热力作用下功能梯度材料的断裂力学行为研究
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摘要
功能梯度材料具有良好的高温热稳定性和抗腐蚀性能,特别是它能有效地缓解热应力和残余应力,从而被广泛的应用于各种高温环境。由于材料设计,生产工艺及工作环境等方面的原因,功能梯度材料会产生大量的微裂纹,而这些微裂纹的扩展及合并会进一步产生一些主裂纹从而导致材料破坏。因此,研究功能梯度材料在热机载荷作用下的断裂力学行为对于功能梯度材料的安全使用及其结构的设计,优化有着非常重要的意义。然而功能梯度材料材料的非均匀特性使得热力学行为非常复杂,通常的解析解只能依靠模型的一再简化和边界条件的理想化,对于复杂的问题还需要借助于数值方法。本文主要尝试着利用数值方法对功能梯度材料在非定常热边界条件和定常的力边界条件作用下的断裂力学性能进行分析,主要研究内容如下:
(1)研究了含有半椭圆表面裂纹的氧化锆/镍铬合金功能梯度材料板条在热冲击载荷作用下的裂纹问题。分析了热边界条件,裂纹纵横比以及裂纹深度对裂纹前沿分布的应力强度因子的影响。
(2)研究了含有半椭圆表面裂纹的氧化锆/镍铬合金功能梯度材料板条在热冲击载荷和机械载荷共同作用下裂纹问题分析。
(3)通过对材料属性变化的研究,分析了不同的材料属性对热力相互作用下的应力强度因子的影响,对高抗热震的梯度材料设计提出了一些建议。
论文的第一章介绍了功能梯度材料的发展历程及热机械力学行为的研究现状。第二章介绍了热弹性力学的数值解法和非均匀梯度材料断裂力学的基本概念。第三章研究了含有表面半椭圆裂纹的功能梯度材料板条在热冲击载荷作用下的断裂问题分析。第四章进一步研究了在热力共同作用下的梯度材料板的断裂问题分析。第五章研究了材料属性变化对应力强度因子的影响。
Functionally Graded Materials (FGMs) have been widely used in the high temperature environments to alleviate the thermal stresses and residual stresses effectively because of its high temperature structural and excellent corrosion-resistant properties. Due to the reasons from the design, manufacture, service environment, etc., all kinds of cracks or defects may cause the failure of FGMs. Therefore, it is very important to investigate the fracture behaviors for the FGMs under thermo-mechanical loads for the design, optimization and application. However, it is very complex to analysis the thermo-mechanical behavior owing to its non-uniform characteristics. Until now, various types of simplified mathematic models and idealized boundary conditions for FGMs can be theoretically solved. However, the numerical methods are further effectively to investigate the fracture behavior of FGMs especially for the more complicated models or boundaries. In this paper, Finite Element Method (FEM) was used to analyse the fracture mechanical performance of FGMs subjected to mechanical loads and thermal loads. The major researches as follows:
(1) The surface fracture was studied for Zirconia / Ni-Cr alloy FGMs strip with a semi-elliptical surface crack subjected to the thermal shock load, and studied the influence of crack depth, aspect ratios and thermal boundary conditions on the normalized stress-intensity factors along a crack-front.
(2) Studied on the semi-elliptical surface crack problems with Zirconia / Ni-Cr alloy FGMs strip subjected to thermal shock loads and mechanical loads.
(3) Changed the material properties, looking for effects with the different properties of materials under thermo-mechanical loading on the stress intensity factors, and propose some recommendations to design the FGMs with higher thermal shock resistance.
The fracture problems of FGMs were reviewed in Chapter One, including the advances of theoretical analysis, numerical simulation and experimental researches. In Chapter Two, numerical solution of thermo-elasticity and the basic concepts of fracture mechanics on non-uniform gradient material were introduced. In Chapter Three , a fracture issue which contained a semi-elliptical surface cracks in functionally graded material strip under thermal shock loading was Investigated. In Chapter four, this fracture issue was discussed while FGMs subjected to thermal shock loading and mechanical loading. In Chapter five, the impact to the stress intensity factor was investigated with the variational material properties.
(1)研究了含有半椭圆表面裂纹的氧化锆/镍铬合金功能梯度材料板条在热冲击载荷作用下的裂纹问题。分析了热边界条件,裂纹纵横比以及裂纹深度对裂纹前沿分布的应力强度因子的影响。
(2)研究了含有半椭圆表面裂纹的氧化锆/镍铬合金功能梯度材料板条在热冲击载荷和机械载荷共同作用下裂纹问题分析。
(3)通过对材料属性变化的研究,分析了不同的材料属性对热力相互作用下的应力强度因子的影响,对高抗热震的梯度材料设计提出了一些建议。
论文的第一章介绍了功能梯度材料的发展历程及热机械力学行为的研究现状。第二章介绍了热弹性力学的数值解法和非均匀梯度材料断裂力学的基本概念。第三章研究了含有表面半椭圆裂纹的功能梯度材料板条在热冲击载荷作用下的断裂问题分析。第四章进一步研究了在热力共同作用下的梯度材料板的断裂问题分析。第五章研究了材料属性变化对应力强度因子的影响。
Functionally Graded Materials (FGMs) have been widely used in the high temperature environments to alleviate the thermal stresses and residual stresses effectively because of its high temperature structural and excellent corrosion-resistant properties. Due to the reasons from the design, manufacture, service environment, etc., all kinds of cracks or defects may cause the failure of FGMs. Therefore, it is very important to investigate the fracture behaviors for the FGMs under thermo-mechanical loads for the design, optimization and application. However, it is very complex to analysis the thermo-mechanical behavior owing to its non-uniform characteristics. Until now, various types of simplified mathematic models and idealized boundary conditions for FGMs can be theoretically solved. However, the numerical methods are further effectively to investigate the fracture behavior of FGMs especially for the more complicated models or boundaries. In this paper, Finite Element Method (FEM) was used to analyse the fracture mechanical performance of FGMs subjected to mechanical loads and thermal loads. The major researches as follows:
(1) The surface fracture was studied for Zirconia / Ni-Cr alloy FGMs strip with a semi-elliptical surface crack subjected to the thermal shock load, and studied the influence of crack depth, aspect ratios and thermal boundary conditions on the normalized stress-intensity factors along a crack-front.
(2) Studied on the semi-elliptical surface crack problems with Zirconia / Ni-Cr alloy FGMs strip subjected to thermal shock loads and mechanical loads.
(3) Changed the material properties, looking for effects with the different properties of materials under thermo-mechanical loading on the stress intensity factors, and propose some recommendations to design the FGMs with higher thermal shock resistance.
The fracture problems of FGMs were reviewed in Chapter One, including the advances of theoretical analysis, numerical simulation and experimental researches. In Chapter Two, numerical solution of thermo-elasticity and the basic concepts of fracture mechanics on non-uniform gradient material were introduced. In Chapter Three , a fracture issue which contained a semi-elliptical surface cracks in functionally graded material strip under thermal shock loading was Investigated. In Chapter four, this fracture issue was discussed while FGMs subjected to thermal shock loading and mechanical loading. In Chapter five, the impact to the stress intensity factor was investigated with the variational material properties.
引文
1郑子樵,梁叔全.梯度功能材料的研究与展望[J].功能材料,1992,10(1): 1-5,16
2 S. Suresh and A. Mortensen. Fundamentals of Functionally Graded Materials—Processing and Thermomechanical Behaviour of Graded Metals and Metal Ceramic Composites. The University press, Cambridge. 1998
3 S. Suresh和A. Mortensen.功能梯度材料基础—制备及热机械行为.国防工业出版社, 2000
4新野正之,平井敏雄,度边龙三.倾斜机能材料[J].日本复合材料学会志,1987,13:257-264.
5郑慧雯,章娴君.功能梯度材料的研究进展.
6 J. C. Nadeau and M. Ferrari. Microstructural Optimization of a Functionally Gradient Layer. ASME, Composites and Functionally Graded Materials.1997, MD-80:3-10
7 S. Nomura and D. M. Sheaben. Green’s Function Approach to the Analysis of Functionally Graded Materials. ASME, Composites and Functionally Graded Materials. 1997, MD-80:19-23
8 W. F. Shelley, S. Wan, K. J. Bowman. Functionally Graded Piezoelectric Ceramics. Materials Science Forum. 1999, 308-311: 515-520
9 T. Taux, A. Killinger, M. Auweter-kurtz et al. Functionally Graded Ceramic Materials for High Temperature Applications for Space Planes. Materials Science Forum. 1999, 308-311: 428-433
10 M. Kambe. Design of High energy Density Thermoelectric Energy Conversion Unit by Using FGM Compliant Pads. Materials Science Forum. 1999, 308-311: 653-658
11 F. Delale, F. Erdogan. The Crack Problem for a Nonhomogeneous Plane. Journal of Applied Mechanics. 1983, 50: 609-614
12 F. Erdogan. The Crack Problem for Bonded Nonhomogeneous Materials under Antiplane Shear Loading. Journal of Applied Mechanics. 1985, 52: 823-828
13 Erdogan, F. Fracture mechanics of functionally graded materials. Composites Engineering 5,1995 753–770.
14 Erdogan, F. and Wu, B.H. Crack problems in FGM layers under thermal stresses. Journal of Thermal Stresses 19,1996 237–265.
15 Erdogan, F. and Wu, B.H. The surface crack problem for a plate with functionally graded properties. ASMEJournal of Applied Mechanics 64,1997, 449–456.
16 Gu, P. and Asaro, R.J. Cracks in functionally graded materials. International Journal of Solids and Structures 34, 1997,1–17.
17 Gu, P. and Asaro, R.J. Crack deflection in functionally graded materials. International Journal of Solids and Structures 34,1997, 3085–3098.
18 Honein, T. and Herrmann, G. (1997). Conservation laws in nonhomogeneous plane elastostatics. Journal of the Mechanics and Physics of Solids 45, 789–805.
19 Ozturk,M, Erdogan, F., 1997. Mode I crack problem in an inhomogeneous orthotropic medium. International Journal of Engineering Science 35, 869–883.
20 Ozturk,M, Erdogan, F., 1999. The mixed mode crack problem in an inhomogeneous orthotropic medium. International Journal ofFracture 98, 243–261.
21 Guo, L.-C., Wu, L.-Z., Zeng, T., Ma, L., 2004. Mode I crack problem for a functionally graded orthotropic strip. European Journal of Mechanics A/Solids 23, 219–234.
22 Guo, L.-C., Wu, L.-Z., Zeng, T., 2005. The dynamic response of an edge crack in a functionally graded orthotropic strip. Mechanics Research Communications 32, 385–400.
23 Noda, N. and Jin, Z.-H. 1993. Thermal stress intensity factors for a crack in a strip of a functionally gradient material. International Journal of Solids and Structures 30, 1039–1056.
24 Y.Tanigawa,T.Muraki,R,Kawamura,JSME Int.J.Ser.A .39 (1996):540–547。
25 M.Nemat-Alla,N.Noda,Acta Mech.144 (2000): 211–229。
26 Jin, Z.-H. and Noda, N. (1994b). Transient thermal stress intensity factors for a crack in a semi-infinite plane of a functionally gradient material. International Journal of Solids and Structures 31, 203–218.
27 Choi, H.J., Jin, T.E. and Lee, K.Y. (1998). Collinear cracks in a layered half-plane with a graded nonhomogeneous Transient thermal stress analysis of an edge crack in a functionally graded material.International Journal of Fracture 107: 73–98, 2001
28 Z.-H. JIN and GLAUCIO H. PAULINO.Transient thermal stress analysis of an edge crack in a functionallygraded material.International Journal of Fracture 107: 73–98, 2001
29 Bao-Lin Wang, Yiu-Wing Mai , Xing-Hong Zhang. Thermal shock resistance offunctionally graded materials .Acta Materialia. 52 (2004) :4961–4972
30 T.Sadowski,A.Neubrand. estimation of the crack length after thermal shock in fgm strip .international Journal of fracture. 127(2004):L135-L140
31 Serkan Dag , Bora Yildirim, Duygu Sarikaya.Mixed-mode fracture analysis of orthotropic functionally graded materials under mechanical and thermal loads International. Journal of Solids and Structures .44 (2007):7816–7840
32 Z.H. Jin,Y.Z. Feng Thermal fracture resistance of a functionally graded coatingwith periodic edge cracks .Surface & Coatings Technology. 202 (2008) :4189–4197
33 N. Noda, L.-C. Guo Thermal shock analysis for a functionally graded plate with a surface crack .Acta Mech.195, 157–166 (2008)
34 Noda, N. (1997). Thermal stress intensity factor for functionally gradient plate with an edge crack. Journal of Thermal Stresses.20, 373–387.
35 G. Bao and L. Wang. Multiple Cracking in Functionally Graded Ceramic/metal Coatings. Int. J. Solids Struct.. 1995, 32(19): 2853-2871.
36 T.C. Miller and R. Chona. Finite Element Analysis of a Thermally Loaded Interface Crack in a Ceramic Coating. Eng. Fracture Mech.1998, 59(2): 203-214.
37 Y.D. Lee and F. Erdogan. Interface Cracking of FGM Coating under Steady State Heat Flow. Eng. Fracture Mech.. 1998, 59(3): 361-380.
38 J.N. Reddy and C.D. Chin. Thermomechanical Analysis of Functionally Graded Cylinders and Plates. J. Thermal Stresses. 1998, 21: 593-626.
39 Kokini, K. and Case, M. (1997). Initiation of surface and interface edge cracks in functionally graded ceramic thermal barrier coatings. ASME Journal of Engineering Materials and Technology 119, 148–152.
40 Y. Xu, S. Saigal. An Element Free Galerkin Formulation for Stable Crack Growth in an Elastic Solid. Comput. Methods Appl. Mech. Engrg. 1998, 154: 331-343
41 J. P. Ponthot, T. Belytschko. Arbitrary Lagrangian-Eulerian Formulation for Element-free Galerkin Method. Comput. Mechods Appl. Mech. Engrg. 1998, 152:19-46
42 J. Chen, L. Z. Wu, S. Y. Du. A Modified J Integral for Functionally Graded Materials. Mechanics Research Communications. 2000, 27(3):301-306
43 P.R.Marur and H.V.Tippur .Dynamic Response of Bimaterrial and Graded Interface Cracks under Impact Loading. International Journal of Fracture.2000,103:95-109
44 J.Abanto-Bueno,J.Lambros.Inverstigation of Crack Growth in Functionally GradedMaterials Using Digital Image Correlation.Engineering Fracture Mechanics.2002,69:1695-1711
45朱景川,来忠红,尹钟大,李明伟. ZrO2 / Ni功能梯度材料的热冲击与热疲劳行为材料科学与工艺. 2001年12月,第9卷,第4期.
46 Jie-Cai Han , Bao-Lin Wang.Thermal shock resistance enhancement of functionally graded materials by multiple cracking.Acta Materialia.54,(2006): 963–973
47 Pavol Hvizdoˇs,Daniel Jonsson , Marc Anglada ,Guy Ann′e,Omer Van Der Biest . Mechanical properties and thermal shock behaviour of an alumina/zirconia functionally graded material prepared by electrophoretic deposition.Journal of the European Ceramic Society .27 (2007): 1365–1371
48 T. Sadowski ,K. Nakonieczny .Thermal shock response of FGM cylindrical plates with various grading patterns.Computational Materials Science .43 (2008): 171–178
49 R.J.Butcher, C.E.Rousseau, H.V.Tippur. A Functionally Graded Particulate Composite: Preparation, Measurements and Failure Analysis. Acta Mater.1999, 47(1):259-268
50 C.E.Rousseau, H.V.Tippur.Compositonally Graded Materials with Cracks Normal to the Elastic Gradient.Acta Mater.2000,48:4021-4033
51吴永礼.计算固体力学方法.科学出版社.2003
52 N. Noda, L.-C. Guo. Thermal shock analysis for a functionally graded plate with a surface crack. Acta Mech .195(2008), 157–166
53 Onur Sayman, Faruk Sen,Erdal Celik , Yusuf Arman .Thermal stress analysis of Wc–Co/Cr– Ni multilayer coatings on 316L steel substrate during cooling process .Materials and Design. 30 (2009) :770–774
54 S.M. Nabavi, A.R. Shahani.Thermal stress intensity factors for a cracked cylinder under transient thermal loading .International Journal of Pressure Vessels and Piping .86 (2009):153–163
55 M.C.Walters.Glaucio H.Paulino,Robert H.Dodds Jr. Stress-intensity Factors for Surface Cracks in Functionally Graded Materials Under Mode-I thermome-chanical Loading. Int. J. Solids Struct.41(2004):1081-1118
56 Serkan Dag , Bora Yildirim , Duygu Sarikaya .Mixed-mode fracture analysis of orthotropic functionally graded materials under mechanical and thermal loads. International Journal of Solids and Structures .44 (2007) :7816–7840
57黄剑锋,曹丽云,曹建坤.有限元在梯度功能材料研究中的应用[J].中国陶瓷,2001 ,37 (6) :37239.
58王慧,于冬梅.梯度功能材料研究进展[J].河北工业科技,2001,18 (5) :44248.
59张幸红,曲伟,张学忠,等. TiC /SiC梯度功能材料的优化设计[J ] .材料科学与工艺,2000 ,8 (1) :81283.
60赵军,王朝霞,董一芬,艾兴.对称型梯度功能材料的瞬态热应力强度因子.山东大学学报(工学版): 2004年6月.第34卷,第3期.
2 S. Suresh and A. Mortensen. Fundamentals of Functionally Graded Materials—Processing and Thermomechanical Behaviour of Graded Metals and Metal Ceramic Composites. The University press, Cambridge. 1998
3 S. Suresh和A. Mortensen.功能梯度材料基础—制备及热机械行为.国防工业出版社, 2000
4新野正之,平井敏雄,度边龙三.倾斜机能材料[J].日本复合材料学会志,1987,13:257-264.
5郑慧雯,章娴君.功能梯度材料的研究进展.
6 J. C. Nadeau and M. Ferrari. Microstructural Optimization of a Functionally Gradient Layer. ASME, Composites and Functionally Graded Materials.1997, MD-80:3-10
7 S. Nomura and D. M. Sheaben. Green’s Function Approach to the Analysis of Functionally Graded Materials. ASME, Composites and Functionally Graded Materials. 1997, MD-80:19-23
8 W. F. Shelley, S. Wan, K. J. Bowman. Functionally Graded Piezoelectric Ceramics. Materials Science Forum. 1999, 308-311: 515-520
9 T. Taux, A. Killinger, M. Auweter-kurtz et al. Functionally Graded Ceramic Materials for High Temperature Applications for Space Planes. Materials Science Forum. 1999, 308-311: 428-433
10 M. Kambe. Design of High energy Density Thermoelectric Energy Conversion Unit by Using FGM Compliant Pads. Materials Science Forum. 1999, 308-311: 653-658
11 F. Delale, F. Erdogan. The Crack Problem for a Nonhomogeneous Plane. Journal of Applied Mechanics. 1983, 50: 609-614
12 F. Erdogan. The Crack Problem for Bonded Nonhomogeneous Materials under Antiplane Shear Loading. Journal of Applied Mechanics. 1985, 52: 823-828
13 Erdogan, F. Fracture mechanics of functionally graded materials. Composites Engineering 5,1995 753–770.
14 Erdogan, F. and Wu, B.H. Crack problems in FGM layers under thermal stresses. Journal of Thermal Stresses 19,1996 237–265.
15 Erdogan, F. and Wu, B.H. The surface crack problem for a plate with functionally graded properties. ASMEJournal of Applied Mechanics 64,1997, 449–456.
16 Gu, P. and Asaro, R.J. Cracks in functionally graded materials. International Journal of Solids and Structures 34, 1997,1–17.
17 Gu, P. and Asaro, R.J. Crack deflection in functionally graded materials. International Journal of Solids and Structures 34,1997, 3085–3098.
18 Honein, T. and Herrmann, G. (1997). Conservation laws in nonhomogeneous plane elastostatics. Journal of the Mechanics and Physics of Solids 45, 789–805.
19 Ozturk,M, Erdogan, F., 1997. Mode I crack problem in an inhomogeneous orthotropic medium. International Journal of Engineering Science 35, 869–883.
20 Ozturk,M, Erdogan, F., 1999. The mixed mode crack problem in an inhomogeneous orthotropic medium. International Journal ofFracture 98, 243–261.
21 Guo, L.-C., Wu, L.-Z., Zeng, T., Ma, L., 2004. Mode I crack problem for a functionally graded orthotropic strip. European Journal of Mechanics A/Solids 23, 219–234.
22 Guo, L.-C., Wu, L.-Z., Zeng, T., 2005. The dynamic response of an edge crack in a functionally graded orthotropic strip. Mechanics Research Communications 32, 385–400.
23 Noda, N. and Jin, Z.-H. 1993. Thermal stress intensity factors for a crack in a strip of a functionally gradient material. International Journal of Solids and Structures 30, 1039–1056.
24 Y.Tanigawa,T.Muraki,R,Kawamura,JSME Int.J.Ser.A .39 (1996):540–547。
25 M.Nemat-Alla,N.Noda,Acta Mech.144 (2000): 211–229。
26 Jin, Z.-H. and Noda, N. (1994b). Transient thermal stress intensity factors for a crack in a semi-infinite plane of a functionally gradient material. International Journal of Solids and Structures 31, 203–218.
27 Choi, H.J., Jin, T.E. and Lee, K.Y. (1998). Collinear cracks in a layered half-plane with a graded nonhomogeneous Transient thermal stress analysis of an edge crack in a functionally graded material.International Journal of Fracture 107: 73–98, 2001
28 Z.-H. JIN and GLAUCIO H. PAULINO.Transient thermal stress analysis of an edge crack in a functionallygraded material.International Journal of Fracture 107: 73–98, 2001
29 Bao-Lin Wang, Yiu-Wing Mai , Xing-Hong Zhang. Thermal shock resistance offunctionally graded materials .Acta Materialia. 52 (2004) :4961–4972
30 T.Sadowski,A.Neubrand. estimation of the crack length after thermal shock in fgm strip .international Journal of fracture. 127(2004):L135-L140
31 Serkan Dag , Bora Yildirim, Duygu Sarikaya.Mixed-mode fracture analysis of orthotropic functionally graded materials under mechanical and thermal loads International. Journal of Solids and Structures .44 (2007):7816–7840
32 Z.H. Jin,Y.Z. Feng Thermal fracture resistance of a functionally graded coatingwith periodic edge cracks .Surface & Coatings Technology. 202 (2008) :4189–4197
33 N. Noda, L.-C. Guo Thermal shock analysis for a functionally graded plate with a surface crack .Acta Mech.195, 157–166 (2008)
34 Noda, N. (1997). Thermal stress intensity factor for functionally gradient plate with an edge crack. Journal of Thermal Stresses.20, 373–387.
35 G. Bao and L. Wang. Multiple Cracking in Functionally Graded Ceramic/metal Coatings. Int. J. Solids Struct.. 1995, 32(19): 2853-2871.
36 T.C. Miller and R. Chona. Finite Element Analysis of a Thermally Loaded Interface Crack in a Ceramic Coating. Eng. Fracture Mech.1998, 59(2): 203-214.
37 Y.D. Lee and F. Erdogan. Interface Cracking of FGM Coating under Steady State Heat Flow. Eng. Fracture Mech.. 1998, 59(3): 361-380.
38 J.N. Reddy and C.D. Chin. Thermomechanical Analysis of Functionally Graded Cylinders and Plates. J. Thermal Stresses. 1998, 21: 593-626.
39 Kokini, K. and Case, M. (1997). Initiation of surface and interface edge cracks in functionally graded ceramic thermal barrier coatings. ASME Journal of Engineering Materials and Technology 119, 148–152.
40 Y. Xu, S. Saigal. An Element Free Galerkin Formulation for Stable Crack Growth in an Elastic Solid. Comput. Methods Appl. Mech. Engrg. 1998, 154: 331-343
41 J. P. Ponthot, T. Belytschko. Arbitrary Lagrangian-Eulerian Formulation for Element-free Galerkin Method. Comput. Mechods Appl. Mech. Engrg. 1998, 152:19-46
42 J. Chen, L. Z. Wu, S. Y. Du. A Modified J Integral for Functionally Graded Materials. Mechanics Research Communications. 2000, 27(3):301-306
43 P.R.Marur and H.V.Tippur .Dynamic Response of Bimaterrial and Graded Interface Cracks under Impact Loading. International Journal of Fracture.2000,103:95-109
44 J.Abanto-Bueno,J.Lambros.Inverstigation of Crack Growth in Functionally GradedMaterials Using Digital Image Correlation.Engineering Fracture Mechanics.2002,69:1695-1711
45朱景川,来忠红,尹钟大,李明伟. ZrO2 / Ni功能梯度材料的热冲击与热疲劳行为材料科学与工艺. 2001年12月,第9卷,第4期.
46 Jie-Cai Han , Bao-Lin Wang.Thermal shock resistance enhancement of functionally graded materials by multiple cracking.Acta Materialia.54,(2006): 963–973
47 Pavol Hvizdoˇs,Daniel Jonsson , Marc Anglada ,Guy Ann′e,Omer Van Der Biest . Mechanical properties and thermal shock behaviour of an alumina/zirconia functionally graded material prepared by electrophoretic deposition.Journal of the European Ceramic Society .27 (2007): 1365–1371
48 T. Sadowski ,K. Nakonieczny .Thermal shock response of FGM cylindrical plates with various grading patterns.Computational Materials Science .43 (2008): 171–178
49 R.J.Butcher, C.E.Rousseau, H.V.Tippur. A Functionally Graded Particulate Composite: Preparation, Measurements and Failure Analysis. Acta Mater.1999, 47(1):259-268
50 C.E.Rousseau, H.V.Tippur.Compositonally Graded Materials with Cracks Normal to the Elastic Gradient.Acta Mater.2000,48:4021-4033
51吴永礼.计算固体力学方法.科学出版社.2003
52 N. Noda, L.-C. Guo. Thermal shock analysis for a functionally graded plate with a surface crack. Acta Mech .195(2008), 157–166
53 Onur Sayman, Faruk Sen,Erdal Celik , Yusuf Arman .Thermal stress analysis of Wc–Co/Cr– Ni multilayer coatings on 316L steel substrate during cooling process .Materials and Design. 30 (2009) :770–774
54 S.M. Nabavi, A.R. Shahani.Thermal stress intensity factors for a cracked cylinder under transient thermal loading .International Journal of Pressure Vessels and Piping .86 (2009):153–163
55 M.C.Walters.Glaucio H.Paulino,Robert H.Dodds Jr. Stress-intensity Factors for Surface Cracks in Functionally Graded Materials Under Mode-I thermome-chanical Loading. Int. J. Solids Struct.41(2004):1081-1118
56 Serkan Dag , Bora Yildirim , Duygu Sarikaya .Mixed-mode fracture analysis of orthotropic functionally graded materials under mechanical and thermal loads. International Journal of Solids and Structures .44 (2007) :7816–7840
57黄剑锋,曹丽云,曹建坤.有限元在梯度功能材料研究中的应用[J].中国陶瓷,2001 ,37 (6) :37239.
58王慧,于冬梅.梯度功能材料研究进展[J].河北工业科技,2001,18 (5) :44248.
59张幸红,曲伟,张学忠,等. TiC /SiC梯度功能材料的优化设计[J ] .材料科学与工艺,2000 ,8 (1) :81283.
60赵军,王朝霞,董一芬,艾兴.对称型梯度功能材料的瞬态热应力强度因子.山东大学学报(工学版): 2004年6月.第34卷,第3期.