平面微裂纹扩展的计算机模拟与相关试验
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摘要
Lankford与Suresh等人曾经假设，自然萌生的微裂纹的“不规则扩展”是与材料
当地的局部晶体结构相关联的。即，相对于尺寸较大的裂纹(与大量的疲劳微裂纹
生长速度的观察数据相比)，疲劳过程中微裂纹扩展速率的分散程度较大，以及较
高的平均疲劳裂纹生长率。在细观尺度上，晶粒取向的变化，会导致应力场的不均
匀。然而，这一现象的重要性并未引起人们足够的重视。
直到1998年12月，在Hawaii由美国工程基金会所筹划的国际专家研讨会上，
X．D Li，和K．S．Ravichandran提出了K的各向异性以及各向异性K对微裂纹扩展行
为的影响等问题，并在随后对此进行了比较深入的研究。
相关的研究表明，由于晶粒的取向、几何形状所诱发的局部各向异性，导致沿
微裂纹前缘应力场强度因子K强烈的各向异性。即多晶体材料中微裂纹前缘的应力
场强度因子K通常存在较大的波动，多晶体材料中的微裂纹萌生与扩展行为，很大
程度上受到与微裂纹前缘相接触的多晶体材料局部区域内晶粒的取向分布、晶粒几
何形状、单晶物性的影响。随着微裂纹尺寸的增加，K的波动程度减小并逐渐趋于
稳定，K各向异性行为消失。
应力场强度因子的各向异性问题，愈来愈受到人们的重视。而微裂纹前缘应力
场强度因子的各向异性这一新概念及其物理意义与几何内涵的提出，更是对传统应
力场强度因子的概念与计算方法的一次重大挑战。
与其它因素相比，微裂纹前缘的K可能是在我们认识细观领域内材料破坏行为
以及工程应用过程中，最具物理意义的一个代表性因素。因此，在评估工程构件的
临界裂纹失效时，各向异性的微观结构对应力场强度因子K的局部影响，就变得尤
为重要。
为了能够可视化地模拟微裂纹的扩展过程，并为建立微裂纹扩展丌裂判据准备
试验数据，本研究涉及了模拟程序设计和相关试验两部分的工作。
模拟程序设计部分旨在开发一个可视化的微裂纹扩展模拟程序，直观地演示在
多晶体材料中，从一个结构弱点(即裂纹源)开始的微裂纹扩展过程；这一可视化
的软件平台同时也为计算微裂纹前缘各向异性的应力场强度因子K提供了一个数
值化的分析基础。
试验部分旨在设计相关试验，以研究微裂纹前缘K的各向异性程度与多晶体材
料当地微观组织的关系，为建立有效的微裂纹丌裂判据准备试验数据及相关资料。
Fatigue damage of engineering materials is often characterized to be a local phenomenon of microcracks initiating and propagating in solids. Lankford and Suresh have supposed that the 'irregular behavior' of naturally initiated microcracks is closely related with the local crystallography. The term 'irregular behavior' means the common observations of large scatter in growth rate data and the noticeably higher average growth rates of microcracks in fatigue, with respect to that of large cracks. Unfortunately, people do not pay enough attention to the importance of this phenomenon.
X.D Li and K.S. Ravichandran put forward the K variation and anisotropy as well as the influence of anisotropic K to the behavior of microcracks' propagation at an international conference. They have done some in-depth research work about these aspects.
It has been found that the grain-orientation-geometry-induced local anisotropy produces large variations in K along front of microcracks, when the crack size is of the order of few grain diameters. Synergetic effect of grain orientation and geometry of broken grains control K variations and evolution along the microcrack front. The K variations may diminish at large crack sizes, signifying a shift of K calculation to bulk stress dependence from local stress dependence.
The phenomenon of K variation and anisotropy is highly regarded increasingly. While the appearance of K anisotropy alone the microcrack front along with its physical significance and geometrical connotation is a great challenge to traditional conception and compute method of K.
Compared with other elements, K along microcrack front should be the most representative one in physical significance during we recognize the material damage behavior and the engineering applying process. For this reason, the local influence of anisotropic microstructure to the stress intensity factor (K) becomes very important when evaluating the critical crack damage of engineering components.
The research work includes modeling programming and correlative experimentation two part. The modeling program part is to develop a visual simulating program, which can illustrate the microcrack propagating process from a material structure weakness. It is also expected to provide a numerical base for computing anisotropy K along microcrack front. The experiment part is to design interrelated exam plans to investigate the relation between anisotropy K along microcrack front and the local microstructure, acquire the correlated exam datum for the establishment of microcrack propagating criterion.
当地的局部晶体结构相关联的。即，相对于尺寸较大的裂纹(与大量的疲劳微裂纹
生长速度的观察数据相比)，疲劳过程中微裂纹扩展速率的分散程度较大，以及较
高的平均疲劳裂纹生长率。在细观尺度上，晶粒取向的变化，会导致应力场的不均
匀。然而，这一现象的重要性并未引起人们足够的重视。
直到1998年12月，在Hawaii由美国工程基金会所筹划的国际专家研讨会上，
X．D Li，和K．S．Ravichandran提出了K的各向异性以及各向异性K对微裂纹扩展行
为的影响等问题，并在随后对此进行了比较深入的研究。
相关的研究表明，由于晶粒的取向、几何形状所诱发的局部各向异性，导致沿
微裂纹前缘应力场强度因子K强烈的各向异性。即多晶体材料中微裂纹前缘的应力
场强度因子K通常存在较大的波动，多晶体材料中的微裂纹萌生与扩展行为，很大
程度上受到与微裂纹前缘相接触的多晶体材料局部区域内晶粒的取向分布、晶粒几
何形状、单晶物性的影响。随着微裂纹尺寸的增加，K的波动程度减小并逐渐趋于
稳定，K各向异性行为消失。
应力场强度因子的各向异性问题，愈来愈受到人们的重视。而微裂纹前缘应力
场强度因子的各向异性这一新概念及其物理意义与几何内涵的提出，更是对传统应
力场强度因子的概念与计算方法的一次重大挑战。
与其它因素相比，微裂纹前缘的K可能是在我们认识细观领域内材料破坏行为
以及工程应用过程中，最具物理意义的一个代表性因素。因此，在评估工程构件的
临界裂纹失效时，各向异性的微观结构对应力场强度因子K的局部影响，就变得尤
为重要。
为了能够可视化地模拟微裂纹的扩展过程，并为建立微裂纹扩展丌裂判据准备
试验数据，本研究涉及了模拟程序设计和相关试验两部分的工作。
模拟程序设计部分旨在开发一个可视化的微裂纹扩展模拟程序，直观地演示在
多晶体材料中，从一个结构弱点(即裂纹源)开始的微裂纹扩展过程；这一可视化
的软件平台同时也为计算微裂纹前缘各向异性的应力场强度因子K提供了一个数
值化的分析基础。
试验部分旨在设计相关试验，以研究微裂纹前缘K的各向异性程度与多晶体材
料当地微观组织的关系，为建立有效的微裂纹丌裂判据准备试验数据及相关资料。
Fatigue damage of engineering materials is often characterized to be a local phenomenon of microcracks initiating and propagating in solids. Lankford and Suresh have supposed that the 'irregular behavior' of naturally initiated microcracks is closely related with the local crystallography. The term 'irregular behavior' means the common observations of large scatter in growth rate data and the noticeably higher average growth rates of microcracks in fatigue, with respect to that of large cracks. Unfortunately, people do not pay enough attention to the importance of this phenomenon.
X.D Li and K.S. Ravichandran put forward the K variation and anisotropy as well as the influence of anisotropic K to the behavior of microcracks' propagation at an international conference. They have done some in-depth research work about these aspects.
It has been found that the grain-orientation-geometry-induced local anisotropy produces large variations in K along front of microcracks, when the crack size is of the order of few grain diameters. Synergetic effect of grain orientation and geometry of broken grains control K variations and evolution along the microcrack front. The K variations may diminish at large crack sizes, signifying a shift of K calculation to bulk stress dependence from local stress dependence.
The phenomenon of K variation and anisotropy is highly regarded increasingly. While the appearance of K anisotropy alone the microcrack front along with its physical significance and geometrical connotation is a great challenge to traditional conception and compute method of K.
Compared with other elements, K along microcrack front should be the most representative one in physical significance during we recognize the material damage behavior and the engineering applying process. For this reason, the local influence of anisotropic microstructure to the stress intensity factor (K) becomes very important when evaluating the critical crack damage of engineering components.
The research work includes modeling programming and correlative experimentation two part. The modeling program part is to develop a visual simulating program, which can illustrate the microcrack propagating process from a material structure weakness. It is also expected to provide a numerical base for computing anisotropy K along microcrack front. The experiment part is to design interrelated exam plans to investigate the relation between anisotropy K along microcrack front and the local microstructure, acquire the correlated exam datum for the establishment of microcrack propagating criterion.
引文
1 J Lankford. The growth of small fatigue cracks in 7075-T6 aluminum[J]. Fatigue &Fracture of Engineering material & Structures, 1982, 5: 233-248．
2 S Suresh. Crack deflection: implications for the growth of long and short fatigue cracks [J]. Metal. Mater. Trans. A, 1983, 14: 2375-2385．
3 Xu-Dong Li. K Variations and Anisotropy: Microstructure Effect and Numerical Predictions [J]. Journal of Engineering and Technology, 2003, 125(1) : 65-74．
4 ' J.V. Carstensen, T. Magnin. Characterization and quantification of multiple crack growth during low cycle fatigue [J]. International Journal of Fatigue, 2001,23: s195-s200．
5 R.J. Roe, and W.R. Krigbaum, Description of crystallite orientation in polycrystalline materials having fiber texture [J]. J. Chem. Phys., 1964, 40: 2608-2615．
6 K. S. Ravichandran and Xu-Dong. Li, Fracture mechanical character of small cracks in polycrystalline materials: Concept and numerical K calculations [J]. Acta Metall., 2000,48(2) : 525-540．
7 Li Xu-dong，Li Hua-qing．K Variations and Anisotropy：Microstructure Effect and Numerical Predictions[J]．材料工程，2003增刊：307-320．
8 Li Xu-Dong. On composite structure weaknesses Part I: simulation, properties and numerical approach [J]. Metallurgical and Materials Transactions, A, 2002, 33(7) : 2205-2215．
9 Khaled. Abdel-Tawab, Gregory J. Rodin, Fracture size effects and polycrystalline in-homogeneity [J]. International Journal of Fracture, 1998, 93: 247-259．
10王从增，刘会亭．材料性能学[M]．北京，北京工业大学出版社，2001．
11 Xu-Dong Li. On Composite-Structure Weaknesses: Part Ⅱ .Computer Experiments, Identification, and Correlation [J]. Metallurgical and Materials Transactions, A, 2002, 33(7) : 2217-2227．
12 季根顺，李旭东．应力场强度因子K的变化及其各向异性：微观组织结构的
影响与数值预测[J]．第十一届全国疲劳与断裂学术会议论文集，2002： 170-173．
13 关于微裂纹现象的再认识与应力场强度因子各向异性．国家自然科学基金资 助项目计划书(批准文号：50271016) (内部资料)．
14 [德]D．罗伯编著，项金钟等译．计算材料学[M]．北京：化学工业出版社，2002．
15 傅庭亮．计算机模拟技术[M]．合肥：中国科学技术大学出版社，2001．
16 Xu-Dong Li. Computational assessment of composite structure weaknesses in short-fiber reinforced MMCs [J]. Mech. Mater, 2002, 34: 191-216．
17 Gill Barequet, matthew T.Dickerson, Robert L. Scot Drysdale. 2-Point site Voronoi diagrams [J]. Discrete Applied Mathematics, 2002, 12: 37-54．
18 Sankaran Mahadevan, Yao-wu Zhao. Advanced computer simulation of polycrystalline microstructure [J]. Comput. Methods Appl. Mech Engrg, 2002, 191:3651-3667．
19 D Weaire, J P Kermode. Computer simulation of a two-dimensional soap froth, Ⅰ . Method and motivation [J]. Philosophical Magazine, B, 1983,48(3) :245-259．
20 D Weaire, J P Kermode. Computer simulation of a two-dimensional soap froth, Ⅱ. Analysis of results [J]. Philosophical Magazine B, 1984, 50(3) : 379-395．
21 宋余九．金属的晶界与强度[M]．西安：西安交通大学出版社，1986．
22 卢光熙．候增寿，金属学教程[M]．上海：上海科学技术出版社，1984．
23 Patrick W Trimby, David J Prior. Microstructure imaging techniques: a comparison between light and scanning electron microscopy [J]. Tectonophysics, 1999,303:71-81．
24 Bernt L Adams, Sturt I Wright, and Karsten Kunze. Orientation Imaging: The Emergence of a New Microscopy [J]. Metallurgical Transactions, A, 1993, 24A: 819-831．
25 F. J. Humphreys. Review Grain and sub-grain characterization by electron backscatter diffraction [J]. Journal of science, 2001, 36: 3833-3854．
26 David P. Field and David J. Dingle. Microstructure Mapping of Interconnects by Orientation Imaging Microscopy [J]. Journal of Electronic Material, 1996, 25:
1767-1771．
27 Dorte Juul Jensen. Applications of orientation mapping by scanning and transmission electron microscopy [J]. Ultramicroscopy, 1997, 67: 25-34．
28 Angus J. Wilkinson. A new method for determining small misorientation from electron back scatter diffraction patterns[J]. Scripta mater, 2001,44: 2379-2385． 29 B. L. Adams. Orientation imaging microscopy: Emerging and future applications [J]. Ultramicroscopy, 1997, 67: 11-17．
30 朱静．取向成像电子显微术[J]．电子显微学报，16(3) ：210-217，1997．
31 H. S. Cannon. A Universal Polishing Method [J]. Met. Prog, 1955, 67: 83-86．
32 黄晓旭等．背散射衍射与透射电镜在单晶铝形变组织研究中的应用[J]．电子显 微学报，2002，21：449-454．
33 宓小川，陈家光．XRD与EBSD在钢板织构研究中的应用[J]．宝钢技术，1998， 5：16-20． 34 英国牛津公司提供资料[A]．
35 毛为民．金属的再结晶与晶粒长大[M]．北京：冶金工业出版社，1994．
36 屠世润，高越等译．金相原理与实践[M]．北京：机械工业出版社，1990．
37 桂立丰，唐汝均等．机械工程材料测试手册．物理金相卷[M]．沈阳：辽宁科 学技术出版社，1999．
38 A. Balasundaram, A.M. Gokhale. Quantitative characterization of spatial arrangement of shrinkage and gas (air) pores in cast magnesium alloys [J]. Materials Characterization, 2001,46:419-426．
39 稀有金属手册编辑委员会．稀有金属手册[M]．北京：冶金工业出版社，1997．
40 刘静安，吴煌良等译．钛合金手册[M]．重庆：科学技术出版社重庆分社，1984．
41 孙珍宝等．合金钢手册[M]．北京：冶金工业出版社，1984．
42 A M Hamed, H.EI-Ghandoor, et al. Analysis of speckle images to assess surface roughness. Optics & Laser Technology, 2004, 36:249-253．
43 Sylvie Yotte, Denys Breysse, et al. Cluster characterization in a metal matrix composite [J]. Materials Characterization, 2001,46:211-219．
44 D. He, N.N. Ekere, L. Cai. New statistic techniques for structure evaluation of
particle packing [J]. Material Science and Engineering, 2001, A298:209-215．
45 Zhaohui Shan, Arun M. Gokhale. Digital image analysis and microstructure modeling tools for microstructure sensitive design of materials [J]. International Journal of Plasticity, 2003 in press.
46 Zhaohui Shan, Arun M. Gokhale. Representative volume element for non-uniform micro-structure [J]. Computational materials science, 2002,24: 361-179．
47 Asin Tewati, Manish Dighe and A.M. Gokhale. Quantitative characterization of spatial arrangement of micro-pores in cast microstructures [J]. Materials Characterization, 1998,40: 119-132．
48 季根顺在上海宝钢集团公司得到的纯锌取向图(内部资料)。
2 S Suresh. Crack deflection: implications for the growth of long and short fatigue cracks [J]. Metal. Mater. Trans. A, 1983, 14: 2375-2385．
3 Xu-Dong Li. K Variations and Anisotropy: Microstructure Effect and Numerical Predictions [J]. Journal of Engineering and Technology, 2003, 125(1) : 65-74．
4 ' J.V. Carstensen, T. Magnin. Characterization and quantification of multiple crack growth during low cycle fatigue [J]. International Journal of Fatigue, 2001,23: s195-s200．
5 R.J. Roe, and W.R. Krigbaum, Description of crystallite orientation in polycrystalline materials having fiber texture [J]. J. Chem. Phys., 1964, 40: 2608-2615．
6 K. S. Ravichandran and Xu-Dong. Li, Fracture mechanical character of small cracks in polycrystalline materials: Concept and numerical K calculations [J]. Acta Metall., 2000,48(2) : 525-540．
7 Li Xu-dong，Li Hua-qing．K Variations and Anisotropy：Microstructure Effect and Numerical Predictions[J]．材料工程，2003增刊：307-320．
8 Li Xu-Dong. On composite structure weaknesses Part I: simulation, properties and numerical approach [J]. Metallurgical and Materials Transactions, A, 2002, 33(7) : 2205-2215．
9 Khaled. Abdel-Tawab, Gregory J. Rodin, Fracture size effects and polycrystalline in-homogeneity [J]. International Journal of Fracture, 1998, 93: 247-259．
10王从增，刘会亭．材料性能学[M]．北京，北京工业大学出版社，2001．
11 Xu-Dong Li. On Composite-Structure Weaknesses: Part Ⅱ .Computer Experiments, Identification, and Correlation [J]. Metallurgical and Materials Transactions, A, 2002, 33(7) : 2217-2227．
12 季根顺，李旭东．应力场强度因子K的变化及其各向异性：微观组织结构的
影响与数值预测[J]．第十一届全国疲劳与断裂学术会议论文集，2002： 170-173．
13 关于微裂纹现象的再认识与应力场强度因子各向异性．国家自然科学基金资 助项目计划书(批准文号：50271016) (内部资料)．
14 [德]D．罗伯编著，项金钟等译．计算材料学[M]．北京：化学工业出版社，2002．
15 傅庭亮．计算机模拟技术[M]．合肥：中国科学技术大学出版社，2001．
16 Xu-Dong Li. Computational assessment of composite structure weaknesses in short-fiber reinforced MMCs [J]. Mech. Mater, 2002, 34: 191-216．
17 Gill Barequet, matthew T.Dickerson, Robert L. Scot Drysdale. 2-Point site Voronoi diagrams [J]. Discrete Applied Mathematics, 2002, 12: 37-54．
18 Sankaran Mahadevan, Yao-wu Zhao. Advanced computer simulation of polycrystalline microstructure [J]. Comput. Methods Appl. Mech Engrg, 2002, 191:3651-3667．
19 D Weaire, J P Kermode. Computer simulation of a two-dimensional soap froth, Ⅰ . Method and motivation [J]. Philosophical Magazine, B, 1983,48(3) :245-259．
20 D Weaire, J P Kermode. Computer simulation of a two-dimensional soap froth, Ⅱ. Analysis of results [J]. Philosophical Magazine B, 1984, 50(3) : 379-395．
21 宋余九．金属的晶界与强度[M]．西安：西安交通大学出版社，1986．
22 卢光熙．候增寿，金属学教程[M]．上海：上海科学技术出版社，1984．
23 Patrick W Trimby, David J Prior. Microstructure imaging techniques: a comparison between light and scanning electron microscopy [J]. Tectonophysics, 1999,303:71-81．
24 Bernt L Adams, Sturt I Wright, and Karsten Kunze. Orientation Imaging: The Emergence of a New Microscopy [J]. Metallurgical Transactions, A, 1993, 24A: 819-831．
25 F. J. Humphreys. Review Grain and sub-grain characterization by electron backscatter diffraction [J]. Journal of science, 2001, 36: 3833-3854．
26 David P. Field and David J. Dingle. Microstructure Mapping of Interconnects by Orientation Imaging Microscopy [J]. Journal of Electronic Material, 1996, 25:
1767-1771．
27 Dorte Juul Jensen. Applications of orientation mapping by scanning and transmission electron microscopy [J]. Ultramicroscopy, 1997, 67: 25-34．
28 Angus J. Wilkinson. A new method for determining small misorientation from electron back scatter diffraction patterns[J]. Scripta mater, 2001,44: 2379-2385． 29 B. L. Adams. Orientation imaging microscopy: Emerging and future applications [J]. Ultramicroscopy, 1997, 67: 11-17．
30 朱静．取向成像电子显微术[J]．电子显微学报，16(3) ：210-217，1997．
31 H. S. Cannon. A Universal Polishing Method [J]. Met. Prog, 1955, 67: 83-86．
32 黄晓旭等．背散射衍射与透射电镜在单晶铝形变组织研究中的应用[J]．电子显 微学报，2002，21：449-454．
33 宓小川，陈家光．XRD与EBSD在钢板织构研究中的应用[J]．宝钢技术，1998， 5：16-20． 34 英国牛津公司提供资料[A]．
35 毛为民．金属的再结晶与晶粒长大[M]．北京：冶金工业出版社，1994．
36 屠世润，高越等译．金相原理与实践[M]．北京：机械工业出版社，1990．
37 桂立丰，唐汝均等．机械工程材料测试手册．物理金相卷[M]．沈阳：辽宁科 学技术出版社，1999．
38 A. Balasundaram, A.M. Gokhale. Quantitative characterization of spatial arrangement of shrinkage and gas (air) pores in cast magnesium alloys [J]. Materials Characterization, 2001,46:419-426．
39 稀有金属手册编辑委员会．稀有金属手册[M]．北京：冶金工业出版社，1997．
40 刘静安，吴煌良等译．钛合金手册[M]．重庆：科学技术出版社重庆分社，1984．
41 孙珍宝等．合金钢手册[M]．北京：冶金工业出版社，1984．
42 A M Hamed, H.EI-Ghandoor, et al. Analysis of speckle images to assess surface roughness. Optics & Laser Technology, 2004, 36:249-253．
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