预制裂缝宽度对变尺寸圆盘试样应力强度因子的影响
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摘要
为研究了预制裂缝宽度对不同尺寸圆盘试样无量纲应力强度因子的影响,采用ABAQUS有限元软件,对圆盘直径分别为40,80,100,120,200 mm,预制裂缝宽度0~2.0 mm内的直裂缝平台巴西圆盘试样进行数值分析,基于等效区域积分法标定了在裂缝长度与圆盘直径比为0.55条件下的无量纲应力强度因子。结果表明,在圆盘直径一定条件下,无量纲应力强度因子随着裂缝宽度增加而增加,最大相对误差为13.53%;随着圆盘直径增大,预制裂缝宽度带来的影响相对减弱,但最大相对误差仍然超过3%。给出了消除预制裂缝宽度影响的无量纲应力强度因子修正公式,为采用含有预制裂缝的圆盘试样准确确定岩石的断裂韧度提供理论支持。
In order to get the influence of prefabricated crack width on the dimensionless stress intensity of disc specimen with different sizes. ABAQUS software was used for,numerical analysis of cracked straight-through flattened Brazilian disc(CSTFBD). In the model,the sizes of disc diameter were 40 mm,80 mm,100 mm,120 mm and 200 mm and the width of prefabricated crack ranged from 0 mm to 2. 0 mm. The dimensionless stress intensity factors were calibrated by the equivalent zone integration method when the ratio of crack length to disc diameter was 0. 55. Results show that the dimensionless stress intensity increase along with the increase of the crack width. The maximum relative error is 13. 53 % when the disc specimens have same diameter sizes. If the size of disc diameter increase,the influence will be decreased,however the maximum relative error is still more than 3 %. A revised formula of the dimensionless stress intensity factor was given to eliminate the influence of the prefabricated crack width. It provides a theoretical basis for determining the fracture toughness value by using cracked straight-through flattened Brazilian disc specimen.
In order to get the influence of prefabricated crack width on the dimensionless stress intensity of disc specimen with different sizes. ABAQUS software was used for,numerical analysis of cracked straight-through flattened Brazilian disc(CSTFBD). In the model,the sizes of disc diameter were 40 mm,80 mm,100 mm,120 mm and 200 mm and the width of prefabricated crack ranged from 0 mm to 2. 0 mm. The dimensionless stress intensity factors were calibrated by the equivalent zone integration method when the ratio of crack length to disc diameter was 0. 55. Results show that the dimensionless stress intensity increase along with the increase of the crack width. The maximum relative error is 13. 53 % when the disc specimens have same diameter sizes. If the size of disc diameter increase,the influence will be decreased,however the maximum relative error is still more than 3 %. A revised formula of the dimensionless stress intensity factor was given to eliminate the influence of the prefabricated crack width. It provides a theoretical basis for determining the fracture toughness value by using cracked straight-through flattened Brazilian disc specimen.
引文
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[12]董世明,方美彦,夏源明.中心裂纹圆盘裂纹形状尺寸对应力强度因子的影响[J].中国科学技术大学学报,2004,34(4):449-455.DONG S M,FANG M Y,XIA Y M.Effect of crack shape and size on stress intensity factors of central cracked circular disk[J].Journal of University of Science and Technology of China,2004,34(4):449-455.
[13]RAJENDRA KOLHE,CHUNG-YUEN HUI,ALAN T.ZEHNDER.Effects of finite notch width on the fracture of chevron-notched specimens[J].International Journal of Fracture.1998,94(2):189-198.
[14]OUINAS D,SAHNOUNE M,BENDERDOUCHE N,et al.Stress intensity factor analysis for notched cracked structure repaired by composite patching[J].Materials&Design,2009,30(7):2302-2308.
[15]BACHIR BOUIADJRA B,OUINAS D,BELHOUARI M,et al.Numerical analysis of the notch effect and the behaviour of notch crack in adhesively bonded composite laminates[J].Computational Materials Science,2007,38(4):759-764.
[16]解德,钱勤,李长安.断裂力学中的数值计算方法及工程应用[M].北京:科学出版社,2009.XIE D,QIAN Q,LI C A.Numerical calculation method of fracture mechanics and the engineering application[M].Beijing:Science Press,2009.
[17]刘明尧,柯孟龙,周祖德,等.裂纹尖端应力强度因子的有限元计算方法分析[J].武汉理工大学学报,2011,33(6):116-121.LIU M X,KE M L,ZHOU Z D,et al.Analysis of finite element calculation methods for crack-tip stress intensity factor[J].Journal of Wuhan University of Technology,2011,33(6):116-121.
[2]张盛,李小军,李大伟.岩石Ⅰ型断裂韧度测试技术和理论研究综述[J].河南理工大学学报:自然科学版,2009,28(1):33-38.ZHANG S,LI X J,LI D W.A review of test technique and theory of modeⅠrock fracture toughness[J].Journal of Henan Polytechnic University:Natural Science,2009,28(1):33-38.
[3]贾学明,王启智.断裂韧度试样CCNBD宽范围应力强度因子标定[J].岩土力学,2003,24(6):907-912.JIA X M,WANG Q Z.Wide range calibration of the stress intensity factor for the fracture toughness specimen CCNBD[J].Rock and Soil Mechanics,2003,24(6):907-912.
[4]吴礼舟,贾学明,王启智.CCNBD断裂韧度试样的SIF新公式和在尺度律分析中的应用[J].岩土力学,2004,25(2):233-237.WU L Z,JIA X M,WANG Q Z.A new stress intensity factor formula of cracked chevron notched Brazilian disc(CCNBD)and its application to analyzing size effect[J].Rock and Soil Mechanics,2004,25(2):233-237.
[5]樊鸿,张盛,苟小平,等.岩石断裂韧度试样CCNBD临界应力强度因子的全新数值标定[J].应用力学学报,2011,28(4):416-422.FAN H,ZHANG S,GOU X P,et al.A new numerical calibration of the critical stress intensity factor for the CCNBD specimens used in rock fracture toughness test[J].Chinese Journal of Applied Mechanics,2011,28(4):416-422.
[6]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分析[J].岩土力学,2015(07):1959-1965.XU J G,DONG S M,HUA W.Effect of confining pressure on stress intensity factors determined by cracked Brazilian disk[J].Rock and Soil Mechanics,2015(07):1959-1965.
[7]罗毅,任利,谢凌志,等.岩石Ⅰ/Ⅱ复合断裂韧度测试的单边切槽深梁试件:数值分析与标定[J].岩石力学与工程学报,2016,(S2):3633-3643.LUO Y,REN L,XIE L Z,et al.Single edge notched deep beam specimen to test I/II mixed-mode fracture toughness of rocks:numerical analysis and calibration[J].Chinese Journal of Rock Mechanics and Engineering,2016,(S2):3633-3643.
[8]CHEN C H,CHEN C S,WU J H.Fracture toughness analysis on cracked ring disks of anisotropic rock[J].Rock Mechanics Rock Engineering,2008,41(4):539-562.
[9]KOURKOULIS S K,MARKIDES CH F.Stresses and displacements in a circular ring under parabolic diametral compression[J].International Journal of Rock Mechanics and Mining Sciences,2014,71:272-292.
[10]戴峰,王启智.有限宽切槽对CCNBD断裂试样应力强度因子的影响[J].岩土力学,2004,25(3):427-431.DAI F,WANG Q Z.Effects of finite notch width on stress intensity factor for CCNBD specimen[J].Rock and Soil Mechanics,2004,25(3):427-431.
[11]赵春风,李晓杰,闫鸿浩,等.Ι型裂纹尖端圆弧对应力强度因子影响的数值研究[J].科学技术与工程,2010,10(4):961-965.ZHAO C F,LI X J,YAN H H,et al.Effect of the crack tip arc of mode-on stress intensity factor using numerical method[J].Science Technology and Engineering,2010,10(4):961-965.
[12]董世明,方美彦,夏源明.中心裂纹圆盘裂纹形状尺寸对应力强度因子的影响[J].中国科学技术大学学报,2004,34(4):449-455.DONG S M,FANG M Y,XIA Y M.Effect of crack shape and size on stress intensity factors of central cracked circular disk[J].Journal of University of Science and Technology of China,2004,34(4):449-455.
[13]RAJENDRA KOLHE,CHUNG-YUEN HUI,ALAN T.ZEHNDER.Effects of finite notch width on the fracture of chevron-notched specimens[J].International Journal of Fracture.1998,94(2):189-198.
[14]OUINAS D,SAHNOUNE M,BENDERDOUCHE N,et al.Stress intensity factor analysis for notched cracked structure repaired by composite patching[J].Materials&Design,2009,30(7):2302-2308.
[15]BACHIR BOUIADJRA B,OUINAS D,BELHOUARI M,et al.Numerical analysis of the notch effect and the behaviour of notch crack in adhesively bonded composite laminates[J].Computational Materials Science,2007,38(4):759-764.
[16]解德,钱勤,李长安.断裂力学中的数值计算方法及工程应用[M].北京:科学出版社,2009.XIE D,QIAN Q,LI C A.Numerical calculation method of fracture mechanics and the engineering application[M].Beijing:Science Press,2009.
[17]刘明尧,柯孟龙,周祖德,等.裂纹尖端应力强度因子的有限元计算方法分析[J].武汉理工大学学报,2011,33(6):116-121.LIU M X,KE M L,ZHOU Z D,et al.Analysis of finite element calculation methods for crack-tip stress intensity factor[J].Journal of Wuhan University of Technology,2011,33(6):116-121.