基于ABAQUS的裂纹扩展仿真软件及应用
摘要
在各类工程中如从机械行业、建筑行业等到微电子封装行业，由于机器设备或器件在使用过程中受到载荷作用或者材料本身的固有缺陷，将会引起裂纹的产生，在一定的条件下裂纹将会扩展，并最终导致设备或器件的失效有时还可能会导致事故的发生。因此研究裂纹及其在一定程度下的扩展行为将会对评定产品的使用寿命和安全性有积极的促进作用，并且可以指导产品的设计以及提高设计的可靠性。
本文采用有限元方法来研究裂纹的扩展。在前人工作的基础上，通过基于ABAQUS软件平台编制裂纹扩展仿真软件。该软件的设计思想是，根据前一步的分析结果确定裂纹是否扩展、求得扩展角，然后在给定的扩展长度下确定新的裂纹尖端，并对该尖端局部区域进行网格自动重建，通过在裂尖邻域采用规则的四边形单元来保证应力，其他区域采用三角形单元。如此往复计算、裂纹尖端推进，直至构件断裂或裂纹止裂。鉴于ABAQUS具有丰富的材料库、单元库和各种分析类型，且计算效率高，本程序可用于分析弹塑性问题、热—机耦合、机—电耦合问题以及多裂纹扩展问题。通过典型算例分析了该软件的实用性和健壮性，然后计算分析了几种形式的裂纹扩展，包括带有边缘斜裂纹板、中心斜裂纹板、平行裂纹板、孔边裂纹和多条裂纹板等的裂纹扩展情况，通过裂纹扩展软件分析计算，可以求得它们在外载荷作用下的裂纹扩展的整个过程。同时分析讨论了裂纹扩展增量Δα对裂纹扩展路径的影响。对于多裂纹扩展问题，分析了裂纹之间的相互作用情况，指出了对于多裂纹扩展，各裂纹之间是相互关联的。
At present, in various kinds of engineering problem from mechanical industry, architectural industry and micro-electronic package, etc, cracks will appear because of the material's inherent flaw or the loads forced on the machine or equipment during the process of service. Under some condition, these cracks will propagate, which causes the ultimate failure of the equipment and in some cases, it can cause the accident. Thus, reaching on cracks and its propagation behavior under certain conditions can help prolong the using life of the product, prevent the appearance of the accident. Furthermore, it can contribute to the design of the product and improve the reliability of the design.
Based on the present development status of Fracture mechanics theory, Numerical method and FEA software, in this paper we use FEA method to simulate the propagation of the crack. First, we design the program for simulating the propagation of the crack based on the platform of ABAQUS and prove its ability using a computational example. The design thought of the software is as follows: first based on the pre-analysis result make sure if the crack will propagate and obtain the propagation angle, then based on the propagation length ensure the new crack tip and use automatic mesh generation in this area. Through the crack tip area, use the regular quad mesh to ensure the stress, in other areas, use the triangular mesh. Through the circular computation, the crack tip will forward until the structure ruptures or stop cracking. Because of ABAQUS has rich material warehouse, cells, various analysis type and high computational efficiency, we can use this software to analyze elastic-plastic problem, thermal-mechanical problem, machine-electrical problem and multiple crack propagation problem. We have proved the utility and robustness of the software, then analyze some kind of crack propagation problem
本文采用有限元方法来研究裂纹的扩展。在前人工作的基础上，通过基于ABAQUS软件平台编制裂纹扩展仿真软件。该软件的设计思想是，根据前一步的分析结果确定裂纹是否扩展、求得扩展角，然后在给定的扩展长度下确定新的裂纹尖端，并对该尖端局部区域进行网格自动重建，通过在裂尖邻域采用规则的四边形单元来保证应力，其他区域采用三角形单元。如此往复计算、裂纹尖端推进，直至构件断裂或裂纹止裂。鉴于ABAQUS具有丰富的材料库、单元库和各种分析类型，且计算效率高，本程序可用于分析弹塑性问题、热—机耦合、机—电耦合问题以及多裂纹扩展问题。通过典型算例分析了该软件的实用性和健壮性，然后计算分析了几种形式的裂纹扩展，包括带有边缘斜裂纹板、中心斜裂纹板、平行裂纹板、孔边裂纹和多条裂纹板等的裂纹扩展情况，通过裂纹扩展软件分析计算，可以求得它们在外载荷作用下的裂纹扩展的整个过程。同时分析讨论了裂纹扩展增量Δα对裂纹扩展路径的影响。对于多裂纹扩展问题，分析了裂纹之间的相互作用情况，指出了对于多裂纹扩展，各裂纹之间是相互关联的。
At present, in various kinds of engineering problem from mechanical industry, architectural industry and micro-electronic package, etc, cracks will appear because of the material's inherent flaw or the loads forced on the machine or equipment during the process of service. Under some condition, these cracks will propagate, which causes the ultimate failure of the equipment and in some cases, it can cause the accident. Thus, reaching on cracks and its propagation behavior under certain conditions can help prolong the using life of the product, prevent the appearance of the accident. Furthermore, it can contribute to the design of the product and improve the reliability of the design.
Based on the present development status of Fracture mechanics theory, Numerical method and FEA software, in this paper we use FEA method to simulate the propagation of the crack. First, we design the program for simulating the propagation of the crack based on the platform of ABAQUS and prove its ability using a computational example. The design thought of the software is as follows: first based on the pre-analysis result make sure if the crack will propagate and obtain the propagation angle, then based on the propagation length ensure the new crack tip and use automatic mesh generation in this area. Through the crack tip area, use the regular quad mesh to ensure the stress, in other areas, use the triangular mesh. Through the circular computation, the crack tip will forward until the structure ruptures or stop cracking. Because of ABAQUS has rich material warehouse, cells, various analysis type and high computational efficiency, we can use this software to analyze elastic-plastic problem, thermal-mechanical problem, machine-electrical problem and multiple crack propagation problem. We have proved the utility and robustness of the software, then analyze some kind of crack propagation problem
引文
[1] 杨卫．宏微观断裂力学．北京：国防工业出版社，1995
[2] 郭乙木，陶伟明，庄茁．线性与非线性有限元及其应用．机械工业出版社，2004
[3] 黎在良等．断裂力学中的边界数值方法[M]，地震出版社，1996．
[4] Aliabadi, M. H. Boundary element formulations in fracture mechanics: a review[C]. Computer Aided Assessment and Control of Localized Damage-Proceedings of the International Conference, Localized Damage Ⅳ, 1996: 3-19
[5] Portela A, et al. The dual BEM: effective implementation for crack problem[J]. Int J for Numerical Methods in engineering, 1992, 33: 269-287
[6] 顾克秋，钱林方，袁人枢．基于边界元法的疲劳裂纹扩展模拟[J]．南京理工大学学报．1995，19(6)：517-520
[7] 宋康机，陆明万，张雄，固体力学中的无网格方法[J]．力学进展，2000，30(1)：55-65
[8] Y. Xu, S. Saigal. Element free galerkin study of steady quasi-static crack growth in plane strain tension in elastic-plastic materials[J]. Computational Mechanics, 1 998, 22: 255-265
[9] M. R. Tabbara, C. M. Stone. A computational method for quasi-static fracture[J]. Computational Mechanics, 1998, 22: 203-210
[10] 杨庆生，杨卫．断裂过程的有限元模拟．计算力学学报．1997，第14卷第4期，407-412
[11] SHI G H. Manifold method[C]. Proceedings of the First International Forum on DDA and Simulation of Discontinuous Media. Berkeley, 1996. 52-204.
[12] 石根华．数值流形方法与非连续变形方法[m]．裴觉民译．北京：清华大学出版社．1997
[13] Shephard MS, Yehlan A. B. Computational strategies for nonlinear and fracture mechanics problem[J]. Computer& structure. 1985, 20: 211-23
[14] Bittencourt T. N, Wawrzynek PA. Quasi automatic simulation of crack propagation for 2D LEFM problem[J]. Engineering Mechanics. 1996, 55(2): 3 21-33
[15] Klein P, Gao H. Crack nucleation and growth as strain localization in a virtual-bond continium[J], Engineering Fracture Mechanics. 1998, 61: 21-48
[16] 黄向平，王建华．裂纹跟踪的网格生成技术[J]．上海交通大学学报．2001，35(4)：493-495
[17] 贾建军，彭颖红，阮雪榆．一种有限元裂纹扩展仿真的网格技术[J]．模具技术．2001，5：4-6
[18] Kaiser P. K, Tang C. A. Numerical simulation of cumulative damage and seismic energy release during brittle rock failure. Int J Rock Mech Sci. 1998, 3 5(2): 113-134
[19] Yao Zhenhan, Chen Yonggiang, Zheng Xiaoping. Numerical Simulation of Failure Processin 3D Heterogeneous Brittle Material. 1CTAM 2000, Chicago, US, August2 7-Stp. 2, 2000
[20] 陈永强等．三维非均匀脆性材料破坏过程的数值模拟[J]．力学学报．2002，34 (3)：351-361
[21] 陈永强等．非均匀材料破坏过程数值模拟的边界元法研究[J]．工程力学，2003，20(3)：19-25
[22] 黄克智，余寿文．弹塑性断裂力学．清华大学出版社．1985
[23] Griffith. The phenomena of rupture and flow in solids. Phil. R. Soc. A221, 1921: 163-198P.
[24] H．L．Ewalds，R．J．H．Wanhill著．朱永昌、浦素云等译．断裂力学．北京航空航天大学出版社，1988年：9-11
[25] Wells, AA. Application of fracture mechanics at beyond general yielding. British Welding Journal, Vol. 10, 1963: 563-570..
[26] Burdekin, Stone. The crack opening displacement approach to fracture mechanics in yielding. Journal of Strain Analysis, Vol. 1, 1966: 145-153P.
[27] 李志安．压力容器断裂理论与缺陷评定．大连：大连理工大学出版社，1994年8月．
[28] Rice. J. R. A path independent integral and approximate analysis of strain Concentration by notches and cracks. Journal of Applied Mechanics, Vol. 35, 19 68: 379-386P.
[29] 陈向平，应道宁．统一于NIP的多边形三角剖分算法．计算机学报，1989，12C3)：194-199．
[30] 丁永祥，夏巨湛，王英，肖景容．任意多边形的Delaunay三角剖分．计算机学报．1994，V17(4)．
[31] M. Bastian, B. Q. Li. An efficient automatic mesh generator for quadrilateral elements implemented using C++. Finite elements in analysis and design. 39 (2003) 905-930.
[32] A. Tradegard, F. Nilsson*, S. Ostlund. FEM-remeshing technique applied to crack growth problems. Comput. Methods Appl. Mech. Engrg. 160(1998)115-131.
[33] Zhiqiang Wang, Toshio Nakamura *. Simulations of crack propagation in elasticplastic graded materials. Mechanics of Materials 36 (2004) 601-622
[34] ABAQUS v6. 5 Document
[35] 王殷成，邵敏．有限单元法基本原理与数值方法[M]，北京：清华大学出版社，1988
[36] 庄茁译．ABAQUS／standard有限元软件入门指南．清华大学出版社．1998
[37] L-S. Niu, H-J. Shi, C. Rbin and G. Pluvinage. Elastic and elastic-plastic fields on circular rings containing a V-notch under inclined loads[J]. Eng. Fracture M ech, 2001, 68(7): 949-962
[38] I. V. Orynyak, A. JA Krasowsky. The modeling of elastic response of A three-point bend specimen under impact loading[J]. Eng. Fracture Mech, 1998, 60(5/6): 563-575
[38] R. Hambli. Finite element model fracture prediction during sheet-metal blanking processes[J]. Eng. Fracture Mech, 2001, 68(3): 365-378
[39] Ramsamooj, D. V. Analytical prediction of short to long fatigue crack growth rate using small and large-scale yielding fracture mechanics. International Journal of Fatigue. 2 003, 25(9-11): 923-933
[40] G T Sha, J K Chen. Weight functions for bimaterial interface cracks.. International Journal of Fracture, 1991, 51: 265～284.
[41] Yimu Guo, Daiheng Cheng, Weiming rao. Fracture and damage of advanced materials. China Machine Press. 2004
[42] Cavendish J C. Automatic triangulation of arbitrary planar domains for the finite element method[J]. International Journal for Numerical Methods in Engineering, 1974(8): 679-696.
[43] 雷永刚，卫原平，阮雪榆．三维有限元网格自动生成典型方法与发展方向[J]．机械科学与技术，1999，18(2)：311-313．
[44] 张玉峰，朱以文．有限元网格自动生成的典型方法与研究前瞻．武汉大学学报(工学版)．第38卷第2期．2005．
[45] 张均锋，刘桂斋，陈刚．有限元平面三角形网格自动划分．山东矿业学院学报(自然 科学版)．第18卷第4期．1999．
[46] Lo, S. H., A New Mesh Generation Scheme for Arbitrary Planar Domains[J]. International Journal of Numerical Methods Engineering, Vol. 21, 1985: 1403-1426.
[47] 李俊，游理华．有限元网格自动生成算法的研究进展．机械研究与应用．1998年第4期．
[48] Woo T C. Thomasma T. An algorithm for generating solid Element in objects with holes. Comp. Struct, 1984, 18(2).
[49] 俞树荣，严志刚，曹睿，陈剑虹．有限元软件模拟裂纹扩展的方法探讨．甘肃科学学报．第15卷第4期，2003．
[50] 张双寅．三角形等参数奇异元[J]．力学与实践．1986．(5)：25—27．
[51] 范天佑．断裂理论基础．科学出版社．2003．
[52] http://www.cfg.cornell.edu.
[53] http://www.zentech.co.uk/zencrack.htm
[54] 王生楠，方旭．改进的多裂纹扩展算法和程序设计．机械科学与技术，第23卷，第8期
[55] Garey M R, Johnson D S, Preparata F P. Triangulating a simple polygon. Inf Proc lett, 1978, 7: 175-179.
[56] Jim Ruppert*. A Delaunay Refinement Algorithm For Quality 2-Dimensional Mesh Generation. Journal of algorithms, 18, 548-585(1995)
[57] 中国航空研究院．应力强度因子手册．科学出版社．1981．
[58] Moes N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engzneerzng, 1999, 46: 131150.
[59] 黄维扬．工程断裂力学．航空工业出版社．1992．
[60] computational geometry in C. isbn 0-521-445922 Jseph o' s Rourke. cambridge CB2 1RP: Cambridge University press, 1994.
[61] Delaunay triangulation using a uniform grid, IEEE computer graphics and applications 1993-05, p36-47, tsung-pao Fang and Les A. piegl, University of Minnesota, USA, 1995 www. geom. umn. edu.
[61] 李录贤，王铁军．扩展有限元法(XFEM)及其应用．力学进展．第35卷，第1期．
[2] 郭乙木，陶伟明，庄茁．线性与非线性有限元及其应用．机械工业出版社，2004
[3] 黎在良等．断裂力学中的边界数值方法[M]，地震出版社，1996．
[4] Aliabadi, M. H. Boundary element formulations in fracture mechanics: a review[C]. Computer Aided Assessment and Control of Localized Damage-Proceedings of the International Conference, Localized Damage Ⅳ, 1996: 3-19
[5] Portela A, et al. The dual BEM: effective implementation for crack problem[J]. Int J for Numerical Methods in engineering, 1992, 33: 269-287
[6] 顾克秋，钱林方，袁人枢．基于边界元法的疲劳裂纹扩展模拟[J]．南京理工大学学报．1995，19(6)：517-520
[7] 宋康机，陆明万，张雄，固体力学中的无网格方法[J]．力学进展，2000，30(1)：55-65
[8] Y. Xu, S. Saigal. Element free galerkin study of steady quasi-static crack growth in plane strain tension in elastic-plastic materials[J]. Computational Mechanics, 1 998, 22: 255-265
[9] M. R. Tabbara, C. M. Stone. A computational method for quasi-static fracture[J]. Computational Mechanics, 1998, 22: 203-210
[10] 杨庆生，杨卫．断裂过程的有限元模拟．计算力学学报．1997，第14卷第4期，407-412
[11] SHI G H. Manifold method[C]. Proceedings of the First International Forum on DDA and Simulation of Discontinuous Media. Berkeley, 1996. 52-204.
[12] 石根华．数值流形方法与非连续变形方法[m]．裴觉民译．北京：清华大学出版社．1997
[13] Shephard MS, Yehlan A. B. Computational strategies for nonlinear and fracture mechanics problem[J]. Computer& structure. 1985, 20: 211-23
[14] Bittencourt T. N, Wawrzynek PA. Quasi automatic simulation of crack propagation for 2D LEFM problem[J]. Engineering Mechanics. 1996, 55(2): 3 21-33
[15] Klein P, Gao H. Crack nucleation and growth as strain localization in a virtual-bond continium[J], Engineering Fracture Mechanics. 1998, 61: 21-48
[16] 黄向平，王建华．裂纹跟踪的网格生成技术[J]．上海交通大学学报．2001，35(4)：493-495
[17] 贾建军，彭颖红，阮雪榆．一种有限元裂纹扩展仿真的网格技术[J]．模具技术．2001，5：4-6
[18] Kaiser P. K, Tang C. A. Numerical simulation of cumulative damage and seismic energy release during brittle rock failure. Int J Rock Mech Sci. 1998, 3 5(2): 113-134
[19] Yao Zhenhan, Chen Yonggiang, Zheng Xiaoping. Numerical Simulation of Failure Processin 3D Heterogeneous Brittle Material. 1CTAM 2000, Chicago, US, August2 7-Stp. 2, 2000
[20] 陈永强等．三维非均匀脆性材料破坏过程的数值模拟[J]．力学学报．2002，34 (3)：351-361
[21] 陈永强等．非均匀材料破坏过程数值模拟的边界元法研究[J]．工程力学，2003，20(3)：19-25
[22] 黄克智，余寿文．弹塑性断裂力学．清华大学出版社．1985
[23] Griffith. The phenomena of rupture and flow in solids. Phil. R. Soc. A221, 1921: 163-198P.
[24] H．L．Ewalds，R．J．H．Wanhill著．朱永昌、浦素云等译．断裂力学．北京航空航天大学出版社，1988年：9-11
[25] Wells, AA. Application of fracture mechanics at beyond general yielding. British Welding Journal, Vol. 10, 1963: 563-570..
[26] Burdekin, Stone. The crack opening displacement approach to fracture mechanics in yielding. Journal of Strain Analysis, Vol. 1, 1966: 145-153P.
[27] 李志安．压力容器断裂理论与缺陷评定．大连：大连理工大学出版社，1994年8月．
[28] Rice. J. R. A path independent integral and approximate analysis of strain Concentration by notches and cracks. Journal of Applied Mechanics, Vol. 35, 19 68: 379-386P.
[29] 陈向平，应道宁．统一于NIP的多边形三角剖分算法．计算机学报，1989，12C3)：194-199．
[30] 丁永祥，夏巨湛，王英，肖景容．任意多边形的Delaunay三角剖分．计算机学报．1994，V17(4)．
[31] M. Bastian, B. Q. Li. An efficient automatic mesh generator for quadrilateral elements implemented using C++. Finite elements in analysis and design. 39 (2003) 905-930.
[32] A. Tradegard, F. Nilsson*, S. Ostlund. FEM-remeshing technique applied to crack growth problems. Comput. Methods Appl. Mech. Engrg. 160(1998)115-131.
[33] Zhiqiang Wang, Toshio Nakamura *. Simulations of crack propagation in elasticplastic graded materials. Mechanics of Materials 36 (2004) 601-622
[34] ABAQUS v6. 5 Document
[35] 王殷成，邵敏．有限单元法基本原理与数值方法[M]，北京：清华大学出版社，1988
[36] 庄茁译．ABAQUS／standard有限元软件入门指南．清华大学出版社．1998
[37] L-S. Niu, H-J. Shi, C. Rbin and G. Pluvinage. Elastic and elastic-plastic fields on circular rings containing a V-notch under inclined loads[J]. Eng. Fracture M ech, 2001, 68(7): 949-962
[38] I. V. Orynyak, A. JA Krasowsky. The modeling of elastic response of A three-point bend specimen under impact loading[J]. Eng. Fracture Mech, 1998, 60(5/6): 563-575
[38] R. Hambli. Finite element model fracture prediction during sheet-metal blanking processes[J]. Eng. Fracture Mech, 2001, 68(3): 365-378
[39] Ramsamooj, D. V. Analytical prediction of short to long fatigue crack growth rate using small and large-scale yielding fracture mechanics. International Journal of Fatigue. 2 003, 25(9-11): 923-933
[40] G T Sha, J K Chen. Weight functions for bimaterial interface cracks.. International Journal of Fracture, 1991, 51: 265～284.
[41] Yimu Guo, Daiheng Cheng, Weiming rao. Fracture and damage of advanced materials. China Machine Press. 2004
[42] Cavendish J C. Automatic triangulation of arbitrary planar domains for the finite element method[J]. International Journal for Numerical Methods in Engineering, 1974(8): 679-696.
[43] 雷永刚，卫原平，阮雪榆．三维有限元网格自动生成典型方法与发展方向[J]．机械科学与技术，1999，18(2)：311-313．
[44] 张玉峰，朱以文．有限元网格自动生成的典型方法与研究前瞻．武汉大学学报(工学版)．第38卷第2期．2005．
[45] 张均锋，刘桂斋，陈刚．有限元平面三角形网格自动划分．山东矿业学院学报(自然 科学版)．第18卷第4期．1999．
[46] Lo, S. H., A New Mesh Generation Scheme for Arbitrary Planar Domains[J]. International Journal of Numerical Methods Engineering, Vol. 21, 1985: 1403-1426.
[47] 李俊，游理华．有限元网格自动生成算法的研究进展．机械研究与应用．1998年第4期．
[48] Woo T C. Thomasma T. An algorithm for generating solid Element in objects with holes. Comp. Struct, 1984, 18(2).
[49] 俞树荣，严志刚，曹睿，陈剑虹．有限元软件模拟裂纹扩展的方法探讨．甘肃科学学报．第15卷第4期，2003．
[50] 张双寅．三角形等参数奇异元[J]．力学与实践．1986．(5)：25—27．
[51] 范天佑．断裂理论基础．科学出版社．2003．
[52] http://www.cfg.cornell.edu.
[53] http://www.zentech.co.uk/zencrack.htm
[54] 王生楠，方旭．改进的多裂纹扩展算法和程序设计．机械科学与技术，第23卷，第8期
[55] Garey M R, Johnson D S, Preparata F P. Triangulating a simple polygon. Inf Proc lett, 1978, 7: 175-179.
[56] Jim Ruppert*. A Delaunay Refinement Algorithm For Quality 2-Dimensional Mesh Generation. Journal of algorithms, 18, 548-585(1995)
[57] 中国航空研究院．应力强度因子手册．科学出版社．1981．
[58] Moes N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engzneerzng, 1999, 46: 131150.
[59] 黄维扬．工程断裂力学．航空工业出版社．1992．
[60] computational geometry in C. isbn 0-521-445922 Jseph o' s Rourke. cambridge CB2 1RP: Cambridge University press, 1994.
[61] Delaunay triangulation using a uniform grid, IEEE computer graphics and applications 1993-05, p36-47, tsung-pao Fang and Les A. piegl, University of Minnesota, USA, 1995 www. geom. umn. edu.
[61] 李录贤，王铁军．扩展有限元法(XFEM)及其应用．力学进展．第35卷，第1期．