合金材料塑性变形过程中位错和溶质原子交互作用的蒙特卡罗模拟
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摘要
位错与溶质原子的交互作用对合金材料的宏观力学行为影响颇大,微观上位错和溶质原子间的交互作用也影响着合金材料的变形方式。随着汽车工业的发展和汽车轻量化要求的迫切,对影响铝合金塑性成形性能的锯齿形屈服效应的研究显得非常重要。对位错和溶质原子的交互作用进行研究,可为合金材料的微观特征物理量与其宏观力学行为的衔接奠定一定的理论基础。本文从微观角度运用动态蒙特卡罗方法,模拟单个刃型位错和置换溶质原子之间的交互作用,主要内容如下:
1.运用动态蒙特卡罗模型,对两种极限情况(位错始终静止和溶质浓度为零)进行模拟。当位错始终静止时模拟得到位错的中心处形成Cottrell气团,远离中心处也有溶质云层形成,同时也检验了模拟方法的可行性。
2.动态模拟中假设溶质原子之间没有相互作用,得到在不同的外加应力下位错的运动特征和溶质原子的分布状态。结果表明,在较小的外加应力下,位错的运动受到溶质原子的迟滞作用很容易被钉扎;在较大的外加应力下,位错的运动基本不受溶质原子的影响;而中等的应力下位错的运动状态具有歧义性,速度出现高低跳跃的状态。
3.研究了溶质原子浓度和溶质原子体积膨胀对位错运动速度和临界脱钉应力的影响。结果表明,随着溶质原子浓度和体积膨胀的改变,位错的运动速度存在高速和低速两个分支;位错的临界脱钉应力值随着溶质原子浓度和体积膨胀的增加而增加。
4.当考虑溶质原子之间的相互作用,分析了溶-溶作用对对静态模拟中溶质原子的分布的影响,以及在动态模拟中对位错运动特征的影响。模拟结果反映出位错的钉扎和脱钉现象的并存,为从微观角度深入研究锯齿形屈服效应奠定了基础。
The influence of the interaction between dislocation and solute atoms on the macroscopic mechanical behavior of the alloys is extraordinary great, and the interaction also influences the way by which alloys deform at the microscopic scale. With the development of automobile industry and urgent requirement of the automobile light weight, the research of the serrated yielding effect which influences the plastic formability of the Al alloys becomes very important. To study the interaction between dislocation and solute atoms may help to establish some theoretical foundation for the link between microscopic parameters and the macroscopic mechanical behavior of alloys. The dynamic Monte Carlo method was used in this paper to simulate the interaction between a single edge dislocation and substitutional solute atoms. The main contents are as follows:
1. A dynamic Monte Carlo model was established to simulate two critical states (the dislocation is always static and the solute concentration is zero). When the dislocation is always static, the simulation results show that there is a Cottrell atmosphere around the dislocation core, and a diffuse solute atmosphere far from the core. The results also verify the feasibility of the simulation method.
2. Supposing there is no interaction between solute atoms, the feature of dislocation motion and the distribution of solutes are obtained at different external stresses in the dynamic simulation. The results reflect that at small external stress the dislocation is efficiently pinned by solute atoms with low velocity; and at high external stress the dislocation motion is nearly unaffected by solute atoms and the velocity is high; whereas bifurcation of dislocation motion typified by velocity jumps has been found at intermediate stress.
3. The influences of solute concentration and solute volume dilation on the dislocation velocity and the dislocation’s critical de-pinning stress were simulated. The results reflect that the dislocation motion have two branches of high velocity and low velocity with the change of the solute concentration and the volume dilation; the dislocation critical de-pinning stress rises with the increment of the solute concentration and the volume dilation.
4. Considering the interaction between the solute atoms, we analyzed the influence of solute-solute interaction on the solute distribution in the static simulation, and the feature of dislocation motion in the dynamic simulation. The simulation results reflect the concurrence of the dislocation pinning and de-pinning, which exhibits the microscopic mechanism of the serrated yielding effect.
1.运用动态蒙特卡罗模型,对两种极限情况(位错始终静止和溶质浓度为零)进行模拟。当位错始终静止时模拟得到位错的中心处形成Cottrell气团,远离中心处也有溶质云层形成,同时也检验了模拟方法的可行性。
2.动态模拟中假设溶质原子之间没有相互作用,得到在不同的外加应力下位错的运动特征和溶质原子的分布状态。结果表明,在较小的外加应力下,位错的运动受到溶质原子的迟滞作用很容易被钉扎;在较大的外加应力下,位错的运动基本不受溶质原子的影响;而中等的应力下位错的运动状态具有歧义性,速度出现高低跳跃的状态。
3.研究了溶质原子浓度和溶质原子体积膨胀对位错运动速度和临界脱钉应力的影响。结果表明,随着溶质原子浓度和体积膨胀的改变,位错的运动速度存在高速和低速两个分支;位错的临界脱钉应力值随着溶质原子浓度和体积膨胀的增加而增加。
4.当考虑溶质原子之间的相互作用,分析了溶-溶作用对对静态模拟中溶质原子的分布的影响,以及在动态模拟中对位错运动特征的影响。模拟结果反映出位错的钉扎和脱钉现象的并存,为从微观角度深入研究锯齿形屈服效应奠定了基础。
The influence of the interaction between dislocation and solute atoms on the macroscopic mechanical behavior of the alloys is extraordinary great, and the interaction also influences the way by which alloys deform at the microscopic scale. With the development of automobile industry and urgent requirement of the automobile light weight, the research of the serrated yielding effect which influences the plastic formability of the Al alloys becomes very important. To study the interaction between dislocation and solute atoms may help to establish some theoretical foundation for the link between microscopic parameters and the macroscopic mechanical behavior of alloys. The dynamic Monte Carlo method was used in this paper to simulate the interaction between a single edge dislocation and substitutional solute atoms. The main contents are as follows:
1. A dynamic Monte Carlo model was established to simulate two critical states (the dislocation is always static and the solute concentration is zero). When the dislocation is always static, the simulation results show that there is a Cottrell atmosphere around the dislocation core, and a diffuse solute atmosphere far from the core. The results also verify the feasibility of the simulation method.
2. Supposing there is no interaction between solute atoms, the feature of dislocation motion and the distribution of solutes are obtained at different external stresses in the dynamic simulation. The results reflect that at small external stress the dislocation is efficiently pinned by solute atoms with low velocity; and at high external stress the dislocation motion is nearly unaffected by solute atoms and the velocity is high; whereas bifurcation of dislocation motion typified by velocity jumps has been found at intermediate stress.
3. The influences of solute concentration and solute volume dilation on the dislocation velocity and the dislocation’s critical de-pinning stress were simulated. The results reflect that the dislocation motion have two branches of high velocity and low velocity with the change of the solute concentration and the volume dilation; the dislocation critical de-pinning stress rises with the increment of the solute concentration and the volume dilation.
4. Considering the interaction between the solute atoms, we analyzed the influence of solute-solute interaction on the solute distribution in the static simulation, and the feature of dislocation motion in the dynamic simulation. The simulation results reflect the concurrence of the dislocation pinning and de-pinning, which exhibits the microscopic mechanism of the serrated yielding effect.
引文
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[48] F.B. Klose , A. Ziegenbein , F. Hagemann,et al. Analysis of Portevin-Le Chatelier serrations of type Bin Al–Mg. Materials Science and Engineering A,2004,369: 76~81
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[50] Weiguo Wang,, Bangxin Zhou. The local internal stress in ferromagneticalloys. Dislocation–solute interaction model for local internal stress source. Materials and Design, 2004,25: 25~29
[51] J.M. Rickman, R. LeSar, D.J. Srolovitz. Solute effects on dislocation glide in metals. Acta Materialia, 2003,51:1199~1210
[52] I.M.Robertson.The effect of Hydrogen on dislocation dynamics.Engineering Fracture Mechanics,2001,68:671~692
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[2] J.M.Silcock , W.J.Tunstall,Phil.Mag.1964,10:361
[3] H.J.Harding, R.W.K.Honeycombe.J.Iron Steel Inst. 1966, 204~259
[4] P.S.Kotval,Trans.Met.Soc.,AIME.1968,242:1651
[5] R.Raty .H.M.Miekk-oja.Phil.Mag, 1968, 18:1105
[6] C.R.Simcoe, A.H.Nehrenberg, V.Biss, et al.Trans. ASM, 1968, 61:834
[7] P.Duwez.Trans.ASM, 1967, 60:834
[8] M.Itagaki, B.C.Giesson, N.J.Grant.Trans.ASM, 1986, 61:1330
[9]刘永才,阮永丰.有限元法用于晶体生长形态的研究.天津大学学报,2000,33(2):185~191
[10] J.弗里埃德尔.位错.北京:科学出版社, 1980
[11]朱永松,袁泽正.π的一种算法研究与软件实现.湖北工业大学学报,2003 ,18(4):63~65
[12]邓凯.随机事件的概率.数学爱好者(高二版) , 2007年06期
[13]周健伟.马尔可夫过程的与时间有关的函数.应用数学, 2000年02期
[14]胡舒合,何泽慧,马松林等.线性过程的大数定律与中心极限定理,2006,30(2):1~5
[15] Bruns, W., I.Motoc, et al. Monte Carlo Application in Polymer Science. Springer Verlag, 1981
[16] Baumgartner,A.In Application of the Monte Carlo in Statistical Physics.Springer Verlag, 1984,35:145
[17] Baumgartner, A.Rev.Phys.Chem,1984,35:419
[18] Smith, R.W. J.Appl.Phys, 1997, 81:1196
[19]徐钟济.蒙特卡罗方法.上海:上海科学技术出版社
[20]朱本仁.蒙特卡罗方法引论.山东:山东大学出版社
[21]徐钟济.伪随机数产生.电子计算机动态,1962,(5):16~18
[22]郑列,宋正义.伪随机数生成算法及比较,2008,23(5)65~68
[23]杨自强,魏公毅.产生伪随机数的若干新方法.数值计算与计算机应用, 2001,(03):201~216
[24]朱阁,卢贵武,李英峰等.晶体生长机制和生长动力学的蒙特卡罗模拟研究.人工晶体学报,2006,35(1):24~31
[25] Gilmer G H, Bennema P . Simulation of Crystal Growth with Surface Diffusion . J. Appl . Phys, 1972, 43: 1347~1360
[26] Malkin A J, Kuznetsov Yu G, Land T A, et al . Mechanisms of Growth for Pr otein and Virus Crystals. Nature Structural biology, 1995, 2(11) : 956~959.
[27]张克从,张乐惠.晶体生长科学与技术(第二版)上册.北京:科学出版社,1997
[28] Anderson M P ,Srolovitz D J , Grest G S ,et al . Computer Simulation of Grain Growth -Ⅰ.Kinetics. Acta. Metal ,1984 ,32 (5) :783 ~ 791
[29] Anderson M P ,Srolovitz D J ,Grest G S ,et al . Computer Siumulation of Grain Growth -Ⅱ. Grain Size Dist ribution .Topology and Local Dynamics. Acta Metal, 1984, 32(5) :793 ~ 802
[30] Cottrell A H, Jaswon M A. Distribution of solute atoms round a slow dislocation. Proc. R. Soc. A,1949, 199:104~114.
[31] Yoshinaga H, Morozumi S. The solute atmosphere round a moving dislocation and its dragging stress. Philosophical Magazine, 1971, 23:1367~1385.
[32] Hirth J P, Lothe J. Theory of dislocations. New York.Wiley,1982.
[33] Nabarro F R N. Distribution of solute atoms round a moving dislocation. Materials Science and Engineering A, 2005, 400/401:22~24.
[34] Chen Z J, Zhang Q C, Jiang Z Y,et al. A macroscopic model for the Portevin-Le Chatelier effect. J Mater. Sci.Technol, 2004, 20(5):535~539.
[35]陈忠家,昌木松,张青川等.铝合金板材塑性性能的研究.实验力学, 2007,22(3/4):413~418.
[36]钱匡武,彭开萍,陈文哲.金属动态应变时效现象中的“锯齿屈服”.福州工程学院学报, 2003,1(1):4~8.
[37]彭开萍,陈文哲,钱匡武.3004铝合金的拉伸变形特征.机械工程材料, 2005,29(12):13~16.
[38]孙亮,张青川,江慧丰.溶质浓度对Al-Cu合金中PLC效应的影响.金属学报,2006,42(12):1248~1252.
[39]江慧丰,张青川,徐志毅等.时效对Al-Cu合金中锯齿形流动的影响.金属学报,2006,42(2):139~142.
[40] Freesengeas C, Beaudoin A J, Lebyodkin M, et al. Dynamic strain aging: a coupled dislocation-solute dynamic model.Materials Science and Engineering A, 2005, 400/401: 226~230.
[41] Ait-Amokhtar H, Fressengeas C, Boudrahem S. The dynamics of Portevin–Le Chatelier bands in an Al–Mg alloy from infrared thermography. Materials Science and Engineering A, 2008,488(1/2):540~546.
[42] Sun Ig Hong. Influence of Solute-Dislocation Interaction on the Superplastic Behavior and Ductility of Al-Mg Alloys. Scripta Materialia,1999,40(2): 217~222
[43] D.H.Xiao, M.Song. Superplastic Deformation of an as-Rolled Al–Cu–Mg–Ag Alloy. Materials and Design, 2008, 30: 424~426
[44] V.G. Gavriljuk, V.N. Shivanyuk B.D. Shanina. Change in the electron structure caused by C, N and H atoms in iron and its effect on their interaction with dislocations. Acta Meteriallia, 2005, 53:5017~5024
[45] Zdenek Drozd, Zuzanka Trojanová, Stanislav Kúdela. Deformation behaviour of Mg–Li–Al alloys. Journal of Alloys and Conpounds,2004,378:192~195
[46] ?. Bremnes, B. Carreno-Morelli, G. Gremaud. Influence of the interaction between dislocations and mobile point-defectson the damping spectrum of aluminium. Journal of Alloys and Conpounds,2000,310:62~67
[47] M. Atodiresei , G. Gremaud, R. Schaller. Study of solute atom-dislocation interactions in Al–Mg alloys by mechanical spectroscopy. Materials Science and Engineering A,2006, 442 :160~164
[48] F.B. Klose , A. Ziegenbein , F. Hagemann,et al. Analysis of Portevin-Le Chatelier serrations of type Bin Al–Mg. Materials Science and Engineering A,2004,369: 76~81
[49] Sanboh Lee , J.C.M. Li, C.T. Liu. Pinning of dislocations by solutes in Ni-Al. Materials Science and Engineering A,1997,239–240: 808~812
[50] Weiguo Wang,, Bangxin Zhou. The local internal stress in ferromagneticalloys. Dislocation–solute interaction model for local internal stress source. Materials and Design, 2004,25: 25~29
[51] J.M. Rickman, R. LeSar, D.J. Srolovitz. Solute effects on dislocation glide in metals. Acta Materialia, 2003,51:1199~1210
[52] I.M.Robertson.The effect of Hydrogen on dislocation dynamics.Engineering Fracture Mechanics,2001,68:671~692
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