-652.
[7]	AYATOLLAHI M R, PAVIER M J, SMITH D J. Determination of T-stress from finite element analysis for mode Ⅰ and mixed mode Ⅰ/Ⅱ loading[J]. International Journal of Fracture,1998,91(3): 283-298.
[8]	HUA W, LI Y, DONG S, et al. T-stress for a centrally cracked Brazilian disk under confining pressure[J]. Engineering Fracture Mechanics,2015,149: 37-44.
[9]	李一凡, 董世明, 华文. 中心裂纹巴西圆盘压缩载荷下T应力研究[J]. 岩土力学, 2016,37(11): 3191-3196.(LI Yifan, DONG Shiming, HUA Wen. T-stress for central cracked Brazilian disk subjected to compression[J]. Rock and Soil Mechanics,2016,37(11): 3191-3196.(in Chinese))
[10]	高玉华, 汪洋, 程长征. 广义T应力对裂纹应力强度因子的影响[J]. 中国科学技术大学学报, 2009,39(12): 1319-1322.(GAO Yuhua, WANG Yang, CHENG Changzheng. Effect of general T-stress on stress intensity factor of a crack[J]. Journal of University of Science And Technology of China,2009,39(12): 1319-1322.(in Chinese))
[11]	DONG S, WANG Y, XIA Y. Stress intensity factors for central cracked circular disk subjected to compression[J]. Engineering Fracture Mechanics,2004,71(7): 1135-1148.
[12]	ATKINSON C, SMELSER R E, SANCHEZ J. Combined mode fracture via the cracked Brazilian disk test[J]. International Journal of Fracture,1982,18(4): 279-291.
[13]	周妍, 张财贵, 杨井瑞, 等. 圆孔内单边(或双边)裂纹平台巴西圆盘应力强度因子的全面标定[J]. 应用数学和力学, 2015,36(1): 16-30.(ZHOU Yan, ZHANG Caigui, YANG Jingrui, et al. Comprehensive calibration of the stress intensityfactor for the holed flattened Brazilian disc withan inner single crack or double cracks[J]. Applied Mathematics and Mechanics,2015,36(1): 16-30.(in Chinese))
[14]	HUA W, DONG S, XU J G. Experimental study on fracture toughness of rust stone under mixed mode loading condition[J]. Materials Research Innovations,2015,19(S8): 531-536.
[15]	徐积刚, 董世明, 华文. 围压对巴西裂纹圆盘应力强度因子影响的分析[J]. 岩土力学, 2015,36(7): 1959-1965.(XU Jigang, DONG Shiming, HUA Wen. Effects of confining pressure on stress intensity factors determined by cracked Brazilian disk[J]. Rock and Soil Mechanics,2015,36(7): 1959-1965.(in Chinese))