金属塑性与超塑性拉伸失稳及其力学解析
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摘要
本论文主要讨论和研究了理想试样的超塑性变形的稳定性。文中建立了描述拉伸变形过程的模型,定义和讨论了变形过程的四个失稳状态,指出Considère、Hart、Ghosh和Jonas所提出的稳定性准则描述的是应变速率敏感性材料在不同变形路径下的失稳发生。γ= 1描述的是恒应变速率拉伸变形中的失稳,γ= 1 + m描述的是恒速率拉伸变形中的失稳,而γ= 1 ? m描述的是定载荷拉伸变形过程中的失稳。由于在定载荷拉伸变形过程中,载荷是恒定的,因此载荷不能做为判断失稳的参考量,故Hart将试样截面积的变化做为判断失稳的参考量。结合数学模型给出了应变速率波动模型,利用数学模型解出了全面反映力学参量与材料参数之间关系的超塑性流动方程。对理想试样的四个失稳状态的失稳应变进行了预测,借助于数值计算的技巧给出了非理想试样断裂应变的预测公式。
Nowadays,the world's development mainly represents on two aspects:science and technology, war industry. While the development andadvancement of them more and more rely on manufacture and application ofnew materials. Then superplastic metals have important roles on above twofields. Therefore,superplastic theory and application need to be studied deeply,in order to give universal answer and regular guidance for the questions inmanufacture. We should understand further the conjunction betweenmacro-mechanical law and micro-physics mechanism , which is veryimportant to develop new materials, simplify superplastic pretreatment andnormalize forming technics.
Superplastic deformation has strong structure sensitivity,and there isclose relationship between stress state and deformation path. Uniaxial tensileis the simplest one-dimension stress state, therefore the relationship betweenmaterial mechanical parameter and deformation path and conditionalparameter can be confirmed by tensile experiment directly. The essencedifference between superplastic deformation of superplastic material andplastic deformation of ductile material is: When load is instable duringsuperplastic deformation, geometrical instability will not happensimultaneously which appears after homogeneous deformation;At the sametime of geometrical instability, stress instability will happen;and failure
instability will not be caused directly after geometrical instability, but arelatively long quasi-stable deformation will be rebuilt. This is themechanical essence of material's superplasticity. Based on reviewing ofsuperplastic tensile deformation instability at home and abroad this paper hasa systemic study on tensile instability.The author's works and achievements are as follows:1、The achievements about superplastic uniaxial tensile deformation inthree aspects since 1885 is reviewed and summarized:①the definition of instability and its determinant rules;②the development of necking and the influence of defect on instabilitydiffusion;③the predicts of instability strain and failure strain.The author point out that there has not form a systemic theory andmethod,that is the shortage of superplastic theory;And the orientation of thedevelopment of superplastic theory is emphasized, one is to develop advancedobservation and experiment equipments, the other is to establish mathematicalmodel which could accurately describe deformation course, and then get abroadly applied constructive equation which reflects superplastic flow.2、Constructive equation which reflects superplastic flow is establishedsuccessfully, combining the Hart's state equation and basic formulae ofsuperplastic deformation. The stability of the model is analysed from the pointof nonlinear systemic kinetics, and it is pointed out that the system will go tobe instable if without control when load attains maximum value.3、Quasi-uniform deformation stage of superplastic deformation isdivided into: load instability,geometry instability,stress instability and failureinstability,then these are analyzed. We got a conclusion that different rules ofinstability is consistent,their expressions are only the beginning of instability
under different deformation path or instable state, and there is nocomparability between the strains corresponding to instability point of eachinstability rules.4、Superplastic uniaxial tensile sample is regarded as a nonlinear kineticsystem,and we obtain strain rate fluctuate model of this system. Load is thedriving force for the system. When initial load is given, initial strain rate canbe confirmed by load and strain hardening property of material;While strainrate sensitivity index is determined by strain rate,test temperature and grainsize of material,and its value represents recovery ability of strain rate,thebigger the value, the higher the recovery ability;Constructive equation isgiven which includes initial condition, stress, strain, strain rate, strain ratesensitivity index and strain hardening index and can represent superplasticdeformation course specifically;Furthermore the important results aboutsuperplastic tensile deformation previously were reappeared by theconstructive equation.5、Necking question of non perfect sample was studied;Instable strainand failure strain were forecasted,then we obtain ideal theoretic predictorformula.In 1964,Backofen put forward constructive equation representingsuperplastic tensile deformation process. Then, Hart gave state equationdescribing superplastic deformation process in 1967. The equation combinedstress, strain, strain rate, strain rate sensitivity index and strain hardeningindex. However, it is too ambiguous to reflect the relationship betweendifferent mechanical variables and material parameters. The mathematicalmodel in the first chapter made up for the shortage of the state equation. Themathematical model which was given by the author is a standard second-ordernonlinear differential equation , which provided theoretical basis for
controlling tensile deformation process automatically. In addition,if we canconfirm the relationship between material parameter and strain or strain rate,then the model will be more definitely to confirm the relationship betweendifferent mechanical variables. Superplastic deformation process is toocomplex to express by one variable function, which is a commonunderstanding to people , thus Backofen's constructive equation seemsextremely simple. On the other hand, Backofen's constructive equation didn'trepresent the relationship between different mechanical variables overall. Wecan obtain a new constructive equation by regarding the material parametersas constant,and Backofen's constructive equation is just a peculiar case of thenew constructive equation. The constructive equation in the third chapterrepresents the relationship of mechanical variables and material parameters. Itis the new constructive equation that can obtain a result consisting withstability criterion under different deformation path. There is innovation in thefirst chapter's mathematical model and the third chapter's constructiveequation,and they will contribute to perfect and develop superplasticdeformation theory. The mechanical analysis about four states of tensileinstability will help us understand deformation process better;Strain ratefluctuate model of superplastic tensile deformation represents strain ratesensitivity of superplastic material more clearly,and gives the effect thatstrain rate sensitivity index on strain rate fluctuate model,this model also canhelp us establish relational expression of strain rate sensitivity index.Moreover, the forecasting of instability strain and failure strain with singledefect or mixed defect sample enrich the theory of strain forecasting.The achievements and results of this paper will contribute to thedevelopment of superplastic theory.
Nowadays,the world's development mainly represents on two aspects:science and technology, war industry. While the development andadvancement of them more and more rely on manufacture and application ofnew materials. Then superplastic metals have important roles on above twofields. Therefore,superplastic theory and application need to be studied deeply,in order to give universal answer and regular guidance for the questions inmanufacture. We should understand further the conjunction betweenmacro-mechanical law and micro-physics mechanism , which is veryimportant to develop new materials, simplify superplastic pretreatment andnormalize forming technics.
Superplastic deformation has strong structure sensitivity,and there isclose relationship between stress state and deformation path. Uniaxial tensileis the simplest one-dimension stress state, therefore the relationship betweenmaterial mechanical parameter and deformation path and conditionalparameter can be confirmed by tensile experiment directly. The essencedifference between superplastic deformation of superplastic material andplastic deformation of ductile material is: When load is instable duringsuperplastic deformation, geometrical instability will not happensimultaneously which appears after homogeneous deformation;At the sametime of geometrical instability, stress instability will happen;and failure
instability will not be caused directly after geometrical instability, but arelatively long quasi-stable deformation will be rebuilt. This is themechanical essence of material's superplasticity. Based on reviewing ofsuperplastic tensile deformation instability at home and abroad this paper hasa systemic study on tensile instability.The author's works and achievements are as follows:1、The achievements about superplastic uniaxial tensile deformation inthree aspects since 1885 is reviewed and summarized:①the definition of instability and its determinant rules;②the development of necking and the influence of defect on instabilitydiffusion;③the predicts of instability strain and failure strain.The author point out that there has not form a systemic theory andmethod,that is the shortage of superplastic theory;And the orientation of thedevelopment of superplastic theory is emphasized, one is to develop advancedobservation and experiment equipments, the other is to establish mathematicalmodel which could accurately describe deformation course, and then get abroadly applied constructive equation which reflects superplastic flow.2、Constructive equation which reflects superplastic flow is establishedsuccessfully, combining the Hart's state equation and basic formulae ofsuperplastic deformation. The stability of the model is analysed from the pointof nonlinear systemic kinetics, and it is pointed out that the system will go tobe instable if without control when load attains maximum value.3、Quasi-uniform deformation stage of superplastic deformation isdivided into: load instability,geometry instability,stress instability and failureinstability,then these are analyzed. We got a conclusion that different rules ofinstability is consistent,their expressions are only the beginning of instability
under different deformation path or instable state, and there is nocomparability between the strains corresponding to instability point of eachinstability rules.4、Superplastic uniaxial tensile sample is regarded as a nonlinear kineticsystem,and we obtain strain rate fluctuate model of this system. Load is thedriving force for the system. When initial load is given, initial strain rate canbe confirmed by load and strain hardening property of material;While strainrate sensitivity index is determined by strain rate,test temperature and grainsize of material,and its value represents recovery ability of strain rate,thebigger the value, the higher the recovery ability;Constructive equation isgiven which includes initial condition, stress, strain, strain rate, strain ratesensitivity index and strain hardening index and can represent superplasticdeformation course specifically;Furthermore the important results aboutsuperplastic tensile deformation previously were reappeared by theconstructive equation.5、Necking question of non perfect sample was studied;Instable strainand failure strain were forecasted,then we obtain ideal theoretic predictorformula.In 1964,Backofen put forward constructive equation representingsuperplastic tensile deformation process. Then, Hart gave state equationdescribing superplastic deformation process in 1967. The equation combinedstress, strain, strain rate, strain rate sensitivity index and strain hardeningindex. However, it is too ambiguous to reflect the relationship betweendifferent mechanical variables and material parameters. The mathematicalmodel in the first chapter made up for the shortage of the state equation. Themathematical model which was given by the author is a standard second-ordernonlinear differential equation , which provided theoretical basis for
controlling tensile deformation process automatically. In addition,if we canconfirm the relationship between material parameter and strain or strain rate,then the model will be more definitely to confirm the relationship betweendifferent mechanical variables. Superplastic deformation process is toocomplex to express by one variable function, which is a commonunderstanding to people , thus Backofen's constructive equation seemsextremely simple. On the other hand, Backofen's constructive equation didn'trepresent the relationship between different mechanical variables overall. Wecan obtain a new constructive equation by regarding the material parametersas constant,and Backofen's constructive equation is just a peculiar case of thenew constructive equation. The constructive equation in the third chapterrepresents the relationship of mechanical variables and material parameters. Itis the new constructive equation that can obtain a result consisting withstability criterion under different deformation path. There is innovation in thefirst chapter's mathematical model and the third chapter's constructiveequation,and they will contribute to perfect and develop superplasticdeformation theory. The mechanical analysis about four states of tensileinstability will help us understand deformation process better;Strain ratefluctuate model of superplastic tensile deformation represents strain ratesensitivity of superplastic material more clearly,and gives the effect thatstrain rate sensitivity index on strain rate fluctuate model,this model also canhelp us establish relational expression of strain rate sensitivity index.Moreover, the forecasting of instability strain and failure strain with singledefect or mixed defect sample enrich the theory of strain forecasting.The achievements and results of this paper will contribute to thedevelopment of superplastic theory.
引文
[1] 宋玉泉. 测定超塑性应变速率敏感性指数 m 的新公式――用长度及其增量测定m 值. 吉林工大学报, 1984(4):116-120.
[2] 宋玉泉. 超塑性均匀大变形动态过程的力学分析.吉林工业大学学报,1985(1):13-21.
[3] 宋玉泉.应变速率敏感性指数 m 的力学解析和测量的规格化理论.吉林工业大学学报,1985(2):1-14.
[4] 宋玉泉,连书君.载荷跃变法测量 m 值.机械工程学报,1989 年 9(Vol.25,No.3):38-42.
[5] 宋玉泉,程永春,王习文.超塑性拉伸似粘性流变方程中本构参数的力学解析.中国科学(E 辑),1997,10(Vol.27,No.5):385-392.
[6] 宋玉泉,高柏恩,王习文.超塑性拉伸似粘性变参数流变方程.中国科学(E 辑),1998 年 6 月,第 28 卷,第 3 期:192-197.
[7] 宋玉泉,程永春,刘颖.拉伸变形应变硬化指数的力学涵义及其规范测量.中国科学(E 辑),2000 年 6 月,(Vol.30)第 3 期: 200-207.
[8] 宋玉泉,程永春,刘术梅.超塑拉伸应变速率敏感性指数的力学解析.机械工程学报,2001 年 3 月:5-10.
[9] 宋玉泉,程永春,刘术梅.超塑性拉伸变形应变速率敏感性指数的试验测量及其精细分析.机械工程学报,2001 年 4 月:1-7.
[10] 宋玉泉,海锦涛,管志平.拉伸变形应变硬化指数的力学解析.中国科学(E 辑),2001 年 4 月,第 2 期:103-108.
[11] 宋玉泉,程永春,王习文.拉伸变形应变硬化指数的实验测量及其精细分析.中国科学(E 辑),2001 年 6 月,(Vol.31,No.3): 193-203.
[12] 宋玉泉,程永春,王习文.拉伸应变速率敏感性指数的力学涵义及 其规范测量.机械工程学报,2001 年 8 月:33-38.
[13] 宋玉泉,刘术梅,侯磊.超塑性拉伸均匀应变值的定量判定.科学通报,2002 年 5 月,第 9 期:717-720.
[14] 宋玉泉.超塑拉伸变形的力学解析.机械工程学报,2003 年 10 月: 64-72.
[15] I.-H.Lin, J.P.Hirth and E.W.Hart.Plastic instability in uniaxial tension tests.Acta Metallurgica, 1981, 29: 819-827.
[16] Pierre VIOLAN.Critere de stabilite de la deformation plastique en traction des metaux cubiques centres.Scripta Metallurgica, Vol.6, 1972:1175-1184.
[17] A.K.Ghosh.Tensile instability and necking in materials with strain hardening and strain-rate hardening.Acta Metallurgica, 1977, 25: 1413-1424.
[18] F.A.Nichols.Overview No.7 Plastic instabilities and uniaxial tensile ductilities. Acta Metallurgica, 1980, 28: 663-673.
[19] J.J.Jonas,R.A.Holt,C.E.Coleman.Plastic stability in tension and compression. Acta Metallurgica,1976,24:911-918.
[20] E.W.Hart.Theory of the tensile test.Acta Metallurgica, 1967, 15: 351-355.
[21] I.-H.Lin, J.P.Hirth and E.W.Hart.Plastic instability in uniaxial tension tests.Acta Metallurgica, 1981, 29: 819-827.
[21] J.J.Jonas, N.Christodoulou, C.G'Sell.The onset of flow localization in tensile samples containing geometric and metallurgical defects.Scripta Metallurgica, 1978, 12: 565-570.
[22] J.W.Hutchinson, K.W.Neale.Influence of strain-rate sensitivity on necking under uniaxial tension.Acta Metallurgica, 1977, 25: 839-846.
[23] Li Chuan Chung, Jung-Ho Cheng.The analysis of instability and strain co ncentration during superplastic deformation.Materials Science and Engineering, 2001, A308: 153-160.
[24] C.H.Cáceres, D.S.Wilkinson.Acta Metall, 1984,32(3):415—422.
[25] J.J.Jonas, B.Baudelet.Effect of crack and cavity generation on tensile stability.Acta Metallurgica, 1977, 25: 43-50.
[26] U.F.Kocks,J.J.Jonas,H.Mecking.The development of strain-rate gradients.Acta Metallurgica,1979,27:419-432.
[27] 畑山東明,和泉 修.Al-33Cu 超塑性合金における不均一形状試料の変形挙動.日本金属学会誌,第 45 巻,第 12 号(1981):1326-1332.
[28] 畑山東明,和泉 修. m 値と塑性不安定.日本金属学会誌,第 45巻,第 12 号(1981):1332-1337.
[29] Farghalli A.Mohamed,Terence G.Langdon.Flow Localization and neck formation in a superplastic metal.Acta Metallurgica,1981,29: 911-920.
[30] 畑山東明, 武井英雄.超塑性材料における m 値と破壊ひずみ. 日本金属学会会報, 第 21 巻, 第 10 号(1982):762—768.
[31] Amit K Ghosh and Robert A Ayres.On Rep[orted Anomalies in Relating Strain-Rate Sensitivity( m ) to Ductility.Metallurgical Transactions A, 1976,Vol.7A:1589-1591.
[32] D.LEE and F.ZAVERL Jr.The influence of material parameters on nonuniform plastic flow in simple tension.Acta Metallurgica, Vol.28,1980:1415-1426.
[33] Jianshe Lian, Bernard Baudelet.Necking development and strain to fracture under uniaxial tension.Materials Science and Engineering, 1986, 84: 157-162.
[34] W.A.Backofen , I.R.Turner and D.H.Avery.Superplasticity in an Al-Zn Alloy.Transactions of the asm,1964 Vol.57: 980—990.
[35] E. W. Hart. A phenomenological theory for plastic deformation of polycrystalline metals. Acta Metallurgica,1970,18(6):599-610.
[36] N.Christodoulou,J.J.Jonas.Work hardening and rate sensitivity material coefficients for OFHC Cu and 99.99%Al.Acta metal,1984,Vol.32,No.10:1655-1668.
[37] 佐藤英一,粟林一彦,堀内 良.ネック形状変化の解析もとづく超塑性変形にぉける.日本金属学会誌,第 52 巻,第 11 号(1988):1051-1056.
[38] 吴艳青,张克实.粗晶超塑性单轴拉伸颈缩模拟.计算力学学报,2004 年 2 月,第 4 期:81~87.
[39] Xing Huilin,Zhang Kaifeng,Z.R.Wang.Study on the optimal mode of superplastic deformation.Journal of Materials Processing Technology,1994,44:29-34.
[40] M.Khantha,D.P.Pope,V.Vitek.Dislocation generation instability and the brittle-to-ductile transition.Materials Science and Engineering, 1995,A192/193:435-442.
[41] B.Wack,A.Tourabi.A new method to quantify Portevin-Le Chatelier instabilities : application to aluminium-lithium alloys.Materials Science and Engineering,1995,A196:79-87.
[42] Sinisa Dj,Mesarovic.Dynamic strain aging and plastic instabilities. J.Mech Phys Solids,1995,43(5):671-700.
[43] P.B.Hirsch , S.G.Roberts.Comment on the brittle-to-ductile transition : A cooperative dislocation generation instability dislocation dynamics and the strain-rate dependence of the transition temperature.Acta Mater,1996,44(6):2361-2371.
[44] H.Moritoki,E.Okuyama.Intrinsic criterion of plastic instability. Journal of Materials Processing Technology,1996,60:649~656.
[45] Michael Zaiser,Peter H?hner.A unified description of strain-rate softening instabilities.Materials Science and Engineering,1997,A238:399-406.
[46] M.Dablij,A.Zeghloul,Portevin-Le Chatelier. Plastic instabilities: characteristics of deformation bands.Materials Science and Engineering,1997,237:1-5.
[47] Petr Wyslych,Eva Mazancóva,Karel Mazanec.The instabilities of plastic deformation in as-quenched martensite.Materials Science and Engineering,1997,A234-236:513-516.
[48] M.Kolbe , K.Neuking , G.Eggeler.Dislocation reactions and microstructural instability during 1025°C shear creep testing of superalloy single crystals.Materials Science and Engineering,1997, A234-236:877-879.
[49] B.I.Smirnov.Superlocalization of plastic deformation in crystals at high temperatures.Materials Science and Engineering,1997,A233: 56-60.
[50] Ming Li,O.Richmond.Intrinsic instability and nonuniformity of plastic deformation.International Journal of Plasticity,1997,13(8-9): 765-784.
[51] Francois Louchet,Mikha?l Lebyodkin.A general approach for stress anomalies and plastic instabilities in intermetallics.Materials Science and Engineering,1997,A239-240:804-807.
[52] P.Lukác,J.Balík,F.Chmelík.Physical aspects of plastic instabilities. Materials Science and Engineering,1997,A234-236:45-51.
[53] G.Bérces,N.Q.Chinh,A.Juhász,J.Lendvai.Kinematic analysis of plastic instabilities occurring in microhardness tests.Acta Mater,1998,46(6):2029-2037.
[54] S.V.S.Narayana Murty , B.Nageswara Rao , B.P.Kashyap. Instability criteria for hot deformation of materials.International Materials Reviews,2000,45(1):15-26.
[55] James C.M. Li. Instabilities in micromechanical deformation. Materials Science and Engineering, 2000, A285: 207-212.
[56] Zs. Kovács, J. Lendvai, G. V?r?s. Localized deformation bands in Portevin–Le Chatelier plastic instabilities at a constant stress rate. Materials Science and Engineering, 2000, A279: 179-184.
[57] Poul V. Lade. Instability shear banding and failure in granular materials. International Journal of Solids and Structures, 2002, 39: 3337-3357.
[58] Daniel Walgraef. Rate equation approach to dislocation dynamics and plastic deformation. Materials Science and Engineering, 2002, A322: 167-175.
[59] N. Q. Chinh, Gy. Horváth, Zs. Kovács, J. Lendvai. Characterization of plastic instability steps occurring in depth-sensing indentation tests. Materials Science and Engineering, 2002, A324: 219-224.
[60] K. W. Neale, K. Inal, P. D. Wu. Effects of texture gradients and strain paths on localization phenomena in polycrystals . International Journal of Mechanics Science, 2003, 45: 1671-1686.
[61] 曲 杰, 金泉林, 徐秉业. 超塑性本构模型材料参数识别方法研究. 工程力学, 2004 年 8 月, 第 4 期: 17~21.
[62] M. A. Burke, W. D. Nix. Plastic instabilities in tension creep. Acta Metallurgica, 1975, 23: 793-798.
[63] 畑山東明, 岡部卓治, 武井英雄, 宝道喜之. 超塑性材料の m値と伸び. 日本金属学会誌, 第 46 巻, 第 2 号(1982):205--210
[64] 崗部卓治, 畑山東明, 武井英雄. 超塑性材料の破壊挙動. 日本金属学会誌, 第 46 巻, 第 2 号(1982):211—216.
[65] T. G. Langdon. Fracture processes in superplastic flow. Metal Science, 1982, 16: 175-183.
[66] Jianshe Lian, Bernard Baudelet, Michel Suery. Numerical analysis of the influence of various defects on superplastic fracture under uniaxial tension. Computational Methods for Predicting Material Processing Defects, edited by M. Predeleanu, 1987.
[67] Galip Said, Suleyman Tasgetiren. An express technique for the determination of static and dynamic fracture toughness (KIC, KId) of bcc metals and alloys . Mechanics of Materials, 2004, 36: 1129-1142.
[68] 陈光南, 胡世光. 板材拉伸成形中损伤、失稳与成形极限曲线的建立. 塑性工程学报, 1994 年 3 月, 第 1 卷, 第 1 期: 31~36.
[69] 赵军, 郑祖伟, 潘文武. 拉深过程智能化控制中的破裂失稳临界条件. 燕山大学学报, 2000 年 10 月, 第 24 卷, 第 4 期: 330~337.
[70] 王祖唐. 金属塑性变形极限判据. 应用力学学报, 2002 年 6 月,第 19 卷, 第 2 期: 104~106.
[71] 金泉林. 超塑变形的行为与本构描述. 力学进展, 1995年5月25, 第 25 卷, 第 2 期: 260―274.
[72] 邓忠勇, 黄伯云, 贺跃辉, 孙坚. 热变形态 TiAl 基合金超塑性拉伸过程中应变速率敏感系数的分析. 稀有金属材料与工程, 1999 年 8 月, 第 28 卷: 第 4 期.
[73] 刘润广, 蒋浩民, 姜勇. GH4169 合金超塑性变形及其力学行为的研究. 宇航材料工艺, 1998 年, 第 2 期.
[74] 刘润广, 蒋浩民, 姜勇. 2214 铝合金超塑性变形机制. 金属学报, 1996 年 12 月, 第 32 卷, 第 12 期: 1244-1247.
[75] 陈征宇. 对影响金属材料塑性变形的重要指标-应变速率敏感性指数的探讨. 机械设计与制造, 1998 年 3 月: 40-42.
[76] 蒋浩民, 姜勇, 刘润广. 2214 铝合金超塑性变形力学行为的研究. 航天工艺, 1996 年第 3 期: 7-10.
[77] 田宝辉, 李焕喜等. Al-Li 单晶体流变应力的应变速率敏感性. 兵器材料科学与工程, 1997年7月, 第20卷, 第4期: 14-19.
[78] 刘润广, 蒋大鸣, 崔约贤, 王仲仁. Al-Zn-Mg-Cu 合金的超塑性变形力学行为. 哈尔滨工业大学学报, 1998 年 10 月,第 30 卷, 第 5 期: 121-123.
[79] 黄伯云, 贺跃辉, 邓忠勇, 王健农. 热变形 TiAl 基合金的超塑性行为. 金属学报,1998 年 11 月, 第 34 卷, 第 11 期: 1173-1177.
[80] 罗兵辉, 周善初. Zn-Al 共析合金室温超塑性变形机理. 材料科 学与工程, 1995 年, 第 13 卷, 第 4 期: 22-24.
[81] 石志强, 叶以富, 李世春. Zn-5Al共晶合金的恒载荷超塑性拉伸试验. 金属热处理, 2002 年, 第 27 卷, 第 1 期: 33-35.
[82] 刘勤. 流变应力的应变速率敏感性指数(m)及其和超塑性之间的关系. 机械工程材料, 1979 年, 第 2 期: 58~69.
[83] J. J. Gracio, A. B. Lopes, E. F. Rauch. Analysis of plastic instability in commercially pure Al alloys. Journal of Materials Processing Technology, 2000, 103: 160-164.
[84] D. Bigoni, B. Loret. Effects of elastic anisotropy on strain localization and flutter instability in plastic solids. Journal of the Mechanics and Physics of Solids, 1999, 47: 1409-1436.
[85] Du Zhixiao, Wu Shichun. A kinetic equation for damage during superplastic deformation. Journal of Materials Processing Technology, 1995, 52: 270-279.
[86] Peter H?hner. A generalized criterion of plastic instabilities and its application to creep damage and superplastic flow. Acta Metall. Meter., 1995, 43(11): 4093-4100.
[87] 赵军, 李硕本. 金属复合板的拉伸失稳判据. 机械工程学报, 1995 年 10 月, 第 31 卷, 第 5 期: 103~108.
[88] 李名尧, 川.比吉特. 应变速率敏感性对板料成形失稳的影响. 上海工程技术大学学报, 2000 年 12 月, 第 14 卷, 第 4 期: 248~258.
[89] 杜志孝, 李森泉, 刘马宝, 吴诗惇. 超塑性板料的成形极限. 应用数学和力学, 1996 年 2 月, 第 17 卷, 第 2 期: 127~132.
[90] 柳玉起, 胡平, 李运兴, 陈塑寰. 金属材料平面应变拉伸变形局部化有限元分析. 应用力学学报, 1995 年 6 月: 17~22.
[91] 李振环, 张克实. 温度、材料不均匀性对粘塑性材料冲击拉伸失稳的影响. 成都科技大学学报, 1994 年 1 月, 第 75 期:95~102.
[92] J. Kajberg, G. Lindkvist. Characterisation of materials subjected to large strains by inverse modelling based on in-plane displacement fields . International Journal of Solids and Structures, 2004, 41: 3439-3459.
[93] Li Chuan Chung, Jung-Ho Cheng. Fracture criterion forming pressure design for superplastic bulging . Materials Science and Engineering, 2002, A333: 146-154.
[94] K. Inal, P.D. Wu, K.W. Neale. Instability and localized deformation in polycrystalline solids under plane-strain tension . International Journal of Solids and Structures, 2002, 39: 983-1002.
[95] G. Nefussi, A. Combescure. Coupled buckling and plastic instability for tube hydroforming. International Journal of Mechanics Science, 2002, 44: 899-914.
[96] G. J. Creus. Instability and damage effects in the modeling of metal forming .Comput. Methods Appl. Mech. Engrg., 2000, 182: 421-437
[97] A.B. Lopes, E.F. Rauch, J.J. Gracio. Textural vs structural plastic instabilities in sheet metal forming. Acta mater., 1999, 47(3): 859-866.
[98] Youngseog Lee, Vikas Prakash. Numerical simulations of dynamic plastic shear instability under conditions of plane strain. Int. J. Solids Structures, 1998, 35(28-29): 3755-3791.
[99] Rodeny Hill. A general theory of plastic deformation and instability in thin-walled tubes under combined loading. J. Mech. Phys. Solids,1996, 44(12): 2041~2057.
[100] Yeong-Maw Hwang, Hung-Hsiou Hsu, Hung-Jen Lee. Analysis of plastic instability during sandwich sheet rolling. Int. J. Mech. Tools Manufact., 1996, 36(1): 47~62.
[101] D. W. A. Rees. Instability limits to the forming of sheet metals. Journal of Materials Processing Technology, 1995, 55: 146-153.
[102] A.K. Ghosh. A Numerical Analysis of the Tensile Test for Sheet Metals. Metallurgical Transactions A 1977, 8A:1221-1232.
[103] 吴诗惇. 考虑空洞演化效应的金属超塑性变形理论. 吉首大学学报(自然科学版), 第 19 卷, 第 4 期: 9~14.
[104] 黄志强. 基于能量分析的韧性金属材料空穴型损伤演化及失稳破坏判据. 武汉交通科技大学学报, 1998 年 2 月, 第 22 卷, 第 1期: 108~110.
[105] Nicolas Trniantafyllidis, Patrick Massin, Yves M. Leroy. A sufficient condition for the linear instability of strain-rate-dependent solids. C. R. Acad. Sci. Paris, 1997, 324(ll b): 151~157.
[106] L. Chen, B. C. Batra. Analysis of material instability at an impact loaded crack tip. Theoretical and Applied Fracture Mechanics, 1998, 29: 213-217.
[107] I.-W. Chen, E. J. Winn, M. Menon. Application of deformation instability to microstructural control in multilayer ceramic composites. Materials Science and Engineering, 2001, 317: 226-235.
[108] D. Bigoni, H. Petryk. A note on divergence and flutter instabilities in elastic–plastic materials. International Journal of Solids and Structures, 2002, 39: 911-926.
[109] E. Ma. Instabilities and ductility of nanocrystalline and ultrafine-grained metals. Scripta Materialia, 2003, 49: 663-668.
[110] H.P. Stüwe, L.S. Tóth. Plastic instability and Lüders bands in the tensile test: the role of crystal orientation. Materials Science and Engineering, 2003, A358: 17-25.
[111] 王高潮, 刘振华, 熊洪淼等. Ti-15-3 合金超塑性拉伸变形过程的计算机优化控制. 江西科学, 1997 年 12 月, 第 15 卷, 第 4期: 212-216.
[112] 周立运, 李普安. 计算及推算结构失稳临界荷载的方法与实测验证. 应用力学学报, 1995 年 3 月, 第 12 卷, 第 1 期: 76~81.
[113] 何大钧, 王孝培, 李中林, 温 彤. DDCAD 系统成型工艺分析及设计模块(二)----应变失稳判据成形极限方程. 金属成形工艺, 1999 年, 第 17 卷, 第 2 期: 46~48.
[114] 梁玉平, 崔振广. 超塑性研究展望. 兵器材料科学与工程, 1994 年 11 月, 第 17 卷, 第 6 期: 68-69.
[115] 丁 桦, 张凯锋. 材料超塑性研究的现状与发展. 中国有色金属学报, 2004 年 7 月, 第 7 期: 1060~1067.
[116] 王仁. 塑性动力学和动态塑性失稳回顾. 力学进展, 2001 年 8月, 第 31 卷, 第 3 期: 461~468.
[117] S. V. S. Narayana Murty, B. Nageswara Rao, B. P. Kashyap. Letter to editor: Clarification on the physical dimension of K in a constitutive equation for superplastic flow: σ =Kεm. Journal of Materials Processing Technology, 2002, 124: 259.
[118] Hiroaki Ohsawa. Foreword: Something ambiguous with superplasticity: a foreword to the special issue on superplasticity and superplastic technology in Japan. Journal of Materials Processing Technology, 1997, 68: 193~195.
[119] B.A.Ash and C.H.Hamilton. Strain and Strain-rate Hardening characteristics of a superplastic Al-Li-Cu-Zr Alloy. Scripta Metallurgica, 1988,Vol. 22: 277—282 .
[120] 王高潮, 刘振华, 杜忠权. Ti-15-3 钛合金超塑性最佳变形模式的研究. 航空材料学报, 1998 年 9 月, 第 18 卷, 第 3 期:22-28.
[121] 宋玉泉,赵军 变m 值超塑性本构方程 金属科学与工艺 1984,9:1-13.
[2] 宋玉泉. 超塑性均匀大变形动态过程的力学分析.吉林工业大学学报,1985(1):13-21.
[3] 宋玉泉.应变速率敏感性指数 m 的力学解析和测量的规格化理论.吉林工业大学学报,1985(2):1-14.
[4] 宋玉泉,连书君.载荷跃变法测量 m 值.机械工程学报,1989 年 9(Vol.25,No.3):38-42.
[5] 宋玉泉,程永春,王习文.超塑性拉伸似粘性流变方程中本构参数的力学解析.中国科学(E 辑),1997,10(Vol.27,No.5):385-392.
[6] 宋玉泉,高柏恩,王习文.超塑性拉伸似粘性变参数流变方程.中国科学(E 辑),1998 年 6 月,第 28 卷,第 3 期:192-197.
[7] 宋玉泉,程永春,刘颖.拉伸变形应变硬化指数的力学涵义及其规范测量.中国科学(E 辑),2000 年 6 月,(Vol.30)第 3 期: 200-207.
[8] 宋玉泉,程永春,刘术梅.超塑拉伸应变速率敏感性指数的力学解析.机械工程学报,2001 年 3 月:5-10.
[9] 宋玉泉,程永春,刘术梅.超塑性拉伸变形应变速率敏感性指数的试验测量及其精细分析.机械工程学报,2001 年 4 月:1-7.
[10] 宋玉泉,海锦涛,管志平.拉伸变形应变硬化指数的力学解析.中国科学(E 辑),2001 年 4 月,第 2 期:103-108.
[11] 宋玉泉,程永春,王习文.拉伸变形应变硬化指数的实验测量及其精细分析.中国科学(E 辑),2001 年 6 月,(Vol.31,No.3): 193-203.
[12] 宋玉泉,程永春,王习文.拉伸应变速率敏感性指数的力学涵义及 其规范测量.机械工程学报,2001 年 8 月:33-38.
[13] 宋玉泉,刘术梅,侯磊.超塑性拉伸均匀应变值的定量判定.科学通报,2002 年 5 月,第 9 期:717-720.
[14] 宋玉泉.超塑拉伸变形的力学解析.机械工程学报,2003 年 10 月: 64-72.
[15] I.-H.Lin, J.P.Hirth and E.W.Hart.Plastic instability in uniaxial tension tests.Acta Metallurgica, 1981, 29: 819-827.
[16] Pierre VIOLAN.Critere de stabilite de la deformation plastique en traction des metaux cubiques centres.Scripta Metallurgica, Vol.6, 1972:1175-1184.
[17] A.K.Ghosh.Tensile instability and necking in materials with strain hardening and strain-rate hardening.Acta Metallurgica, 1977, 25: 1413-1424.
[18] F.A.Nichols.Overview No.7 Plastic instabilities and uniaxial tensile ductilities. Acta Metallurgica, 1980, 28: 663-673.
[19] J.J.Jonas,R.A.Holt,C.E.Coleman.Plastic stability in tension and compression. Acta Metallurgica,1976,24:911-918.
[20] E.W.Hart.Theory of the tensile test.Acta Metallurgica, 1967, 15: 351-355.
[21] I.-H.Lin, J.P.Hirth and E.W.Hart.Plastic instability in uniaxial tension tests.Acta Metallurgica, 1981, 29: 819-827.
[21] J.J.Jonas, N.Christodoulou, C.G'Sell.The onset of flow localization in tensile samples containing geometric and metallurgical defects.Scripta Metallurgica, 1978, 12: 565-570.
[22] J.W.Hutchinson, K.W.Neale.Influence of strain-rate sensitivity on necking under uniaxial tension.Acta Metallurgica, 1977, 25: 839-846.
[23] Li Chuan Chung, Jung-Ho Cheng.The analysis of instability and strain co ncentration during superplastic deformation.Materials Science and Engineering, 2001, A308: 153-160.
[24] C.H.Cáceres, D.S.Wilkinson.Acta Metall, 1984,32(3):415—422.
[25] J.J.Jonas, B.Baudelet.Effect of crack and cavity generation on tensile stability.Acta Metallurgica, 1977, 25: 43-50.
[26] U.F.Kocks,J.J.Jonas,H.Mecking.The development of strain-rate gradients.Acta Metallurgica,1979,27:419-432.
[27] 畑山東明,和泉 修.Al-33Cu 超塑性合金における不均一形状試料の変形挙動.日本金属学会誌,第 45 巻,第 12 号(1981):1326-1332.
[28] 畑山東明,和泉 修. m 値と塑性不安定.日本金属学会誌,第 45巻,第 12 号(1981):1332-1337.
[29] Farghalli A.Mohamed,Terence G.Langdon.Flow Localization and neck formation in a superplastic metal.Acta Metallurgica,1981,29: 911-920.
[30] 畑山東明, 武井英雄.超塑性材料における m 値と破壊ひずみ. 日本金属学会会報, 第 21 巻, 第 10 号(1982):762—768.
[31] Amit K Ghosh and Robert A Ayres.On Rep[orted Anomalies in Relating Strain-Rate Sensitivity( m ) to Ductility.Metallurgical Transactions A, 1976,Vol.7A:1589-1591.
[32] D.LEE and F.ZAVERL Jr.The influence of material parameters on nonuniform plastic flow in simple tension.Acta Metallurgica, Vol.28,1980:1415-1426.
[33] Jianshe Lian, Bernard Baudelet.Necking development and strain to fracture under uniaxial tension.Materials Science and Engineering, 1986, 84: 157-162.
[34] W.A.Backofen , I.R.Turner and D.H.Avery.Superplasticity in an Al-Zn Alloy.Transactions of the asm,1964 Vol.57: 980—990.
[35] E. W. Hart. A phenomenological theory for plastic deformation of polycrystalline metals. Acta Metallurgica,1970,18(6):599-610.
[36] N.Christodoulou,J.J.Jonas.Work hardening and rate sensitivity material coefficients for OFHC Cu and 99.99%Al.Acta metal,1984,Vol.32,No.10:1655-1668.
[37] 佐藤英一,粟林一彦,堀内 良.ネック形状変化の解析もとづく超塑性変形にぉける.日本金属学会誌,第 52 巻,第 11 号(1988):1051-1056.
[38] 吴艳青,张克实.粗晶超塑性单轴拉伸颈缩模拟.计算力学学报,2004 年 2 月,第 4 期:81~87.
[39] Xing Huilin,Zhang Kaifeng,Z.R.Wang.Study on the optimal mode of superplastic deformation.Journal of Materials Processing Technology,1994,44:29-34.
[40] M.Khantha,D.P.Pope,V.Vitek.Dislocation generation instability and the brittle-to-ductile transition.Materials Science and Engineering, 1995,A192/193:435-442.
[41] B.Wack,A.Tourabi.A new method to quantify Portevin-Le Chatelier instabilities : application to aluminium-lithium alloys.Materials Science and Engineering,1995,A196:79-87.
[42] Sinisa Dj,Mesarovic.Dynamic strain aging and plastic instabilities. J.Mech Phys Solids,1995,43(5):671-700.
[43] P.B.Hirsch , S.G.Roberts.Comment on the brittle-to-ductile transition : A cooperative dislocation generation instability dislocation dynamics and the strain-rate dependence of the transition temperature.Acta Mater,1996,44(6):2361-2371.
[44] H.Moritoki,E.Okuyama.Intrinsic criterion of plastic instability. Journal of Materials Processing Technology,1996,60:649~656.
[45] Michael Zaiser,Peter H?hner.A unified description of strain-rate softening instabilities.Materials Science and Engineering,1997,A238:399-406.
[46] M.Dablij,A.Zeghloul,Portevin-Le Chatelier. Plastic instabilities: characteristics of deformation bands.Materials Science and Engineering,1997,237:1-5.
[47] Petr Wyslych,Eva Mazancóva,Karel Mazanec.The instabilities of plastic deformation in as-quenched martensite.Materials Science and Engineering,1997,A234-236:513-516.
[48] M.Kolbe , K.Neuking , G.Eggeler.Dislocation reactions and microstructural instability during 1025°C shear creep testing of superalloy single crystals.Materials Science and Engineering,1997, A234-236:877-879.
[49] B.I.Smirnov.Superlocalization of plastic deformation in crystals at high temperatures.Materials Science and Engineering,1997,A233: 56-60.
[50] Ming Li,O.Richmond.Intrinsic instability and nonuniformity of plastic deformation.International Journal of Plasticity,1997,13(8-9): 765-784.
[51] Francois Louchet,Mikha?l Lebyodkin.A general approach for stress anomalies and plastic instabilities in intermetallics.Materials Science and Engineering,1997,A239-240:804-807.
[52] P.Lukác,J.Balík,F.Chmelík.Physical aspects of plastic instabilities. Materials Science and Engineering,1997,A234-236:45-51.
[53] G.Bérces,N.Q.Chinh,A.Juhász,J.Lendvai.Kinematic analysis of plastic instabilities occurring in microhardness tests.Acta Mater,1998,46(6):2029-2037.
[54] S.V.S.Narayana Murty , B.Nageswara Rao , B.P.Kashyap. Instability criteria for hot deformation of materials.International Materials Reviews,2000,45(1):15-26.
[55] James C.M. Li. Instabilities in micromechanical deformation. Materials Science and Engineering, 2000, A285: 207-212.
[56] Zs. Kovács, J. Lendvai, G. V?r?s. Localized deformation bands in Portevin–Le Chatelier plastic instabilities at a constant stress rate. Materials Science and Engineering, 2000, A279: 179-184.
[57] Poul V. Lade. Instability shear banding and failure in granular materials. International Journal of Solids and Structures, 2002, 39: 3337-3357.
[58] Daniel Walgraef. Rate equation approach to dislocation dynamics and plastic deformation. Materials Science and Engineering, 2002, A322: 167-175.
[59] N. Q. Chinh, Gy. Horváth, Zs. Kovács, J. Lendvai. Characterization of plastic instability steps occurring in depth-sensing indentation tests. Materials Science and Engineering, 2002, A324: 219-224.
[60] K. W. Neale, K. Inal, P. D. Wu. Effects of texture gradients and strain paths on localization phenomena in polycrystals . International Journal of Mechanics Science, 2003, 45: 1671-1686.
[61] 曲 杰, 金泉林, 徐秉业. 超塑性本构模型材料参数识别方法研究. 工程力学, 2004 年 8 月, 第 4 期: 17~21.
[62] M. A. Burke, W. D. Nix. Plastic instabilities in tension creep. Acta Metallurgica, 1975, 23: 793-798.
[63] 畑山東明, 岡部卓治, 武井英雄, 宝道喜之. 超塑性材料の m値と伸び. 日本金属学会誌, 第 46 巻, 第 2 号(1982):205--210
[64] 崗部卓治, 畑山東明, 武井英雄. 超塑性材料の破壊挙動. 日本金属学会誌, 第 46 巻, 第 2 号(1982):211—216.
[65] T. G. Langdon. Fracture processes in superplastic flow. Metal Science, 1982, 16: 175-183.
[66] Jianshe Lian, Bernard Baudelet, Michel Suery. Numerical analysis of the influence of various defects on superplastic fracture under uniaxial tension. Computational Methods for Predicting Material Processing Defects, edited by M. Predeleanu, 1987.
[67] Galip Said, Suleyman Tasgetiren. An express technique for the determination of static and dynamic fracture toughness (KIC, KId) of bcc metals and alloys . Mechanics of Materials, 2004, 36: 1129-1142.
[68] 陈光南, 胡世光. 板材拉伸成形中损伤、失稳与成形极限曲线的建立. 塑性工程学报, 1994 年 3 月, 第 1 卷, 第 1 期: 31~36.
[69] 赵军, 郑祖伟, 潘文武. 拉深过程智能化控制中的破裂失稳临界条件. 燕山大学学报, 2000 年 10 月, 第 24 卷, 第 4 期: 330~337.
[70] 王祖唐. 金属塑性变形极限判据. 应用力学学报, 2002 年 6 月,第 19 卷, 第 2 期: 104~106.
[71] 金泉林. 超塑变形的行为与本构描述. 力学进展, 1995年5月25, 第 25 卷, 第 2 期: 260―274.
[72] 邓忠勇, 黄伯云, 贺跃辉, 孙坚. 热变形态 TiAl 基合金超塑性拉伸过程中应变速率敏感系数的分析. 稀有金属材料与工程, 1999 年 8 月, 第 28 卷: 第 4 期.
[73] 刘润广, 蒋浩民, 姜勇. GH4169 合金超塑性变形及其力学行为的研究. 宇航材料工艺, 1998 年, 第 2 期.
[74] 刘润广, 蒋浩民, 姜勇. 2214 铝合金超塑性变形机制. 金属学报, 1996 年 12 月, 第 32 卷, 第 12 期: 1244-1247.
[75] 陈征宇. 对影响金属材料塑性变形的重要指标-应变速率敏感性指数的探讨. 机械设计与制造, 1998 年 3 月: 40-42.
[76] 蒋浩民, 姜勇, 刘润广. 2214 铝合金超塑性变形力学行为的研究. 航天工艺, 1996 年第 3 期: 7-10.
[77] 田宝辉, 李焕喜等. Al-Li 单晶体流变应力的应变速率敏感性. 兵器材料科学与工程, 1997年7月, 第20卷, 第4期: 14-19.
[78] 刘润广, 蒋大鸣, 崔约贤, 王仲仁. Al-Zn-Mg-Cu 合金的超塑性变形力学行为. 哈尔滨工业大学学报, 1998 年 10 月,第 30 卷, 第 5 期: 121-123.
[79] 黄伯云, 贺跃辉, 邓忠勇, 王健农. 热变形 TiAl 基合金的超塑性行为. 金属学报,1998 年 11 月, 第 34 卷, 第 11 期: 1173-1177.
[80] 罗兵辉, 周善初. Zn-Al 共析合金室温超塑性变形机理. 材料科 学与工程, 1995 年, 第 13 卷, 第 4 期: 22-24.
[81] 石志强, 叶以富, 李世春. Zn-5Al共晶合金的恒载荷超塑性拉伸试验. 金属热处理, 2002 年, 第 27 卷, 第 1 期: 33-35.
[82] 刘勤. 流变应力的应变速率敏感性指数(m)及其和超塑性之间的关系. 机械工程材料, 1979 年, 第 2 期: 58~69.
[83] J. J. Gracio, A. B. Lopes, E. F. Rauch. Analysis of plastic instability in commercially pure Al alloys. Journal of Materials Processing Technology, 2000, 103: 160-164.
[84] D. Bigoni, B. Loret. Effects of elastic anisotropy on strain localization and flutter instability in plastic solids. Journal of the Mechanics and Physics of Solids, 1999, 47: 1409-1436.
[85] Du Zhixiao, Wu Shichun. A kinetic equation for damage during superplastic deformation. Journal of Materials Processing Technology, 1995, 52: 270-279.
[86] Peter H?hner. A generalized criterion of plastic instabilities and its application to creep damage and superplastic flow. Acta Metall. Meter., 1995, 43(11): 4093-4100.
[87] 赵军, 李硕本. 金属复合板的拉伸失稳判据. 机械工程学报, 1995 年 10 月, 第 31 卷, 第 5 期: 103~108.
[88] 李名尧, 川.比吉特. 应变速率敏感性对板料成形失稳的影响. 上海工程技术大学学报, 2000 年 12 月, 第 14 卷, 第 4 期: 248~258.
[89] 杜志孝, 李森泉, 刘马宝, 吴诗惇. 超塑性板料的成形极限. 应用数学和力学, 1996 年 2 月, 第 17 卷, 第 2 期: 127~132.
[90] 柳玉起, 胡平, 李运兴, 陈塑寰. 金属材料平面应变拉伸变形局部化有限元分析. 应用力学学报, 1995 年 6 月: 17~22.
[91] 李振环, 张克实. 温度、材料不均匀性对粘塑性材料冲击拉伸失稳的影响. 成都科技大学学报, 1994 年 1 月, 第 75 期:95~102.
[92] J. Kajberg, G. Lindkvist. Characterisation of materials subjected to large strains by inverse modelling based on in-plane displacement fields . International Journal of Solids and Structures, 2004, 41: 3439-3459.
[93] Li Chuan Chung, Jung-Ho Cheng. Fracture criterion forming pressure design for superplastic bulging . Materials Science and Engineering, 2002, A333: 146-154.
[94] K. Inal, P.D. Wu, K.W. Neale. Instability and localized deformation in polycrystalline solids under plane-strain tension . International Journal of Solids and Structures, 2002, 39: 983-1002.
[95] G. Nefussi, A. Combescure. Coupled buckling and plastic instability for tube hydroforming. International Journal of Mechanics Science, 2002, 44: 899-914.
[96] G. J. Creus. Instability and damage effects in the modeling of metal forming .Comput. Methods Appl. Mech. Engrg., 2000, 182: 421-437
[97] A.B. Lopes, E.F. Rauch, J.J. Gracio. Textural vs structural plastic instabilities in sheet metal forming. Acta mater., 1999, 47(3): 859-866.
[98] Youngseog Lee, Vikas Prakash. Numerical simulations of dynamic plastic shear instability under conditions of plane strain. Int. J. Solids Structures, 1998, 35(28-29): 3755-3791.
[99] Rodeny Hill. A general theory of plastic deformation and instability in thin-walled tubes under combined loading. J. Mech. Phys. Solids,1996, 44(12): 2041~2057.
[100] Yeong-Maw Hwang, Hung-Hsiou Hsu, Hung-Jen Lee. Analysis of plastic instability during sandwich sheet rolling. Int. J. Mech. Tools Manufact., 1996, 36(1): 47~62.
[101] D. W. A. Rees. Instability limits to the forming of sheet metals. Journal of Materials Processing Technology, 1995, 55: 146-153.
[102] A.K. Ghosh. A Numerical Analysis of the Tensile Test for Sheet Metals. Metallurgical Transactions A 1977, 8A:1221-1232.
[103] 吴诗惇. 考虑空洞演化效应的金属超塑性变形理论. 吉首大学学报(自然科学版), 第 19 卷, 第 4 期: 9~14.
[104] 黄志强. 基于能量分析的韧性金属材料空穴型损伤演化及失稳破坏判据. 武汉交通科技大学学报, 1998 年 2 月, 第 22 卷, 第 1期: 108~110.
[105] Nicolas Trniantafyllidis, Patrick Massin, Yves M. Leroy. A sufficient condition for the linear instability of strain-rate-dependent solids. C. R. Acad. Sci. Paris, 1997, 324(ll b): 151~157.
[106] L. Chen, B. C. Batra. Analysis of material instability at an impact loaded crack tip. Theoretical and Applied Fracture Mechanics, 1998, 29: 213-217.
[107] I.-W. Chen, E. J. Winn, M. Menon. Application of deformation instability to microstructural control in multilayer ceramic composites. Materials Science and Engineering, 2001, 317: 226-235.
[108] D. Bigoni, H. Petryk. A note on divergence and flutter instabilities in elastic–plastic materials. International Journal of Solids and Structures, 2002, 39: 911-926.
[109] E. Ma. Instabilities and ductility of nanocrystalline and ultrafine-grained metals. Scripta Materialia, 2003, 49: 663-668.
[110] H.P. Stüwe, L.S. Tóth. Plastic instability and Lüders bands in the tensile test: the role of crystal orientation. Materials Science and Engineering, 2003, A358: 17-25.
[111] 王高潮, 刘振华, 熊洪淼等. Ti-15-3 合金超塑性拉伸变形过程的计算机优化控制. 江西科学, 1997 年 12 月, 第 15 卷, 第 4期: 212-216.
[112] 周立运, 李普安. 计算及推算结构失稳临界荷载的方法与实测验证. 应用力学学报, 1995 年 3 月, 第 12 卷, 第 1 期: 76~81.
[113] 何大钧, 王孝培, 李中林, 温 彤. DDCAD 系统成型工艺分析及设计模块(二)----应变失稳判据成形极限方程. 金属成形工艺, 1999 年, 第 17 卷, 第 2 期: 46~48.
[114] 梁玉平, 崔振广. 超塑性研究展望. 兵器材料科学与工程, 1994 年 11 月, 第 17 卷, 第 6 期: 68-69.
[115] 丁 桦, 张凯锋. 材料超塑性研究的现状与发展. 中国有色金属学报, 2004 年 7 月, 第 7 期: 1060~1067.
[116] 王仁. 塑性动力学和动态塑性失稳回顾. 力学进展, 2001 年 8月, 第 31 卷, 第 3 期: 461~468.
[117] S. V. S. Narayana Murty, B. Nageswara Rao, B. P. Kashyap. Letter to editor: Clarification on the physical dimension of K in a constitutive equation for superplastic flow: σ =Kεm. Journal of Materials Processing Technology, 2002, 124: 259.
[118] Hiroaki Ohsawa. Foreword: Something ambiguous with superplasticity: a foreword to the special issue on superplasticity and superplastic technology in Japan. Journal of Materials Processing Technology, 1997, 68: 193~195.
[119] B.A.Ash and C.H.Hamilton. Strain and Strain-rate Hardening characteristics of a superplastic Al-Li-Cu-Zr Alloy. Scripta Metallurgica, 1988,Vol. 22: 277—282 .
[120] 王高潮, 刘振华, 杜忠权. Ti-15-3 钛合金超塑性最佳变形模式的研究. 航空材料学报, 1998 年 9 月, 第 18 卷, 第 3 期:22-28.
[121] 宋玉泉,赵军 变m 值超塑性本构方程 金属科学与工艺 1984,9:1-13.