孔穴不稳定增长导致高聚物电子封装材料“爆米花”失效的弹塑性理论研究
|
摘要
高密度集成电子技术的迅速发展对电子封装可靠性的要求日趋提高。高聚物电子封装材料在回流焊过程中的“popcorn”失效严重影响了产品的合格率,是电子封装领域关注的热点之一。本文利用非线性材料有限变形的基本理论对“popcorn”失效进行了弹-塑性分析和数值计算。本文的主要工作及获得的结果如下:
1.对方形扁平封装(QFP)、球栅阵列封装(BGA)等封装器件中常用的GR9810和KL-G900HC高聚物材料进行了热分析实验。测得两类典型材料的热膨胀系数与玻璃态转化温度。为采用有限变形孔穴不稳定理论对“popcorn”失效研究提供了必要的实验支持。
2.利用孔穴不稳定增长问题的基本理论,对七类具有典型储能形式的高聚物材料的“popcorn”失效进行了弹性分析。推导了各材料中的孔穴增长与湿热应力之间的解析关系。对解析关系的数值分析发现是否发生“popcorn”失效与储能函数的形式紧密相关。对于发生失效的高聚物材料,讨论了“popcorn”失效的极限载荷与极限孔穴率与本构模型中的各储能项之间的关系。对于利用弹性稳定性理论分析不发生失效的高聚物材料,我们补充极限伸长的失效准则,分析了其“popcorn”失效的可能性。
3.考虑了温度变化对高聚物材料体积的影响,将材料的不可压缩假定修正为可压缩假定,推导了各类典型储能材料与温度相关的广义σ?f解析关系。由实验测得的热膨胀系数分析了考虑可压缩假定下“popcorn”失效的极限载荷与极限孔穴率。
4.针对“popcorn”失效问题,对具有各典型储能形式高聚物材料的孔穴增长行为进行了弹-塑性稳定性分析。推导了考虑弹-塑性特点时孔穴增长规律的控制方程组。分析了考虑高聚物材料的弹-塑性特性的“popcorn”失效问题并与弹性分析的结果进行了对比。
本文二、三、四、五章的工作是对现有的“popcorn”失效理论研究工作的系统化。第六章的工作是“popcorn”失效问题理论研究工作的进一步深入。另外本文的工作对类橡胶材料孔穴不稳定增长与空穴突然生成问题的理论研究工作的统一具有促进意义,使有限变形的稳定性理论应用到了更广泛的工程实际中。
The rapid development of high-density integrated electronic technology sets a higher request to reliability of electronic packing. During the solder-reflow process, popcorn failure of plastic electronic packages has a strong impact on proportion of qualified products, which is one of the hottest research points. In this paper, elasto-plastic analysis of popcorn failure was made and the numerical results were given by using nonlinear materials’finite deformation theory. The main results contain as follows:
1. Thermal analysis of polymer materials(GR9810 and KL-G900HC) used in package devices such as QFP, BGA etc. was carried out. The coefficients of thermal expansion and glass transition temperature were obtained, which provide necessary lab support for applying finite deformation theory about unstable void growth to analyze popcorn failure.
2. Popcorn failure about seven kinds of typical polymer materials which have different strain energy functions under elastic stage was analyzed according to finite deformation theory about unstable void growth. Analytical relationships were gained between void growth and the sum of the vapor pressure and thermal stress. Numerical analyses show that popcorn failure is related to stored energy function closely. The relations between critical values and energy storage forms were discussed when popcorn failure occurred. If popcorn failure didn’t happen, we added failure criterions of ultimate elongation to discuss the probability of popcorn failure.
3. The assumption of materials' incompressibility was revised to compressibility when the effect of temperature change on the volume of polymer materials was taken under consideration, and the generalized temperature-dependent relationship forσ?f was given. Critical traction and void growth for popcorn failure were discussed by measurement of thermal expansion coefficient.
4. In view of the problem of popcorn failure, the void growth behavior of polymer materials which have typical strain energy functions respectively was analyzed according to by using elasto-plastic stability theory. The governing equations of void growth considering elasto-plastic property were given. The elasto-plastic analysis and elastic analysis of popcorn failure about polymer materials was carried out.
The chapter 2 to chapter 5 of this paper make the present theoretical research on popcorn failure systematic. The chapter 6 makes theoretical research on popcorn failure further. In addition, this paper can promote harmonization of theories research on void formation and growth, and bring stability theory of finite deformation into boarder use in engineering.
1.对方形扁平封装(QFP)、球栅阵列封装(BGA)等封装器件中常用的GR9810和KL-G900HC高聚物材料进行了热分析实验。测得两类典型材料的热膨胀系数与玻璃态转化温度。为采用有限变形孔穴不稳定理论对“popcorn”失效研究提供了必要的实验支持。
2.利用孔穴不稳定增长问题的基本理论,对七类具有典型储能形式的高聚物材料的“popcorn”失效进行了弹性分析。推导了各材料中的孔穴增长与湿热应力之间的解析关系。对解析关系的数值分析发现是否发生“popcorn”失效与储能函数的形式紧密相关。对于发生失效的高聚物材料,讨论了“popcorn”失效的极限载荷与极限孔穴率与本构模型中的各储能项之间的关系。对于利用弹性稳定性理论分析不发生失效的高聚物材料,我们补充极限伸长的失效准则,分析了其“popcorn”失效的可能性。
3.考虑了温度变化对高聚物材料体积的影响,将材料的不可压缩假定修正为可压缩假定,推导了各类典型储能材料与温度相关的广义σ?f解析关系。由实验测得的热膨胀系数分析了考虑可压缩假定下“popcorn”失效的极限载荷与极限孔穴率。
4.针对“popcorn”失效问题,对具有各典型储能形式高聚物材料的孔穴增长行为进行了弹-塑性稳定性分析。推导了考虑弹-塑性特点时孔穴增长规律的控制方程组。分析了考虑高聚物材料的弹-塑性特性的“popcorn”失效问题并与弹性分析的结果进行了对比。
本文二、三、四、五章的工作是对现有的“popcorn”失效理论研究工作的系统化。第六章的工作是“popcorn”失效问题理论研究工作的进一步深入。另外本文的工作对类橡胶材料孔穴不稳定增长与空穴突然生成问题的理论研究工作的统一具有促进意义,使有限变形的稳定性理论应用到了更广泛的工程实际中。
The rapid development of high-density integrated electronic technology sets a higher request to reliability of electronic packing. During the solder-reflow process, popcorn failure of plastic electronic packages has a strong impact on proportion of qualified products, which is one of the hottest research points. In this paper, elasto-plastic analysis of popcorn failure was made and the numerical results were given by using nonlinear materials’finite deformation theory. The main results contain as follows:
1. Thermal analysis of polymer materials(GR9810 and KL-G900HC) used in package devices such as QFP, BGA etc. was carried out. The coefficients of thermal expansion and glass transition temperature were obtained, which provide necessary lab support for applying finite deformation theory about unstable void growth to analyze popcorn failure.
2. Popcorn failure about seven kinds of typical polymer materials which have different strain energy functions under elastic stage was analyzed according to finite deformation theory about unstable void growth. Analytical relationships were gained between void growth and the sum of the vapor pressure and thermal stress. Numerical analyses show that popcorn failure is related to stored energy function closely. The relations between critical values and energy storage forms were discussed when popcorn failure occurred. If popcorn failure didn’t happen, we added failure criterions of ultimate elongation to discuss the probability of popcorn failure.
3. The assumption of materials' incompressibility was revised to compressibility when the effect of temperature change on the volume of polymer materials was taken under consideration, and the generalized temperature-dependent relationship forσ?f was given. Critical traction and void growth for popcorn failure were discussed by measurement of thermal expansion coefficient.
4. In view of the problem of popcorn failure, the void growth behavior of polymer materials which have typical strain energy functions respectively was analyzed according to by using elasto-plastic stability theory. The governing equations of void growth considering elasto-plastic property were given. The elasto-plastic analysis and elastic analysis of popcorn failure about polymer materials was carried out.
The chapter 2 to chapter 5 of this paper make the present theoretical research on popcorn failure systematic. The chapter 6 makes theoretical research on popcorn failure further. In addition, this paper can promote harmonization of theories research on void formation and growth, and bring stability theory of finite deformation into boarder use in engineering.
引文
[1] Moore G E. Cramming more components on integrated circuits[J]. Electronics, 1965, 38(8): 144-147.
[2]Zhang G Q. The Challenges of Nanoelectronics for Reliability[C].IEEE 7th Internationl conference on electronic packaging technology. Shanghai: Institute of Electrical and Electronics Engineers inc, 2006:16-18.
[3]毕克允.电子与封装[J].把握“十一五”契机推进封装业持续发展. 6( 6):1-2.
[4]Tummala等著,电子封装丛书编辑委员会组织译校.微电子封装手册[M].北京:电子工业出版社,2001,1-30.
[5]Tummala著,黄庆安,唐洁影译.微系统封装基础[M].南京:东南大学出版社,2005:16-18.
[6] Zhang G Q, Fan X J.Mechanics of Microelectronics[M]. Dordrecht :Springer,2006:1-10.
[7]鲜飞. CPU芯片封装技术的发展演变[J].IC工程, 2004, 11: 60-61.
[8]Zhang G Q. More than Moore-The changing international landscape, strategy and solutions of micro/nanoelectronics[R].太原:太原理工大学,2007.
[9]Zhang G Q, Tay A A O, Ernst L J, etc. Virtual Thermo-Mechanical Prototy-ping of Electronic Packaging-Challenges in material characterization and modeling[C]. Electronic Components and Technology Conference Proceedings 51st, 2001:1479-1486.
[10]王珺,含湿热的耦合粘弹性本构、断裂及应用[D].成都:西南交通大学,2002.
[11]徐步陆.电子封装可靠性研究[D].上海:中国科学院上海微系统与信息技术研究所,2002.
[12]彩霞.高密度电子封装可靠性研究[D].中国科学院上海微系统与信息技术研究所,2002.
[13]Lau J H, Lee S W R, Chang C. Effects of underfill material properties on the reliability of solder bumped flip chip on board with imperfect underfill encapsulants[J]. IEEE Trans Compon Packag Technol, 2000, 23 (2) : 323-328.
[14] Cheng Z N, etc. Influences of packaging materials on solder joint reliability of chip scale package assemblies[C] . International Symposium on Advanced packaging Materials, Braselt-on,Georgia ,1999 :144-150.
[15] Cheng Z N, Cai X, Chen L , etc. Thermal fatigue failure analysis of SnPb solder bumped flip chip on low-cost board with and without underfill encapsulants[C]. Proceedings of the Fourth International Symposium on Electronic Packaging Technology, 2001: 403-450.
[16] Cheng Z N, Xu B, Zhang Q , et al. Underfill delamination analysis of flip chip on low cost board[C]. Proceedings of 2001 International Symposium on Electronic Materials & Packaging,2001: 280-288.
[17]徐步陆,张群,程兆年.倒装焊底充胶分层和焊点失效[J].半导体学报. 2001, 37(10) 1135-1140.
[18] Desai C.S. , Whitenack R. Review of models and the disturbed State concept for thermo mechanical analysis in electronic packaging[J]. Journal of Electronic Packaging, 2001,123(1):19-33.
[19]Evans A.G.,Hutchinson J.W. Thermo mechanical integrity of thin films and multilayers[J]. Acta Metallurgica et Materialia.1995. 43(7): 2507-2530.
[20]Crank J, Park G S. Diffusion in Polymers [M].London : Academic Press, 1968: 1-39.
[21]Crank J. The mathematics of diffusion[M]. Oxford, [Eng] :Clarendon Press,1975:1-40.
[22]Schapery R A, Sun C T. Time dependent and nonlinear effects in polymers and composites[C].Proceedings of the ASTM Symposium, Atlanta, 1998:353- 377.
[23]Browning C E. The mechanisms of elevated temperature property losses in high performance structural epoxy resin matrix materials after exposure to high humidity environments[J]. Polymer Engineering & Science, 1978,1(1): 18-24.
[24]Malyshev B M, Salganik R L. The strength of adhesive joints using the theory of cracks[J]. International Journal of Fracture Mechanics, 1965,1: 114-128.
[25]Belton D J, Sullivan E A, Molter M J. Moisture sorption and its effects upon the microstructure of epoxy moulding compounds[C], Proc.3rd Int.Electron. Manufact. Technol. Symp., 1987:158-169.
[26]Brewis D M, Comyn J, Cope B C, etc. Effect of carrier on the performance of aluminum alloy joints bonded with a structural film adhesive. Polymer Engineering & Science, 1981, 21(12): 797-803.
[27]De'N eve B, Shanahan M E R. Water absorption by an epoxy resin and its effect on themechanical properties and infra-red spectra. Polymer, 1993,34(24): 5099-5105.
[28]Wong E H, Teo Y C, Lim T B. Moisture diffusion and vapor pressure modeling of IC packaging[C]. Proceedings of Electronic Components and Technology Conference, 1998:1372-1378.
[29]Wong E H, Koh S W, Lee K H. Advanced moisture diffusion modeling and characterization for electronic packaging[C]. Proceedings of Electronic Components and Technology Conference, 2002:1297-1303.
[30]Kitano M, Nishimura A, Kawai S. Analysis of packages cracking during reflow soldering process[C]. IEEE International Reliability Physics Symposium, Monterey, 1988: 90-95.
[31]Tay A A O, Lin T .Moisture diffusion and heat transfer in plastic IC packages[J]. IEEE Components Packaging and Manufacturing Technology, 1996, 19(2): 186-193.
[32]Tee T Y, Ng H S. Whole field pressure modeling of QFN during reflow with coupled hygro-mechanical and thermo-mechanical stresses[C]. IEEE 52nd Proceedings of Electronic Components and Technology Conference, 2002: 1552-1559.
[33]Lam T F. FEA simulation on moisture absorption in PBGA packages under various moisture pre-conditioning[C]. Electronic Components and Technology Conference, 2000: 1078-082.
[34]Fan X J, Tee T Y, Lim T B. Modeling of whole field vapor pressure during reflow for flip chip BGA and wire-bond PBGA packages[C]. 1st International Workshop on Electronic Materials and Packaging, Singapore, 1999: 38-45.
[35]S Ning, Lin D, Yang D. Analysis of thermal-moisture induced failure of Pb-free soldered IC packages in SMT reflow soldering process[C]. IEEEE 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and MicroSystems, EuroSimE,2004:341-344.
[36]S Ning, Lin D, Yang D. Finite element analysis of hygro-thermal induced failure in plastic packages[C]. IEEE 5th International Conference on Electronic Packaging Technology Proceedings, ICEPT 2003: 381-385.
[37]巫松,蒋迁彪,杨道国. PBGA器件潮湿扩散和湿应力的有限元分析[J].电子元件与材料,2004,23(6):42-44.
[38]彩霞,黄卫东,徐步陆.电子封装材料中水的形态[J].材料研究学报,2002,16(5): 507-511.
[39]Galloway J E, Miles B M. Moisture absorption and desorption predictions for plastic ball grid array packages[J]. IEEE Components, IEEE Packaging and Manufacturing Technology, 1997, 20(3):274-279.
[40]Stellrecht E, Hand B, Pecht M G. Characterization of hygroscopic swelling behavior of mold compounds and plastic packages[J]. IEEE Compounds and packaging Technologies, 2004, 27(3): 499-506.
[41]Ardebili H, Wong E H, Pecht M. Hygroscopic swelling and sorption characteristics of epoxy molding compounds used in electronic packaging[J]. IEEE Components and Packaging Technologies, 2003, 26 (1): 206-214.
[42]Wong E H, Rajoo R, Lim T B. The mechanics and impact of hygroscopic swelling of polymeric materials in electronics packaging[J]. ASME Journal of Electronic Packaging, 2002: 124-126.
[43]Wong E H, Koh S W, Rajoo R, etc. Underfill swelling and temperature-humidity performance of flip chip PBGA package[C]. Proceedings of Electronics Packaging Technology Conference, 2000: 258-262.
[44]Stellrecht E, Han B, Pecht M. Measurement of the hygroscopic swelling coefficient in mold compounds using Moire interferometry[J]. Experimental Techniques, 2003, 27(4): 40-44.
[45]Stellrecht E, Han B. Measurement of hygroscopic swelling in mold compounds and its effect on PEM reliability[C]. ASME International Electronics Packaging Technology Conference and Exhibition, 2003: 497-502.
[46]Chen X, Zhao S F, Zhai L. Moisture absorption and diffusion characterization of molding compound[J]. ASME Trans Journal of Electronic Packaging .2005, 127(4): 460-465.
[47]Ardebili H, Hillman C, Natishan A E. A comparison of the theory of moisture diffusion in plastic encapsulated microelectronics with moisture sensor chip and weigh-gain measurements[J]. IEEE Components and Packaging Technologies, 2000, 25(1): 132-139.
[48]Ken H, Saka M. Measurement of water absorption in ball grid array package[J]. IEEE Components and Packaging Technologies, 2002, 25(1): 164-168.
[49]别俊龙.电子塑封器件中湿气吸收及扩散的相关研究[D].北京:清华大学,2006.
[50]Fukuzawa I, Ishiguro S, Nanbu S. Moisture resistance degradation of plastic LSI’s by reflow soldering[C]. IEEE Proc IRPS, 1985:192-197.
[51]Pecht M G ,Govind A. In-situ measurements of surface mount IC Package deformations during reflow soldering[J]. IEEE Transactions on Components, Packaging, & Manufacturing Technology Part C: Manufacturing, 1997: 207-212.
[52]Gektin V, Bar-Cohen A. Mechanistic figures of merit for die-attach materials[C]. In Inter-Society Conference on Thermal Phenomena in Electronic Systems, 1996: 306-313.
[53]Lau, J H. Ball grid array technology[C]. Electronic packaging and interconnection series. 1995: 636-638.
[54]Nguyen L T, Chen K L, Schaefe J. A new criterion for Package integrity under solder reflow conditions[C]. In 45th ECTC,1995: 478-490.
[55]Liu S, Mei Y.Behavior of delaminated Plastic IC Packages subjected to encapsulation cooling, moisture absorption, and wave soldering[J]. IEEE Transactions on Components Packaging & Manufacturing Technology PartA, 1995,18(3): 634-645.
[56]Tanaka N, Kitano M T, Kumazawa, etc. Evaluation of interface delamination in IC Packages by considering swelling of the molding compound due to moisture absorption[C]. In 47th ECTC. 1997:120-122.
[57]Lin T Y, Tay A O. Dynamics of moisture diffusion, hygrothermal stresses and delamination in plastic IC packages[J]. ASME Advances in Electronic Packaging, 1997, 19(1): 1429-1436.
[58]Wong E H., Chan K C. Compasive treatment of moisture induced failure in IC packaging[C]. In 3rd IEMT, 1999:822-832.
[59]Tay A O, Lin T Y. Moisture-induced interfacial delamination growth in plastic IC packages during solder reflow[C]. Proceedings-Electronic Components and Technology Conference,1998: 371-378.
[60]Lam D C, Wang J, Yang F. The role of steam evaporation in interfacial failures in electronics packages[C]. In International Conference on Materials for Advanced Technologies. Singapore, 2001: 352-360.
[61]王珺,杨帆,陈大鹏.湿热导致电子元件封装脱层断裂的分析[J].西南交通大学学报,2002,37(2):125-128.
[62]Fan X J, Zhang G Q, Ernst L J. A micro-mechanics approach for polymeric material failures in microelectronic packaging[C]. 3rd International Conference on Thermal and Thermo-mechanical Simulation in Microelectronics, France, 2002:5-15.
[63]Fan X J, Lim T B. Mechanism analysis for moisture-induced failure in IC packages[C]. In:ASME International Mechanical Engineering Congress & Exposition, 11th Symposium on Mechanics of surface Mount Technology. Nov, 1999:311-321.
[64]Fan X J, Zhou J, Zhng G Q, etc.A micromechanics-based vapor pressure model in electronic packages[J]. ASME Journal of Electronics Packaging, 2005, 127: 262-267.
[65]Fan X J. Mechanism-based delamination prediction during reflow with moisture preconditioning[C].Proceeding of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Micro-electronic and Micro-System, EuroSimE, 2004: 329-335.
[66]Fan X J. Analytical solution for moisture-induced interface delamination in electronic packaging[C]. Proceedings of Electronic Components and Technology Conference, 2003: 733-738.
[67]Fan X J. Modeling of vapor pressure during reflow for electronic packages[C]. ESIME2000. Kluwer Academic, Boston, MA, 2000: 75-92.
[68]Guo T F, Cheng L. Thermal and vapor pressure effects on cavitation and void growth.[J] Journal of Materials Science 2001, 36 (24):5871-5879.
[69]Guo, T F, Cheng L. Modeling vapor pressure effects on void rupture and crack growth resistance[J]. Acta Materialia ,2002,50 (13):3487-3500.
[70]Guo T F, Cheng L. Vapor pressure and void size effects on failure of a constrained ductile film[J]. Journal of the Mechanics and Physics of Solids ,2003,51(6):993-1014.
[71]任九生.非线性材料中的空穴生成与增长问题[D].上海:上海大学,2003.
[72] Rivlin R S. Finite elasticity[M].ASME-AMD, New York:ASME, 1977:110-127.
[73]Ogden R W . Extremum principles in non-linear elasticity and their application to composites—I : Theory[J] . International Journal of Solids and Structures, 1978, 14( 4): 265- 282.
[74]Gent A N, Lindley P B. Internal rupture of bonded rubber cylinders in tension [J ] . Proc R Soc Lond, 1958 , A249 :195-205.
[75]Williams M L, Schapery R A. Spherical flaw instability in hydrostatic tension[J], Internat -ional Journal of Fracture,1965,1(1): 64 -71. [76 ]Ball J M. Discontinuous equilibrium solutions and cavitations in nonlinear elasticity [J ] . Philos Trans Roy Soc Lond Ser A, 1982 , 306(3) : 557-611.
[77]Horgan C O, Abeyaratne R .A bifurcation problem for a compressible non- linearly elastic medium : growth of a micro-void[J], Journal of Elasticity, 1986, 16(1):189 -200.
[78]Sivaloganothan J.Uniqueness of regular and singular equlibrium for spherically symmetr -ic problems of nonlinear elasticity[J],Arch. Rat. Mech. Anal., 1986,96(1):97-136.
[79]Horgan C O, Polignone D A. Cavitation in nonlinearly elastic solids[J]. A review,Applied Mechanics Review,1995,48(2):471-485.
[80]程昌钧,尚新春.超弹性矩形板单向拉伸时微孔的增长[J].应用数学和力学, 1997, 18(7):573-579.
[81]尚新春,程昌钧.弹性固体材料中的空穴萌生与增长[J].北京科学技术大学,2002, 24(3):380-382.
[82]任九生,程昌钧.不可压超弹性材料中的空穴分叉[J].应用数学和力学,2002,23(8) : 783-789.
[83]任九生,程昌钧,朱正佑.可压超弹性材料组合球休中心的空穴生成[J],应用数学和力学, 2003, 24(9):892-898.
[84]任九生,程昌钧.多孔Mooney-Riviin材料矩形板的单向拉伸[J].力学季刊, 2003, 23(3):347-353.
[85]程昌钧,任九生.横观各向同性多孔超弹性矩形板的单向拉伸[J].应用数学和力学, 2003, 24:675-683.
[86]任九生,程昌钧.超弹性材料中空穴的动态生成[J].固体力学学报, 2004, 25(1): 42-46.
[87]程昌钧,任九生.非线性材料中空穴生成和增长问题的一些进展[J].自然杂志,2004, 26(1):1-6.
[88]Murhy J G, Biwa S. Nonmontonic cavity growth in finite, compressible elasticity[J]. International Journal of Solid and Structures, 1997, (34):3859-3872.
[89]Ren Jiu-sheng , Cheng Chang-jun. Bifurcation of cavitation solutions for incompressible transversely isotropic hyper-elastic materials[J] . Journal Engineering Mathematics, 2002, 44 (5):245-257.
[90]Shang Xin-chun, Cheng Chang-jun. Cavition in Hookean elastic membranes[J], Acta Mechanica Solida Sinica, 2002,15(1):89-94.
[91]Yuan Xue-gang, Zhu Zheng-you, Cheng Chang-Jun. Qualitative analyses of Spherical cavity nucleation and growth for incompressible generalized Valanis - landel hyperelastic material[J]. Acta Mechanical Solida Sinica, 2004,17(2):158-165.
[92]Yuan Xue-gang, Zhang Ruo-jing. Effect of constituive parameters on cavity formation and growth in a class of incompressible transversely isotropic nonlinearly elastic solid spheres [J] . Computers,Materials & Continua , 2005, 2:201- 211.
[93]Yuan Xue-gang, Zhu Zheng-you, Cheng Chang-jun. Study on cavitated bifurcation problem for sphere composed of hyper-elastic materials[J] , Journal of Engineering Mathemat -ics, 2005,51:15-34.
[94]金明,黄克服,武际可. Poisson比为1/ 2材料中球形空穴突变和球形空穴萌生的分岔问题研究.应用数学和力学[J],1999,20(8):867-873.
[95]唐立强,范志强,杨勇.哈尔滨工程大学学报[J].不可压缩球体的空穴和叉,2005, 26(5):624-627.
[96]Fu Y B, Ogden R W. Nonlinear Elasticity: Theory and Applications [M].Cambridge, UK:Cambridge University Press, 2001:1-20.
[97]Charles A Harper著,沈桌身,贾松良译.电子封装材料与工艺[M].北京:化学工业出版社,2006:476-510.
[98]Zhou Jiang .Transient analysis on hygroscopic swelling characterization using sequential- lly coupled moisture diffusion and hygroscopic stress modeling method[J] .Microelectronics Reliability, 2008,48(6): 805-810.
[99]匡震邦.非线性连续介质力学[M].上海:上海交通大学出版社,2002:179-196.
[100]I.M著,漆宗能译.固体高聚物的力学性能[M].北京:科学出版社,1988:1-90.
[101]黄筑平.连续介质力学基础[M].北京:高等教育出版社,2003:60-80.
[102]Treloar L R G .The mechanics of rubber elasticity[J]. Proc Roy SocLond, 1976,A351:301-330.
[103] Treloar L R G. The elasticity of a network of long chain molecules ( I and II)[J]. Trans -actions of the Faraday Society ,1943,36:241.
[104]Wall F T .Statistical thermodynamics of rubber [J]. Journal of Chemical Physics,1942, 10(2): 485-488.
[105]Flory P J, Rechner J .Statistical mechanics of cross-linked polymer networks [J]: Journal of Chemical Physics,1943, 11:512-520.
[106]James H M, Guth E . Theory of elastic properties of rubber[J]. Journal of Chemical Physics,1943, 11:455 -481.
[107]Treloar L R G. Stress-strain data for vulcanized rubber under various types of deformation[J]. Transactions of the Faraday Society ,1944 ,40: 59.
[108]Kuhn W , Grün F. Beziehungen zwischen elastischen Kon2 stanten und Dehnungsdopp- elbrechung hochelastischer Stof2 fe[J]. Kolloid2Zeit schrift , 1942 ,101 (3) :248.
[109]Flory P J . Network structure and the elastic properties of vulcanized rubber. chemical reviews[J] ,1944 ,35 :51.
[110]Arruda E M ,Boyce M C. A There-dimensional constitutive model for the larges stretch behavior of rubber elastic materials[J]. Journal of t he Mechanics and Physics of Solids, 1993, 41(2):389-412.
[111] Thomas A G, Derham C J. The design and use of rubber bearings for vibration isolation and seismic protection of structures[J]Engineering Structures, 1980 2(3) :171-175.
[112]Treloar L R G. The elasticity of a network of long chain molecules (Ⅲ) [J]. Transactions of the Faraday Society ,1946 ,42(1) :83-93.
[113]Mooney M. A theory of large elastic deformation[J] . Journal of Applied Physics, 1940, 11(6):582-592.
[114]Rivlin R S. Large elastic deformations of isot ropic materials [A]. Philosophical Transactions of the Royal Society of London ,Physical Sciences and Engineer [C] . London , U K:1948, 491-510.
[115]Tschoegl N W. Constitutive equations for elastomers[J]. Polymer Science, 1971 A1:1959-1970.
[116]Gent A N.A new constitutive relation for rubbe[J], Rubber Chemistry and Technology,1996, 69(1):59-61.
[117]Pucci E, Saccomandi G. A note on the Gent model for rubber-like materials[J]. Rubber Chemistry and Technology, 2002,75(6):839-852.
[118]Takamizawa K, Hayashi K. Strain energy density function and uniform strain hypothesis for arterial mechanics[J].Biomech,1987,20(1):7-17.
[119]Yeoh O H. Some forms of the strain energy for rubber[J]. Rubber Chemistry and Technology, 1993,66(5):754-771.
[120]Blatz P J. The finite elastic plane strain deformation of a mooney-rivlin body[J]. International Journal of Engineering Science, 1964,2(4) 405-411.
[121]Ogden R W. Large deformation isotropic elasticity :On the correlation of theory and experiment for incompressible rubbe-rlike solids [C].Proceeding of the royal society of London, 1972a, series A 326:565-584.
[122]Ogden R W, Chadwick P. On the deformation of solid and tubular cylinders of incompressible isotropic elastic material[J]. Journal of the Mechanics and Physics of Solids, 1972, 20(2): 77-90.
[123]Ogden R W. Volume changes associated with the deformation of rubber-like solids[J]. Journal of the Mechanics and Physics of Solids, 1976, 24(6):323-338.
[124]朱艳峰.橡胶类材料硬化的本构研究与非线性有限元分析[D].广州:华南理工大学,2005.
[125]高玉臣.固体力学基础[M].北京:中国铁道出版社,1999:10-30.
[126]Boyce M C, Arruda E M. Constitutive models of rubber elasticity[J] .A review,Rubber Chemistry and Technology,2000,73:504-23.
[127]Valanis K C, Landel R F. The strain energy function of a hyper-elastic material in terms of the extension ratios[J]. Applied Physics,1967 ,38:2997.
[128]徐明.橡胶类超弹性材料本构关系研究及有限元分析[D].北京:北京航空航天大学, 2002.
[129]Ting T C T. Effects of change of reference coordinates on the stress analyses of anisotropic elastic materials[J]. International Journal of Solids and Structures.1982,18(2): 139-152.
[130]Ting T C, Yan Gongpu. The anisotropic elastic solid with an elliptic hole or rigidinclusion[J]. International Journal of Solids and Structures, 1991, 27(15): 1879-1894.
[131]Ting T C T. Recent developments in anisotropic elasticity[J]. International Journal of Solids and Structures . 2000, 37(1):401-409.
[132]Ting T C T. Three-dimensional solutions for general anisotropy[J]. Journal of the Mechanics and Physics of Solids,2007, 55(9): 1993-2006.
[133]Polignone D A, Horgan C O. Cavitation for incompressible anisotropic nonlinearly elastic spheres[J]. Journal of Elasticity,1993,33:27 -65.
[134]Zidi M. Large shearing of a prestressed tube[J]. Journal of Applied Mechanics. 2000, 67: 209-211.
[135]Zidi M. Effects of a prestress on a reinforced, nonlinearly elastic and compressible tubes subjected to combined deformations[J].International Journal of Solids and Structures.2001,38(26): 4657-4669.
[136]Zidi M, Cheref M. Finite deformations of a hyperelastic compressible and fiber-reinforced tube[J], European Journal of Mechanics - A/Solids,2002, 21(6): 971-980.
[137]Nicholson DW, Nelson N. Finite element analysis in design with rubber elasticity [J], Rubber Chem Technol.1990,63 :358-406.
[138]Nicholson D W, Lin B. Theory of thermoelasticity for bear-incompressible elastomers [J], Acta Mech.,1996,116:15-28.
[139]Horgan C O, Saccomandi Giuseppe. Finite thermoelasticity with limiting chain extensibility[J] .Journal of mechanics and physics of solids. 2003,51:1127-1146.
[140]Wu P D , Van der Giessen E.On improved network models for rubber elasticity and their applications to orientation hardening in glassy polymers[J]. Mechanics and Physics of Solids , 1993 ,41 (3):427.
[141]Marckmann G, Verron E , etc. A theory of net-work alteration for the Mullins effect[J] . Mechanics and Physics of Solids, 2002 ,50 (9) :2011.
[142]Elias-Zuniga A , Beatty M F. Constitutive equations for amended non-Gaussian network models of rubber elasticity[J]. Int Eng Sci , 2002 ,40 (20) :2265.
[143]Lim G T. Scratch behavior of polymers[D].Texas A &M University , 2005.
[144]Yuan Xue-gang, Zhu Zheng-you .Qualitative study of cavitated bifurcation for a class of incompressible generalized neo-hookean spheres[J] .Applied Mathematics and Mechanics,2005, 26 (2):185-194.
[145]Merodio Jose, Saccommandi Giuseppe. Remarks on cavity formation in fiber-reinforced incompressible non-linearly elastic solids[J] ,European journal of Mechanics A/solids 2006,25:778-792.
[146]袁学刚.具有缺陷的超弹性材料球体中的空穴分岔[D].上海:上海大学,2003.
[147]Chang W J, Pan J. Cavitation instability in rubber with consideration of failure[J]. Journal of Materials science, 2001, 36: 1901-1909.
[148]任九生,程昌钧.固体力学学报[J].热超弹性材料中的空穴生成问题, 2004, l5(3):275-277.
[2]Zhang G Q. The Challenges of Nanoelectronics for Reliability[C].IEEE 7th Internationl conference on electronic packaging technology. Shanghai: Institute of Electrical and Electronics Engineers inc, 2006:16-18.
[3]毕克允.电子与封装[J].把握“十一五”契机推进封装业持续发展. 6( 6):1-2.
[4]Tummala等著,电子封装丛书编辑委员会组织译校.微电子封装手册[M].北京:电子工业出版社,2001,1-30.
[5]Tummala著,黄庆安,唐洁影译.微系统封装基础[M].南京:东南大学出版社,2005:16-18.
[6] Zhang G Q, Fan X J.Mechanics of Microelectronics[M]. Dordrecht :Springer,2006:1-10.
[7]鲜飞. CPU芯片封装技术的发展演变[J].IC工程, 2004, 11: 60-61.
[8]Zhang G Q. More than Moore-The changing international landscape, strategy and solutions of micro/nanoelectronics[R].太原:太原理工大学,2007.
[9]Zhang G Q, Tay A A O, Ernst L J, etc. Virtual Thermo-Mechanical Prototy-ping of Electronic Packaging-Challenges in material characterization and modeling[C]. Electronic Components and Technology Conference Proceedings 51st, 2001:1479-1486.
[10]王珺,含湿热的耦合粘弹性本构、断裂及应用[D].成都:西南交通大学,2002.
[11]徐步陆.电子封装可靠性研究[D].上海:中国科学院上海微系统与信息技术研究所,2002.
[12]彩霞.高密度电子封装可靠性研究[D].中国科学院上海微系统与信息技术研究所,2002.
[13]Lau J H, Lee S W R, Chang C. Effects of underfill material properties on the reliability of solder bumped flip chip on board with imperfect underfill encapsulants[J]. IEEE Trans Compon Packag Technol, 2000, 23 (2) : 323-328.
[14] Cheng Z N, etc. Influences of packaging materials on solder joint reliability of chip scale package assemblies[C] . International Symposium on Advanced packaging Materials, Braselt-on,Georgia ,1999 :144-150.
[15] Cheng Z N, Cai X, Chen L , etc. Thermal fatigue failure analysis of SnPb solder bumped flip chip on low-cost board with and without underfill encapsulants[C]. Proceedings of the Fourth International Symposium on Electronic Packaging Technology, 2001: 403-450.
[16] Cheng Z N, Xu B, Zhang Q , et al. Underfill delamination analysis of flip chip on low cost board[C]. Proceedings of 2001 International Symposium on Electronic Materials & Packaging,2001: 280-288.
[17]徐步陆,张群,程兆年.倒装焊底充胶分层和焊点失效[J].半导体学报. 2001, 37(10) 1135-1140.
[18] Desai C.S. , Whitenack R. Review of models and the disturbed State concept for thermo mechanical analysis in electronic packaging[J]. Journal of Electronic Packaging, 2001,123(1):19-33.
[19]Evans A.G.,Hutchinson J.W. Thermo mechanical integrity of thin films and multilayers[J]. Acta Metallurgica et Materialia.1995. 43(7): 2507-2530.
[20]Crank J, Park G S. Diffusion in Polymers [M].London : Academic Press, 1968: 1-39.
[21]Crank J. The mathematics of diffusion[M]. Oxford, [Eng] :Clarendon Press,1975:1-40.
[22]Schapery R A, Sun C T. Time dependent and nonlinear effects in polymers and composites[C].Proceedings of the ASTM Symposium, Atlanta, 1998:353- 377.
[23]Browning C E. The mechanisms of elevated temperature property losses in high performance structural epoxy resin matrix materials after exposure to high humidity environments[J]. Polymer Engineering & Science, 1978,1(1): 18-24.
[24]Malyshev B M, Salganik R L. The strength of adhesive joints using the theory of cracks[J]. International Journal of Fracture Mechanics, 1965,1: 114-128.
[25]Belton D J, Sullivan E A, Molter M J. Moisture sorption and its effects upon the microstructure of epoxy moulding compounds[C], Proc.3rd Int.Electron. Manufact. Technol. Symp., 1987:158-169.
[26]Brewis D M, Comyn J, Cope B C, etc. Effect of carrier on the performance of aluminum alloy joints bonded with a structural film adhesive. Polymer Engineering & Science, 1981, 21(12): 797-803.
[27]De'N eve B, Shanahan M E R. Water absorption by an epoxy resin and its effect on themechanical properties and infra-red spectra. Polymer, 1993,34(24): 5099-5105.
[28]Wong E H, Teo Y C, Lim T B. Moisture diffusion and vapor pressure modeling of IC packaging[C]. Proceedings of Electronic Components and Technology Conference, 1998:1372-1378.
[29]Wong E H, Koh S W, Lee K H. Advanced moisture diffusion modeling and characterization for electronic packaging[C]. Proceedings of Electronic Components and Technology Conference, 2002:1297-1303.
[30]Kitano M, Nishimura A, Kawai S. Analysis of packages cracking during reflow soldering process[C]. IEEE International Reliability Physics Symposium, Monterey, 1988: 90-95.
[31]Tay A A O, Lin T .Moisture diffusion and heat transfer in plastic IC packages[J]. IEEE Components Packaging and Manufacturing Technology, 1996, 19(2): 186-193.
[32]Tee T Y, Ng H S. Whole field pressure modeling of QFN during reflow with coupled hygro-mechanical and thermo-mechanical stresses[C]. IEEE 52nd Proceedings of Electronic Components and Technology Conference, 2002: 1552-1559.
[33]Lam T F. FEA simulation on moisture absorption in PBGA packages under various moisture pre-conditioning[C]. Electronic Components and Technology Conference, 2000: 1078-082.
[34]Fan X J, Tee T Y, Lim T B. Modeling of whole field vapor pressure during reflow for flip chip BGA and wire-bond PBGA packages[C]. 1st International Workshop on Electronic Materials and Packaging, Singapore, 1999: 38-45.
[35]S Ning, Lin D, Yang D. Analysis of thermal-moisture induced failure of Pb-free soldered IC packages in SMT reflow soldering process[C]. IEEEE 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and MicroSystems, EuroSimE,2004:341-344.
[36]S Ning, Lin D, Yang D. Finite element analysis of hygro-thermal induced failure in plastic packages[C]. IEEE 5th International Conference on Electronic Packaging Technology Proceedings, ICEPT 2003: 381-385.
[37]巫松,蒋迁彪,杨道国. PBGA器件潮湿扩散和湿应力的有限元分析[J].电子元件与材料,2004,23(6):42-44.
[38]彩霞,黄卫东,徐步陆.电子封装材料中水的形态[J].材料研究学报,2002,16(5): 507-511.
[39]Galloway J E, Miles B M. Moisture absorption and desorption predictions for plastic ball grid array packages[J]. IEEE Components, IEEE Packaging and Manufacturing Technology, 1997, 20(3):274-279.
[40]Stellrecht E, Hand B, Pecht M G. Characterization of hygroscopic swelling behavior of mold compounds and plastic packages[J]. IEEE Compounds and packaging Technologies, 2004, 27(3): 499-506.
[41]Ardebili H, Wong E H, Pecht M. Hygroscopic swelling and sorption characteristics of epoxy molding compounds used in electronic packaging[J]. IEEE Components and Packaging Technologies, 2003, 26 (1): 206-214.
[42]Wong E H, Rajoo R, Lim T B. The mechanics and impact of hygroscopic swelling of polymeric materials in electronics packaging[J]. ASME Journal of Electronic Packaging, 2002: 124-126.
[43]Wong E H, Koh S W, Rajoo R, etc. Underfill swelling and temperature-humidity performance of flip chip PBGA package[C]. Proceedings of Electronics Packaging Technology Conference, 2000: 258-262.
[44]Stellrecht E, Han B, Pecht M. Measurement of the hygroscopic swelling coefficient in mold compounds using Moire interferometry[J]. Experimental Techniques, 2003, 27(4): 40-44.
[45]Stellrecht E, Han B. Measurement of hygroscopic swelling in mold compounds and its effect on PEM reliability[C]. ASME International Electronics Packaging Technology Conference and Exhibition, 2003: 497-502.
[46]Chen X, Zhao S F, Zhai L. Moisture absorption and diffusion characterization of molding compound[J]. ASME Trans Journal of Electronic Packaging .2005, 127(4): 460-465.
[47]Ardebili H, Hillman C, Natishan A E. A comparison of the theory of moisture diffusion in plastic encapsulated microelectronics with moisture sensor chip and weigh-gain measurements[J]. IEEE Components and Packaging Technologies, 2000, 25(1): 132-139.
[48]Ken H, Saka M. Measurement of water absorption in ball grid array package[J]. IEEE Components and Packaging Technologies, 2002, 25(1): 164-168.
[49]别俊龙.电子塑封器件中湿气吸收及扩散的相关研究[D].北京:清华大学,2006.
[50]Fukuzawa I, Ishiguro S, Nanbu S. Moisture resistance degradation of plastic LSI’s by reflow soldering[C]. IEEE Proc IRPS, 1985:192-197.
[51]Pecht M G ,Govind A. In-situ measurements of surface mount IC Package deformations during reflow soldering[J]. IEEE Transactions on Components, Packaging, & Manufacturing Technology Part C: Manufacturing, 1997: 207-212.
[52]Gektin V, Bar-Cohen A. Mechanistic figures of merit for die-attach materials[C]. In Inter-Society Conference on Thermal Phenomena in Electronic Systems, 1996: 306-313.
[53]Lau, J H. Ball grid array technology[C]. Electronic packaging and interconnection series. 1995: 636-638.
[54]Nguyen L T, Chen K L, Schaefe J. A new criterion for Package integrity under solder reflow conditions[C]. In 45th ECTC,1995: 478-490.
[55]Liu S, Mei Y.Behavior of delaminated Plastic IC Packages subjected to encapsulation cooling, moisture absorption, and wave soldering[J]. IEEE Transactions on Components Packaging & Manufacturing Technology PartA, 1995,18(3): 634-645.
[56]Tanaka N, Kitano M T, Kumazawa, etc. Evaluation of interface delamination in IC Packages by considering swelling of the molding compound due to moisture absorption[C]. In 47th ECTC. 1997:120-122.
[57]Lin T Y, Tay A O. Dynamics of moisture diffusion, hygrothermal stresses and delamination in plastic IC packages[J]. ASME Advances in Electronic Packaging, 1997, 19(1): 1429-1436.
[58]Wong E H., Chan K C. Compasive treatment of moisture induced failure in IC packaging[C]. In 3rd IEMT, 1999:822-832.
[59]Tay A O, Lin T Y. Moisture-induced interfacial delamination growth in plastic IC packages during solder reflow[C]. Proceedings-Electronic Components and Technology Conference,1998: 371-378.
[60]Lam D C, Wang J, Yang F. The role of steam evaporation in interfacial failures in electronics packages[C]. In International Conference on Materials for Advanced Technologies. Singapore, 2001: 352-360.
[61]王珺,杨帆,陈大鹏.湿热导致电子元件封装脱层断裂的分析[J].西南交通大学学报,2002,37(2):125-128.
[62]Fan X J, Zhang G Q, Ernst L J. A micro-mechanics approach for polymeric material failures in microelectronic packaging[C]. 3rd International Conference on Thermal and Thermo-mechanical Simulation in Microelectronics, France, 2002:5-15.
[63]Fan X J, Lim T B. Mechanism analysis for moisture-induced failure in IC packages[C]. In:ASME International Mechanical Engineering Congress & Exposition, 11th Symposium on Mechanics of surface Mount Technology. Nov, 1999:311-321.
[64]Fan X J, Zhou J, Zhng G Q, etc.A micromechanics-based vapor pressure model in electronic packages[J]. ASME Journal of Electronics Packaging, 2005, 127: 262-267.
[65]Fan X J. Mechanism-based delamination prediction during reflow with moisture preconditioning[C].Proceeding of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Micro-electronic and Micro-System, EuroSimE, 2004: 329-335.
[66]Fan X J. Analytical solution for moisture-induced interface delamination in electronic packaging[C]. Proceedings of Electronic Components and Technology Conference, 2003: 733-738.
[67]Fan X J. Modeling of vapor pressure during reflow for electronic packages[C]. ESIME2000. Kluwer Academic, Boston, MA, 2000: 75-92.
[68]Guo T F, Cheng L. Thermal and vapor pressure effects on cavitation and void growth.[J] Journal of Materials Science 2001, 36 (24):5871-5879.
[69]Guo, T F, Cheng L. Modeling vapor pressure effects on void rupture and crack growth resistance[J]. Acta Materialia ,2002,50 (13):3487-3500.
[70]Guo T F, Cheng L. Vapor pressure and void size effects on failure of a constrained ductile film[J]. Journal of the Mechanics and Physics of Solids ,2003,51(6):993-1014.
[71]任九生.非线性材料中的空穴生成与增长问题[D].上海:上海大学,2003.
[72] Rivlin R S. Finite elasticity[M].ASME-AMD, New York:ASME, 1977:110-127.
[73]Ogden R W . Extremum principles in non-linear elasticity and their application to composites—I : Theory[J] . International Journal of Solids and Structures, 1978, 14( 4): 265- 282.
[74]Gent A N, Lindley P B. Internal rupture of bonded rubber cylinders in tension [J ] . Proc R Soc Lond, 1958 , A249 :195-205.
[75]Williams M L, Schapery R A. Spherical flaw instability in hydrostatic tension[J], Internat -ional Journal of Fracture,1965,1(1): 64 -71. [76 ]Ball J M. Discontinuous equilibrium solutions and cavitations in nonlinear elasticity [J ] . Philos Trans Roy Soc Lond Ser A, 1982 , 306(3) : 557-611.
[77]Horgan C O, Abeyaratne R .A bifurcation problem for a compressible non- linearly elastic medium : growth of a micro-void[J], Journal of Elasticity, 1986, 16(1):189 -200.
[78]Sivaloganothan J.Uniqueness of regular and singular equlibrium for spherically symmetr -ic problems of nonlinear elasticity[J],Arch. Rat. Mech. Anal., 1986,96(1):97-136.
[79]Horgan C O, Polignone D A. Cavitation in nonlinearly elastic solids[J]. A review,Applied Mechanics Review,1995,48(2):471-485.
[80]程昌钧,尚新春.超弹性矩形板单向拉伸时微孔的增长[J].应用数学和力学, 1997, 18(7):573-579.
[81]尚新春,程昌钧.弹性固体材料中的空穴萌生与增长[J].北京科学技术大学,2002, 24(3):380-382.
[82]任九生,程昌钧.不可压超弹性材料中的空穴分叉[J].应用数学和力学,2002,23(8) : 783-789.
[83]任九生,程昌钧,朱正佑.可压超弹性材料组合球休中心的空穴生成[J],应用数学和力学, 2003, 24(9):892-898.
[84]任九生,程昌钧.多孔Mooney-Riviin材料矩形板的单向拉伸[J].力学季刊, 2003, 23(3):347-353.
[85]程昌钧,任九生.横观各向同性多孔超弹性矩形板的单向拉伸[J].应用数学和力学, 2003, 24:675-683.
[86]任九生,程昌钧.超弹性材料中空穴的动态生成[J].固体力学学报, 2004, 25(1): 42-46.
[87]程昌钧,任九生.非线性材料中空穴生成和增长问题的一些进展[J].自然杂志,2004, 26(1):1-6.
[88]Murhy J G, Biwa S. Nonmontonic cavity growth in finite, compressible elasticity[J]. International Journal of Solid and Structures, 1997, (34):3859-3872.
[89]Ren Jiu-sheng , Cheng Chang-jun. Bifurcation of cavitation solutions for incompressible transversely isotropic hyper-elastic materials[J] . Journal Engineering Mathematics, 2002, 44 (5):245-257.
[90]Shang Xin-chun, Cheng Chang-jun. Cavition in Hookean elastic membranes[J], Acta Mechanica Solida Sinica, 2002,15(1):89-94.
[91]Yuan Xue-gang, Zhu Zheng-you, Cheng Chang-Jun. Qualitative analyses of Spherical cavity nucleation and growth for incompressible generalized Valanis - landel hyperelastic material[J]. Acta Mechanical Solida Sinica, 2004,17(2):158-165.
[92]Yuan Xue-gang, Zhang Ruo-jing. Effect of constituive parameters on cavity formation and growth in a class of incompressible transversely isotropic nonlinearly elastic solid spheres [J] . Computers,Materials & Continua , 2005, 2:201- 211.
[93]Yuan Xue-gang, Zhu Zheng-you, Cheng Chang-jun. Study on cavitated bifurcation problem for sphere composed of hyper-elastic materials[J] , Journal of Engineering Mathemat -ics, 2005,51:15-34.
[94]金明,黄克服,武际可. Poisson比为1/ 2材料中球形空穴突变和球形空穴萌生的分岔问题研究.应用数学和力学[J],1999,20(8):867-873.
[95]唐立强,范志强,杨勇.哈尔滨工程大学学报[J].不可压缩球体的空穴和叉,2005, 26(5):624-627.
[96]Fu Y B, Ogden R W. Nonlinear Elasticity: Theory and Applications [M].Cambridge, UK:Cambridge University Press, 2001:1-20.
[97]Charles A Harper著,沈桌身,贾松良译.电子封装材料与工艺[M].北京:化学工业出版社,2006:476-510.
[98]Zhou Jiang .Transient analysis on hygroscopic swelling characterization using sequential- lly coupled moisture diffusion and hygroscopic stress modeling method[J] .Microelectronics Reliability, 2008,48(6): 805-810.
[99]匡震邦.非线性连续介质力学[M].上海:上海交通大学出版社,2002:179-196.
[100]I.M著,漆宗能译.固体高聚物的力学性能[M].北京:科学出版社,1988:1-90.
[101]黄筑平.连续介质力学基础[M].北京:高等教育出版社,2003:60-80.
[102]Treloar L R G .The mechanics of rubber elasticity[J]. Proc Roy SocLond, 1976,A351:301-330.
[103] Treloar L R G. The elasticity of a network of long chain molecules ( I and II)[J]. Trans -actions of the Faraday Society ,1943,36:241.
[104]Wall F T .Statistical thermodynamics of rubber [J]. Journal of Chemical Physics,1942, 10(2): 485-488.
[105]Flory P J, Rechner J .Statistical mechanics of cross-linked polymer networks [J]: Journal of Chemical Physics,1943, 11:512-520.
[106]James H M, Guth E . Theory of elastic properties of rubber[J]. Journal of Chemical Physics,1943, 11:455 -481.
[107]Treloar L R G. Stress-strain data for vulcanized rubber under various types of deformation[J]. Transactions of the Faraday Society ,1944 ,40: 59.
[108]Kuhn W , Grün F. Beziehungen zwischen elastischen Kon2 stanten und Dehnungsdopp- elbrechung hochelastischer Stof2 fe[J]. Kolloid2Zeit schrift , 1942 ,101 (3) :248.
[109]Flory P J . Network structure and the elastic properties of vulcanized rubber. chemical reviews[J] ,1944 ,35 :51.
[110]Arruda E M ,Boyce M C. A There-dimensional constitutive model for the larges stretch behavior of rubber elastic materials[J]. Journal of t he Mechanics and Physics of Solids, 1993, 41(2):389-412.
[111] Thomas A G, Derham C J. The design and use of rubber bearings for vibration isolation and seismic protection of structures[J]Engineering Structures, 1980 2(3) :171-175.
[112]Treloar L R G. The elasticity of a network of long chain molecules (Ⅲ) [J]. Transactions of the Faraday Society ,1946 ,42(1) :83-93.
[113]Mooney M. A theory of large elastic deformation[J] . Journal of Applied Physics, 1940, 11(6):582-592.
[114]Rivlin R S. Large elastic deformations of isot ropic materials [A]. Philosophical Transactions of the Royal Society of London ,Physical Sciences and Engineer [C] . London , U K:1948, 491-510.
[115]Tschoegl N W. Constitutive equations for elastomers[J]. Polymer Science, 1971 A1:1959-1970.
[116]Gent A N.A new constitutive relation for rubbe[J], Rubber Chemistry and Technology,1996, 69(1):59-61.
[117]Pucci E, Saccomandi G. A note on the Gent model for rubber-like materials[J]. Rubber Chemistry and Technology, 2002,75(6):839-852.
[118]Takamizawa K, Hayashi K. Strain energy density function and uniform strain hypothesis for arterial mechanics[J].Biomech,1987,20(1):7-17.
[119]Yeoh O H. Some forms of the strain energy for rubber[J]. Rubber Chemistry and Technology, 1993,66(5):754-771.
[120]Blatz P J. The finite elastic plane strain deformation of a mooney-rivlin body[J]. International Journal of Engineering Science, 1964,2(4) 405-411.
[121]Ogden R W. Large deformation isotropic elasticity :On the correlation of theory and experiment for incompressible rubbe-rlike solids [C].Proceeding of the royal society of London, 1972a, series A 326:565-584.
[122]Ogden R W, Chadwick P. On the deformation of solid and tubular cylinders of incompressible isotropic elastic material[J]. Journal of the Mechanics and Physics of Solids, 1972, 20(2): 77-90.
[123]Ogden R W. Volume changes associated with the deformation of rubber-like solids[J]. Journal of the Mechanics and Physics of Solids, 1976, 24(6):323-338.
[124]朱艳峰.橡胶类材料硬化的本构研究与非线性有限元分析[D].广州:华南理工大学,2005.
[125]高玉臣.固体力学基础[M].北京:中国铁道出版社,1999:10-30.
[126]Boyce M C, Arruda E M. Constitutive models of rubber elasticity[J] .A review,Rubber Chemistry and Technology,2000,73:504-23.
[127]Valanis K C, Landel R F. The strain energy function of a hyper-elastic material in terms of the extension ratios[J]. Applied Physics,1967 ,38:2997.
[128]徐明.橡胶类超弹性材料本构关系研究及有限元分析[D].北京:北京航空航天大学, 2002.
[129]Ting T C T. Effects of change of reference coordinates on the stress analyses of anisotropic elastic materials[J]. International Journal of Solids and Structures.1982,18(2): 139-152.
[130]Ting T C, Yan Gongpu. The anisotropic elastic solid with an elliptic hole or rigidinclusion[J]. International Journal of Solids and Structures, 1991, 27(15): 1879-1894.
[131]Ting T C T. Recent developments in anisotropic elasticity[J]. International Journal of Solids and Structures . 2000, 37(1):401-409.
[132]Ting T C T. Three-dimensional solutions for general anisotropy[J]. Journal of the Mechanics and Physics of Solids,2007, 55(9): 1993-2006.
[133]Polignone D A, Horgan C O. Cavitation for incompressible anisotropic nonlinearly elastic spheres[J]. Journal of Elasticity,1993,33:27 -65.
[134]Zidi M. Large shearing of a prestressed tube[J]. Journal of Applied Mechanics. 2000, 67: 209-211.
[135]Zidi M. Effects of a prestress on a reinforced, nonlinearly elastic and compressible tubes subjected to combined deformations[J].International Journal of Solids and Structures.2001,38(26): 4657-4669.
[136]Zidi M, Cheref M. Finite deformations of a hyperelastic compressible and fiber-reinforced tube[J], European Journal of Mechanics - A/Solids,2002, 21(6): 971-980.
[137]Nicholson DW, Nelson N. Finite element analysis in design with rubber elasticity [J], Rubber Chem Technol.1990,63 :358-406.
[138]Nicholson D W, Lin B. Theory of thermoelasticity for bear-incompressible elastomers [J], Acta Mech.,1996,116:15-28.
[139]Horgan C O, Saccomandi Giuseppe. Finite thermoelasticity with limiting chain extensibility[J] .Journal of mechanics and physics of solids. 2003,51:1127-1146.
[140]Wu P D , Van der Giessen E.On improved network models for rubber elasticity and their applications to orientation hardening in glassy polymers[J]. Mechanics and Physics of Solids , 1993 ,41 (3):427.
[141]Marckmann G, Verron E , etc. A theory of net-work alteration for the Mullins effect[J] . Mechanics and Physics of Solids, 2002 ,50 (9) :2011.
[142]Elias-Zuniga A , Beatty M F. Constitutive equations for amended non-Gaussian network models of rubber elasticity[J]. Int Eng Sci , 2002 ,40 (20) :2265.
[143]Lim G T. Scratch behavior of polymers[D].Texas A &M University , 2005.
[144]Yuan Xue-gang, Zhu Zheng-you .Qualitative study of cavitated bifurcation for a class of incompressible generalized neo-hookean spheres[J] .Applied Mathematics and Mechanics,2005, 26 (2):185-194.
[145]Merodio Jose, Saccommandi Giuseppe. Remarks on cavity formation in fiber-reinforced incompressible non-linearly elastic solids[J] ,European journal of Mechanics A/solids 2006,25:778-792.
[146]袁学刚.具有缺陷的超弹性材料球体中的空穴分岔[D].上海:上海大学,2003.
[147]Chang W J, Pan J. Cavitation instability in rubber with consideration of failure[J]. Journal of Materials science, 2001, 36: 1901-1909.
[148]任九生,程昌钧.固体力学学报[J].热超弹性材料中的空穴生成问题, 2004, l5(3):275-277.