固体推进剂药柱表面裂纹动态力学特性研究
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摘要
固体火箭发动机作为战术导弹或野战火箭的动力装置和关键部件,其安全性非常重要。从己知的导弹及火箭故障来看,固体火箭发动机失效是导致灾难性故障的最主要原因,而失效主要是由于药柱结构完整性的破坏。因此,在固体火箭发动机设计阶段,需要大力开展发动机的结构完整性分析,其中药柱的结构完整性是关键技术之一。在药柱结构完整性分析中,形变和断裂特性研究一直是十分活跃的研究课题。
本文通过建立由三维非线性粘弹性本构关系描述的固体推进剂药柱有限元模型,利用数值方法分析药柱表面裂纹的动态场特性,对裂纹尖端应力应变场的分布及其动态场对加载率的响应特征进行了研究。主要研究内容为:
1.通过研究广义粘弹性本构方程在固体推进剂材料中的适应性,利用非线性有限元分析中的通用求解方法对单轴和多轴粘弹性本构关系进行了分析,运用递归迭代算法编制了用户材料子程序。
2.建立由三维非线性粘弹性本构关系描述的有限元模型,通过数值计算结果与实验结果对比的方式对方程的有效性进行验证。
3.利用三种加载方式对带裂纹的典型药柱结构的裂纹尖端场进行了数值计算。通过将三维非线性粘弹性数值方程转化成动态条件下本构模型,编制VUMAT(动态分析用户材料子程序),分别对施加三种不同加载率的不同长度裂纹进行有限元计算,考虑裂纹对动态载荷的响应,分析了应力应变场的变化规律。
4.利用典型药柱结构的裂纹尖端场数值计算结果分析了加载率对裂尖前方张开应力场的影响,并预测了动态加载条件下的断裂韧性。
通过本文的研究,得到了固体推进剂表面裂纹在动态加载条件下的力学响应特性、场变化规律和裂纹起裂特征。本文的研究工作将对固体火箭发动机结构完整性分析,特别是对固体推进剂药柱结构完整性分析奠定坚实的基
The safety of a solid rocket motor, which serves as the propulsion system and the key component of a tactical missile or a field rocket, was extraordinary important. Known from the View of solid missile fault, solid rocket engine failure led to the catastrophic failure was the main reason, and the failure was mainly due to the structural integrity of the grain damage. As a result, study on analysis of structural integrity of the engine should be energetically developped on solid rocket design stage, the structural integrity of grain was one of the key technologies. In the analysis of the structural integrity of grain, study on deformation and fracture characteristics was always a very active research subject.
In this paper, the solid propellant grain finite element model charactered by three-dimensional nonlinear viscoelastic constitutive relationship was established, the dynamic field characteristics of solid propellant surface crack was simulated from numerical methods, the distribution of crack tip stress-strain field and the response characteristics of dynamic field on loading rate were studied. The main contents were as follows:
1. By studying applicability of generalized viscoelastic constitutive relation in solid propellant material, uniaxial and multi-axial viscoelastic constitutive relation were analyzed by using currency resolving method in nonlinear finite element analysis, and UMAT was programmed by recursion-iterative arithmetic.
2. Finite element model charactered by three-dimensional viscoelastic constitutive relation was established and analyzed ,the validity of three-dimensional viscoelastic constitutive relation was validated by comparing numerical result with test result.
3. Crack-tip fields of representative grains structure contained precrack was conputed by numerical mothed in three loaded type.VUMAT was programmed by changing the three-dimensional viscoelastic constitutive numerical equation into dynamic constitutive numerical model, the different length crack applied three type load was computed by finite element method, the reponse of crack in dynamic applied load was calculated and the law of crack-tip fields was analyzed.
4.The effect loading rate on open stress fields in crack-tip ahead was analyzed by numerical competed result of the crack-tip fields in representative grains structure, and fracture roughness in dynamic applied load was predicted.
Through research of this paper, the response to the mechanical properties, the law of Field changes and the start features of crack of solid propellant surface crack with dynamic load conditions were obtained. laid a solid foundation to the analysis of structural integrity of rocket engine, especially to the structural integrity of grain.
本文通过建立由三维非线性粘弹性本构关系描述的固体推进剂药柱有限元模型,利用数值方法分析药柱表面裂纹的动态场特性,对裂纹尖端应力应变场的分布及其动态场对加载率的响应特征进行了研究。主要研究内容为:
1.通过研究广义粘弹性本构方程在固体推进剂材料中的适应性,利用非线性有限元分析中的通用求解方法对单轴和多轴粘弹性本构关系进行了分析,运用递归迭代算法编制了用户材料子程序。
2.建立由三维非线性粘弹性本构关系描述的有限元模型,通过数值计算结果与实验结果对比的方式对方程的有效性进行验证。
3.利用三种加载方式对带裂纹的典型药柱结构的裂纹尖端场进行了数值计算。通过将三维非线性粘弹性数值方程转化成动态条件下本构模型,编制VUMAT(动态分析用户材料子程序),分别对施加三种不同加载率的不同长度裂纹进行有限元计算,考虑裂纹对动态载荷的响应,分析了应力应变场的变化规律。
4.利用典型药柱结构的裂纹尖端场数值计算结果分析了加载率对裂尖前方张开应力场的影响,并预测了动态加载条件下的断裂韧性。
通过本文的研究,得到了固体推进剂表面裂纹在动态加载条件下的力学响应特性、场变化规律和裂纹起裂特征。本文的研究工作将对固体火箭发动机结构完整性分析,特别是对固体推进剂药柱结构完整性分析奠定坚实的基
The safety of a solid rocket motor, which serves as the propulsion system and the key component of a tactical missile or a field rocket, was extraordinary important. Known from the View of solid missile fault, solid rocket engine failure led to the catastrophic failure was the main reason, and the failure was mainly due to the structural integrity of the grain damage. As a result, study on analysis of structural integrity of the engine should be energetically developped on solid rocket design stage, the structural integrity of grain was one of the key technologies. In the analysis of the structural integrity of grain, study on deformation and fracture characteristics was always a very active research subject.
In this paper, the solid propellant grain finite element model charactered by three-dimensional nonlinear viscoelastic constitutive relationship was established, the dynamic field characteristics of solid propellant surface crack was simulated from numerical methods, the distribution of crack tip stress-strain field and the response characteristics of dynamic field on loading rate were studied. The main contents were as follows:
1. By studying applicability of generalized viscoelastic constitutive relation in solid propellant material, uniaxial and multi-axial viscoelastic constitutive relation were analyzed by using currency resolving method in nonlinear finite element analysis, and UMAT was programmed by recursion-iterative arithmetic.
2. Finite element model charactered by three-dimensional viscoelastic constitutive relation was established and analyzed ,the validity of three-dimensional viscoelastic constitutive relation was validated by comparing numerical result with test result.
3. Crack-tip fields of representative grains structure contained precrack was conputed by numerical mothed in three loaded type.VUMAT was programmed by changing the three-dimensional viscoelastic constitutive numerical equation into dynamic constitutive numerical model, the different length crack applied three type load was computed by finite element method, the reponse of crack in dynamic applied load was calculated and the law of crack-tip fields was analyzed.
4.The effect loading rate on open stress fields in crack-tip ahead was analyzed by numerical competed result of the crack-tip fields in representative grains structure, and fracture roughness in dynamic applied load was predicted.
Through research of this paper, the response to the mechanical properties, the law of Field changes and the start features of crack of solid propellant surface crack with dynamic load conditions were obtained. laid a solid foundation to the analysis of structural integrity of rocket engine, especially to the structural integrity of grain.
引文
[1]萨顿.G.P,比布拉兹.O.火箭发动机基础.北京:科学出版社,2003
[2]Graham.G.A.C.The Correspondence Principle of Linear Viscoelasticity Theory for mixed Boundary Value Problems Involving Time-dependent Boundary Regions.Quart.Appl.Math.,1968,22:10-20
[3]Graham.G.A.C.The Correspondence Principle of Llinear Viscoelasticity for Problems that Involve Time-dePendent Regions.Int.J.Engrg.Sci,1973
[4]魏培君,张双寅,吴永礼.粘弹性力学的对应原理及其数值反演方法.力学进展,1999,29(3):317-330
[5]王元有.推进剂药柱在内压力载荷下的应力、应变的粘弹性分析.兵工学报,1993,3:20-33
[6]Christensen.R.M.Theory of Viscoelasticity.New York:Academic Press,1982.
[7]杨挺青.粘弹性力学.北京:华中理工大学出版社,1990
[8]Schapery.R.A.Nonlinear Constitutive Equations for Solid Propellant Based on a Work Potential and Micromechanical Model.In Proc.1987 JANNAF Structures and Mechanical Behavior Meeting,17-19 March,CPIA,Huntsville,AL
[9]王礼立,施绍裘,陈江英等.ZWT非线性热粘弹性本构关系的研究与应用.宁波大学学报(理1版),2000,13(4):141-149
[10]Swanson.S.R,Christensen.L.W.A Constitutive Formulation for High Elongation Propellants.J.Spacecraft,1983,20(6):559-566
[11]强洪夫.固体火箭发动机药柱结构完整性数值仿真与实验研究.西安交通大学博士学位论文,1998
[12]Jung.G D,Youn.S K,Kim.B K.A Three-dimensional Nonlinear Viscoelastic Constitutive Model of Solid Propelant.Int.J.Solids Structures,2000,37(34):4715-4732
[13]Zienkiewicz.O C,Watson.M.Some Creep Effects Stress Analysis with Particular Reference to Concrete Pressure Vessel.Nuclear Engineering and Design,1966,4:406-412
[14]Zienkiewicz.O C,Watson.M,King.I P.A Numerical Method of Visco-elastic Stress Aanalysis.Int J Mech Sci,1968,10:807-827
[15]White.J L.The finite element mothod of 3 dimensional nonnlinear viscoelastic large deformation problems.Proceedings of the 2nd Conference on Matrix method in Structural Mechanics,1968:489-516
[16]Argyris.J H,Pister.K S,Szimmat.J,William.K J.Computer Methods in Applied Mechanics and Engineering.Unified concepts of constitutive modelling and numerical solution methods for concrete creep problems.Journal of the Engineering Mechanics,1977,10:199-246
[17]Adey.R A,Brebbia.C A.Efficient Method for Solution of Viscoelastic Problem.Journal of the Engineering Mechanics,1973:1119-1127
[18]Srinatha.H R,Lewis.R W.A Finite Element Method for Thermovisoelastic Analysis of Plane Problems.Computer Methods in Applied Mechanics and Engineering,1981,25:21-33
[19]Yadagari.S,Reddy.C P,Reddy.T S.Viscoelatstic Analysis of Adhesively bonded Joints.Computers and Structures,1987,27(4):445-454
[20]Jones.I W,E.Pierre-Louis.A Linear Thermoviscoelastic Material Model for Solid Rocket Motor Structural Analyses.Computers and Structures,1985,21(12):235-243
[21]Styrk Finne,Cecilia Futsaether,Jan Ivar Botnan.Three-Dimensional Analysis of Solid Propelant Grain Using a Nonlinear Viscoelastic Model.AIAA-2090,1990:1-8
[22]Reggi.A Nonlinear Viscoelastic Constitutive Model for Solid Propellant.Technical Report BMO-TR-93-61,Failure Analysis Associates,1993,4
[23]Lai.J,Bakker A.3-D Schapery Representation for Non-linear Viscoelasticity and Finite Element Implementation.Computional Mechenics,1996,18:182-191
[24]李录贤等.三维药柱的热粘弹性有限元分析.推进技术.1997,18(3):45-50
[25]王馄,田维平.固体火箭发动机前、后翼药柱三维有限元分析.推进技术,1997,18(4):36-41
[26]朱智春等.固体火箭发动机药柱三维温度场有限元分析.推进技术,1997,18(2):21-26
[27]唐国金,周建平.自由装填药柱的结构完整性分析.固体火箭技术,1994,(6):13-19
[28]Feng.Z G,Zhou.J P.The Long-term Aging Effects of Viscoelastic Polymers and Its Finite Element Method.Proc.of Int.Conf.on Deformation,Yield and Fracture of Polymers,Cambrige,U K.1994
[29]蒋辉国.粘弹结构应力应变场与温度场全耦合的计算机程序及其应用.推进技术,1990,1:7-13
[30]杨卫国.ADINA软件在固体发动机设计中的应用.固体火箭技术,1992,4:15-19
[31]沈亚鹏,王晓明,梁汉梁.用Total Lagrangian法的三维粘弹性大变形问题的有限元分析.航空学报(A辑),1989,7:387-393
[32]Shen Ya peng,Zhou Zhe,Xue Qi.Analysis of Deformation of Nozzleless Rocket Propellant.Acta Mechanica Solid Sinica,1990,3(2):193-200
[33]杜建科,朱祖念等.固体发动机药柱损伤粘弹有限元分析.固体火箭技术,2001,24(1):1-5
[34]魏卫,王宇飞.高加速度冲击下固体推进剂药柱轴向形变的数值模拟.固体火箭技术,2003,26(2):42-45
[35]刘中兵,利凤祥,李越森,胡春波.高过载条件下固体推进剂药柱结构完整性分析计算.固体火箭技术,2003,(6):12-16
[36]利凤祥,刘中兵,李越森,胡春波.药柱结构对其抗轴向过载能力的影响.推进技术,2004,25(2):165-169
[37]沈亚鹏,李录贤,王晓明.粘弹性准静态、动态问题的数值解法.力学进展,1994,25(2):265-272
[38]王本华,张戈,黄涵,刘晓.粘弹结构动力响应的有限元分析.强度与环境,1993.3:49-52
[39]王本华,张戈.三维粘弹大变形动力响应分析.推进技术,1994,3:21-27
[40]杨挺青,王胜凯,黄玉盈.粘弹性轴对称平面问题的动态响应.固体力学学报,1987,1:78-86
[41]Murray.J W,Mikeska.A J,Tonkin.M E.Nozzleless Performance Program Grain Deflection Model.AIAA/SAE/ASME,18th Joint Propulsion Conference,Clevland,Ohio,1982
[42]陈前,朱德悉.复合结构振动分析的数值方法.计算结构力学及其用,1990,7(3):27-35
[43]李录贤,沈亚鹏.粘弹性大变形动力响应的有限元分析.计算结构力学及其应用,1994,11(4):349-355
[44]Mott.N.F.Brittle Fracture in Mild Steel Plates.Engineering,1948,165:16-18
[45]Yoffe.E.H.The moving Grifith crack.Phil.Mag.1951,42:739-750
[46]Baker.B.R.Dynamic Stresses Created by a Moving Crack.J.Appl.Mech,1962,29:449-458
[47]K.B.Broberg.The Propagation of a Britle Crack.Archiv fur Fysik,1960,18:159-192
[48]Craggs.J.W.On the Propagation of a Crack in an Elastic-britle Solid.J.Mech.Phys.Solids,1960,8:66-75
[49]Gao.Y.C,Rousselier.G.Near Tip Quasi-static Crack Growth Behavior in Strain Hardening and Softening Material.Theoretical and Applied Fracture Mechanics,1994,20:149-155
[50]Li J,Zhang.X.B.Elastic-plastic Analysis of an Arbitrarily-oriented Mode ⅢCrack Touching an Iinterface.International Journal of Fracture Mechanics,1996,80:311-337
[51]Erdogan.F.Fracture Mechanics.International journal of solids and structures,2000,37:171-183
[52]Griffith.A.A.The Phenomenon of Rupture and Flow in Solids.London:Philosophical Transactions of Royal Society,1920
[53]Irwin.G R.Fracture Dynamics.Fracturing of Metals.Cleveland:Am.Soc.Metals,1948
[54]Orowan.E.Fracture and Strength of Solids.On Prog.In Phys.Ⅴ-Ⅶ,1948
[55]Irwin.G R.Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate.Journal of Applied Mechanics,1957,24:361-364
[56]范天佑.断裂动力学引论.北京:北京理工大学出版社,1990
[57]Hult.J.A,McClintock.F.A Elastic-plastic Distribution around Sharp Notches under Repeated Shear.Proceedings of 9~(th)International Congress on Applied Mechanics,Brussels.1956,8:51-62
[58]Rice.J.R.Stress due to a Sharp Notch in a Work-hardening Elastic-plastic Material Loaded by Longitudinal Shear.Journal of Applied Mechanics,1967,34(2):287-298
[59]Rice.J.R.Contained Plastic Deformation Near Cracks and Notches under Longitudinal Shear.International Journal of Fracture Mechanics,1966,2(2):426-447
[60]Amazigo.J.A.Fully Plastic Center-cracked Strip Antiplane Shear.International Journal of Solids and Structures,1975,11(12):1291-1299
[61]Hutchinson.J.W.Singular Behavior at the End of Tensile Crack in a Hardening Material.Journal of Mechanics and Physics of Solids,1968,16(1):13-21
[62]Rice J.R,Rosengren.G.F.Plane Strain Deformation Near Crack Tip in a Power Law Hardening Material.Journal of Mechanics and Physics of Solids,1968,16(1):1-12
[63]Begley J.A,Landes.J.D.The J-integral as a Fracture Criterion.Fracture Toughness,ASTM.STP 1972,514:1-20
[64]Shib.C.F.Small-scale Yielding Analysis of Mixed Mode Plane Strain Crack Problems.In Fracture analysis,ASTM.STP.1974,560:187-210
[65]Hutchinson.J.W.Plastic Stress and Strain Field at a Crack Tip.Journal of Mechanics and Physics of Solids,1968,16(4):337-347
[66]黄克智,余寿文.弹塑性断裂力学.北京:清华大学出版社,1985
[67]高玉臣.裂纹起始扩展的弹塑性场.固体力学学报,1980,12(1):67-76
[68]高玉臣,黄克智.理想弹塑性平面应变问题.力学学报1981年特刊:111-120
[69]Gao.Y.C,Hwang.K.C.Elastic-plastic Fields in Steady Crack Growth in a Strain-hardening Material.ICF5 in Advances in Fracture Research.Francois D.ed.V2,Pergamon Press,1981
[70]高玉臣.理想弹塑性平面应力问题.固体力学学报,1982,3(3):339-350
[71]Gao.Y.C,Hwang.K.C.On the Formulation of Plane Strain Problems for Elastic Perfectly-plastic medium.International Journal of Engineering Science,1983,21(7):765-780
[72]Gao.Y.C,Hwang.K.C.Elastic-plastic Fields in Steady Crack Growth.In Three-Dimensional Constitutive Relations and Ductile Fracture.Nemat-Nasser S.ed,North-Holland Publication Company,1980
[73]靳志和,余寿文.理想弹塑性材料平面应力Ⅰ型裂纹尖端的弹塑性场.力学学报,1986,18(1):88-92
[74]章梓茂,马兴瑞,高玉臣.理想塑性介质中平面应力静止裂纹的尖端弹塑性场.力学学报,1990,22(2):229-235
[75]Riedel.H.Cracks Loaded in Anti-plane Shear under Creep Conditions.Z.Metall,1978,69(12):755-760
[76]Riedel.H,Rice.J.R.Tensile Cracks in Creeping Solids.Fracture Mechanics.Twelfth Conference,ASTM.STP700,American Society for Testing and Materials,1980,112-130
[77]Riedel.H.Creep Deformation at Crack Tips in Elastic-viscoplastic Solids.J.Mech.Phys.Solids,1981,29:35-49
[78]Hui.C.Y.The Mechanics of Self-similar Crack Growth in an Elastic Power-law Creeping Material.J.Solids Structs,1986,22(4):357-372
[79]Wang.T.C.Elastic-plastic Asymptotic Fields for Cracks on Bi-material Interfaces.Engineering Fracture Mechanics,1990,37(3):527-538
[80]Li F.Z,Needleman.A,Shih.C.F.Characterization of Near Tip Stress and Deformation Fields in Creeping Solids.International Journal of Fracture,1988,36:163-186
[81]Bassani.J.L.Cracks in Materials with Hyperbolic-sine-law Creep Behavior.Elastic-Plastic Fracture:Second Symposium.Volume I-Inelastic Crack Analysis,ASTM.STP803,1983,532-550
[82]Gao.Y.C.Uniparameter Plastic Field Near a Dynamic Crack-tip.Mechanics Research Communications,1988,15(5):307-313
[83]Eran Sharon,Steven.P,Gross,Jay Fineberg.Energy Dissipation in Dynamic Fracture.Physical Review Letters,1996,76(12):2117-2120
[84]Lu Meng,Yiu-Wing Mai,Lin Ye.Crack-tip Field for Fast Fracture of an Elastic-plastic-viscoplastic Material Incorporated with Quasi-brittle Damage.Part 1.Large damage regime,International Journal of Solids and Structures,2001,38:9383-9402
[85]Ueda.S.Impact Response of a Piezoelectric Layered Composite Plate with a Crack.Theoretical and Applied Fracture Mechanics,2002,38:221-242
[86]蔡艳红.粘弹性材料动态扩展裂纹尖端场.哈尔滨工程大学博士学位论文,2003
[87]Zhang.Ch,Savaidis.A,Savaidis.G,Zhu.H.Transient Dynamic Analysis of a Cracked Functionally Graded Material by a BIEM.Computational Materials Science,2003,26:167-174
[88]Tang Li-qiang,Yang Jing-yuan,Wu Guo-hui.The Asymptotic Fields of a Dynamically Growing Crack in a Viscoelastic Material.Journal of Marine Science and Application,2007,6(4):62-67
[89]Fagerstr(o|¨)m.M,Larsson.R.Approaches to Dynamic Fracture Modelling at Finite Deformations.Journal of the Mechanics and Physics of Solids,2008,56:613-639
[90]尹双增.断裂·损伤理论及应用.北京:清华大学出版社,1992
[91]沈成康.断裂力学.上海:同济大学出版社,1996
[92]匡震邦,马法尚.裂纹端部场.西安:西安交通大学出版社,2002
[93]Shockey.D A,Kalthoff.J F,Erlich.D C.Evaluation of Dynamic Instability Criteria.Int J Frac,1983,22:217-229
[94]Homma.H,Shockey.D.A,Murayama.Y.Response of Cracks in Structural Materials to Short Pulse Loads.Journal of Mechanics and Physics of Solids,1983,31:261-279
[95]Ravi-chandar.K,Knauss.W.G.An Experimental Investigation into Dynamic Fracture:Ⅰ.Crack iinitiation and arrest.International Journal of Fracture,1984,25:247-262
[96]黄风雷,王泽平,丁敬.复合固体推进剂动态断裂研究.兵工学报,1995,2:47-50
[97]Koppenhoefer.K C,Dodds.R H.Constraint Effect on Fracture Toughness of Impact-loaded,Pre-cracked Charpy Specimens.Nucl Eng Des,1996,162:145-158
[98]LIU.C,Knauss.W.G,Rosakis.A.J.Loading Rates and the Dynamic Initiation Toughness in Brittle Solids.Intemational Journal of Fracture,1998,90:103-118
[99]Sumit Basu,Narasimhan.R.A Numerical Investigation of Loss of Crack Trip Constraint in a Dynamically Loaded Ductile Specimen.Joumal of the Mechanics and Physics of Solids,2000,48:1967-1985
[100]Jayadevan.K R,Narasimhan.R,Ramamurthy.T S,Dattaguru.B.A Numerical Study of T-stress in Dynamically Loaded Fracture Specimens.In J Solids Struct,2001,38:4987-5005
[101]Kim.Y,Chao.Y.J.Effect of Loading Rate on Dynamic Fracture Initiation Toughness.Int J Fract,2007,145:195-204
[102]Svob.G J,Bills.Jr.K.W.Predictive Surveillance Technique for Air-launched Rocket motors.J Spacecraft,1984,21(2):162-167
[103]Jana.M K,Renganathan.K,Rao G.Venkateswara.A Method of Non-linear Viscoelastic Analysis of Solid Propellant Grains for Pressure Load.Comput Struct,1994,52(1):61-67
[104]Shiang-Woei Chyuan.A Study of Loading History Effect for Thermoviscoelastic Solid Propellant Grains.Computers and Structures,2000,77:735-745
[105]Sebnem(O|¨)z(u|¨)pek.Constitutive Equations for Solid Propellant.The University of Texas,Ph.D,1997
[106]李葆萱.固体推进剂性能.西安:西北工业大学出版社,1990
[107]Coleman.B D,Gurtin.M E.Thermodynamics with Internal State Variables.J Chem.Phys,1967,47:597-613
[108]Valanis.K C.Thermodynamics of Large Viscoelastic Deformations.J Maths Phys,1966,45(2):197-212
[109]杨挺青.粘弹性力学.武汉:华中理工大学出版社,1992
[110]周建平.粘弹性材料的变形动力学模型.固体力学学报,1994,15(1):80-85
[111]李如生.非平衡态热力学和耗散结构.北京:清华大学出版社,1986
[112]Biot.M.A.Theory of Stress-strain Relation in Anisotropic Viscoelasticity and Relation Phenomene.J Appl Physics,1954,25(11):1358-1391
[113]余寿文,冯西桥.损伤力学.北京:清华大学出版社,1997
[114]Allen.D.H,Holmberg.J.A,Ericson.M,Lans.L,Svensson.N,Holmberg.S.Modeling the Viscoelastic Response of GMT Structural Components.Composites Science and Technology,2001,61:503-515
[115]Martin L(?)vesque.Mechamical Behavior Modelling of Nonlinear Viscoelastic Composite Materials by a Homogenisation Approach.L'(?)cole Nationale Superieure D'arts Et Metiers,Ph.D,2004
[116]Green.A.E,Rivlin.R.S.The Mechanics of Nonlinear Materials with Memory.Archive for Rational Mechanics and Analysis,1957,1:1-21
[117]Green.A.E,Rivlin.R.S.The Mechanics of Nonlinear Materials with Memory-Part Ⅲ.Archive for Rational Mechanics and Analysis,1960,4:387-404
[118]Green.A.E,Rivlin.R.S,Spencer.A.J.S.The Mechanics of Nonlinear Materials with Memory-Part Ⅱ.Archive for Rational Mechanics and Analysis,1959,3:82-90
[119]Lockett.F.J.Creep and Stress-relaxation Experiments for Non-linear Materials.International Journal of Engineering Science,1965,3:59-75
[120]Buckley.C.P.Multiaxial nonlinear Viscoelasticity in Solid polymers.Polymer Engineering and Science,1987,27(2):155-164
[121]Schapery.R.A.Application of Thermodynamics to Thermomechanical,Fracture,and Berefringent Phenomena in Viscoelastic Media.Journal of Applied Physiscs,1964,35(5):1451-1465
[122]Bathe.K.J.Finite Element Procedures.2~(nd)edition,Prentice Hall,1995
[123]Zienkiewicz.O.C,Taylor.R.L著.有限元方法:固体力学.北京:清华大学出版社,2006
[124]Findley.W N,Lai.J S,Onaran.K.Creep and Relaxation of Non-linear Viscoelastic Materials.New York:Dover Publication,1976
[125]Henriksen.M.Nonlinear Viscoelastic Stress Analysis—a Finite Element Approach.Computers and Structures,1984,18(1):133-139.
[126]Taylor.R L,Pister.K S,Goudreau.G L.Thermomechanical Analysis of Viscoelastic Solids.International Journal for Numerical Methods in Engineering,1970,2:45-59
[127]Rami.M,Haj-Ali,H.Anastasia,Muliana.Numerical Finite Element Formulation of the Schapery Non-linear Viscoelastic Material Model.International Journal for Numerical Methods in Engineering,2004,59:25-45
[128]Lou.Y.C,Schapery.R.A.Viscoelastic Characterisation of a Nonlinear Fibre-reinforced Plastic.Journal of Composite Materials,1971,5:208-234
[129]王至存.定速拉伸的固体推进剂双轴板条的应力分析.固体火箭技术,1995,18(1):54-59
[130]张永敬,赵光辉,阳建红,强洪夫.HTPB复合固体推进剂非线性本构研究.推进技术,2000,4(21):69-72
[131]Wang Lei.Study of Surface Cracks in a Simulated Solid Rocket Propellant Grain with an Iinternal Star Perforation,Ph.D,1992
[132]Thepenier.J,Gondouin.B,Menez-Coutanceau.H.Reliability of Solid Propellant Grains:Mechanical Analog Motors and Testing.AIAA-87-1987
[133]范天佑.断裂理论基础.北京:科学出版社,2003
[134]FenghuaZhou,Jean-FrancoisMolinari,YulongLi.Three-dimensional Numerical Simulations of Dynamic Fracture in Silicon Carbide Reinforced Aluminum.Engineering Fracture Mechanics,2004,71:1357-1378
[135]范天佑.断裂动力学引论.北京:北京理大大学出版社,1990
[136]Williams.M L.On the Stress Distribution at the Base of a Stationary Crack.J Appl Mech,1957,24:109-114
[137]Rice.J R.A Path Independent Iintegral and the Approximate Analysis of Strain Concentration by Notches and Cracks.J Appl Mech,1968,35:370-386
[138]Larsson S G,Carlsson.A J.Influence of Non-singular Stress Term and Specimen Geometry on Small-scale Yielding at Crack Tips in Elastic-plastic Materials.J Mech Phys Solids,1973,21:263-278
[139]Al-Ani.A M,Hancock.J W.J.Dominance of Short Cracks in Tension and Bending.J Mech Phys Solids,1991,39:23-43
[140]O'Dowd.N P, Shih.C F.Family of Crack-tip Fields Characterized by a Triaxiality Parameter-Ⅱ: Fracture applications.J Mech Phys Solids, 1992.40:939-963
[141]Chao.Y J, Yang.S, Sutton.M A.On the Fracture of Solids Haracterized by One or Two Parameters: Theory and Practice.J Mech Phys Solids, 1994, 42:629-647
[142]Chao.Y J, Zhang.X.Constraint Effect in Brittle Fracture.In: Piascik R(ed) Fatigue and fracture mechanics, 1997, 27:41-60
[143]Chao.Y J, Reuter.W G.Fracture of Surface Cracks Under Bending loads.American Society for Testing and Materials, 1997,128:214-242
[144]Chao.Y J, Liu.S, Broviak.B.Brittle Fracture: Constraint Effect and Crack Curving under Mode I conditions.Exp Mech, 2001,41(3):232-241
[145]Liu.S, Chao.Y J.Variation Fracture Toughness with Constraint.Int J Frac, 2003,124:113-117
[146]Kim.Y, Chao.Y.J.Effect of Lloading Rate on Dynamic Fracture Initiation Toughness.Int J Fract, 2007, 145:195-204
[147]Anderson.T L.Dynamic and Time-dependent Fracture.In: Fracture Mechanics, Fundamentals and Applications.CRC press, 1995
[148]Sih.G C.Some Elastodynamic Problems of Cracks.Int J Frac, 1968, 4:51-68
[149]Ravera.R J, Sih.G C.Transient Analysis of Stress Waves around Cracks under Antiplane Strain.J Acoust Soc Am, 1969, 47:875-880
[150]Sih.C G, Embley.G T, Ravera.R J.Impact Response of a Plane Crack in Extension.Int J Solids Struct, 1972, 8:977-993
[151]Achenbach.J D.Brittle and Ductile Extension of a Finite Crack by a Horizontally Polarized Shear Wave.Int J Eng Sci, 1970, 8:947-966
[152]Sih.G C.Some Elastodynamic Problems of Cracks.Int J Frac, 1968, 4:51-68
[153]Achenbach.J D.Brittle and Ductile Extension of a Finite Crack by a Horizontally Polarized Shear Wave.Int J Eng Sci, 1970, 8:947-966
[154]Achenbach.J D.Dynamic Effects in Brittle Fracture.In:Nemat-Nasser S(ed) Mechanics today, Newyork: Pergamon Press, 1972
[155]Shockey.D A, Curran.D R.A Method of KIC at very Highs Train Rate.ASTM Special Technical Publication No.536, 1973
[156]Shockey.D A.Erlich.D C, KalthoffJ F, Homma.H.Short Pulse Fracture Mechanics.Eng Frac Mech, 1986, 23(1):311-319
[157]Kalthoff.J F, Shockey.D A.Instability of Cracks under Iimpulse Loads.J Appl Phys, 1977,48(3):986-993
[158]Petrov.Y V, Morozov.N F.On the Modeling of Fracture of Brittle Solids.J Appl Mech, 1994.61:710-712
[159]Petrov.Y V, Morozov.N F, Smirnov.V I.Structural Macromechanics Approach in Dynamics of Fracture.Fatigue Fract Eng Mater Struct, 2003,26:363-372
[160]Freund.L B.Fracture Initiation due to Dynamic Loading.In: Dynamic Fracture Mechanics.Cambridge University Press, 1990
[161]Freund.L B.Crack Propagation in an Elastic Solid Subjected to General Loading.Ⅲ.Stress Wave Loading.J Mech Phys Solids, 1973, 21:47-61
[162]Nakamura T, Shih.C F, Freund.L B.Analysis of a Ddynamically Loaded Tthree-point Bend Ductile Fracture Specimen.Eng Frac Mech, 1986,25:333-339
[2]Graham.G.A.C.The Correspondence Principle of Linear Viscoelasticity Theory for mixed Boundary Value Problems Involving Time-dependent Boundary Regions.Quart.Appl.Math.,1968,22:10-20
[3]Graham.G.A.C.The Correspondence Principle of Llinear Viscoelasticity for Problems that Involve Time-dePendent Regions.Int.J.Engrg.Sci,1973
[4]魏培君,张双寅,吴永礼.粘弹性力学的对应原理及其数值反演方法.力学进展,1999,29(3):317-330
[5]王元有.推进剂药柱在内压力载荷下的应力、应变的粘弹性分析.兵工学报,1993,3:20-33
[6]Christensen.R.M.Theory of Viscoelasticity.New York:Academic Press,1982.
[7]杨挺青.粘弹性力学.北京:华中理工大学出版社,1990
[8]Schapery.R.A.Nonlinear Constitutive Equations for Solid Propellant Based on a Work Potential and Micromechanical Model.In Proc.1987 JANNAF Structures and Mechanical Behavior Meeting,17-19 March,CPIA,Huntsville,AL
[9]王礼立,施绍裘,陈江英等.ZWT非线性热粘弹性本构关系的研究与应用.宁波大学学报(理1版),2000,13(4):141-149
[10]Swanson.S.R,Christensen.L.W.A Constitutive Formulation for High Elongation Propellants.J.Spacecraft,1983,20(6):559-566
[11]强洪夫.固体火箭发动机药柱结构完整性数值仿真与实验研究.西安交通大学博士学位论文,1998
[12]Jung.G D,Youn.S K,Kim.B K.A Three-dimensional Nonlinear Viscoelastic Constitutive Model of Solid Propelant.Int.J.Solids Structures,2000,37(34):4715-4732
[13]Zienkiewicz.O C,Watson.M.Some Creep Effects Stress Analysis with Particular Reference to Concrete Pressure Vessel.Nuclear Engineering and Design,1966,4:406-412
[14]Zienkiewicz.O C,Watson.M,King.I P.A Numerical Method of Visco-elastic Stress Aanalysis.Int J Mech Sci,1968,10:807-827
[15]White.J L.The finite element mothod of 3 dimensional nonnlinear viscoelastic large deformation problems.Proceedings of the 2nd Conference on Matrix method in Structural Mechanics,1968:489-516
[16]Argyris.J H,Pister.K S,Szimmat.J,William.K J.Computer Methods in Applied Mechanics and Engineering.Unified concepts of constitutive modelling and numerical solution methods for concrete creep problems.Journal of the Engineering Mechanics,1977,10:199-246
[17]Adey.R A,Brebbia.C A.Efficient Method for Solution of Viscoelastic Problem.Journal of the Engineering Mechanics,1973:1119-1127
[18]Srinatha.H R,Lewis.R W.A Finite Element Method for Thermovisoelastic Analysis of Plane Problems.Computer Methods in Applied Mechanics and Engineering,1981,25:21-33
[19]Yadagari.S,Reddy.C P,Reddy.T S.Viscoelatstic Analysis of Adhesively bonded Joints.Computers and Structures,1987,27(4):445-454
[20]Jones.I W,E.Pierre-Louis.A Linear Thermoviscoelastic Material Model for Solid Rocket Motor Structural Analyses.Computers and Structures,1985,21(12):235-243
[21]Styrk Finne,Cecilia Futsaether,Jan Ivar Botnan.Three-Dimensional Analysis of Solid Propelant Grain Using a Nonlinear Viscoelastic Model.AIAA-2090,1990:1-8
[22]Reggi.A Nonlinear Viscoelastic Constitutive Model for Solid Propellant.Technical Report BMO-TR-93-61,Failure Analysis Associates,1993,4
[23]Lai.J,Bakker A.3-D Schapery Representation for Non-linear Viscoelasticity and Finite Element Implementation.Computional Mechenics,1996,18:182-191
[24]李录贤等.三维药柱的热粘弹性有限元分析.推进技术.1997,18(3):45-50
[25]王馄,田维平.固体火箭发动机前、后翼药柱三维有限元分析.推进技术,1997,18(4):36-41
[26]朱智春等.固体火箭发动机药柱三维温度场有限元分析.推进技术,1997,18(2):21-26
[27]唐国金,周建平.自由装填药柱的结构完整性分析.固体火箭技术,1994,(6):13-19
[28]Feng.Z G,Zhou.J P.The Long-term Aging Effects of Viscoelastic Polymers and Its Finite Element Method.Proc.of Int.Conf.on Deformation,Yield and Fracture of Polymers,Cambrige,U K.1994
[29]蒋辉国.粘弹结构应力应变场与温度场全耦合的计算机程序及其应用.推进技术,1990,1:7-13
[30]杨卫国.ADINA软件在固体发动机设计中的应用.固体火箭技术,1992,4:15-19
[31]沈亚鹏,王晓明,梁汉梁.用Total Lagrangian法的三维粘弹性大变形问题的有限元分析.航空学报(A辑),1989,7:387-393
[32]Shen Ya peng,Zhou Zhe,Xue Qi.Analysis of Deformation of Nozzleless Rocket Propellant.Acta Mechanica Solid Sinica,1990,3(2):193-200
[33]杜建科,朱祖念等.固体发动机药柱损伤粘弹有限元分析.固体火箭技术,2001,24(1):1-5
[34]魏卫,王宇飞.高加速度冲击下固体推进剂药柱轴向形变的数值模拟.固体火箭技术,2003,26(2):42-45
[35]刘中兵,利凤祥,李越森,胡春波.高过载条件下固体推进剂药柱结构完整性分析计算.固体火箭技术,2003,(6):12-16
[36]利凤祥,刘中兵,李越森,胡春波.药柱结构对其抗轴向过载能力的影响.推进技术,2004,25(2):165-169
[37]沈亚鹏,李录贤,王晓明.粘弹性准静态、动态问题的数值解法.力学进展,1994,25(2):265-272
[38]王本华,张戈,黄涵,刘晓.粘弹结构动力响应的有限元分析.强度与环境,1993.3:49-52
[39]王本华,张戈.三维粘弹大变形动力响应分析.推进技术,1994,3:21-27
[40]杨挺青,王胜凯,黄玉盈.粘弹性轴对称平面问题的动态响应.固体力学学报,1987,1:78-86
[41]Murray.J W,Mikeska.A J,Tonkin.M E.Nozzleless Performance Program Grain Deflection Model.AIAA/SAE/ASME,18th Joint Propulsion Conference,Clevland,Ohio,1982
[42]陈前,朱德悉.复合结构振动分析的数值方法.计算结构力学及其用,1990,7(3):27-35
[43]李录贤,沈亚鹏.粘弹性大变形动力响应的有限元分析.计算结构力学及其应用,1994,11(4):349-355
[44]Mott.N.F.Brittle Fracture in Mild Steel Plates.Engineering,1948,165:16-18
[45]Yoffe.E.H.The moving Grifith crack.Phil.Mag.1951,42:739-750
[46]Baker.B.R.Dynamic Stresses Created by a Moving Crack.J.Appl.Mech,1962,29:449-458
[47]K.B.Broberg.The Propagation of a Britle Crack.Archiv fur Fysik,1960,18:159-192
[48]Craggs.J.W.On the Propagation of a Crack in an Elastic-britle Solid.J.Mech.Phys.Solids,1960,8:66-75
[49]Gao.Y.C,Rousselier.G.Near Tip Quasi-static Crack Growth Behavior in Strain Hardening and Softening Material.Theoretical and Applied Fracture Mechanics,1994,20:149-155
[50]Li J,Zhang.X.B.Elastic-plastic Analysis of an Arbitrarily-oriented Mode ⅢCrack Touching an Iinterface.International Journal of Fracture Mechanics,1996,80:311-337
[51]Erdogan.F.Fracture Mechanics.International journal of solids and structures,2000,37:171-183
[52]Griffith.A.A.The Phenomenon of Rupture and Flow in Solids.London:Philosophical Transactions of Royal Society,1920
[53]Irwin.G R.Fracture Dynamics.Fracturing of Metals.Cleveland:Am.Soc.Metals,1948
[54]Orowan.E.Fracture and Strength of Solids.On Prog.In Phys.Ⅴ-Ⅶ,1948
[55]Irwin.G R.Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate.Journal of Applied Mechanics,1957,24:361-364
[56]范天佑.断裂动力学引论.北京:北京理工大学出版社,1990
[57]Hult.J.A,McClintock.F.A Elastic-plastic Distribution around Sharp Notches under Repeated Shear.Proceedings of 9~(th)International Congress on Applied Mechanics,Brussels.1956,8:51-62
[58]Rice.J.R.Stress due to a Sharp Notch in a Work-hardening Elastic-plastic Material Loaded by Longitudinal Shear.Journal of Applied Mechanics,1967,34(2):287-298
[59]Rice.J.R.Contained Plastic Deformation Near Cracks and Notches under Longitudinal Shear.International Journal of Fracture Mechanics,1966,2(2):426-447
[60]Amazigo.J.A.Fully Plastic Center-cracked Strip Antiplane Shear.International Journal of Solids and Structures,1975,11(12):1291-1299
[61]Hutchinson.J.W.Singular Behavior at the End of Tensile Crack in a Hardening Material.Journal of Mechanics and Physics of Solids,1968,16(1):13-21
[62]Rice J.R,Rosengren.G.F.Plane Strain Deformation Near Crack Tip in a Power Law Hardening Material.Journal of Mechanics and Physics of Solids,1968,16(1):1-12
[63]Begley J.A,Landes.J.D.The J-integral as a Fracture Criterion.Fracture Toughness,ASTM.STP 1972,514:1-20
[64]Shib.C.F.Small-scale Yielding Analysis of Mixed Mode Plane Strain Crack Problems.In Fracture analysis,ASTM.STP.1974,560:187-210
[65]Hutchinson.J.W.Plastic Stress and Strain Field at a Crack Tip.Journal of Mechanics and Physics of Solids,1968,16(4):337-347
[66]黄克智,余寿文.弹塑性断裂力学.北京:清华大学出版社,1985
[67]高玉臣.裂纹起始扩展的弹塑性场.固体力学学报,1980,12(1):67-76
[68]高玉臣,黄克智.理想弹塑性平面应变问题.力学学报1981年特刊:111-120
[69]Gao.Y.C,Hwang.K.C.Elastic-plastic Fields in Steady Crack Growth in a Strain-hardening Material.ICF5 in Advances in Fracture Research.Francois D.ed.V2,Pergamon Press,1981
[70]高玉臣.理想弹塑性平面应力问题.固体力学学报,1982,3(3):339-350
[71]Gao.Y.C,Hwang.K.C.On the Formulation of Plane Strain Problems for Elastic Perfectly-plastic medium.International Journal of Engineering Science,1983,21(7):765-780
[72]Gao.Y.C,Hwang.K.C.Elastic-plastic Fields in Steady Crack Growth.In Three-Dimensional Constitutive Relations and Ductile Fracture.Nemat-Nasser S.ed,North-Holland Publication Company,1980
[73]靳志和,余寿文.理想弹塑性材料平面应力Ⅰ型裂纹尖端的弹塑性场.力学学报,1986,18(1):88-92
[74]章梓茂,马兴瑞,高玉臣.理想塑性介质中平面应力静止裂纹的尖端弹塑性场.力学学报,1990,22(2):229-235
[75]Riedel.H.Cracks Loaded in Anti-plane Shear under Creep Conditions.Z.Metall,1978,69(12):755-760
[76]Riedel.H,Rice.J.R.Tensile Cracks in Creeping Solids.Fracture Mechanics.Twelfth Conference,ASTM.STP700,American Society for Testing and Materials,1980,112-130
[77]Riedel.H.Creep Deformation at Crack Tips in Elastic-viscoplastic Solids.J.Mech.Phys.Solids,1981,29:35-49
[78]Hui.C.Y.The Mechanics of Self-similar Crack Growth in an Elastic Power-law Creeping Material.J.Solids Structs,1986,22(4):357-372
[79]Wang.T.C.Elastic-plastic Asymptotic Fields for Cracks on Bi-material Interfaces.Engineering Fracture Mechanics,1990,37(3):527-538
[80]Li F.Z,Needleman.A,Shih.C.F.Characterization of Near Tip Stress and Deformation Fields in Creeping Solids.International Journal of Fracture,1988,36:163-186
[81]Bassani.J.L.Cracks in Materials with Hyperbolic-sine-law Creep Behavior.Elastic-Plastic Fracture:Second Symposium.Volume I-Inelastic Crack Analysis,ASTM.STP803,1983,532-550
[82]Gao.Y.C.Uniparameter Plastic Field Near a Dynamic Crack-tip.Mechanics Research Communications,1988,15(5):307-313
[83]Eran Sharon,Steven.P,Gross,Jay Fineberg.Energy Dissipation in Dynamic Fracture.Physical Review Letters,1996,76(12):2117-2120
[84]Lu Meng,Yiu-Wing Mai,Lin Ye.Crack-tip Field for Fast Fracture of an Elastic-plastic-viscoplastic Material Incorporated with Quasi-brittle Damage.Part 1.Large damage regime,International Journal of Solids and Structures,2001,38:9383-9402
[85]Ueda.S.Impact Response of a Piezoelectric Layered Composite Plate with a Crack.Theoretical and Applied Fracture Mechanics,2002,38:221-242
[86]蔡艳红.粘弹性材料动态扩展裂纹尖端场.哈尔滨工程大学博士学位论文,2003
[87]Zhang.Ch,Savaidis.A,Savaidis.G,Zhu.H.Transient Dynamic Analysis of a Cracked Functionally Graded Material by a BIEM.Computational Materials Science,2003,26:167-174
[88]Tang Li-qiang,Yang Jing-yuan,Wu Guo-hui.The Asymptotic Fields of a Dynamically Growing Crack in a Viscoelastic Material.Journal of Marine Science and Application,2007,6(4):62-67
[89]Fagerstr(o|¨)m.M,Larsson.R.Approaches to Dynamic Fracture Modelling at Finite Deformations.Journal of the Mechanics and Physics of Solids,2008,56:613-639
[90]尹双增.断裂·损伤理论及应用.北京:清华大学出版社,1992
[91]沈成康.断裂力学.上海:同济大学出版社,1996
[92]匡震邦,马法尚.裂纹端部场.西安:西安交通大学出版社,2002
[93]Shockey.D A,Kalthoff.J F,Erlich.D C.Evaluation of Dynamic Instability Criteria.Int J Frac,1983,22:217-229
[94]Homma.H,Shockey.D.A,Murayama.Y.Response of Cracks in Structural Materials to Short Pulse Loads.Journal of Mechanics and Physics of Solids,1983,31:261-279
[95]Ravi-chandar.K,Knauss.W.G.An Experimental Investigation into Dynamic Fracture:Ⅰ.Crack iinitiation and arrest.International Journal of Fracture,1984,25:247-262
[96]黄风雷,王泽平,丁敬.复合固体推进剂动态断裂研究.兵工学报,1995,2:47-50
[97]Koppenhoefer.K C,Dodds.R H.Constraint Effect on Fracture Toughness of Impact-loaded,Pre-cracked Charpy Specimens.Nucl Eng Des,1996,162:145-158
[98]LIU.C,Knauss.W.G,Rosakis.A.J.Loading Rates and the Dynamic Initiation Toughness in Brittle Solids.Intemational Journal of Fracture,1998,90:103-118
[99]Sumit Basu,Narasimhan.R.A Numerical Investigation of Loss of Crack Trip Constraint in a Dynamically Loaded Ductile Specimen.Joumal of the Mechanics and Physics of Solids,2000,48:1967-1985
[100]Jayadevan.K R,Narasimhan.R,Ramamurthy.T S,Dattaguru.B.A Numerical Study of T-stress in Dynamically Loaded Fracture Specimens.In J Solids Struct,2001,38:4987-5005
[101]Kim.Y,Chao.Y.J.Effect of Loading Rate on Dynamic Fracture Initiation Toughness.Int J Fract,2007,145:195-204
[102]Svob.G J,Bills.Jr.K.W.Predictive Surveillance Technique for Air-launched Rocket motors.J Spacecraft,1984,21(2):162-167
[103]Jana.M K,Renganathan.K,Rao G.Venkateswara.A Method of Non-linear Viscoelastic Analysis of Solid Propellant Grains for Pressure Load.Comput Struct,1994,52(1):61-67
[104]Shiang-Woei Chyuan.A Study of Loading History Effect for Thermoviscoelastic Solid Propellant Grains.Computers and Structures,2000,77:735-745
[105]Sebnem(O|¨)z(u|¨)pek.Constitutive Equations for Solid Propellant.The University of Texas,Ph.D,1997
[106]李葆萱.固体推进剂性能.西安:西北工业大学出版社,1990
[107]Coleman.B D,Gurtin.M E.Thermodynamics with Internal State Variables.J Chem.Phys,1967,47:597-613
[108]Valanis.K C.Thermodynamics of Large Viscoelastic Deformations.J Maths Phys,1966,45(2):197-212
[109]杨挺青.粘弹性力学.武汉:华中理工大学出版社,1992
[110]周建平.粘弹性材料的变形动力学模型.固体力学学报,1994,15(1):80-85
[111]李如生.非平衡态热力学和耗散结构.北京:清华大学出版社,1986
[112]Biot.M.A.Theory of Stress-strain Relation in Anisotropic Viscoelasticity and Relation Phenomene.J Appl Physics,1954,25(11):1358-1391
[113]余寿文,冯西桥.损伤力学.北京:清华大学出版社,1997
[114]Allen.D.H,Holmberg.J.A,Ericson.M,Lans.L,Svensson.N,Holmberg.S.Modeling the Viscoelastic Response of GMT Structural Components.Composites Science and Technology,2001,61:503-515
[115]Martin L(?)vesque.Mechamical Behavior Modelling of Nonlinear Viscoelastic Composite Materials by a Homogenisation Approach.L'(?)cole Nationale Superieure D'arts Et Metiers,Ph.D,2004
[116]Green.A.E,Rivlin.R.S.The Mechanics of Nonlinear Materials with Memory.Archive for Rational Mechanics and Analysis,1957,1:1-21
[117]Green.A.E,Rivlin.R.S.The Mechanics of Nonlinear Materials with Memory-Part Ⅲ.Archive for Rational Mechanics and Analysis,1960,4:387-404
[118]Green.A.E,Rivlin.R.S,Spencer.A.J.S.The Mechanics of Nonlinear Materials with Memory-Part Ⅱ.Archive for Rational Mechanics and Analysis,1959,3:82-90
[119]Lockett.F.J.Creep and Stress-relaxation Experiments for Non-linear Materials.International Journal of Engineering Science,1965,3:59-75
[120]Buckley.C.P.Multiaxial nonlinear Viscoelasticity in Solid polymers.Polymer Engineering and Science,1987,27(2):155-164
[121]Schapery.R.A.Application of Thermodynamics to Thermomechanical,Fracture,and Berefringent Phenomena in Viscoelastic Media.Journal of Applied Physiscs,1964,35(5):1451-1465
[122]Bathe.K.J.Finite Element Procedures.2~(nd)edition,Prentice Hall,1995
[123]Zienkiewicz.O.C,Taylor.R.L著.有限元方法:固体力学.北京:清华大学出版社,2006
[124]Findley.W N,Lai.J S,Onaran.K.Creep and Relaxation of Non-linear Viscoelastic Materials.New York:Dover Publication,1976
[125]Henriksen.M.Nonlinear Viscoelastic Stress Analysis—a Finite Element Approach.Computers and Structures,1984,18(1):133-139.
[126]Taylor.R L,Pister.K S,Goudreau.G L.Thermomechanical Analysis of Viscoelastic Solids.International Journal for Numerical Methods in Engineering,1970,2:45-59
[127]Rami.M,Haj-Ali,H.Anastasia,Muliana.Numerical Finite Element Formulation of the Schapery Non-linear Viscoelastic Material Model.International Journal for Numerical Methods in Engineering,2004,59:25-45
[128]Lou.Y.C,Schapery.R.A.Viscoelastic Characterisation of a Nonlinear Fibre-reinforced Plastic.Journal of Composite Materials,1971,5:208-234
[129]王至存.定速拉伸的固体推进剂双轴板条的应力分析.固体火箭技术,1995,18(1):54-59
[130]张永敬,赵光辉,阳建红,强洪夫.HTPB复合固体推进剂非线性本构研究.推进技术,2000,4(21):69-72
[131]Wang Lei.Study of Surface Cracks in a Simulated Solid Rocket Propellant Grain with an Iinternal Star Perforation,Ph.D,1992
[132]Thepenier.J,Gondouin.B,Menez-Coutanceau.H.Reliability of Solid Propellant Grains:Mechanical Analog Motors and Testing.AIAA-87-1987
[133]范天佑.断裂理论基础.北京:科学出版社,2003
[134]FenghuaZhou,Jean-FrancoisMolinari,YulongLi.Three-dimensional Numerical Simulations of Dynamic Fracture in Silicon Carbide Reinforced Aluminum.Engineering Fracture Mechanics,2004,71:1357-1378
[135]范天佑.断裂动力学引论.北京:北京理大大学出版社,1990
[136]Williams.M L.On the Stress Distribution at the Base of a Stationary Crack.J Appl Mech,1957,24:109-114
[137]Rice.J R.A Path Independent Iintegral and the Approximate Analysis of Strain Concentration by Notches and Cracks.J Appl Mech,1968,35:370-386
[138]Larsson S G,Carlsson.A J.Influence of Non-singular Stress Term and Specimen Geometry on Small-scale Yielding at Crack Tips in Elastic-plastic Materials.J Mech Phys Solids,1973,21:263-278
[139]Al-Ani.A M,Hancock.J W.J.Dominance of Short Cracks in Tension and Bending.J Mech Phys Solids,1991,39:23-43
[140]O'Dowd.N P, Shih.C F.Family of Crack-tip Fields Characterized by a Triaxiality Parameter-Ⅱ: Fracture applications.J Mech Phys Solids, 1992.40:939-963
[141]Chao.Y J, Yang.S, Sutton.M A.On the Fracture of Solids Haracterized by One or Two Parameters: Theory and Practice.J Mech Phys Solids, 1994, 42:629-647
[142]Chao.Y J, Zhang.X.Constraint Effect in Brittle Fracture.In: Piascik R(ed) Fatigue and fracture mechanics, 1997, 27:41-60
[143]Chao.Y J, Reuter.W G.Fracture of Surface Cracks Under Bending loads.American Society for Testing and Materials, 1997,128:214-242
[144]Chao.Y J, Liu.S, Broviak.B.Brittle Fracture: Constraint Effect and Crack Curving under Mode I conditions.Exp Mech, 2001,41(3):232-241
[145]Liu.S, Chao.Y J.Variation Fracture Toughness with Constraint.Int J Frac, 2003,124:113-117
[146]Kim.Y, Chao.Y.J.Effect of Lloading Rate on Dynamic Fracture Initiation Toughness.Int J Fract, 2007, 145:195-204
[147]Anderson.T L.Dynamic and Time-dependent Fracture.In: Fracture Mechanics, Fundamentals and Applications.CRC press, 1995
[148]Sih.G C.Some Elastodynamic Problems of Cracks.Int J Frac, 1968, 4:51-68
[149]Ravera.R J, Sih.G C.Transient Analysis of Stress Waves around Cracks under Antiplane Strain.J Acoust Soc Am, 1969, 47:875-880
[150]Sih.C G, Embley.G T, Ravera.R J.Impact Response of a Plane Crack in Extension.Int J Solids Struct, 1972, 8:977-993
[151]Achenbach.J D.Brittle and Ductile Extension of a Finite Crack by a Horizontally Polarized Shear Wave.Int J Eng Sci, 1970, 8:947-966
[152]Sih.G C.Some Elastodynamic Problems of Cracks.Int J Frac, 1968, 4:51-68
[153]Achenbach.J D.Brittle and Ductile Extension of a Finite Crack by a Horizontally Polarized Shear Wave.Int J Eng Sci, 1970, 8:947-966
[154]Achenbach.J D.Dynamic Effects in Brittle Fracture.In:Nemat-Nasser S(ed) Mechanics today, Newyork: Pergamon Press, 1972
[155]Shockey.D A, Curran.D R.A Method of KIC at very Highs Train Rate.ASTM Special Technical Publication No.536, 1973
[156]Shockey.D A.Erlich.D C, KalthoffJ F, Homma.H.Short Pulse Fracture Mechanics.Eng Frac Mech, 1986, 23(1):311-319
[157]Kalthoff.J F, Shockey.D A.Instability of Cracks under Iimpulse Loads.J Appl Phys, 1977,48(3):986-993
[158]Petrov.Y V, Morozov.N F.On the Modeling of Fracture of Brittle Solids.J Appl Mech, 1994.61:710-712
[159]Petrov.Y V, Morozov.N F, Smirnov.V I.Structural Macromechanics Approach in Dynamics of Fracture.Fatigue Fract Eng Mater Struct, 2003,26:363-372
[160]Freund.L B.Fracture Initiation due to Dynamic Loading.In: Dynamic Fracture Mechanics.Cambridge University Press, 1990
[161]Freund.L B.Crack Propagation in an Elastic Solid Subjected to General Loading.Ⅲ.Stress Wave Loading.J Mech Phys Solids, 1973, 21:47-61
[162]Nakamura T, Shih.C F, Freund.L B.Analysis of a Ddynamically Loaded Tthree-point Bend Ductile Fracture Specimen.Eng Frac Mech, 1986,25:333-339
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