圆柱体表面椭圆裂纹应力强度因子的有限元分析和研究
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摘要
本文以断裂力学理论为基础，利用有限元分析方法，对圆柱体表面椭圆裂纹的应力强度因子进行了分析和研究：
论述了表面裂纹应力强度因子的国内外研究现状，比较了表面裂纹应力强度因子研究中各种方法的优缺点，可以看到，有限元法的优点为：单元的布局和节点的配置方式比较灵活，对裂纹的形状和位置无特殊的限制。
对利用ANSYS参数化设计语言APDL分析问题时所涉及的一些带有共性的基础性问题进行了探讨，研究了ANSYS命令流及APDL语言在断裂力学数值模拟中的应用。
研究了奇异单元的尺度对计算结果的影响，选取了奇异单元最佳尺度范围，使该方法具有通用性强和精度高的特点。
本文研究表明，圆柱体表面椭圆裂纹应力强度因子的最大值除了出现在裂纹前缘的最深点和表面点之外，中间某些点(中间某点和椭圆中点的连线与短半轴夹角φ的弧度值在1.066到1.327之间)也会出现最大值。
通过分析，得出了圆柱体表面椭圆裂纹最深点和表面点应力强度因子的变化规律，绘制了圆柱体表面椭圆裂纹应力强度因子的变化曲线。
本文的计算结果与实验结果进吻合良好，对断裂力学在工程实际中的应用提供重要的参考价值。
In light of the theory of the fracture mechanics, the stress intensity factorof cylinder surface elliptical crack has been analysed and researched bymeans of finite element method:
Domestic and foreign present state of making researches on the stressintensity factor for surface crack is discussed, the merits and drawbacks ofvarious methods in researching into stress intensity factor of surface crack arecompared .It can be seen the advantages of the finite element method are thatthe layout of elements and nodes is flexible and it has no special restrict to theshape and position of crack.
General and basic problems are discussed when problems are analysedby using ANSYS parametric design language APDL. The application of bothANSYS command stream and language of APDL in numerical simulation ofthe fracture mechanics is researched.
The study of the dimensions of singularity element affecting results hasbeen done. The best dimensions scope of singularity element are selected soas to make versatility and accuracy of the method very high.
The research indicates that the biggest value of stress intensity factor ofcrack tip in cylinder surface elliptical crack presents in the deepest point orthe surface point, it also presents in some center points (the radian value ofseparation angel from line which ties center point to the middle point ofellipse to semi-minor axis is at 1.066-1.327).
Through analysis, change regularity of stress intensity factor of thedeepest and surface point in the cylinder surface elliptical crack have beenobtained and the variety curve of stress intensity factor of advancing edge in cylinder surface elliptical crack have been described.
The results obtained in this paper are consistent well with theexperimental results. It provides the important reference value towards thefracture mechanics applying in engineering practice.
论述了表面裂纹应力强度因子的国内外研究现状，比较了表面裂纹应力强度因子研究中各种方法的优缺点，可以看到，有限元法的优点为：单元的布局和节点的配置方式比较灵活，对裂纹的形状和位置无特殊的限制。
对利用ANSYS参数化设计语言APDL分析问题时所涉及的一些带有共性的基础性问题进行了探讨，研究了ANSYS命令流及APDL语言在断裂力学数值模拟中的应用。
研究了奇异单元的尺度对计算结果的影响，选取了奇异单元最佳尺度范围，使该方法具有通用性强和精度高的特点。
本文研究表明，圆柱体表面椭圆裂纹应力强度因子的最大值除了出现在裂纹前缘的最深点和表面点之外，中间某些点(中间某点和椭圆中点的连线与短半轴夹角φ的弧度值在1.066到1.327之间)也会出现最大值。
通过分析，得出了圆柱体表面椭圆裂纹最深点和表面点应力强度因子的变化规律，绘制了圆柱体表面椭圆裂纹应力强度因子的变化曲线。
本文的计算结果与实验结果进吻合良好，对断裂力学在工程实际中的应用提供重要的参考价值。
In light of the theory of the fracture mechanics, the stress intensity factorof cylinder surface elliptical crack has been analysed and researched bymeans of finite element method:
Domestic and foreign present state of making researches on the stressintensity factor for surface crack is discussed, the merits and drawbacks ofvarious methods in researching into stress intensity factor of surface crack arecompared .It can be seen the advantages of the finite element method are thatthe layout of elements and nodes is flexible and it has no special restrict to theshape and position of crack.
General and basic problems are discussed when problems are analysedby using ANSYS parametric design language APDL. The application of bothANSYS command stream and language of APDL in numerical simulation ofthe fracture mechanics is researched.
The study of the dimensions of singularity element affecting results hasbeen done. The best dimensions scope of singularity element are selected soas to make versatility and accuracy of the method very high.
The research indicates that the biggest value of stress intensity factor ofcrack tip in cylinder surface elliptical crack presents in the deepest point orthe surface point, it also presents in some center points (the radian value ofseparation angel from line which ties center point to the middle point ofellipse to semi-minor axis is at 1.066-1.327).
Through analysis, change regularity of stress intensity factor of thedeepest and surface point in the cylinder surface elliptical crack have beenobtained and the variety curve of stress intensity factor of advancing edge in cylinder surface elliptical crack have been described.
The results obtained in this paper are consistent well with theexperimental results. It provides the important reference value towards thefracture mechanics applying in engineering practice.
引文
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[2] Manuel da Fonte, Manuel da Freitas, Stress intensity factor for semi-elliptical surface cracks in round bars under bending and torsion[J]. International journal of fatigue, 1999, 21: 457-463
[3] 徐克明，钟伯明，魏嘉荃等．拉伸圆杆表面裂纹应力强度因子实验研究[J]．大庆石油学院学报，1991，15(2)：65-70
[4] 刘荣佩，轴表面半椭圆裂纹应力强度因子的求解[J]，昆明理工大学学报，1996，2l(1)：55-62
[5] 沈海军，郭万林，李海军．拉伸螺杆半椭圆表面裂纹应力强度因子[J]．力学与实践，2003，25(3)：32-34
[6] 尹峰．关于表面裂纹理论的研究与进展[J]．沈阳航空工业学院学报，2003，20(3)：88-91
[7] Paris, P. C., Sih, G. C. Fracture toughness testing and its application [J], ASTM, stp381, 1981
[8] 崔振源．表面裂纹理论及其应用[M]，西安：西北工业大学出版社，1987
[9] 颜声远，孟溪．直三点弯曲试样K的数值解法[J]．哈尔滨船舶工程学院学报，1989，10(2)：256-261
[10] Xiao, Q. Z., Karihaloo, B. L., Liu, X. Y. Direct determination of SIF and higher order terms of mixed mode crack by a hybrid element[J]. International Journal of Fracture, 2004, 125(3-4): 207-225
[11] Dong, C. Y., Lo, S. H., Cheumg, Y. K. Anisotropic thin plate bending problem by Trefftz boundary collocation method[J]. Engineering Analysis with Boundary Element, 2004, 28(9): 1017-1024
[12] E. Madenci, B. Sergeev, S. Shkaragev. Boundary collocation in an anisotropic finite region[J]. Formerly Kluwer Academic Problem B. V, 1998, 94(4): 339-355
[13] Wany, Y. H.. Tham, L. G., Lee, P. KK. A Boundary Collocation method for crack plates[J]. Computer & Structure, 2003, 81: 2621-2637
[14] Z. Zong. A complex variable boundary collocation method for plane elastic problem[J]. Springer-Verlag Gmbh, 2003, 31(3-4): 284-292
[15] 闫相祯．Williams级数收敛性与边界配位法计算的可行性[J]．石油大学学报，1996，20(1)：67-70
[16] 朱哲明，谢和平．裂纹表面承受均布载荷时的应力强度因子及裂纹张开位移的边界配位法[J]．计算力学学报，1997，14(2)：182-188．
[17] 高洪，吕新生．用数值方法求弯圆轴的应力强度因子K1[J]．合肥工业大学学报(自然科学版)，2002，25(4)：590-594
[18] 陈道礼．基于有限元分析的表面裂纹应力强度因子的拟合估算[J]．机械设计与制造，2003，3：6-7
[19] I. S. Raju, J. C. Newman. Stress-intensity factor for circum-ferencial surface crack in pipes and rods under tension and bending loads[J]. ASTM. STP905, 1986, 789-805
[20] 赵丹．有限板半椭圆表面裂纹应力强度因子—Irwin深埋椭圆裂纹解法的推广[J]．应用力学学报，1986，4：57-63
[21] Fabrikant, V. I. The stress intensity factor for an eternal elliptical crack[J]. Int. J. Fract, 1987, 23(4): 466-467
[22] Shah, R. C., Kobayasli, A. S. The surface crack[J]. ASTM, STPS13, 1996, 3: 45-52
[23] Williamson. R. L, Wright. J. K., Cannon, R. M. Finite element analysis of surface crack at corners in protective oxide scales[J]. Proceedings of the Symposium on High Temperature Corrosion and Materials Chemistry, 1998, 6: 41-52
[24] Zhao, W., Newman, J. C., Sutton, M. A. Stress intensity factors for surface cracks at a hole by a three-dimensional weight function method with stresses from the finite element method[J]. Fatigue &Fracture of Engineering Materials &Structures, 1998, 21(2): 39-229
[25] L. P. Pook. A finite element analysis of cracked square plates and bars under antiplane loading[J]. Fatigue Fract Engng Mater Struct, 2002, 26: 533-541
[26] Kamays, M,. Nishioka, T. Analysis of surface crack in cylinder by finite element alternating method[J]. Journal of Pressure Vessel Technology, 2005, 127(2): 72-165
[27] 李翠华．计算应力强度因子的奇异单元法[J]．西安交通大学学报，1991，25(6)：23-29
[28] 钱俊．三维表面半椭圆裂纹应力强度因子的计算[J]．华东工学院学报，1992，3：86-91
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