Please wait a minute...
《材料导报》期刊社  2017, Vol. 31 Issue (3): 70-74    https://doi.org/10.11896/j.issn.1005-023X.2017.03.012
  材料综述 |
扩展有限元法在裂纹扩展问题中的应用*
底月兰, 王海斗, 董丽虹, 邢志国, 王晓丽
中国人民解放军装甲兵工程学院装备再制造技术国防科技重点实验室,北京100072;
Application of the Extended Finite Element Method in Crack Propagation
DI Yuelan, WANG Haidou, DONG Lihong, XING Zhiguo, WANG Xiaoli
Science and Technology on Remanufacturing Laboratory, Academy of Armored Forces Engineering, Beijing 100072;
下载:  全 文 ( PDF ) ( 1173KB ) 
输出:  BibTeX | EndNote (RIS)      
摘要 扩展有限元法(Extended finite element method, XFEM)是近几年发展起来的数值方法,属于传统有限元法的扩展,具有区别于传统有限元法的优点,在求解不连续断裂问题上具有更高的精度及效率。本文针对影响裂纹扩展的主要因素进行探讨,继而介绍扩展有限元的基本原理,并对其在裂纹扩展中的应用进行综述,同时对该方法的下一步研究进行了展望。
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
底月兰
王海斗
董丽虹
邢志国
王晓丽
关键词:  裂纹扩展  扩展有限元  应力强度因子  断裂韧度    
Abstract: Extended finite element method (XFEM) is a novel numerical method developed in recent years, which belongs to the extension of the traditional finite element method. It has the special advantage compared to traditional finite element method, and has higher accuracy and efficiency to solve the discontinuous fracture problem. In this paper, major factors in the process of crack propagation are discussed, the basic principle for XFEM and its application in crack growth are reviewed. Besides, further development of this method is proposed.
Key words:  crack propagation    extended finite element    stress intensity factor    fracture toughness
               出版日期:  2017-02-10      发布日期:  2018-05-02
ZTFLH:  O242.21  
基金资助: *国家自然科学基金重点项目(51535011);国防973计划(61328304)
作者简介:  底月兰:女,1986年生,博士,研究方向为涂层表界面、疲劳寿命 E-mail:dylxinjic031@163.com
引用本文:    
底月兰, 王海斗, 董丽虹, 邢志国, 王晓丽. 扩展有限元法在裂纹扩展问题中的应用*[J]. 《材料导报》期刊社, 2017, 31(3): 70-74.
DI Yuelan, WANG Haidou, DONG Lihong, XING Zhiguo, WANG Xiaoli. Application of the Extended Finite Element Method in Crack Propagation. Materials Reports, 2017, 31(3): 70-74.
链接本文:  
http://www.mater-rep.com/CN/10.11896/j.issn.1005-023X.2017.03.012  或          http://www.mater-rep.com/CN/Y2017/V31/I3/70
1 范天佑.断裂理论基础[M].北京:科学出版社,2003:23.
2 Paris, Erdogan P C. A critical analysis of crack propagation laws[J]. J Basic Eng,1963,85:528.
3 Paris, Gomez P C, Anderson M P. A rational analytic theory of fatigue[J]. Trend Eng,1961,13:9.
4 Erdogan F, Gupta G D. On the numerical solution of singular integral equations[J]. Quarterly Appl Math,1973,30(4):525.
5 Theocaris P S, Loakimids N I. A comparison between the direct and classical numerical methods for solution of Cauchy-type singular integral equations [J]. SIAM J Numer Anal,1980,17:115.
6 Theocaris P S, Loakimids N I. Numerical integration methods for the solution of singular integral equation[J]. Quarterly Appl Math,1977,35:173.
7 Erdogan F, Wu B H. The surface crack problem for a plate with functionally graded properties[J].J Appl Mech,1997,64:449.
8 Shbeeb N I, Binienda W K. Analysis of an interface crack for a functionally graded strip sandwiched between two homogeneous layers of finite thickness[J]. Eng Fract Mech,1999,64:693.
9 Gu B, Yu S W, Feng X Q. Transient response of an insulating crack between dissimilar piezoelectric layers under mechanical and electrical impacts[J]. Archive Appl Mech,2002,72:615.
10 Matbuly M S. Electrostatic analysis of edge cracked orthotropic strips[J]. Acta Mech,2003,165:17.
11 Yuan J H, Tang G J, Zhou J P. The application of singular integral equation to the dynamic fracture analysis of cracked strip(Ⅰ)[J]. J National University of Defense Technology,1999,21(3):9(in Chinese).
袁杰红,唐国金,周建平.奇异积分方程在裂纹板条动态断裂分析中的应用(Ⅰ)[J].国防科技大学学报,1999,21(3):9.
12 Yu Z H. Fatigue life and reliability analysis of No.17 coupler and coupler yoke[D]. Beijing: Beijing Jiaotong Unversity,2009(in Chinese).
于兆华.17号车钩、钩尾框疲劳寿命及可靠性分析[D].北京:北京交通大学,2009.
13 Lin X B, et al. Calculation of stress intensity factors using the 3d finite element method[J]. Chin Mech Eng,1998,9(11):39(in Chinese).
林晓斌,等.应用三维有限单元法计算应力强度因子[J].中国机械工程,1998,9(11):39.
14 Song M, Li Y T, Wei X C. Finite element method for stress intensity factor of a crack perpendicular to biomaterial interface[J]. Sci Technol Eng,2008,8(20):5543(in Chinese).
宋鸣,李有堂,魏兴春.双材料垂直于界面裂纹应力强度因子的有限元法[J].科学技术与工程,2008,8(20):5543.
15 Li C W, Luo X Q, Yang B Y, et al. Stress intensity factor calculation for aero-engine compressor blade with finite element method[J]. Chinese J Appl Mech,2013,30(3):373(in Chinese).
李春旺,罗秀芹,杨百愚,等. 基于有限元方法的航空发动机叶片应力强度因子计算[J].应用力学学报,2013,30(3):373.
16 Rybicki E F, Kanninen M F. A finite element calculation of stress intensity factors by a modified crack closure integral [J]. Eng Fract Mech,1977,9(4):931.
17 Fawaz S A. Application of the virtual crack closure technique to calculate stress intensity factors for through cracks with an elliptical crack front [J]. Eng Fract Mechan,1997,59(3):327.
18 Belytsehko T, Black T. Elastic crack growth in finite elements with minimal remeshing[J]. Int J Numer Meth Eng,1999,45(5):601.
19 Moës N, Dolbow J, Belytsehko T. A finite element method for crack growth without remeshing[J].Int J Numer Meth Eng,1999,46(1):131.
20 Gross B, Srawley J E, Brown W F. Stress intensity factor for a single-edge-notch tension specimen by boundary collocation of a stress function[R]. NASA TN D-2395,1964.
21 Gross B, Srwley J E. Stress intensity factor for single-edge-notch specimen in bending and tension[R]. NASA TN D-2603,1965.
22 Kabayashi A S, Cherepy R D, Kincel W C. A numerical procedure for estimating the stress intensity factor of a crack in a finite plate[J]. ASME J Bas Eng,1964,86(4):681.
23 Wilson W K. Numerical method for determining stress intensity factors of an interior crack in a finite plate[J]. ASME J Bas Eng,1971,93:685.
24 Cao X L, You Y G, Sheng S W, et al. Application of boundary collocation method to two-dimensional wave propagation[J]. Chin Ocean Eng,2015,29(4):579.
25 Li X, You X M. Stress intensity factors for a finite plate with an inclined crack by boundary collocation[J]. Anal Theory Appl,2005,21(3):258.
26 Tomes Y, Casellas D, Anglada M, et al. Fracture toughness evaluation of hardmetals: Influence of testing procedure[J]. Int J Refract Metals Hard Mater,2001,19(1):27.
27 Krishnamurthy S, Reimanis I E, Berger J, et al. Fracture toughness measurement of chromium nitride films on brass[J]. J Am Ceram Soc,2004,87(7):1306.
28 Emrich A,Muhlich U M,Kuna M,et al.Indirect measuring of crack growth by means of a key-curve-method in pre-cracked Charpy specimens made of nodular cast iron[J]. Int J Fract,2007,45(1):47.
29 Fan Z X, Li Y Z, Wang Y X, et al. Study on fracture toughness and residual strength of aluminum alloy thin sheet with crack[J]. Adv Aeronaut Sci Eng,2015,6(1):52(in Chinese).
樊振兴,李亚智,王亚星,等.含裂纹铝合金薄板的断裂韧度与剩余强度研究[J].航空工程进展,2015,6(1):52.
30 Minguez J M. Study of the fracture toughness by finite element methods[J]. Int J Solids Struct,2000,37(7):991.
31 Folch L C, Burdekin F M. Application of coupled brittle-ductile model to study correlation between Charpy energy and fracture toughness values[J]. Eng Fract Mech,1999,63(1):57.
32 Gao Y. Research on dynamic fracture toughness of granite and finite element analysis[D]. Huainan: Anhui University of Science and Technology,2012(in Chinese).
高远.花岗岩动态断裂韧性的试验研究以及有限元分析[D].淮南:安徽理工大学,2012.
33 Dong W, He H N, Wu Z M, et al. Study on KR-curves based on crack propagation criterion in concrete[J]. Eng Mech,2011,28(7):13(in Chinese).
董伟,何化南,吴智敏,等.基于裂缝扩展准则的KR阻力曲线研究[J].工程力学,2011,28(7):13.
34 Yang W, Grace W R, Shah S P. A geometry and size dependent fracture resistance curve[J]. Int J Fract,2001,109(3):L23.
35 Neimitz A.The jump-like crack growth model, the estimation of fracture energy and J(R) curve[J]. Eng Fract Mech,2008,75(2):236.
36 Yang J Y, Zhang X, Zhang M. Research on relation between crack extension resistance curve and sample thickness[J]. J Beijing University of Aeronautics and Astronautics,2003,29(7):575(in Chinese).
杨继运,张行,张珉.裂纹扩展阻力曲线与试样厚度关系[J].北京航空航天大学学报,2003,29(7):575.
37 Yang J Y, Zhang X. Mathematical research on the relation between resistance curve of crack growth and residual strength[J]. J Mech Strength,2003,25(3):334(in Chinese).
杨继运,张行.裂纹扩展阻力曲线与剩余强度关系的理论研究[J].机械强度,2003,25(3):334.
38 Melenk J M, Babuska I. The partition of unity finite element me-thod: Basic theory and applications[J].Computer Meth Appl Mech Eng,1996,139(1-4):289.
39 Chen D H. A crack normal to and terminating at a bimaterial interface[J]. Eng Fract Mech,1994,49:517.
40 Sukumar N, Prevost J H. Modeling quasi-static crack growth with the extended finite element method part Ⅰ: Computer implementation[J]. Int J Solids Struct,2003,40:7513.
41 Huang R,Sukumar N,Prevost J. Modeling quasi-static crack growth with the extended finite element method pare Ⅱ: Numerical applications[J].Int J Solids Struct,2003,40:7359.
42 Sukumar N, Huang Z Y, Prevost J H, et al.Partition of unity enrichment for bimaterial interface cracks[J]. Int J Numerical Methods in Eng,2004,59:1075.
43 Sukumar N, Moёs N,Moran B, Belytschko T. Extended finite element method for three-dimensional crack modelling[J]. Int J Numer Meth Eng,2000,48:1549.
44 Moës N, Gravouil A, Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets. Part I: Mechanical model[J]. Int J Numer Meth Eng,2002,53:2549.
45 Béchet E, Scherzer M,Kuna M. Application of the XFEM to the fracture of piezoelectric materials[J]. Int J Numer Meth Eng,2009,77:1535.
46 Asadpoure A, Mohammadi S. Developing new enrichment functions for crack simulation in orthotropic media by the extend finite element method[J]. Int J Numer Meth Eng,2007,69:2150.
47 Yang Z F, Zhou C Y, Dai Q. Elastic-plastic crack propagation based on extended finite element method[J]. J Nanjing Tech University: Nat Sci Ed,2014,36(4):50(in Chinese).
杨志峰,周昌玉,代巧.基于扩展有限元法的弹塑性裂纹扩展研究[J].南京工业大学学报:自然版,2014,36(4):50.
48 Nagashima T, Omoto Y, Tani S. Stress intensity factor analysis of interface cracks using XFEM[J]. Int J Numer Meth Eng,2003,56:1151.
49 Liu X Y, Xiao Q Z, Karihaloo B L. XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials[J]. Int J Numer Meth Eng,2004,59:1103.
50 Jiang S Y, Du C B, Gu C S, et al. Computation of stress intensity factors for interface cracks between two dissimilar materials using extended finite element methods[J]. Eng Mech,2015,32(3):22(in Chinese).
江守燕,杜成斌,顾冲时,等.求解双材料界面裂纹应力强度因子的扩展有限元法[J].工程力学,2015,32(3):22.
51 Shi F, Gao F, Yang Y G. Application of extended finite element method to study crack propagation problems of orthotropic rock mass[J]. Rock Soil Mech,2014,35(4):1203(in Chinese).
师访,高峰,杨玉贵.正交各向异性岩体裂纹扩展的扩展有限元方法研究[J].岩土力学,2014,35(4):1203.
52 Su Y, Wang S N, Liu J H. Investigation of stress intensity factors for nonhomogeneous materials using extended finite element method[J]. J Northwestern Polytechnical University,2014,32(1):62(in Chinese).
苏毅,王生楠,刘俭辉.基于扩展有限元研究非均质材料的应力强度因子[J].西北工业大学学报,2014,32(1):62.
53 Wang M, Liu G, Huang Y. Shear locking avoidance in the analysis of plate with a through crack by XFEM[J]. J Ship Mech,2015,19(1-2):126(in Chinese).
王敏,刘刚,黄一.用扩展有限元方法来分析含裂纹板时剪切闭锁问题消除[J].船舶力学,2015,19(1-2):126.
54 Dolbow J E, Devan A. Enrichment of enhanced assumed strain approximations for representing strong discontinuities: Addressing vo-lumetric incompressibility and the discontinuous patch test[J].Int J Numer Meth Eng,2004,59(1):47.
55 Wang Z, Yu T T. Adaptive multiscale extended finite element me-thod for modeling three dimensional crack problems[J].Eng Mech,2016,33(1):32(in Chinese).
王振,余天堂.模拟三维裂纹问题的自适应多尺度扩展有限元法[J].工程力学,2016,33(1):32.
56 Jiang S Y, Du C B. Evaluation on stress intensity factors at the crack tip under dynamic loads using extended finite element methods[J]. Appl Math Mech,2013,34(6):586(in Chinese).
江守燕,杜成斌.动载下缝端应力强度因子计算的扩展有限元法[J].应用数学和力学,2013,34(6):586.
57 Shu Y X, Li Y Z, Jiang W. Analyzing multiple crack propagation using extended finite element method (X-FEM)[J]. J Northwestern Polytechnical University,2015,33(2):197(in Chinese).
束一秀,李亚智,姜薇.基于扩展有限元的多裂纹扩展分析[J].西北工业大学学报,2015,33(2):197.
58 Lee C K, Liu X, Fan S C. On solving singular interface problems using the enriched partition-of-unity finite element methods[J]. Eng Comput,2003,20:998.
59 Bellec J, Dolbow J E. A note on enrichment functions for modeling crack nucleartion[J]. Commun Numer Meth Eng,2003,19:921.
60 Iarve E V. Mesh independent modeling of cracks by using higher order shape functions[J]. Int J Numer Meth Eng,2003,56:869.
61 Stazi F L, Budyn E, Chessa J, et al. An extended finite element method with higher-order elements for curved cracks[J]. Comput Mech,2003,31:38.
62 Daux C, Moës N,Dolbow J, et al. Arbitrary branched and intersecting cracks with the extended finite element method[J].Int J Numer Meth Eng,2000,48:1741.
63 Sukumar N, Chopp D L, Moran B. Extended finite element method and fast marching method for three-dimensional fatigue crack propagation [J]. Eng Fract Mech,2003,70:29.
64 Wells G N, Sluys L J. A new method for modeling cohesive cracks using finite elements[J].Int J Numer Meth Eng,2001,50(12):2667.
65 Moës N, Belytschko T. Extended finite element method for cohesive crack growth[J]. Eng Fract Mech,2002,69(7):813.
66 Zi G, Belytschko T.New crack-tip elements for XFEM and applications to cohesive cracks[J]. Int J Numer Meth Eng,2003,57:2221.
67 Stolarska M, Chopp D L. Modeling thermal fatigue cracking in integrated circuits by level sets and the extended finite element method[J]. Int J Eng Sci,2003,41:2381.
68 Gravouil A, Moës N, Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets-Part Ⅱ: Level set update[J]. Int J Numer Meth Eng,2002,53(11):2569.
69 Budyn E, Zi G Moes N, Belytschko T.A method for multiple crack growth in brittle materials without remeshing[J]. Int J Numer Meth Eng,2004,61:1741.
70 Chopp D L,Sukumar N.Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element and fast marching method[J]. Int J Eng Sci,2003,41(8):845.
[1] 李雪换, 底月兰, 王海斗, 李国禄, 董丽虹, 马懿泽. 基于内聚力模型的热障涂层失效行为研究[J]. 材料导报, 2019, 33(9): 1500-1504.
[2] 崔巍, 张煜杭, 张强, 冯子明. 考虑流体渗透压力的管道焊缝内裂纹扩展流固磁耦合方法[J]. 材料导报, 2019, 33(6): 1036-1041.
[3] 盛鹰, 朱星亮, 曾祥国, 贾彬, 文军. 裂纹扩展和裂尖变形机理的多尺度耦合数值模拟方法[J]. 材料导报, 2019, 33(14): 2419-2425.
[4] 陈宇强, 宋文炜, 潘素平, 刘文辉, 宋宇锋, 张浩. 沉积颗粒对7N01-T6铝合金疲劳裂纹扩展行为的影响[J]. 材料导报, 2019, 33(10): 1697-1701.
[5] 赵伦, 何晓聪, 张先炼, 丁燕芳, 刘洋, 邓聪. TA1钛合金自冲铆接头力学性能及微动行为[J]. 材料导报, 2018, 32(20): 3579-3583.
[6] 崔巍, 王珂, 姜民政, 马春阳, 冯子明, 冷建成. 管道焊缝裂纹扩展的流固磁耦合表征[J]. 材料导报, 2018, 32(16): 2852-2858.
[7] 葛茂忠, 项建云, 范真. 激光熔覆修复对TC4钛合金疲劳裂纹扩展速率的影响[J]. 材料导报, 2018, 32(16): 2803-2808.
[8] 温飞娟, 董丽虹, 王海斗, 吕振林, 底月兰. 热喷涂零件界面裂纹扩展行为影响因素研究[J]. 材料导报, 2018, 32(16): 2793-2797.
[9] 王顺风, 马雪, 张祖华, 王爱国, 李亚林. 粉煤灰-偏高岭土基地质聚合物的孔结构及抗压强度[J]. 材料导报, 2018, 32(16): 2757-2762.
[10] 李革, 徐泽华, 牛建刚. 塑钢纤维轻骨料混凝土细观破坏过程的数值模拟[J]. 《材料导报》期刊社, 2018, 32(14): 2412-2417.
[11] 冷建成,田洪旭,周国强,吴泽民. 基于磁记忆方法的抽油杆裂纹扩展监测[J]. 《材料导报》期刊社, 2017, 31(24): 178-190.
[12] 方瑞杰,刘军,陈建恩,王肖锋. 多耦合拘束效应对P92钢蠕变裂纹扩展行为的影响*[J]. 材料导报编辑部, 2017, 31(22): 153-158.
[13] 张玉波, 郭荣鑫, 夏海廷, 颜峰, 王时越, 李一博. 颗粒和微观结构对Cu/WCp复合材料疲劳裂纹萌生和扩展行为的影响*[J]. 《材料导报》期刊社, 2017, 31(18): 85-91.
[14] 陈林, 王慧军, 郭飞翔. 淬火微观组织对重轨钢疲劳裂纹扩展速率的影响*[J]. 《材料导报》期刊社, 2017, 31(14): 109-112.
[1] Bingwei LUO,Dabo LIU,Fei LUO,Ye TIAN,Dongsheng CHEN,Haitao ZHOU. Research on the Two Typical Infrared Detection Materials Serving at Low Temperatures: a Review[J]. Materials Reports, 2018, 32(3): 398 -404 .
[2] Huimin PAN,Jun FU,Qingxin ZHAO. Sulfate Attack Resistance of Concrete Subjected to Disturbance in Hardening Stage[J]. Materials Reports, 2018, 32(2): 282 -287 .
[3] Siyuan ZHOU,Jianfeng JIN,Lu WANG,Jingyi CAO,Peijun YANG. Multiscale Simulation of Geometric Effect on Onset Plasticity of Nano-scale Asperities[J]. Materials Reports, 2018, 32(2): 316 -321 .
[4] Xu LI,Ziru WANG,Li YANG,Zhendong ZHANG,Youting ZHANG,Yifan DU. Synthesis and Performance of Magnetic Oil Absorption Material with Rice Chaff Support[J]. Materials Reports, 2018, 32(2): 219 -222 .
[5] Ninghui LIANG,Peng YANG,Xinrong LIU,Yang ZHONG,Zheqi GUO. A Study on Dynamic Compressive Mechanical Properties of Multi-size Polypropylene Fiber Concrete Under High Strain Rate[J]. Materials Reports, 2018, 32(2): 288 -294 .
[6] XU Zhichao, FENG Zhongxue, SHI Qingnan, YANG Yingxiang, WANG Xiaoqi, QI Huarong. Microstructure of the LPSO Phase in Mg98.5Zn0.5Y1 Alloy Prepared by Directional Solidification and Its Effect on Electromagnetic Shielding Performance[J]. Materials Reports, 2018, 32(6): 865 -869 .
[7] ZHOU Rui, LI Lulu, XIE Dong, ZHANG Jianguo, WU Mengli. A Determining Method of Constitutive Parameters for Metal Powder Compaction Based on Modified Drucker-Prager Cap Model[J]. Materials Reports, 2018, 32(6): 1020 -1025 .
[8] WANG Tong, BAO Yan. Advances on Functional Polyacrylate/Inorganic Nanocomposite Latex for Leather Finishing[J]. Materials Reports, 2017, 31(1): 64 -71 .
[9] HUANG Dajian, MA Zonghong, MA Chenyang, WANG Xinwei. Preparation and Properties of Gelatin/Chitosan Composite Films Enhanced by Chitin Nanofiber[J]. Materials Reports, 2017, 31(8): 21 -24 .
[10] YUAN Xinjian, LI Ci, WANG Haodong, LIANG Xuebo, ZENG Dingding, XIE Chaojie. Effects of Micro-alloying of Chromium and Vanadium on Microstructure and Mechanical Properties of High Carbon Steel[J]. Materials Reports, 2017, 31(8): 76 -81 .
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed