铝合金中Portevin-Le Chatelier效应的多尺度实验和机理研究
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摘要
Portevin-Le Chatelier (PLC)效应是合金材料在一定的应变率、温度或合适的预变形下所出现的特殊失稳现象。它表现为时域上的锯齿形应力屈服和空域上的应变局域化。对PLC效应的微观解释,目前被广泛接受的是动态应变时效(dynamic strain aging, DSA)理论,即可动位错与溶质原子之间动态的交互作用。PLC效应作为一个横跨宏观变形带、细观晶粒变形、微观位错运动的多尺度问题,长期得到学术界重视。铝合金以其较高的强度质量比、良好的耐腐蚀性等一系列优点,在国民经济的各个领域都获得了广泛的应用。但其在室温变形时的PLC效应却严重地降低了材料的可加工成形性能。因此,开展铝合金PLC效应的多尺度实验和机理研究具有重要的理论和现实意义。
本文首先基于数字散斑干涉法系统研究了Al-Mg合金和Al-Cu合金中的PLC效应,分析了加载应变率、试验温度、热处理方式、合金成分等条件对PLC效应的影响,并结合DSA微观机制,对上述现象进行了定性的解释。这部分工作侧重应力场的研究。接着借助红外测温法重点研究了Al-Mg合金中PLC效应的空域行为,讨论了PLC效应不同的温升模式,分析了带的倾角转向现象,并计算了带形成时带内的应变率及变形量。这部分工作侧重温度场的研究。然后使用透射电子显微镜观测了析出相的形貌、成分及其在不同情况下的分布形态,考察了随着应变的增加位错的增殖和演化过程,并探讨了位错与析出相的相互作用形式。最后综合宏观与微观的实验结果,提出了基于析出相与溶质原子共同作用的广义管扩散动态应变时效机制。
在PLC效应的时域行为方面,研究了应力跌落幅值、重加载时间和临界应变随应变率、试验温度、退火温度、淬火温度、时效、合金成分等参数的演化规律。应力跌幅的统计分析结果显示,随着应变率的减小、试验温度的升高或者Al-Mg合金中Mg含量的增加,PLC效应出现了从自组织临界性向混沌的转变行为。通过对淬火实验和合金成分实验各时域特征量的分析,发现析出相在PLC效应中也起到了重要作用。进一步的低温实验表明,没有溶质原子的参与,仅有析出相不能产生PLC效应。
在PLC效应的空域行为方面,基于实验获得的温度场数据,分析了三类PLC带的形成与演化过程,求得了局域变形带的带宽、倾角、传播速度等特征参数；发现了PLC效应的两种温升模式,并确定了带发生倾角转向的位置；实验和计算都表明,A类型带形成时不存在带外收缩,而B、C类型带形成时带外存在收缩变形,由此首次提出了将是否存在带外收缩作为定量划分PLC效应A、B类型带的标准。
在微观实验方面,通过透射电镜和能谱分析仪观测了析出相的形貌和成分；使用透射电镜验证了讨论淬火温度和合金成分的影响时对析出相含量的推断；显微观察发现,随着塑性变形的增加,位错密度逐渐增大,其形态从散布、缠结演化为胞状结构,这验证了位错的增殖机制；在正在发生PLC效应的试件中观察到可动位错与析出相相互作用的现象,说明析出相也参与了动态应变时效过程。
在机理研究方面,基于宏观实验分析和显微观测结果,综合考虑溶质原子和析出相两个方面的影响,对原有解释PLC效应的管扩散DSA理论进行改进,提出了广义管扩散DSA机制。并进一步指出,析出相对可动位错的运动只是起到类似林位错的阻拦作用,溶质原子的参与是动态应变时效产生必不可少的条件。
The Portevin-Le Chatelier (PLC) effect refers to special plastic instability in many alloys in a certain range of strain rate, temperature and appropriate pre-deformation, which shows serrated flow in stress-strain curves and strain localization in specimen. It is widely accepted that the physical origin of the PLC effect is dynamic strain aging (DSA), i.e. dynamic interaction between mobile dislocations and diffusing solute atoms. As a multi-scale problem ranging from macro deformation bands, meso grains deformation to micro dislocations motion, the PLC effect has been increasingly attractive to researchers after its discovery. Aluminum alloys have been widely used due to a series of advantages such as their high strength-weight ratio and good corrosion resistance, but their formability at room temperature has been severely harmed by the PLC effect. Therefore, it has important theoretical and practical significance to carry out multi-scale experimental and theoretical research on the Portevin-Le Chatelier effect in Al alloys.
At first, by the digital speckle pattern interferometry (DSPI) technique, the PLC effect in Al-Mg alloys and Al-Cu alloys is systematic investigated in the present work. The influences of strain rate, test temperature, heat treatment, alloy composition on the PLC effect are studied. A qualitative explanation for above phenomena is made according to the mechanism of DSA. This work is focused on stress field. Then, based on infrared pyrometry, the spatial domain behavior of the PLC effect in Al-Mg alloys is investigated. The modes of temperature rise and the obliquity change of PLC band are analyzed and discussed. The strain rate and deformation inside the PLC band during its formation are also calculated. This work is focused on temperature field. After that, the morphology, composition and distribution under different circumstances of the precipitates are observed by transmission electron microscope (TEM). The multiplication and evolution of dislocations with the increase of strain are studied, as well as the interaction type between dislocations and precipitates. Finally, from the comprehensive analysis of macro and micro experimental results, the extended DSA mechanism based on pipe diffusion is proposed, in which the joint effects of precipitates and solute atoms are considered.
On the time domain behavior of the PLC effect, the evolution of stress drop amplitude, reloading time and critical strain with the parameters such as strain rate, test temperature, annealing temperature, quenching temperature, aging, and alloy composition are investigated. The statistical analysis of stress drop amplitude shows that, the PLC effect changes from the self organized criticality to chaos, with the decrease of strain rate, the increase of test temperature or the increase of Mg content in Al-Mg alloys. It displays that precipitates play an important role in the PLC effect from the analysis of quenching and alloy composition experiments. By low temperature experiments, we know that, without the participation of solute atoms, only precipitates can't create the PLC effect.
On the spatial domain behavior of the PLC effect, according to temperature field data, the formation and propagation of the three types of PLC bands (type A, B, C) are discussed and some characteristic parameters of the bands such as bandwidth, orientation, and apparent velocity are also obtained. Two modes of temperature rise in the PLC effect are found, and the location of the obliquity change of PLC band is forecasted. Both the experimental and computational results show that elastic shrinkage deformation exists outside the band only during the formation of the type B, C band. Based on this, whether or not shrinkage deformation exists outside the band is proposed as a new standard to define type A, B band.
In the microcosmic experiments, the morphology and composition of precipitates are recorded by TEM and energy dispersive spectrometer (EDS). These inferences about content of precipitates in quenching and alloy composition experiments are verified. With the increase of plastic deformation, the dislocation density increases and dislocation configuration evolves from spread, tangled to cell structure. This verifies the proliferation mechanism of dislocation. The phenomenon of interaction between mobile dislocations and precipitates when the PLC effect appears is observed, which shows that the precipitates are also involved in the process of DSA.
In the research of mechanism, based on experimental results of macro and micro, according to comprehensive consideration of solute atoms and precipitates, the original DSA mechanism based on pipe diffusion is improved and the general DSA mechanism based on pipe diffusion is proposed. Further more, precipitates only play a role of mobile dislocations blocking similar to forest dislocations, and the participation of solute atoms is a necessary condition to cause the dynamic strain aging.
本文首先基于数字散斑干涉法系统研究了Al-Mg合金和Al-Cu合金中的PLC效应,分析了加载应变率、试验温度、热处理方式、合金成分等条件对PLC效应的影响,并结合DSA微观机制,对上述现象进行了定性的解释。这部分工作侧重应力场的研究。接着借助红外测温法重点研究了Al-Mg合金中PLC效应的空域行为,讨论了PLC效应不同的温升模式,分析了带的倾角转向现象,并计算了带形成时带内的应变率及变形量。这部分工作侧重温度场的研究。然后使用透射电子显微镜观测了析出相的形貌、成分及其在不同情况下的分布形态,考察了随着应变的增加位错的增殖和演化过程,并探讨了位错与析出相的相互作用形式。最后综合宏观与微观的实验结果,提出了基于析出相与溶质原子共同作用的广义管扩散动态应变时效机制。
在PLC效应的时域行为方面,研究了应力跌落幅值、重加载时间和临界应变随应变率、试验温度、退火温度、淬火温度、时效、合金成分等参数的演化规律。应力跌幅的统计分析结果显示,随着应变率的减小、试验温度的升高或者Al-Mg合金中Mg含量的增加,PLC效应出现了从自组织临界性向混沌的转变行为。通过对淬火实验和合金成分实验各时域特征量的分析,发现析出相在PLC效应中也起到了重要作用。进一步的低温实验表明,没有溶质原子的参与,仅有析出相不能产生PLC效应。
在PLC效应的空域行为方面,基于实验获得的温度场数据,分析了三类PLC带的形成与演化过程,求得了局域变形带的带宽、倾角、传播速度等特征参数；发现了PLC效应的两种温升模式,并确定了带发生倾角转向的位置；实验和计算都表明,A类型带形成时不存在带外收缩,而B、C类型带形成时带外存在收缩变形,由此首次提出了将是否存在带外收缩作为定量划分PLC效应A、B类型带的标准。
在微观实验方面,通过透射电镜和能谱分析仪观测了析出相的形貌和成分；使用透射电镜验证了讨论淬火温度和合金成分的影响时对析出相含量的推断；显微观察发现,随着塑性变形的增加,位错密度逐渐增大,其形态从散布、缠结演化为胞状结构,这验证了位错的增殖机制；在正在发生PLC效应的试件中观察到可动位错与析出相相互作用的现象,说明析出相也参与了动态应变时效过程。
在机理研究方面,基于宏观实验分析和显微观测结果,综合考虑溶质原子和析出相两个方面的影响,对原有解释PLC效应的管扩散DSA理论进行改进,提出了广义管扩散DSA机制。并进一步指出,析出相对可动位错的运动只是起到类似林位错的阻拦作用,溶质原子的参与是动态应变时效产生必不可少的条件。
The Portevin-Le Chatelier (PLC) effect refers to special plastic instability in many alloys in a certain range of strain rate, temperature and appropriate pre-deformation, which shows serrated flow in stress-strain curves and strain localization in specimen. It is widely accepted that the physical origin of the PLC effect is dynamic strain aging (DSA), i.e. dynamic interaction between mobile dislocations and diffusing solute atoms. As a multi-scale problem ranging from macro deformation bands, meso grains deformation to micro dislocations motion, the PLC effect has been increasingly attractive to researchers after its discovery. Aluminum alloys have been widely used due to a series of advantages such as their high strength-weight ratio and good corrosion resistance, but their formability at room temperature has been severely harmed by the PLC effect. Therefore, it has important theoretical and practical significance to carry out multi-scale experimental and theoretical research on the Portevin-Le Chatelier effect in Al alloys.
At first, by the digital speckle pattern interferometry (DSPI) technique, the PLC effect in Al-Mg alloys and Al-Cu alloys is systematic investigated in the present work. The influences of strain rate, test temperature, heat treatment, alloy composition on the PLC effect are studied. A qualitative explanation for above phenomena is made according to the mechanism of DSA. This work is focused on stress field. Then, based on infrared pyrometry, the spatial domain behavior of the PLC effect in Al-Mg alloys is investigated. The modes of temperature rise and the obliquity change of PLC band are analyzed and discussed. The strain rate and deformation inside the PLC band during its formation are also calculated. This work is focused on temperature field. After that, the morphology, composition and distribution under different circumstances of the precipitates are observed by transmission electron microscope (TEM). The multiplication and evolution of dislocations with the increase of strain are studied, as well as the interaction type between dislocations and precipitates. Finally, from the comprehensive analysis of macro and micro experimental results, the extended DSA mechanism based on pipe diffusion is proposed, in which the joint effects of precipitates and solute atoms are considered.
On the time domain behavior of the PLC effect, the evolution of stress drop amplitude, reloading time and critical strain with the parameters such as strain rate, test temperature, annealing temperature, quenching temperature, aging, and alloy composition are investigated. The statistical analysis of stress drop amplitude shows that, the PLC effect changes from the self organized criticality to chaos, with the decrease of strain rate, the increase of test temperature or the increase of Mg content in Al-Mg alloys. It displays that precipitates play an important role in the PLC effect from the analysis of quenching and alloy composition experiments. By low temperature experiments, we know that, without the participation of solute atoms, only precipitates can't create the PLC effect.
On the spatial domain behavior of the PLC effect, according to temperature field data, the formation and propagation of the three types of PLC bands (type A, B, C) are discussed and some characteristic parameters of the bands such as bandwidth, orientation, and apparent velocity are also obtained. Two modes of temperature rise in the PLC effect are found, and the location of the obliquity change of PLC band is forecasted. Both the experimental and computational results show that elastic shrinkage deformation exists outside the band only during the formation of the type B, C band. Based on this, whether or not shrinkage deformation exists outside the band is proposed as a new standard to define type A, B band.
In the microcosmic experiments, the morphology and composition of precipitates are recorded by TEM and energy dispersive spectrometer (EDS). These inferences about content of precipitates in quenching and alloy composition experiments are verified. With the increase of plastic deformation, the dislocation density increases and dislocation configuration evolves from spread, tangled to cell structure. This verifies the proliferation mechanism of dislocation. The phenomenon of interaction between mobile dislocations and precipitates when the PLC effect appears is observed, which shows that the precipitates are also involved in the process of DSA.
In the research of mechanism, based on experimental results of macro and micro, according to comprehensive consideration of solute atoms and precipitates, the original DSA mechanism based on pipe diffusion is improved and the general DSA mechanism based on pipe diffusion is proposed. Further more, precipitates only play a role of mobile dislocations blocking similar to forest dislocations, and the participation of solute atoms is a necessary condition to cause the dynamic strain aging.
引文
[1]Luders W., Uber die Ausserung der Elasticitat an stahlartigen Eisenstaben und Stahlstaben, und uber eine beim Biegen solcher Stabe beobachtete Molecularbewegung, Dingler's Polytechnisches J.,1860,5:18.
[2]Portevin A., Le Chatelier F., Sur un phenomene observe lors de l'essai detraction d'alliages en cours de transformation, Comptes Rendus de l'Academiedes Sciences Paris,1923,176:507.
[3]Subramanian K.H., Duncan A. J., Tensile Properties for Application to Type Ⅰ and Type Ⅱ Waste Tank Flaw Stability Analysis, WSRC-TR-2000-00232,2000.
[4]Nadai A., Plasticity:A Mechanics of the Plastic State of Matter, New York:McGraw-Hill, 1931.
[5]冯端等,金属物理学,第三卷,金属力学性质,北京：科学出版社,1999.
[6]Zhang Q.C., Jiang Z.Y., Jiang H.R, Chen Z.J., Wu X. P., On the propagation and pulsation of Portevin-Le Chatelier deformation bands:an experimental study with digital speckle pattern metrology, International Journal of Plasticity,2005,21:2150.
[7]Ardley G.W., Cottrell A.H., Dislocation theory of yielding and strain ageing of iron, Proc. Roval. Soc.,1953, A219:328.
[8]Sleeswyk A.W., Slow Strain-hardening of ingot iron, Acta Metall.,1958,6:598.
[9]Brindley B.J., Corderoy D.J.H., Honeycombe R.W.K., Yield points and Luders bands in single crystal of copper-base alloys, Acta Metall.,1962,10:1043.
[10]Estrin Y, Kubin, L.P., Spatial coupling and propagative plastic instabilities, in Continumm Models for Materials with Microstructures, Muhlhaus H.B., Editor, Wiley:New York,1995, 395.
[11]国家自然科学基金委员会数学物理科学部,力学学科发展研究报告,北京：科学出版社,2007.
[12]国家自然科学基金委员会工程与材料科学部,金属材料科学,北京：科学出版社,2006.
[13]潘复生,张丁非等,铝合金及应用,北京：化学工业出版社,2006.
[14]Bell J.F., The Experimental foundations of Solid Mechanics, Encyclopedia of Physics-Mechanics of Solids I, ed. S. Flugge and C. Truesdell, Vol. VIa/1, Berlin:Springer-Verlag, 1973.
[15]Savart F., Recherches sue les vibrations longitudinales, Ann. Chem. Phys., second series 1837, 65:337.
[16]Franklin S.V., Mertens F., Marder M., Portevin-Le Chatelier effect, Phys. Rev. E,2000,62: 8195.
[17]Masson A.P., Sur l'easticite des corpes solides, Ann. Chem. Phys., third series 1841,3:451.
[18]Portevin A., Le Chatelier F., Heat treatment of aluminium-copper alloys, Transactions of the American Society of Steel Treating,1924,5:457.
[19]Cottrell A.H., A Note on the Portevin-Le Chatelier effect, Philosophical Magazine,1953, 44(355):829.
[20]Andrade ENdaC., The viscous flow in metals and allied phenomena, Proc. R. Soc.,1910,84: 1.
[21]Da Silveira T.L., Monteiro S.N., Jumps in the creep curve of austentic stainless steels, Met. Trans.,1979, A10:1795.
[22]Bell J.F., Stein A., The incremental loading wave in the pre-stressed plastic field, Journal de Mechanique,1962,1:395.
[23]Dillon O.W., Experimental data on aluminum as a mechanically unstable solid, Journal of Mechanics and Physics of Solids,1963,11:289.
[24]Kovacs Z., Chinh N.Q., Lendvai J., Orientation dependence of Portevin-Le Chatelier plastic instabilities in depth-sensing microindentation, Journal of Materials Research,2001,16(4): 1171.
[25]Weinhandl H., Mitter F., Bernt W., Kumar S., Pink E., Computer-assisted recording of tensile tests for the evaluation of serrated flow, Scripta Metallurgica et Materialia,1994,31(11): 1567.
[26]田宝辉,张永刚,陈昌麒,Al—Li单晶体锯齿流变的形态特征,金属学报,1996,32(3)：249.
[27]Tian B., Comparing characteristics of serrations in Al-Li and Al-Mg alloys. Materials Science and Engineering A,2003,360:330.
[28]钱匡武,李效琦,彭开萍,张好国,高强度铝合金LC4中锯齿屈服特征的研究,福州大学学报,1995,23(2)：53.
[29]Kumar S., Pink E., Serrated flow in aluminium alloys containing lithium, Acta Materialia, 1997,45(12):5295.
[30]Pink E., Bruckbauer P., Weinhandl H., Stress-Drop rates in serrated flow of aluminium alloys, Scripta Metallurgica,1998,38(6):945.
[31]Pink E., Arsenault R.J., Stress-drop rates in serrated flow and their strain and temperature dependences:A comparison of an aluminum'Cmagnesium alloy and a mild steel, Materials Science and Engineering A,1999,272:57.
[32]Pink E., Kumar S., Tian B., Serrated flow of aluminium alloys influenced by precipitates, Materials Science and Engineering A,2000,280:17.
[33]Brindley B.J., Worthington P.J., Yield point phenomena in substitutional alloys, Metallurgical Reviews,1970,145:101.
[34]Cuddy L.J., Leslie W.C., Some aspects of serrated yielding in substitutional solid solutions of iron. Acta Metallurgica,1972,20:1157.
[35]Pink E., Grinberg A., Serrated flow in a ferritic stainless steel. Materials Science and Engineering A,1981,51(1):1.
[36]McCormick P.G., Dynamic strain ageing. Transactions of the Indian Institute of Metals,1986, 39:98.
[37]Rizzi E., Hahner P., On the Portevin-Le Chatelier effect:theoretical modeling and numerical results, International Journal of Plasticity,2004,20:121.
[38]Lebyodkin M., Dunin-Barkovskii L., Brechet Y., Estrin Y., Kubin L., Spatio-temporal dynamics of the Portevin-Le Chatelier effect:experiment and modeling, Acta Materialia, 2000,48:2529.
[39]Yoshinaga H., Toma K., Abe K., Morozumi, S., Portevin-Le Chatelier effect in vanadium, Philosophical Magazine,1971,23:1387.
[40]Lebyodkin M., Brechet Y., Estrin Y, Kubin L.P., Statistics of the catastrophic slip events in the Portevin-Le Chatelier effect, Physical Review Letters,1995,74:4758.
[41]Lebyodkin M., Brechet Y., Estrin Y., Kubin L.P., Statistical behavior and strain localization patterns in the Portevin-Le Chatelier effect. Acta Materialia,1996,44:4531.
[42]Lebyodkin M., Dunin-Barkovskii L., Brechet Y, Kubin L., Estrin Y., Kinetics and statistics of jerky flow: experiments and computer simulations, Materials Science and Engineering A, 1997,115:234.
[43]Lebyodkin M., Fressengeas C., Ananthakrishna G., Kubin L.P., Statistical and Multifractal analysis of the Portevin-Le Chatelier effect, Materials Science and Engineering A,2001,170: 319.
[44]Bharathi M.S., Lebyodkin M., Ananthakrishna G., Fressengeas C., Kubin L.P., The hidden order behind jerky flow, Acta Materialia,2002,50:2813.
[45]Packard N.H., Crutchfield J.P., Farmer J.D., Shaw R.S., Geometry from a time series, Physical Review Letters,1980,45:712.
[46]Takens F., Detecting strange attractors in turbulence, in Dynamical systems and turbulence,
Warwick 1980, Edited by Rand D.A. and Yong L.S., Lecture notes in mathematics 898 (Springer, Berlin,1980):366.
[47]Ananthakrishna G, Fressengeas C., Grosbras M., Vergnol J., Engelke C., Plessing J., Neuhauser H., Bouchaud E., Planes J., Kubin L.P., On the existence of chaos in jerky flow, Scripta Metallurgia et Materialia,1995,32(11):1731.
[48]Ananthakrishna G, Fressengeas C., Kubin L.P., Chaos and the jerky flow in Al-Mg polycrystals, Materials Science and Engineering A,1997,234-236:314.
[49]Bharathi M.S., Lebyodkin M., Ananthakrishna G, Fressengeas C., Kubin L.P., Multifractal burst in the spatiotemporal dynamics of jerky flow. Physical Review Letters,2001,87(16): 165508-1.
[50]Ananthakrishna G, Bharathi M.S., Dynamical approach to the spatiotemporal aspects of the Portevin-Le Chatelier effect:chaos, turbulence and band propagation, Physical Review E, 2004,70:026111.
[51]Ananthakrishna G, Noronha S.J., Fressengeas C., Kubin L.P., Crossover from chaotic to self-organized critical dynamics in jerky flow of single crystals, Physical Review E,1999,60: 5455.
[52]Ananthakrishna G, Noronha S.J., Fressengeas C., Kubin L.P., Crossover in the dynamics of Portevin-Le Chatelier effect from chaos to SOC, Mater. Sci. Eng. A.2001,309-310:316.
[53]McReynolds A.W., Plastic deformation waves in aluminum, Transactions of the American Institute of Mining and Metallurgical Engineers,1949,185:32.
[54]Sharpe W.N., The Portevin-Le Chatelier effect in aluminum single crystals and polycrystals, Ph.D. Dissertation, Baltimore, Maryland:The Johns Hopkins University,1966.
[55]Bell J.F., The Physics of Large Deformation of Crystalline Solids, Springer Tracts in Natural Philosophy, Berlin-Heidelberg-New York:Springer,1968.
[56]Caceres C.H., Rodriguez A.H., Acoustic emission and deformation bands in Al-2.5% Mg and Cu-30% Zn, Acta Metall.,1987,35(12):2851.
[57]Cetlin P.R., Gulec A.S., Reed-Hill R.E., Serrated Flow in Al 6061 Alloy, Metall. Trans.,1973, 4:513.
[58]Chihab K., Estrin Y, Kubin L.P., Vergnol J., The kinetics of the Portevin-Le Chatelier bands in an Al-5at%Mg alloy, Scripta Metallurgica,1987,21:203.
[59]Ziegenbein A., Hahner P., Neuhauser H., Correlation of temporal instabilities and spatial localization during Portevin-Le Chatelier deformation of Cu-10 at.%Al and Cu-15 at.%Al. Computational Materials Science,2000,19:27.
[60]Ziegenbein A., Hahner P., Neuhauser H., Propagating Portevin-Le Chatelier deformation bands in Cu-15 at.%Al polycrystals:experiments and thoeretical description, Materials Science and Engineering A,2001,309-310:336.
[61]Xiang G.F., Zhang Q.C., Liu H.W., Wu X.P., Ju X.Y., Time-resolved deformation measurements of the Portevin-Le Chatelier bands, Scripta Metall.,2007,56:721.
[62]龚兴龙,变形的实时光学测量,博士论文,合肥：中国科学技术大学,1995.
[63]Gong X., Toyooka S., Investigation on mechanism of plastic deformation by digital speckle pattern interferometry, Experimental Mechanics,1999,39(1):25.
[64]Zhang Q., Toyooka S., Meng Z., Suprapedi, Investigation of slipband propagation in aluminum alloy with dynamic speckle interferometry, in Part of the SPIE conference on Nondestructive Evaluation of Aging Materials and Composites Ⅲ,1999, Newport Beach, California:SPIE.
[65]Zhang Q., Toyooka S., Wu X, Study of propagation and pulsation of slip band using dynamic digital speckle interferometry, in Third International Conference on Experimental Mechanics, 2001, Beijing:SPIE.
[66]Zhang Q.C., Jiang Z.Y., Jiang H.F., Chen Z.J., Wu X.P., On the propagation and pulsation of Portevin-Le Chatelier deformation bands an experimental study with digital speckle pattern metrology, International Journal of Plasticity,2005,21:2150.
[67]Shabadi R., Kumar S., Roven H.J., Dwarakadasa, E.S., Characterisation of PLC band parameters using laser speckle technique, Materials Science and Engineering A,2004,364: 140.
[68]Shabadi R., Kumar S., Roven H.J., Dwarakadasa E.S., Effect of specimen condition, orientation and alloy composition on PLC band parameters. Materials Science and Engineering A,2004,382:203.
[69]Ranc N., Wagner D., Some aspects of Portevin-Le Chatelier plastic instabilities investigated by infrared pyrometry, Mater. Sci. Eng. A,2005,394:87.
[70]Louche H., Vacher P., Arrieux R., Thermal observations associated with the Portevin-Le Chatelier effect in an Al-Mg alloy, Mater. Sci. Eng. A,2005,404:188,.
[71]Tabata T., Fujita H., Nakajima Y., Behavior of dislocations in Al-Mg single crystals observed by high voltage electron microscopy, Acta Metallurgica,1980,28:795.
[72]Flor S., Nortmann A., Dierke H., Neuhaeuser H., TEM study of the dislocation structure at the transition from discontinuous to viscous glide in Cu-Al and Cu-Mn alloys at elevated temperatures, Zeitschrift Fuer Metallkunde,2003,94(5):572.
[73]Cottrell A.H., Bilby B.A., Dislocation theory of yielding and stain ageing of iron, Proceedings of the Physical Society,1949, LXII(I-A):49.
[74]McCormick P.G, A model for the Portevin-Le Chatelier effect in substitutional alloys, Acta Metallurgica,1972,20:351.
[75]Beukel A.V.D., Theory of the effect of dynamic strain aging of mechanical properties. Physica Status Solidi A,1975,30:197.
[76]Sleeswyk A.W., Slow Strain-hardening of ingot iron, Acta Metallurgica,1958,6:598.
[77]Mulford R.A., Kocks U.F., New observations on the mechanisms of dynamic strain aging and of jerky flow, Acta Metallurgica,1979,27:1125.
[78]Nortmann A., Schwink Ch., Characteristics of dynamic strain ageing in binary f.c.c. copper alloys-Ⅰ. Results on solid solutions of Cu Al, Acta Metall.,1997,45:2043.
[79]Nortmann A., Schwink Ch., Characteristics of dynamic strain ageing in binary f.c.c. copper alloys-Ⅱ. Comparison and analysis of experiments on Cu Al and Cu Mn, Acta Metall.,1997, 45:2051.
[80]Springer F., Nortmann A., Schwink Ch., A study of basic processes characterizing dynamic strain ageing, Phys. Status Solidi A,1998,170:63.
[81]Klose F.B., Ziegenbein A., Weidenmuller J., Neuhauser H., Hahner P., Portevin-Le Chatelier effect in strain and stress controlled tensile tests, Computational Materials Science,2003,26: 80.
[82]Picu R.C., Zhang D., Atomistic study of pipe diffusion in Al-Mg alloys, Acta Mater.,2004, 52:161.
[83]Picu R.C., A mechanism for the negative strain-rate sensitivity of dilute solid solutions, Acta Mater.,2004,52:3447.
[84]Picu R.C., Vincze G, Ozturk F., Gracio J.J., Barlat F., Maniatty A.M., Strain rate sensitivity of the commercial aluminum alloy AA5182-0, Mater. Sci. Eng. A,2005,390:334.
[85]陈忠家,Al合金锯齿形屈服现象的机理研究和数值模拟,博士论文,合肥：中国科学技术大学,2004。
[86]McCormick P.G., Ling C.P., Numerical modeling of the Portevin-Le Chatelier effect. Acta Metall. Mater.,1995,43:1969.
[87]Ananthakrishna G., Sahoo D., A model based on nonlinear oscillations to explain jumps on creep curves. Journal of Physics D:Applied Physics,1981,14:2081.
[88]Schoeck G., The Portevin-Le Chatelier effect, a kinetic theory, Acta Metall.,1984,32:1229.
[89]Kubin L.P., Estrin Y., The Portevin-Le Chatelier effect in deformation with constant stress rate. Acta Metall.,1985,33:397.
[90]Hahner P., Ziegenbein A., Rizzi E., Neuhauser H., Spatiotemporal analysis of Portevin-Le Chatelier deformation bands:Theory, simulation, and experiment. Physical Review B,2002, 65:134109.
[91]Zhang S., McCormick P.G., Estrin Y., The morphology of Portevin-Le Chatelier bands: Finite element simulation for Al-Mg-Si, Acta Mater.,2001,49:1087.
[92]Kok S., Bharathi M.S., Beaudoin A.J., Fressengeas C., Ananthakrishna G., Kubin L.P., Lebyodkin M., Spatial coupling in jerky flow using polycrystal plasticity, Acta. Mater., 2003,51:3651.
[93]Glimm J., Sharp D., Multiscale science:a challenge for the twenty-first century, Siam News, 1997,30(8):1.
[94]何国威,夏蒙棼,柯孚久,白以龙,多尺度耦合现象：挑战和机遇,自然科学进展,2004,14(2)：121.
[1]Pink E., Grinberg A., Stress drops in serrated flow curves of A15Mg, Acta Metallurgica,1982, 30:2153.
[2]Lebyodkin M., Brechet Y., Estrin Y., Kubin L.P., Statistics of the catastrophic slip events in the Portevin-Le Chatelier effect, Physical Review Letters,1995,74:4758.
[3]卢俊勇,蒋震宇,张青川,江慧丰,刘颢文,Al-Cu多晶锯齿形屈服现象中的尺度效应,物理学报,2006,55：3558.
[4]Cetlin P.R., Gulec A.S., Reed-Hill R.E., Serrated Flow in Al 6061 Alloy, Metall. Trans.,1973, 4:513.
[5]Zhang Q.C., Jiang Z.Y., Jiang H.F., Chen Z.J., Wu X.P., On the propagation and pulsation of Portevin-Le Chatelier deformation bands an experimental study with digital speckle pattern metrology, International Journal of Plasticity,2005,21:2150.
[6]孙亮,张青川,晏顺平,江慧丰,刘颢文,卢俊勇,伍小平,Al-4.5wt%Cu合金中溶质原子及析出相对锯齿形屈服时空特性的影响,物理学报,2007,56：3411.
[7]Jiang H.F., Zhang Q.C., Jiang Z.Y., Chen Z.J., Wu X.P., Investigation of Kinematics of the Portevin-Le Chatelier Deformation Bands with Dynamic Digital Speckle Pattern Interferometry, Chinese Physics Letters,2005,22(1):99.
[8]江慧丰,张青川,徐毅豪,伍小平,固溶处理对Al-Cu合金中Portevin-Le Chatelier效应空域行为的影响,物理学报,2006,55(1)：409.
[9]江慧丰,张青川,徐毅豪,伍小平,时效对Al-Cu合金中锯齿形流动的影响,金属学报,2006,42(4)：139.
[10]丹蒂J.C.,激光斑纹及有关现象,北京：科学出版社,1981.
[11]尹协振,续伯钦,张寒虹,实验力学讲义,合肥：中国科学技术大学,1999.
[12]伍小平,何世平,李志超,空间散斑运动规律,物理学报,1980,29：1142.
[13]伍小平,何世平,李志超,空间散斑运动规律(续),物理学报,1983,32：973.
[14]Leendertz J.A., Butters J.N., An image-shearing speckle pattern interferomete for measuring bending moments. Journal of Physics E:Scientific Instruments,1973,6:1107.
[15]武恭等,铝及铝合金材料手册,北京：科学出版社,1997.
[16]Penning P., Mathematics of the Portevin-Le Chatelier effect, Acta Metall.,1972,20:1169.
[17]Sleeswyk A.W., Slow Strain-hardening of ingot iron, Acta Metallurgica,1958,6:598.
[18]Mulford R.A., Kocks U.F., New observations on the mechanisms of dynamic strain aging and of jerky flow, Acta Metallurgica,1979,27:1125.
[19]冯端等,金属物理学,第一卷,结构与缺陷,北京：科学出版社,2000.
[20]Schlipf J., Collective dynamic aging of moving dislocations, Materials Science and Engineering A,1991,137:135.
[21]Ananthakrishna A., Noronha S.J., Fressengeas C., Kubin L.P., Crossover from chaotic to self-organized critical dynamics in jerky flow of single crystals, Physical Review E,1999,60: 5455.
[22]Ananthakrishna G., Noronha S.J., Fressengeas C., Kubin L.P., Crossover in the dynamics of Portevin-Le Chatelier effect from chaos to SOC, Materials Science and Engineering A,2001, 309-310:316.
[23]冯端等,金属物理学,第三卷,金属力学性质,北京：科学出版社,1999.
[24]王群骄,有色金属热处理技术,北京：化学工业出版社,2008.
[25]潘复生,张丁非等,铝合金及应用,北京：化学工业出版社,2006.
[26]张士林,任颂赞,简明铝合金手册,上海：上海科学技术文献出版社,2001.
[27]Jiang H.F., Zhang Q.C., Wu X.P., Fan J.H., Spatiotemporal aspects of the Portevin-Le Chatelier effect in annealed and solution-treated aluminum alloys, Scripta Materialia,2006, 54:2041.
[28]Chihab K., Estrin Y., Kubin L.P., Vergnol J., The kinetics of the Portevin-Le Chatelier bands in an Al-5at%Mg alloy, Scripta Metallurgica,1987,21:203.
[29]崔忠圻,覃耀春,金属学与热处理,第2版,北京：机械工业出版社,2007.
[30]Kumar S., McShane H.B., Serrated yielding in Al-Li alloys, Scripta Metall. et Mater.,1993, 28(9):1149.
[31]Kumar S., Pink E., Effect of δ' precipitates on serrated flow, Scripta Metall. et Mater.,1995, 32(5):749.
[32]Brechet Y., Estrin Y., On the influence of precipitation on the Portevin-Le Chatelier effect. Acta metall. mater.,1995,43(3):955.
[33]Chmelik F., Pink E., Krol J., Balik J., Peika J., Luka P., Mechanisms of serrated flow in aluminium alloys with precipitates investigated by acoustic emission, Acta mater.,1998, 46(12):4435.
[34]Pink E., Kumar S., Tian B.H., Serrated flow of aluminium alloys influenced by precipitates, Materials Science and Engineering A,2000,280:17.
[1]Chihab K., Estrin Y., Kubin L.P., Vergnol J., The kinetics of the Portevin-Le Chatelier bands in an Al-5at%Mg alloy, Scripta Metallurgica, 1987,21:203.
[2]Ziegenbein A., Hahner P., Neuhauser H., Correlation of temporal instabilities and spatial localization during Portevin-Le Chatelier deformation of Cu-10 at.%Al and Cu-15 at.%Al. Computational Materials Science,2000,19:27.
[3]Xiang G.F., Zhang Q.C., Liu H.W., Jiang H.F., Wu X.P., Deformation measurements of three types of Portevin-Le Chatelier bands, Chinese Physics B,2006,15:2378.
[4]Zhang Q.C., Toyooka S., Meng Z.B., Slipband propagation in aluminum alloy with dynamic speckle interferometry, Proc. of SPIE,1999,3585:389.
[5]Ranc N., Wagner D., Some aspects of Portevin-Le Chatelier plastic instabilities investigated by infrared pyrometry, Mater. Sci. Eng. A,2005,394:87.
[6]Louche H., Vacher P., Arrieux R., Thermal observations associated with the Portevin-Le Chatelier effect in an Al-Mg alloy, Mater. Sci. Eng. A,2005,404:188.
[7]Ranc N., Wagner D., Experimental study by pyrometry of Portevin-Le Chatelier plastic instabilities—Type A to type B transition, Mater. Sci. Eng. A,2008,474:188.
[8]Ait-Amokhtar H., Fressengeas C., Boudrahem S., The dynamics of Portevin-Le Chatelier bands in an Al-Mg alloy from infrared thermography, Mater. Sci. Eng. A,2008,488:540.
[9]Thomson W., On the dynamical theory of heat, Trans. Roy. Soc.,1853,20:261.
[10]Taylor G.I., Quiney H., The Latent heat remaining in a metal after cold work, Proc. Roy. Soc., 1934,143:307.
[11]Shabadi R., Kumar S., Roven H.J., Dwarakadasa, E.S., Characterisation of PLC band parameters using laser speckle technique, Mater. Sci. Eng. A,2004,364:140.
[12]杨世铭等,传热学,北京：高等教育出版社,2006.
[13]Pink E., Grinberg A., Stress drops in serrated flow curves of A15Mg, Acta Metallurgica,1982, 30:2153.
[14]Lebyodkin M., Brechet Y., Estrin Y., Kubin L.P., Statistical behavior and strain localization patterns in the Portevin-Le Chatelier effect, Acta Materialia,1996,44:4531.
[15]Neuhauser H., Klose F.B., Hagemann F., Weidenmuller J., Dierke H., Hahner P., On the PLC effect in strain-rate and stress-rate controlled tests-studies by laser scanning extensometry, J. Alloys Comp.,2004,378:13.
[1]Cottrell A.H., Bilby B.A., Dislocation theory of yielding and stain ageing of iron, Proceedings of the Physical Society,1949, LXII(I-A):49.
[2]Tabata T., Fujita H., Nakajima Y., Behavior of dislocations in Al-Mg single crystals observed by high voltage electron microscopy, Acta Metallurgica,1980,28:795.
[3]Flor S., Nortmann A., Dierke H., Neuhaeuser H., TEM study of the dislocation structure at the transition from discontinuous to viscous glide in Cu-Al and Cu-Mn alloys at elevated temperatures, Zeitschrift Fuer Metallkunde,2003,94(5):572.
[4]孟庆昌,透射电子显微学,哈尔滨：哈尔滨工业大学出版社,1998.
[5]潘复生,张丁非等,铝合金及应用,北京：化学工业出版社,2006.
[6]冯端等,金属物理学,第一卷,结构与缺陷,北京：科学出版社,2000.
[7]崔忠圻,覃耀春,金属学与热处理,第2版,北京：机械工业出版社,2007.
[2]Portevin A., Le Chatelier F., Sur un phenomene observe lors de l'essai detraction d'alliages en cours de transformation, Comptes Rendus de l'Academiedes Sciences Paris,1923,176:507.
[3]Subramanian K.H., Duncan A. J., Tensile Properties for Application to Type Ⅰ and Type Ⅱ Waste Tank Flaw Stability Analysis, WSRC-TR-2000-00232,2000.
[4]Nadai A., Plasticity:A Mechanics of the Plastic State of Matter, New York:McGraw-Hill, 1931.
[5]冯端等,金属物理学,第三卷,金属力学性质,北京：科学出版社,1999.
[6]Zhang Q.C., Jiang Z.Y., Jiang H.R, Chen Z.J., Wu X. P., On the propagation and pulsation of Portevin-Le Chatelier deformation bands:an experimental study with digital speckle pattern metrology, International Journal of Plasticity,2005,21:2150.
[7]Ardley G.W., Cottrell A.H., Dislocation theory of yielding and strain ageing of iron, Proc. Roval. Soc.,1953, A219:328.
[8]Sleeswyk A.W., Slow Strain-hardening of ingot iron, Acta Metall.,1958,6:598.
[9]Brindley B.J., Corderoy D.J.H., Honeycombe R.W.K., Yield points and Luders bands in single crystal of copper-base alloys, Acta Metall.,1962,10:1043.
[10]Estrin Y, Kubin, L.P., Spatial coupling and propagative plastic instabilities, in Continumm Models for Materials with Microstructures, Muhlhaus H.B., Editor, Wiley:New York,1995, 395.
[11]国家自然科学基金委员会数学物理科学部,力学学科发展研究报告,北京：科学出版社,2007.
[12]国家自然科学基金委员会工程与材料科学部,金属材料科学,北京：科学出版社,2006.
[13]潘复生,张丁非等,铝合金及应用,北京：化学工业出版社,2006.
[14]Bell J.F., The Experimental foundations of Solid Mechanics, Encyclopedia of Physics-Mechanics of Solids I, ed. S. Flugge and C. Truesdell, Vol. VIa/1, Berlin:Springer-Verlag, 1973.
[15]Savart F., Recherches sue les vibrations longitudinales, Ann. Chem. Phys., second series 1837, 65:337.
[16]Franklin S.V., Mertens F., Marder M., Portevin-Le Chatelier effect, Phys. Rev. E,2000,62: 8195.
[17]Masson A.P., Sur l'easticite des corpes solides, Ann. Chem. Phys., third series 1841,3:451.
[18]Portevin A., Le Chatelier F., Heat treatment of aluminium-copper alloys, Transactions of the American Society of Steel Treating,1924,5:457.
[19]Cottrell A.H., A Note on the Portevin-Le Chatelier effect, Philosophical Magazine,1953, 44(355):829.
[20]Andrade ENdaC., The viscous flow in metals and allied phenomena, Proc. R. Soc.,1910,84: 1.
[21]Da Silveira T.L., Monteiro S.N., Jumps in the creep curve of austentic stainless steels, Met. Trans.,1979, A10:1795.
[22]Bell J.F., Stein A., The incremental loading wave in the pre-stressed plastic field, Journal de Mechanique,1962,1:395.
[23]Dillon O.W., Experimental data on aluminum as a mechanically unstable solid, Journal of Mechanics and Physics of Solids,1963,11:289.
[24]Kovacs Z., Chinh N.Q., Lendvai J., Orientation dependence of Portevin-Le Chatelier plastic instabilities in depth-sensing microindentation, Journal of Materials Research,2001,16(4): 1171.
[25]Weinhandl H., Mitter F., Bernt W., Kumar S., Pink E., Computer-assisted recording of tensile tests for the evaluation of serrated flow, Scripta Metallurgica et Materialia,1994,31(11): 1567.
[26]田宝辉,张永刚,陈昌麒,Al—Li单晶体锯齿流变的形态特征,金属学报,1996,32(3)：249.
[27]Tian B., Comparing characteristics of serrations in Al-Li and Al-Mg alloys. Materials Science and Engineering A,2003,360:330.
[28]钱匡武,李效琦,彭开萍,张好国,高强度铝合金LC4中锯齿屈服特征的研究,福州大学学报,1995,23(2)：53.
[29]Kumar S., Pink E., Serrated flow in aluminium alloys containing lithium, Acta Materialia, 1997,45(12):5295.
[30]Pink E., Bruckbauer P., Weinhandl H., Stress-Drop rates in serrated flow of aluminium alloys, Scripta Metallurgica,1998,38(6):945.
[31]Pink E., Arsenault R.J., Stress-drop rates in serrated flow and their strain and temperature dependences:A comparison of an aluminum'Cmagnesium alloy and a mild steel, Materials Science and Engineering A,1999,272:57.
[32]Pink E., Kumar S., Tian B., Serrated flow of aluminium alloys influenced by precipitates, Materials Science and Engineering A,2000,280:17.
[33]Brindley B.J., Worthington P.J., Yield point phenomena in substitutional alloys, Metallurgical Reviews,1970,145:101.
[34]Cuddy L.J., Leslie W.C., Some aspects of serrated yielding in substitutional solid solutions of iron. Acta Metallurgica,1972,20:1157.
[35]Pink E., Grinberg A., Serrated flow in a ferritic stainless steel. Materials Science and Engineering A,1981,51(1):1.
[36]McCormick P.G., Dynamic strain ageing. Transactions of the Indian Institute of Metals,1986, 39:98.
[37]Rizzi E., Hahner P., On the Portevin-Le Chatelier effect:theoretical modeling and numerical results, International Journal of Plasticity,2004,20:121.
[38]Lebyodkin M., Dunin-Barkovskii L., Brechet Y., Estrin Y., Kubin L., Spatio-temporal dynamics of the Portevin-Le Chatelier effect:experiment and modeling, Acta Materialia, 2000,48:2529.
[39]Yoshinaga H., Toma K., Abe K., Morozumi, S., Portevin-Le Chatelier effect in vanadium, Philosophical Magazine,1971,23:1387.
[40]Lebyodkin M., Brechet Y., Estrin Y, Kubin L.P., Statistics of the catastrophic slip events in the Portevin-Le Chatelier effect, Physical Review Letters,1995,74:4758.
[41]Lebyodkin M., Brechet Y., Estrin Y., Kubin L.P., Statistical behavior and strain localization patterns in the Portevin-Le Chatelier effect. Acta Materialia,1996,44:4531.
[42]Lebyodkin M., Dunin-Barkovskii L., Brechet Y, Kubin L., Estrin Y., Kinetics and statistics of jerky flow: experiments and computer simulations, Materials Science and Engineering A, 1997,115:234.
[43]Lebyodkin M., Fressengeas C., Ananthakrishna G., Kubin L.P., Statistical and Multifractal analysis of the Portevin-Le Chatelier effect, Materials Science and Engineering A,2001,170: 319.
[44]Bharathi M.S., Lebyodkin M., Ananthakrishna G., Fressengeas C., Kubin L.P., The hidden order behind jerky flow, Acta Materialia,2002,50:2813.
[45]Packard N.H., Crutchfield J.P., Farmer J.D., Shaw R.S., Geometry from a time series, Physical Review Letters,1980,45:712.
[46]Takens F., Detecting strange attractors in turbulence, in Dynamical systems and turbulence,
Warwick 1980, Edited by Rand D.A. and Yong L.S., Lecture notes in mathematics 898 (Springer, Berlin,1980):366.
[47]Ananthakrishna G, Fressengeas C., Grosbras M., Vergnol J., Engelke C., Plessing J., Neuhauser H., Bouchaud E., Planes J., Kubin L.P., On the existence of chaos in jerky flow, Scripta Metallurgia et Materialia,1995,32(11):1731.
[48]Ananthakrishna G, Fressengeas C., Kubin L.P., Chaos and the jerky flow in Al-Mg polycrystals, Materials Science and Engineering A,1997,234-236:314.
[49]Bharathi M.S., Lebyodkin M., Ananthakrishna G, Fressengeas C., Kubin L.P., Multifractal burst in the spatiotemporal dynamics of jerky flow. Physical Review Letters,2001,87(16): 165508-1.
[50]Ananthakrishna G, Bharathi M.S., Dynamical approach to the spatiotemporal aspects of the Portevin-Le Chatelier effect:chaos, turbulence and band propagation, Physical Review E, 2004,70:026111.
[51]Ananthakrishna G, Noronha S.J., Fressengeas C., Kubin L.P., Crossover from chaotic to self-organized critical dynamics in jerky flow of single crystals, Physical Review E,1999,60: 5455.
[52]Ananthakrishna G, Noronha S.J., Fressengeas C., Kubin L.P., Crossover in the dynamics of Portevin-Le Chatelier effect from chaos to SOC, Mater. Sci. Eng. A.2001,309-310:316.
[53]McReynolds A.W., Plastic deformation waves in aluminum, Transactions of the American Institute of Mining and Metallurgical Engineers,1949,185:32.
[54]Sharpe W.N., The Portevin-Le Chatelier effect in aluminum single crystals and polycrystals, Ph.D. Dissertation, Baltimore, Maryland:The Johns Hopkins University,1966.
[55]Bell J.F., The Physics of Large Deformation of Crystalline Solids, Springer Tracts in Natural Philosophy, Berlin-Heidelberg-New York:Springer,1968.
[56]Caceres C.H., Rodriguez A.H., Acoustic emission and deformation bands in Al-2.5% Mg and Cu-30% Zn, Acta Metall.,1987,35(12):2851.
[57]Cetlin P.R., Gulec A.S., Reed-Hill R.E., Serrated Flow in Al 6061 Alloy, Metall. Trans.,1973, 4:513.
[58]Chihab K., Estrin Y, Kubin L.P., Vergnol J., The kinetics of the Portevin-Le Chatelier bands in an Al-5at%Mg alloy, Scripta Metallurgica,1987,21:203.
[59]Ziegenbein A., Hahner P., Neuhauser H., Correlation of temporal instabilities and spatial localization during Portevin-Le Chatelier deformation of Cu-10 at.%Al and Cu-15 at.%Al. Computational Materials Science,2000,19:27.
[60]Ziegenbein A., Hahner P., Neuhauser H., Propagating Portevin-Le Chatelier deformation bands in Cu-15 at.%Al polycrystals:experiments and thoeretical description, Materials Science and Engineering A,2001,309-310:336.
[61]Xiang G.F., Zhang Q.C., Liu H.W., Wu X.P., Ju X.Y., Time-resolved deformation measurements of the Portevin-Le Chatelier bands, Scripta Metall.,2007,56:721.
[62]龚兴龙,变形的实时光学测量,博士论文,合肥：中国科学技术大学,1995.
[63]Gong X., Toyooka S., Investigation on mechanism of plastic deformation by digital speckle pattern interferometry, Experimental Mechanics,1999,39(1):25.
[64]Zhang Q., Toyooka S., Meng Z., Suprapedi, Investigation of slipband propagation in aluminum alloy with dynamic speckle interferometry, in Part of the SPIE conference on Nondestructive Evaluation of Aging Materials and Composites Ⅲ,1999, Newport Beach, California:SPIE.
[65]Zhang Q., Toyooka S., Wu X, Study of propagation and pulsation of slip band using dynamic digital speckle interferometry, in Third International Conference on Experimental Mechanics, 2001, Beijing:SPIE.
[66]Zhang Q.C., Jiang Z.Y., Jiang H.F., Chen Z.J., Wu X.P., On the propagation and pulsation of Portevin-Le Chatelier deformation bands an experimental study with digital speckle pattern metrology, International Journal of Plasticity,2005,21:2150.
[67]Shabadi R., Kumar S., Roven H.J., Dwarakadasa, E.S., Characterisation of PLC band parameters using laser speckle technique, Materials Science and Engineering A,2004,364: 140.
[68]Shabadi R., Kumar S., Roven H.J., Dwarakadasa E.S., Effect of specimen condition, orientation and alloy composition on PLC band parameters. Materials Science and Engineering A,2004,382:203.
[69]Ranc N., Wagner D., Some aspects of Portevin-Le Chatelier plastic instabilities investigated by infrared pyrometry, Mater. Sci. Eng. A,2005,394:87.
[70]Louche H., Vacher P., Arrieux R., Thermal observations associated with the Portevin-Le Chatelier effect in an Al-Mg alloy, Mater. Sci. Eng. A,2005,404:188,.
[71]Tabata T., Fujita H., Nakajima Y., Behavior of dislocations in Al-Mg single crystals observed by high voltage electron microscopy, Acta Metallurgica,1980,28:795.
[72]Flor S., Nortmann A., Dierke H., Neuhaeuser H., TEM study of the dislocation structure at the transition from discontinuous to viscous glide in Cu-Al and Cu-Mn alloys at elevated temperatures, Zeitschrift Fuer Metallkunde,2003,94(5):572.
[73]Cottrell A.H., Bilby B.A., Dislocation theory of yielding and stain ageing of iron, Proceedings of the Physical Society,1949, LXII(I-A):49.
[74]McCormick P.G, A model for the Portevin-Le Chatelier effect in substitutional alloys, Acta Metallurgica,1972,20:351.
[75]Beukel A.V.D., Theory of the effect of dynamic strain aging of mechanical properties. Physica Status Solidi A,1975,30:197.
[76]Sleeswyk A.W., Slow Strain-hardening of ingot iron, Acta Metallurgica,1958,6:598.
[77]Mulford R.A., Kocks U.F., New observations on the mechanisms of dynamic strain aging and of jerky flow, Acta Metallurgica,1979,27:1125.
[78]Nortmann A., Schwink Ch., Characteristics of dynamic strain ageing in binary f.c.c. copper alloys-Ⅰ. Results on solid solutions of Cu Al, Acta Metall.,1997,45:2043.
[79]Nortmann A., Schwink Ch., Characteristics of dynamic strain ageing in binary f.c.c. copper alloys-Ⅱ. Comparison and analysis of experiments on Cu Al and Cu Mn, Acta Metall.,1997, 45:2051.
[80]Springer F., Nortmann A., Schwink Ch., A study of basic processes characterizing dynamic strain ageing, Phys. Status Solidi A,1998,170:63.
[81]Klose F.B., Ziegenbein A., Weidenmuller J., Neuhauser H., Hahner P., Portevin-Le Chatelier effect in strain and stress controlled tensile tests, Computational Materials Science,2003,26: 80.
[82]Picu R.C., Zhang D., Atomistic study of pipe diffusion in Al-Mg alloys, Acta Mater.,2004, 52:161.
[83]Picu R.C., A mechanism for the negative strain-rate sensitivity of dilute solid solutions, Acta Mater.,2004,52:3447.
[84]Picu R.C., Vincze G, Ozturk F., Gracio J.J., Barlat F., Maniatty A.M., Strain rate sensitivity of the commercial aluminum alloy AA5182-0, Mater. Sci. Eng. A,2005,390:334.
[85]陈忠家,Al合金锯齿形屈服现象的机理研究和数值模拟,博士论文,合肥：中国科学技术大学,2004。
[86]McCormick P.G., Ling C.P., Numerical modeling of the Portevin-Le Chatelier effect. Acta Metall. Mater.,1995,43:1969.
[87]Ananthakrishna G., Sahoo D., A model based on nonlinear oscillations to explain jumps on creep curves. Journal of Physics D:Applied Physics,1981,14:2081.
[88]Schoeck G., The Portevin-Le Chatelier effect, a kinetic theory, Acta Metall.,1984,32:1229.
[89]Kubin L.P., Estrin Y., The Portevin-Le Chatelier effect in deformation with constant stress rate. Acta Metall.,1985,33:397.
[90]Hahner P., Ziegenbein A., Rizzi E., Neuhauser H., Spatiotemporal analysis of Portevin-Le Chatelier deformation bands:Theory, simulation, and experiment. Physical Review B,2002, 65:134109.
[91]Zhang S., McCormick P.G., Estrin Y., The morphology of Portevin-Le Chatelier bands: Finite element simulation for Al-Mg-Si, Acta Mater.,2001,49:1087.
[92]Kok S., Bharathi M.S., Beaudoin A.J., Fressengeas C., Ananthakrishna G., Kubin L.P., Lebyodkin M., Spatial coupling in jerky flow using polycrystal plasticity, Acta. Mater., 2003,51:3651.
[93]Glimm J., Sharp D., Multiscale science:a challenge for the twenty-first century, Siam News, 1997,30(8):1.
[94]何国威,夏蒙棼,柯孚久,白以龙,多尺度耦合现象：挑战和机遇,自然科学进展,2004,14(2)：121.
[1]Pink E., Grinberg A., Stress drops in serrated flow curves of A15Mg, Acta Metallurgica,1982, 30:2153.
[2]Lebyodkin M., Brechet Y., Estrin Y., Kubin L.P., Statistics of the catastrophic slip events in the Portevin-Le Chatelier effect, Physical Review Letters,1995,74:4758.
[3]卢俊勇,蒋震宇,张青川,江慧丰,刘颢文,Al-Cu多晶锯齿形屈服现象中的尺度效应,物理学报,2006,55：3558.
[4]Cetlin P.R., Gulec A.S., Reed-Hill R.E., Serrated Flow in Al 6061 Alloy, Metall. Trans.,1973, 4:513.
[5]Zhang Q.C., Jiang Z.Y., Jiang H.F., Chen Z.J., Wu X.P., On the propagation and pulsation of Portevin-Le Chatelier deformation bands an experimental study with digital speckle pattern metrology, International Journal of Plasticity,2005,21:2150.
[6]孙亮,张青川,晏顺平,江慧丰,刘颢文,卢俊勇,伍小平,Al-4.5wt%Cu合金中溶质原子及析出相对锯齿形屈服时空特性的影响,物理学报,2007,56：3411.
[7]Jiang H.F., Zhang Q.C., Jiang Z.Y., Chen Z.J., Wu X.P., Investigation of Kinematics of the Portevin-Le Chatelier Deformation Bands with Dynamic Digital Speckle Pattern Interferometry, Chinese Physics Letters,2005,22(1):99.
[8]江慧丰,张青川,徐毅豪,伍小平,固溶处理对Al-Cu合金中Portevin-Le Chatelier效应空域行为的影响,物理学报,2006,55(1)：409.
[9]江慧丰,张青川,徐毅豪,伍小平,时效对Al-Cu合金中锯齿形流动的影响,金属学报,2006,42(4)：139.
[10]丹蒂J.C.,激光斑纹及有关现象,北京：科学出版社,1981.
[11]尹协振,续伯钦,张寒虹,实验力学讲义,合肥：中国科学技术大学,1999.
[12]伍小平,何世平,李志超,空间散斑运动规律,物理学报,1980,29：1142.
[13]伍小平,何世平,李志超,空间散斑运动规律(续),物理学报,1983,32：973.
[14]Leendertz J.A., Butters J.N., An image-shearing speckle pattern interferomete for measuring bending moments. Journal of Physics E:Scientific Instruments,1973,6:1107.
[15]武恭等,铝及铝合金材料手册,北京：科学出版社,1997.
[16]Penning P., Mathematics of the Portevin-Le Chatelier effect, Acta Metall.,1972,20:1169.
[17]Sleeswyk A.W., Slow Strain-hardening of ingot iron, Acta Metallurgica,1958,6:598.
[18]Mulford R.A., Kocks U.F., New observations on the mechanisms of dynamic strain aging and of jerky flow, Acta Metallurgica,1979,27:1125.
[19]冯端等,金属物理学,第一卷,结构与缺陷,北京：科学出版社,2000.
[20]Schlipf J., Collective dynamic aging of moving dislocations, Materials Science and Engineering A,1991,137:135.
[21]Ananthakrishna A., Noronha S.J., Fressengeas C., Kubin L.P., Crossover from chaotic to self-organized critical dynamics in jerky flow of single crystals, Physical Review E,1999,60: 5455.
[22]Ananthakrishna G., Noronha S.J., Fressengeas C., Kubin L.P., Crossover in the dynamics of Portevin-Le Chatelier effect from chaos to SOC, Materials Science and Engineering A,2001, 309-310:316.
[23]冯端等,金属物理学,第三卷,金属力学性质,北京：科学出版社,1999.
[24]王群骄,有色金属热处理技术,北京：化学工业出版社,2008.
[25]潘复生,张丁非等,铝合金及应用,北京：化学工业出版社,2006.
[26]张士林,任颂赞,简明铝合金手册,上海：上海科学技术文献出版社,2001.
[27]Jiang H.F., Zhang Q.C., Wu X.P., Fan J.H., Spatiotemporal aspects of the Portevin-Le Chatelier effect in annealed and solution-treated aluminum alloys, Scripta Materialia,2006, 54:2041.
[28]Chihab K., Estrin Y., Kubin L.P., Vergnol J., The kinetics of the Portevin-Le Chatelier bands in an Al-5at%Mg alloy, Scripta Metallurgica,1987,21:203.
[29]崔忠圻,覃耀春,金属学与热处理,第2版,北京：机械工业出版社,2007.
[30]Kumar S., McShane H.B., Serrated yielding in Al-Li alloys, Scripta Metall. et Mater.,1993, 28(9):1149.
[31]Kumar S., Pink E., Effect of δ' precipitates on serrated flow, Scripta Metall. et Mater.,1995, 32(5):749.
[32]Brechet Y., Estrin Y., On the influence of precipitation on the Portevin-Le Chatelier effect. Acta metall. mater.,1995,43(3):955.
[33]Chmelik F., Pink E., Krol J., Balik J., Peika J., Luka P., Mechanisms of serrated flow in aluminium alloys with precipitates investigated by acoustic emission, Acta mater.,1998, 46(12):4435.
[34]Pink E., Kumar S., Tian B.H., Serrated flow of aluminium alloys influenced by precipitates, Materials Science and Engineering A,2000,280:17.
[1]Chihab K., Estrin Y., Kubin L.P., Vergnol J., The kinetics of the Portevin-Le Chatelier bands in an Al-5at%Mg alloy, Scripta Metallurgica, 1987,21:203.
[2]Ziegenbein A., Hahner P., Neuhauser H., Correlation of temporal instabilities and spatial localization during Portevin-Le Chatelier deformation of Cu-10 at.%Al and Cu-15 at.%Al. Computational Materials Science,2000,19:27.
[3]Xiang G.F., Zhang Q.C., Liu H.W., Jiang H.F., Wu X.P., Deformation measurements of three types of Portevin-Le Chatelier bands, Chinese Physics B,2006,15:2378.
[4]Zhang Q.C., Toyooka S., Meng Z.B., Slipband propagation in aluminum alloy with dynamic speckle interferometry, Proc. of SPIE,1999,3585:389.
[5]Ranc N., Wagner D., Some aspects of Portevin-Le Chatelier plastic instabilities investigated by infrared pyrometry, Mater. Sci. Eng. A,2005,394:87.
[6]Louche H., Vacher P., Arrieux R., Thermal observations associated with the Portevin-Le Chatelier effect in an Al-Mg alloy, Mater. Sci. Eng. A,2005,404:188.
[7]Ranc N., Wagner D., Experimental study by pyrometry of Portevin-Le Chatelier plastic instabilities—Type A to type B transition, Mater. Sci. Eng. A,2008,474:188.
[8]Ait-Amokhtar H., Fressengeas C., Boudrahem S., The dynamics of Portevin-Le Chatelier bands in an Al-Mg alloy from infrared thermography, Mater. Sci. Eng. A,2008,488:540.
[9]Thomson W., On the dynamical theory of heat, Trans. Roy. Soc.,1853,20:261.
[10]Taylor G.I., Quiney H., The Latent heat remaining in a metal after cold work, Proc. Roy. Soc., 1934,143:307.
[11]Shabadi R., Kumar S., Roven H.J., Dwarakadasa, E.S., Characterisation of PLC band parameters using laser speckle technique, Mater. Sci. Eng. A,2004,364:140.
[12]杨世铭等,传热学,北京：高等教育出版社,2006.
[13]Pink E., Grinberg A., Stress drops in serrated flow curves of A15Mg, Acta Metallurgica,1982, 30:2153.
[14]Lebyodkin M., Brechet Y., Estrin Y., Kubin L.P., Statistical behavior and strain localization patterns in the Portevin-Le Chatelier effect, Acta Materialia,1996,44:4531.
[15]Neuhauser H., Klose F.B., Hagemann F., Weidenmuller J., Dierke H., Hahner P., On the PLC effect in strain-rate and stress-rate controlled tests-studies by laser scanning extensometry, J. Alloys Comp.,2004,378:13.
[1]Cottrell A.H., Bilby B.A., Dislocation theory of yielding and stain ageing of iron, Proceedings of the Physical Society,1949, LXII(I-A):49.
[2]Tabata T., Fujita H., Nakajima Y., Behavior of dislocations in Al-Mg single crystals observed by high voltage electron microscopy, Acta Metallurgica,1980,28:795.
[3]Flor S., Nortmann A., Dierke H., Neuhaeuser H., TEM study of the dislocation structure at the transition from discontinuous to viscous glide in Cu-Al and Cu-Mn alloys at elevated temperatures, Zeitschrift Fuer Metallkunde,2003,94(5):572.
[4]孟庆昌,透射电子显微学,哈尔滨：哈尔滨工业大学出版社,1998.
[5]潘复生,张丁非等,铝合金及应用,北京：化学工业出版社,2006.
[6]冯端等,金属物理学,第一卷,结构与缺陷,北京：科学出版社,2000.
[7]崔忠圻,覃耀春,金属学与热处理,第2版,北京：机械工业出版社,2007.