EB-PVD热障涂层的断裂行为研究
|
摘要
目前,在航天、航空等许多工业领域,各种热涂层技术已经广泛用于提高机械构件的性能,延长其使用寿命。而涂层与母材基体的完整性是构件安全的关键,涂层的结合强度成为评价涂层适用性的重要标准之一。电子束物理气相沉积(EB-PVD)技术制备的热障涂层(TBCs)主要应用在航天发动机涡轮上,已经在航空领域起到重要作用。
本文从断裂力学对涂层/基体界面结合强度分析出发,对热障涂层的力学性能、涂层的断裂行为基本特性、涂层与基体间界面的断裂参量计算等几个方面进行了研究。
通过扫描电镜观察了EB-PVD制备的热障涂层(TBCs)的微观形貌,分析了各层成分,并分析了粘结层MCrAlY对于热障涂层性能的作用。
通过三点弯曲试验测量了热障涂层的弹性模量(E),相同厚度涂层的E具有一定的分散性。
通过对三点弯曲试样中热障涂层断裂行为的观察,发现涂层中某位置所受力矩达到一定值时,该处会产生垂直于界面的裂纹,故可将力矩是否达到临界值作为该位置产生裂纹的条件。有限元分析结果也证明了上述结论,对于三个不同位置的裂纹,当裂纹产生时该位置处界面附近的应力水平基本接近。
提出在拉伸涂层试样的涂层与基体之间预制裂纹的方法,对采用有限元方法计算涂层/基体界面断裂参量(应力强度因子K和J积分)的方法进行了研究。模拟结果表明,在拉伸试样中拉伸载荷主导界面裂纹尖端附近区域,且拉伸效果远大于剪切效果。研究发现模拟试样的界面裂纹尖端附近存在K主导区,即K有效。
At present, in astronautics, aviation and so many industry domains, each kind of thermal spraying coating technology has already been widely used in enhancing the performance of the mechanical components and lengthened their service life.The integrity of coating/substrate system is critical for the components’security, and the union intensity of coatings has become one of many important standards in the applicability of coatings. Electron beam-physical vapor deposited(EB-PVD) thermal barrier coatings(TBCs) are mostly used on the hot section of aircraft engine turbines and have played an important role in the field of aviation. For the purpose of analyzing the cohesion strength of coating/substrate system, the mechanical property of TBCs, fracture behavior characteristics of coatings, interface fracture parameters had been studied in this paper.
The microcosmic appear of EB-PVD-TBCs had been observed and the component of each coating had been analyzed by SEM. The important function of bond coating (MCrAlY) was found.
The 3-point bend test had been used to measure the Young’s modulus (E) of the TBCs. E of coatings with same thickness have large disperse.
The fracture behavior of TBCs in 3-point bend specimen had been observed. It was found that the crack normal to the interface in the coating occurred where a fixed moment of force was reached. So whether the moment reached to the critical value can be used as the condition of crack occurrence. The FEA results proved the previous conclusion. The stress levels at the different locations where the cracks occurred near the interface almost were same.
A method of simulating a crack in the interface between TBCs and substrate has been put forward. FEA had been used to study interface fracture parameters of the interface between TBCs and substrate(the complex stress intensity factor K and JC).The result of FEA showed the tensile load near the crack tip were dominant, and the tensile load had higher effect than the shear load. The research found the K-dominant zone existed near the crack tip for total specimens in this tensile test .
本文从断裂力学对涂层/基体界面结合强度分析出发,对热障涂层的力学性能、涂层的断裂行为基本特性、涂层与基体间界面的断裂参量计算等几个方面进行了研究。
通过扫描电镜观察了EB-PVD制备的热障涂层(TBCs)的微观形貌,分析了各层成分,并分析了粘结层MCrAlY对于热障涂层性能的作用。
通过三点弯曲试验测量了热障涂层的弹性模量(E),相同厚度涂层的E具有一定的分散性。
通过对三点弯曲试样中热障涂层断裂行为的观察,发现涂层中某位置所受力矩达到一定值时,该处会产生垂直于界面的裂纹,故可将力矩是否达到临界值作为该位置产生裂纹的条件。有限元分析结果也证明了上述结论,对于三个不同位置的裂纹,当裂纹产生时该位置处界面附近的应力水平基本接近。
提出在拉伸涂层试样的涂层与基体之间预制裂纹的方法,对采用有限元方法计算涂层/基体界面断裂参量(应力强度因子K和J积分)的方法进行了研究。模拟结果表明,在拉伸试样中拉伸载荷主导界面裂纹尖端附近区域,且拉伸效果远大于剪切效果。研究发现模拟试样的界面裂纹尖端附近存在K主导区,即K有效。
At present, in astronautics, aviation and so many industry domains, each kind of thermal spraying coating technology has already been widely used in enhancing the performance of the mechanical components and lengthened their service life.The integrity of coating/substrate system is critical for the components’security, and the union intensity of coatings has become one of many important standards in the applicability of coatings. Electron beam-physical vapor deposited(EB-PVD) thermal barrier coatings(TBCs) are mostly used on the hot section of aircraft engine turbines and have played an important role in the field of aviation. For the purpose of analyzing the cohesion strength of coating/substrate system, the mechanical property of TBCs, fracture behavior characteristics of coatings, interface fracture parameters had been studied in this paper.
The microcosmic appear of EB-PVD-TBCs had been observed and the component of each coating had been analyzed by SEM. The important function of bond coating (MCrAlY) was found.
The 3-point bend test had been used to measure the Young’s modulus (E) of the TBCs. E of coatings with same thickness have large disperse.
The fracture behavior of TBCs in 3-point bend specimen had been observed. It was found that the crack normal to the interface in the coating occurred where a fixed moment of force was reached. So whether the moment reached to the critical value can be used as the condition of crack occurrence. The FEA results proved the previous conclusion. The stress levels at the different locations where the cracks occurred near the interface almost were same.
A method of simulating a crack in the interface between TBCs and substrate has been put forward. FEA had been used to study interface fracture parameters of the interface between TBCs and substrate(the complex stress intensity factor K and JC).The result of FEA showed the tensile load near the crack tip were dominant, and the tensile load had higher effect than the shear load. The research found the K-dominant zone existed near the crack tip for total specimens in this tensile test .
引文
[1]徐滨士,刘世参.表面工程新技术[M].北京:国防工业出版社,2002.
[2]钱苗根,陶寿山.张少宗.现代表面技术[M].北京:机械工业出版社,2000.
[3]Li Y, Zhao J P,Zeng G et al. Ni/Ni3 Al microlaminate composite produced by EB-PVD and the mechanical properties[J]. Materials Letters,2004,58:1629-1633.
[4]Movchen B A. Functionally graded EB-PVD coatings[J]. Surface and Coatings Technology, 2002,149:252-262.
[5]关春龙,李垚,赫晓东.电子束物理气相沉积技术及其应用现状[J].航空制造技术,2003,11:35-37.
[6]StenveA.High-tech coating for turbine blades.Mechanical Engineering,1995(10): 66~69
[7]Movchen B A,MarinskiG S.Gradient protective coatings of different application produced by EB-PVD[J].Surface and Coatings Technology,1998,100-101:309-315.
[8]Movchen B A. EB-PVD technology in the gas turbine industry: present and future [J].JOM,1996,(11):40-45.
[9]Movchen B A,Lemkey F D. Some approaches to producing microporous materials and coatings by EB-PVD[J].Surface and Coatings Technology,2003,165:90-100.
[10]刘福顺,宫声凯,徐惠彬.大功率EB-PVD陶瓷热障涂层的研究与应用[J].航空学报,2002,21(增刊):30-34.
[11]武洪臣,姚振中,冯建基等.先进的涂层技术EB-PVD[J].航空制造技术,2005,13 (5):28-30.
[12]关春龙.EB-PVD设备大尺寸Ni-Cr-Al合金薄板组织及性能研究[D].哈尔滨工业大学博士论文.2005,6.
[13]徐惠彬,宫声凯,刘福顺.乌克兰巴顿焊接研究所电子束物理气相沉积技术[J].航空制造工程,1997,6:6-8.
[14]Youchison D L,Gallis M A,Nygren R E et al.Effects of ion beam assisted deposition, beam sharing and pivoting in EB-PVD processing of graded thermal barrier coating[J].Surface and Coatings Technology,2004,177-178:158-164.
[15]Rhys-JonesTN.The use of thermally sprayed coatings for compressor and turbine application in aeroengines. Surface and Coatings Technology,1990,42:1-11.
[16]李美姮,胡望宇,孙晓峰,等.热障涂层的研究进展与发展趋势[J].材料导报,2005, 19(4):41-45.
[17]徐惠彬,宫声凯,陶冶,等.电子束物理气相沉积技术及其应用现状[J].航空制造工程,1995,11:23-25.
[18]胡传顺,王福会,吴维.热障涂层研究进展.2000,12(3):160~163.
[19]沈成康.断裂力学.上海:同济大学出版社,1996.
[20]Williams M L. The stress around a fault or crack in dissimilar media. Bulletin of the seismological society of America, 1959, 49(2): 199-204.
[21]Williams M L. On the stress distribution at the base of a stationary crack. Journal of applied mechanics. Trans. ASME, 1957,79: 109-114.
[22]Zak A R, Williams M L. Crack point stress singularities at a bi-material interface. Transactions of the ASME, 1963, 30: 142-143.
[23]Erdogan Fazil. Stress Distribution in a Nonhomogeneous elastic plane with cracks. Transactions of the ASME, 1963, 30: 232-236.
[24]Sih G C, Rice J R. The bending of plates of dissimilar materials with cracks. Journal of applied mechanics, 1964, 31: 477-482.
[25]Rice J R, Sih G C. Plane problems of cracks in dissimilar media. Transactions of the ASME, 1965, 32: 418-423.
[26]Park J H, Earmme Y Y. Application of conservation integrals to interfacial crack problems. Mechanics materials, 1986(5): 261-276.
[27]Shih C F, Asaro R. Elastic-plastic analysis of crack on bimaterial interfaces; Part I: Small scale yielding. Journal of applied mechanics. Transactions ASME, 1988, 55(2): 299-313.
[28]Hutchinson J W, Wear M, Rice J R. Crack paralleling an interface between dissimilar materials. Journal of applied mechanics. Transactions ASME 1987, 54(4): 828-832.
[29]Rice JR, Sih G C. Mathematical analysis in the mechanics of fracture. Fracture: An advance treatise. H.Liebowitz, ed., 1968, l2: 17-26.
[30]Cherepanov G P. The stress state in a heterogeneous plate with slits. In Russian, Izvestia AN SSSR, OTN, Mekhan. i Mashin. 1962, Vol.1: 131-137.
[31]Cherepanov G P. Mechanics of brittle fracture. McGraw-Hill, New York, 1979.
[32]England A H. A crack between dissimilar media. Journal of applied mechanics, 1965(32): 400-402.
[33]Erdogan F. Stress distribution in bonded dissimilar materials with cracks. Journal of applied mechanics, 1965(32): 403-410.
[34]Rice J R. Elastic fracture mechanics concepts for interfacial cracks. Journal of applied mechanics.Transactions of the ASME, 1988, 55 (1): 98-103.
[35]Comninou M. The interface crack. Journal of applied mechanics. Transactions of the ASME, 1977, 44(4): 631-636.
[36]Comninou M. Interface crack with friction in the contact zone. Journal of applied mechanics.Transactions of the ASME, 1977, 44 (4): 780-781.
[37]Comninou M, Schmueser D. The interface crack in a combined tension-compression and shear field. Journal of applied mechanics. Transactions of the ASME, 1979, 46(2): 345-348.
[38]Malyshev B M, Salgnik R L. The strength of adhesive joints using the theory of crack. International journal fracture mechanics, 1965, 1: 114-128.
[39]Hutchinson J W.Singular behavior at the end of a tensile crack in a hardening material.Mech.Phys.Solids,1968,16:13-31.
[40]Smelser R E. Evaluation of stress intensity factors for bimaterial bodies using numerical crack flank displacement data. Interational journal of fracture, 1979, 15(2): 135-143.
[41]Matos P P L, McMeeking R M, Charalambides P G. et al. Method for calculating stress intensities in bimaterial fracture. International Journal of Fracture, 1989, 40(4): 235-254.
[42]Muller D, Cho YR, Berg S. et al. Fracture Mechanics Tests for Measuring the Adhesion of Magnetron Sputtered TiN coatings. International Journal of Refractory Metals & Hard Materials, 1996(14): 207-211.
[43]Qian G., Nakamura T, Berndt C.C. Tensile Toughness Test and High Temperature Fracture Analysis of Thermal Barrier Coatings. Acta Materialia, 1997, 45 (4): 1767-1784.
[44]Eshelby J D, Read W T, Shockley W. Anisotropic elasticity with applications to dislocation theory. Acta Metallurgica, 1953, 1: 251-259.
[45]Stroh A N. Dislocations and cracks in anisotropic elasticity. Philosophical Magazine, 1958, 7: 625-646.
[46]Tang T C T. Explicit solution and invariance of the singularities at an interface crack in anisotropic composites. International Journal of Solids and Structures, 1986, 22(9): 965-83.
[47]Qu J, Li Q. Interfacial dislocation and its applications to interface cracks in anisotropic bimaterials. Journal of Elasticity, 1991, 26(2): 169-195.
[48]Atkinson C, Eftaxiopoulos D A. Interaction between a crack and a free or welded boundary in media with arbitrary anisotropy. International Journal of Fracture, 1991, 50(3): 159-182.
[49]Civelek M B, Erdogan F. Crack problems for a rectangular plate and an infinite stripSource: International Journal of Fracture, 1982,19(2): 139-59.
[50]Suo Zhigang. Delamination specimens for orthotropic materialsSource: Transactions of the ASME. Journal of Applied Mechanics, 1990, 57(3): 627-634.
[51]Suo Zhigang, Hutchinson J W. Interface crack between two elastic layersSource.International Journal of Fracture, 1990, 43(1): 1-18.
[52]Jagannadham K, Marcinkowski M J. Surface dislocation model of a finite stressed solid. Material Science and Engineering, 1979, 38(3): 259-270.
[53]Huang Haiying, Kardomateas G A. Single-edge and double-edge cracks in a fully anisotropic strip.Transactions of the ASME. Journal of Engineering Materials and Technology, 1999, 121(4): 422-429.
[54]O’Brien T K, Hooper S J. Local delamination in laminates with angle ply matrix cracks, Part I: Tension tests and stress analysis. In: Stinchcomb, W.W., Ashbaugh, N.E.(Eds.), Composite Materials: Fatigue and Fracture, vol,4, ASTM STP 1156, American Society for Testing and Materials, Philadelphia, 491-506.
[55]Qian W, Sun C T. Calculation of stress intensity factors for interlaminar cracks in composite laminates. Composites Science and Technology, 1997, 57(6): 637-650.
[56]Cao H C, Evans A G. An experimental study of the fracture resistance of bimaterial interfaces. Mechanics of materials. 1989, 7(4): 295-304.
[57]Evans A G., Hutchinson J W. Effects of non-planarity on the mixed mode fracture resistance of bimaterial interfaces. Acta Metallurgica. 1989, 37(3): 909-916.
[58]Charalambides P G, Lund J, Evans A G. et al. A test specimen for determining the fracture resistance of bimaterial interfaces. Journal of applied mechanics. Transactions of the ASME, 1989, 56(1): 77-82.
[59]Chung H G.P, Swain M V, Mori T. Evaluation of the Strain Energy Release Rate for the Fracture of Titanium-porcelain Interfacial Bonding. Biomaterials. 1997, 18 (23): 1553-1557.
[60]Li H, Khor K A, Cheang P. Young’modulus and fracture toughness determination of high velocity oxy-fuel-sprayed bioceramic coatings. Surface and Coatings Technology, 2002, 155(1): 21-32.
[61]G.C. Shih. Mechanics of Fracture Initiation and Propagation, Kluwer Academic, USA, 1991.
[62]O'Dowd N P, Shih C F, Stout M G. Test geometries for measuring interfacial fracture toughness. International Journal of Solids and Structures, 1992, 29(5): 571-589.
[63]Becker Jr T L, McNaney J M, Cannon R M et al. Limitations on the use of the mixed-mode delaminating beam test specimen: effects of the size of the region of K-dominance. Mechanics of Materials, 1997, 25(4): 291-308.
[64]Oh Tae Sung, Cannon R M, Ritchie R O. Subcritical crack growth along ceramic-metal interfaces. Journal of the American Ceramic Society, 1987, 70(12): C352-C355.
[65]Cannon R M, Dalgleish B J, Dauskardt R H et al. Cyclic fatigue-crack propagation along ceramic/metal interfaces. Acta Metallurgica et Materialia, 1991,39(8): 2145-2156.
[66]Thun G, Schneider G A, Bahr H-A et al. Toughness Anisotropy and Damage Behavior of Plasma Sprayed ZrO2 Thermal Barrier Coatings. Surface and Coatings Technology, 2000, 123(2-3): 147-158.
[67]Dornowski Wojciech, Perzyna Piotr. Numerical analysis of macrocrack propagation along a bimaterial interface under dynamic loading processes. International Journal of Solids and Structures, 2002, 39(19): 4949-4977.
[68]Moran B, Shih C F. A General Treatment of crack Tip Integrals. International Journal of Fracture, 1987, 35 (4): 295-310.
[69]Moran B, Shih C F. Crack Tip and Associated Domain Integrals from Momentum and Energy Balance. Engineering Fracture Mechanics, 1987, 27 (6): 615-642.
[70]Li F Z, Shih C F, Needleman A. A Comparison of Methods for Calculating Energy Release rates. Engineering Fracture Mechanics, 1985, 25 (2): 405-421.
[71]Shih C F, Moran B, Nakamura T. Energy Release Rate along a Three-dimensional Crack Front in a Thermally Stressed Body. International Journal of Fracture, 1986, 30 (2): 79-102.
[72]Nikishkov G P, Atluri S N. Calculation of Fracture Mechanics Parameters for an Arbitrary Three-dimensional Crack by the‘Equivalent Domain Integral Method’. International Journal for Numerical Methods in Engineering, 1987, 24 (9): 1801-1821.
[73]Shih C F, Asaro R J. Elastic-plastic Analysis of Cracks on Bimaterial Interfaces: Part I-Small Scale Yielding. Transactions of the ASME. Journal of Applied Mechanics, 1988, 55(2): 299-316.
[74]Nakamura T. Three-dimensional Stress Fields of Elastic Interface Cracks. Transactions of the ASME. Journal of Applied Mechanics, 1991, 58 (4): 939-946.
[75]Nakamura T, Parks D M. Determination of Elastic T-stress along Three-dimensional Crack Front Using Interaction Integral. International Journal of Solids and Structures. 1992, 29(13): 1597-1611.
[76]Charalambides P G, Evans AG. Debonding Properties of Residually Stressed Brittle-matrix Composites. Journal of the American Ceramic Society. 1989, 72(5): 746-753.
[77]陈孟成,吴凤筠,沈文雁.陶瓷热障涂层和热循环试验研究,材料工程,1999/04.
[78]Edward H,Goldman,Ramgopal Darolia.U.S.Patent,Number5,316,866,1993.
[79]Timoshenko S P, James M Gere. Mechanics of Materials. Van Nostrand Reinhold Co., Inc., Molly Millars Lane, Workingham, Berkshire, England.
[80]Y.C.Zhou,T.Hashida.Coupled effects of temperature gradient and oxidation on thermal stress in thermal barrier coating system [J].International Journal of Solidsand Structures 38(2001)4235-4264.
[81]曹学强,热障涂层材料[M],北京:科学出版社,2007.
[82]Smeylser R E, Gurtin M E. On the J-integral for biomaterial bodies. Internation- al Journal of Fracture, 1971, 13: 382-384.
[83]刘刘,杨晓光,耿瑞. TBC界面裂纹K因子的有限元求解方法.航空动力学报, 2001, 16(2):16-174.
[84]Hutchinson J W. Fundamentals of the phenomenological theory of nonlinear fracture mechanics. Journal of Applied Mechanics, 1983, 50(4b): 1042-1050.
[85]Rice J R. A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics, 1968, 35: 379-386.
[86]Hutchinson J W. Singular behavior at the end of a tensile crack tip in a hardening material. Journal of Mechanics and Physics of Solids, 1968, 16(1): 13-31.
[87]Parks D M. The virtual crack extension method for nonlinear material behaviour. Computer Methods in Applied Mechanics and Engineering, 1977, 12(3): 353-364.
[88]Hellen T K. On the method of virtual crack extensions. International Journal for Numerical Methods in Engineering, 1975, 9(1): 187-196.
[89]Nakamura T, Shih C F, Freund L B. Analysis of a dynamicaly loaded three-point-bend ductile fracture specimen. Engineering Fracture Mechanics, 1986, 25(3): 323-339.
[90]Li F Z, Shih C F, Needleman A. A comparison of methods for calculating energy release rates. Engineering Fracture Mechanics, 1985, 21(2): 405-21.
[91]Shih C F, Moran B, Nakamura T. Energy release rate along a three-dimensional crack front in a thermally stressed body. International Journal of Fracture, 1986, 30(2): 79-102.
[92]de Lorenzi H G. On the energy release rate and the J-integral for 3D crack configurations. International Journal of Fracture, 1982, 19(3): 183-193.
[93]雷和荣,虞吉林.虚裂纹扩展法计算J积分的研究.中国科学技术大学学报, 1994, 24(2): 201-213.
[94]杨新岐,霍立兴,张玉凤.三维能量释放率虚拟裂纹扩展算法及工程应用.天津大学学报, 1997, 30(1): 37-42.
[95]王利民,陈浩然. J积分在多层介质中的守恒性和其应用.应用数学和力学. 2001, 22 (10):1097-1104.
[96]C633-79 Standard Test Method for Adhesion of Cohesive Strength of Flame- Sprayed Coatings, Annual Book of ASTM Standards, Vol.03.01, 1993, P.665.
[97]Elssner G, Suga T, Turwitt M. Fracture of ceramic-to-metal interfaces. Journal dePhysique Colloque, 1985, 46 (C-4): 597-612.
[98]Han W, Rybicki E F, Shadley J R. In Thermal Spray Coating: Research, Design and Application (edited by C.C. Berndt and T.E. Bernecki), 1993. 55.
[99]徐连勇,涂层/基体界面的断裂行为研究:[博士学位论文],天津;天津大学,2006
[2]钱苗根,陶寿山.张少宗.现代表面技术[M].北京:机械工业出版社,2000.
[3]Li Y, Zhao J P,Zeng G et al. Ni/Ni3 Al microlaminate composite produced by EB-PVD and the mechanical properties[J]. Materials Letters,2004,58:1629-1633.
[4]Movchen B A. Functionally graded EB-PVD coatings[J]. Surface and Coatings Technology, 2002,149:252-262.
[5]关春龙,李垚,赫晓东.电子束物理气相沉积技术及其应用现状[J].航空制造技术,2003,11:35-37.
[6]StenveA.High-tech coating for turbine blades.Mechanical Engineering,1995(10): 66~69
[7]Movchen B A,MarinskiG S.Gradient protective coatings of different application produced by EB-PVD[J].Surface and Coatings Technology,1998,100-101:309-315.
[8]Movchen B A. EB-PVD technology in the gas turbine industry: present and future [J].JOM,1996,(11):40-45.
[9]Movchen B A,Lemkey F D. Some approaches to producing microporous materials and coatings by EB-PVD[J].Surface and Coatings Technology,2003,165:90-100.
[10]刘福顺,宫声凯,徐惠彬.大功率EB-PVD陶瓷热障涂层的研究与应用[J].航空学报,2002,21(增刊):30-34.
[11]武洪臣,姚振中,冯建基等.先进的涂层技术EB-PVD[J].航空制造技术,2005,13 (5):28-30.
[12]关春龙.EB-PVD设备大尺寸Ni-Cr-Al合金薄板组织及性能研究[D].哈尔滨工业大学博士论文.2005,6.
[13]徐惠彬,宫声凯,刘福顺.乌克兰巴顿焊接研究所电子束物理气相沉积技术[J].航空制造工程,1997,6:6-8.
[14]Youchison D L,Gallis M A,Nygren R E et al.Effects of ion beam assisted deposition, beam sharing and pivoting in EB-PVD processing of graded thermal barrier coating[J].Surface and Coatings Technology,2004,177-178:158-164.
[15]Rhys-JonesTN.The use of thermally sprayed coatings for compressor and turbine application in aeroengines. Surface and Coatings Technology,1990,42:1-11.
[16]李美姮,胡望宇,孙晓峰,等.热障涂层的研究进展与发展趋势[J].材料导报,2005, 19(4):41-45.
[17]徐惠彬,宫声凯,陶冶,等.电子束物理气相沉积技术及其应用现状[J].航空制造工程,1995,11:23-25.
[18]胡传顺,王福会,吴维.热障涂层研究进展.2000,12(3):160~163.
[19]沈成康.断裂力学.上海:同济大学出版社,1996.
[20]Williams M L. The stress around a fault or crack in dissimilar media. Bulletin of the seismological society of America, 1959, 49(2): 199-204.
[21]Williams M L. On the stress distribution at the base of a stationary crack. Journal of applied mechanics. Trans. ASME, 1957,79: 109-114.
[22]Zak A R, Williams M L. Crack point stress singularities at a bi-material interface. Transactions of the ASME, 1963, 30: 142-143.
[23]Erdogan Fazil. Stress Distribution in a Nonhomogeneous elastic plane with cracks. Transactions of the ASME, 1963, 30: 232-236.
[24]Sih G C, Rice J R. The bending of plates of dissimilar materials with cracks. Journal of applied mechanics, 1964, 31: 477-482.
[25]Rice J R, Sih G C. Plane problems of cracks in dissimilar media. Transactions of the ASME, 1965, 32: 418-423.
[26]Park J H, Earmme Y Y. Application of conservation integrals to interfacial crack problems. Mechanics materials, 1986(5): 261-276.
[27]Shih C F, Asaro R. Elastic-plastic analysis of crack on bimaterial interfaces; Part I: Small scale yielding. Journal of applied mechanics. Transactions ASME, 1988, 55(2): 299-313.
[28]Hutchinson J W, Wear M, Rice J R. Crack paralleling an interface between dissimilar materials. Journal of applied mechanics. Transactions ASME 1987, 54(4): 828-832.
[29]Rice JR, Sih G C. Mathematical analysis in the mechanics of fracture. Fracture: An advance treatise. H.Liebowitz, ed., 1968, l2: 17-26.
[30]Cherepanov G P. The stress state in a heterogeneous plate with slits. In Russian, Izvestia AN SSSR, OTN, Mekhan. i Mashin. 1962, Vol.1: 131-137.
[31]Cherepanov G P. Mechanics of brittle fracture. McGraw-Hill, New York, 1979.
[32]England A H. A crack between dissimilar media. Journal of applied mechanics, 1965(32): 400-402.
[33]Erdogan F. Stress distribution in bonded dissimilar materials with cracks. Journal of applied mechanics, 1965(32): 403-410.
[34]Rice J R. Elastic fracture mechanics concepts for interfacial cracks. Journal of applied mechanics.Transactions of the ASME, 1988, 55 (1): 98-103.
[35]Comninou M. The interface crack. Journal of applied mechanics. Transactions of the ASME, 1977, 44(4): 631-636.
[36]Comninou M. Interface crack with friction in the contact zone. Journal of applied mechanics.Transactions of the ASME, 1977, 44 (4): 780-781.
[37]Comninou M, Schmueser D. The interface crack in a combined tension-compression and shear field. Journal of applied mechanics. Transactions of the ASME, 1979, 46(2): 345-348.
[38]Malyshev B M, Salgnik R L. The strength of adhesive joints using the theory of crack. International journal fracture mechanics, 1965, 1: 114-128.
[39]Hutchinson J W.Singular behavior at the end of a tensile crack in a hardening material.Mech.Phys.Solids,1968,16:13-31.
[40]Smelser R E. Evaluation of stress intensity factors for bimaterial bodies using numerical crack flank displacement data. Interational journal of fracture, 1979, 15(2): 135-143.
[41]Matos P P L, McMeeking R M, Charalambides P G. et al. Method for calculating stress intensities in bimaterial fracture. International Journal of Fracture, 1989, 40(4): 235-254.
[42]Muller D, Cho YR, Berg S. et al. Fracture Mechanics Tests for Measuring the Adhesion of Magnetron Sputtered TiN coatings. International Journal of Refractory Metals & Hard Materials, 1996(14): 207-211.
[43]Qian G., Nakamura T, Berndt C.C. Tensile Toughness Test and High Temperature Fracture Analysis of Thermal Barrier Coatings. Acta Materialia, 1997, 45 (4): 1767-1784.
[44]Eshelby J D, Read W T, Shockley W. Anisotropic elasticity with applications to dislocation theory. Acta Metallurgica, 1953, 1: 251-259.
[45]Stroh A N. Dislocations and cracks in anisotropic elasticity. Philosophical Magazine, 1958, 7: 625-646.
[46]Tang T C T. Explicit solution and invariance of the singularities at an interface crack in anisotropic composites. International Journal of Solids and Structures, 1986, 22(9): 965-83.
[47]Qu J, Li Q. Interfacial dislocation and its applications to interface cracks in anisotropic bimaterials. Journal of Elasticity, 1991, 26(2): 169-195.
[48]Atkinson C, Eftaxiopoulos D A. Interaction between a crack and a free or welded boundary in media with arbitrary anisotropy. International Journal of Fracture, 1991, 50(3): 159-182.
[49]Civelek M B, Erdogan F. Crack problems for a rectangular plate and an infinite stripSource: International Journal of Fracture, 1982,19(2): 139-59.
[50]Suo Zhigang. Delamination specimens for orthotropic materialsSource: Transactions of the ASME. Journal of Applied Mechanics, 1990, 57(3): 627-634.
[51]Suo Zhigang, Hutchinson J W. Interface crack between two elastic layersSource.International Journal of Fracture, 1990, 43(1): 1-18.
[52]Jagannadham K, Marcinkowski M J. Surface dislocation model of a finite stressed solid. Material Science and Engineering, 1979, 38(3): 259-270.
[53]Huang Haiying, Kardomateas G A. Single-edge and double-edge cracks in a fully anisotropic strip.Transactions of the ASME. Journal of Engineering Materials and Technology, 1999, 121(4): 422-429.
[54]O’Brien T K, Hooper S J. Local delamination in laminates with angle ply matrix cracks, Part I: Tension tests and stress analysis. In: Stinchcomb, W.W., Ashbaugh, N.E.(Eds.), Composite Materials: Fatigue and Fracture, vol,4, ASTM STP 1156, American Society for Testing and Materials, Philadelphia, 491-506.
[55]Qian W, Sun C T. Calculation of stress intensity factors for interlaminar cracks in composite laminates. Composites Science and Technology, 1997, 57(6): 637-650.
[56]Cao H C, Evans A G. An experimental study of the fracture resistance of bimaterial interfaces. Mechanics of materials. 1989, 7(4): 295-304.
[57]Evans A G., Hutchinson J W. Effects of non-planarity on the mixed mode fracture resistance of bimaterial interfaces. Acta Metallurgica. 1989, 37(3): 909-916.
[58]Charalambides P G, Lund J, Evans A G. et al. A test specimen for determining the fracture resistance of bimaterial interfaces. Journal of applied mechanics. Transactions of the ASME, 1989, 56(1): 77-82.
[59]Chung H G.P, Swain M V, Mori T. Evaluation of the Strain Energy Release Rate for the Fracture of Titanium-porcelain Interfacial Bonding. Biomaterials. 1997, 18 (23): 1553-1557.
[60]Li H, Khor K A, Cheang P. Young’modulus and fracture toughness determination of high velocity oxy-fuel-sprayed bioceramic coatings. Surface and Coatings Technology, 2002, 155(1): 21-32.
[61]G.C. Shih. Mechanics of Fracture Initiation and Propagation, Kluwer Academic, USA, 1991.
[62]O'Dowd N P, Shih C F, Stout M G. Test geometries for measuring interfacial fracture toughness. International Journal of Solids and Structures, 1992, 29(5): 571-589.
[63]Becker Jr T L, McNaney J M, Cannon R M et al. Limitations on the use of the mixed-mode delaminating beam test specimen: effects of the size of the region of K-dominance. Mechanics of Materials, 1997, 25(4): 291-308.
[64]Oh Tae Sung, Cannon R M, Ritchie R O. Subcritical crack growth along ceramic-metal interfaces. Journal of the American Ceramic Society, 1987, 70(12): C352-C355.
[65]Cannon R M, Dalgleish B J, Dauskardt R H et al. Cyclic fatigue-crack propagation along ceramic/metal interfaces. Acta Metallurgica et Materialia, 1991,39(8): 2145-2156.
[66]Thun G, Schneider G A, Bahr H-A et al. Toughness Anisotropy and Damage Behavior of Plasma Sprayed ZrO2 Thermal Barrier Coatings. Surface and Coatings Technology, 2000, 123(2-3): 147-158.
[67]Dornowski Wojciech, Perzyna Piotr. Numerical analysis of macrocrack propagation along a bimaterial interface under dynamic loading processes. International Journal of Solids and Structures, 2002, 39(19): 4949-4977.
[68]Moran B, Shih C F. A General Treatment of crack Tip Integrals. International Journal of Fracture, 1987, 35 (4): 295-310.
[69]Moran B, Shih C F. Crack Tip and Associated Domain Integrals from Momentum and Energy Balance. Engineering Fracture Mechanics, 1987, 27 (6): 615-642.
[70]Li F Z, Shih C F, Needleman A. A Comparison of Methods for Calculating Energy Release rates. Engineering Fracture Mechanics, 1985, 25 (2): 405-421.
[71]Shih C F, Moran B, Nakamura T. Energy Release Rate along a Three-dimensional Crack Front in a Thermally Stressed Body. International Journal of Fracture, 1986, 30 (2): 79-102.
[72]Nikishkov G P, Atluri S N. Calculation of Fracture Mechanics Parameters for an Arbitrary Three-dimensional Crack by the‘Equivalent Domain Integral Method’. International Journal for Numerical Methods in Engineering, 1987, 24 (9): 1801-1821.
[73]Shih C F, Asaro R J. Elastic-plastic Analysis of Cracks on Bimaterial Interfaces: Part I-Small Scale Yielding. Transactions of the ASME. Journal of Applied Mechanics, 1988, 55(2): 299-316.
[74]Nakamura T. Three-dimensional Stress Fields of Elastic Interface Cracks. Transactions of the ASME. Journal of Applied Mechanics, 1991, 58 (4): 939-946.
[75]Nakamura T, Parks D M. Determination of Elastic T-stress along Three-dimensional Crack Front Using Interaction Integral. International Journal of Solids and Structures. 1992, 29(13): 1597-1611.
[76]Charalambides P G, Evans AG. Debonding Properties of Residually Stressed Brittle-matrix Composites. Journal of the American Ceramic Society. 1989, 72(5): 746-753.
[77]陈孟成,吴凤筠,沈文雁.陶瓷热障涂层和热循环试验研究,材料工程,1999/04.
[78]Edward H,Goldman,Ramgopal Darolia.U.S.Patent,Number5,316,866,1993.
[79]Timoshenko S P, James M Gere. Mechanics of Materials. Van Nostrand Reinhold Co., Inc., Molly Millars Lane, Workingham, Berkshire, England.
[80]Y.C.Zhou,T.Hashida.Coupled effects of temperature gradient and oxidation on thermal stress in thermal barrier coating system [J].International Journal of Solidsand Structures 38(2001)4235-4264.
[81]曹学强,热障涂层材料[M],北京:科学出版社,2007.
[82]Smeylser R E, Gurtin M E. On the J-integral for biomaterial bodies. Internation- al Journal of Fracture, 1971, 13: 382-384.
[83]刘刘,杨晓光,耿瑞. TBC界面裂纹K因子的有限元求解方法.航空动力学报, 2001, 16(2):16-174.
[84]Hutchinson J W. Fundamentals of the phenomenological theory of nonlinear fracture mechanics. Journal of Applied Mechanics, 1983, 50(4b): 1042-1050.
[85]Rice J R. A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics, 1968, 35: 379-386.
[86]Hutchinson J W. Singular behavior at the end of a tensile crack tip in a hardening material. Journal of Mechanics and Physics of Solids, 1968, 16(1): 13-31.
[87]Parks D M. The virtual crack extension method for nonlinear material behaviour. Computer Methods in Applied Mechanics and Engineering, 1977, 12(3): 353-364.
[88]Hellen T K. On the method of virtual crack extensions. International Journal for Numerical Methods in Engineering, 1975, 9(1): 187-196.
[89]Nakamura T, Shih C F, Freund L B. Analysis of a dynamicaly loaded three-point-bend ductile fracture specimen. Engineering Fracture Mechanics, 1986, 25(3): 323-339.
[90]Li F Z, Shih C F, Needleman A. A comparison of methods for calculating energy release rates. Engineering Fracture Mechanics, 1985, 21(2): 405-21.
[91]Shih C F, Moran B, Nakamura T. Energy release rate along a three-dimensional crack front in a thermally stressed body. International Journal of Fracture, 1986, 30(2): 79-102.
[92]de Lorenzi H G. On the energy release rate and the J-integral for 3D crack configurations. International Journal of Fracture, 1982, 19(3): 183-193.
[93]雷和荣,虞吉林.虚裂纹扩展法计算J积分的研究.中国科学技术大学学报, 1994, 24(2): 201-213.
[94]杨新岐,霍立兴,张玉凤.三维能量释放率虚拟裂纹扩展算法及工程应用.天津大学学报, 1997, 30(1): 37-42.
[95]王利民,陈浩然. J积分在多层介质中的守恒性和其应用.应用数学和力学. 2001, 22 (10):1097-1104.
[96]C633-79 Standard Test Method for Adhesion of Cohesive Strength of Flame- Sprayed Coatings, Annual Book of ASTM Standards, Vol.03.01, 1993, P.665.
[97]Elssner G, Suga T, Turwitt M. Fracture of ceramic-to-metal interfaces. Journal dePhysique Colloque, 1985, 46 (C-4): 597-612.
[98]Han W, Rybicki E F, Shadley J R. In Thermal Spray Coating: Research, Design and Application (edited by C.C. Berndt and T.E. Bernecki), 1993. 55.
[99]徐连勇,涂层/基体界面的断裂行为研究:[博士学位论文],天津;天津大学,2006