Please wait a minute...
金属学报  2013, Vol. 49 Issue (8): 981-988    DOI: 10.3724/SP.J.1037.2013.00164
  论文 本期目录 | 过刊浏览 |
相场法研究含第二相颗粒多晶体系的晶粒粗化标度律
赵彦,张洪宇,韦华,郑启,金涛,孙晓峰
中国科学院金属研究所, 沈阳 110016
A PHASE FIELD STUDY FOR SCALING RULES OF GRAIN COARSENING IN POLYCRYSTALLINE SYSTEM CONTAINING SECOND-PHASE PARTICLES
ZHAO Yan, ZHANG Hongyu, WEI Hua, ZHENG Qi, JIN Tao, SUN Xiaofeng
Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016
引用本文:

赵彦,张洪宇,韦华,郑启,金涛,孙晓峰. 相场法研究含第二相颗粒多晶体系的晶粒粗化标度律[J]. 金属学报, 2013, 49(8): 981-988.
ZHAO Yan, ZHANG Hongyu, WEI Hua, ZHENG Qi, JIN Tao, SUN Xiaofeng. A PHASE FIELD STUDY FOR SCALING RULES OF GRAIN COARSENING IN POLYCRYSTALLINE SYSTEM CONTAINING SECOND-PHASE PARTICLES[J]. Acta Metall Sin, 2013, 49(8): 981-988.

全文: PDF(750 KB)  
摘要: 

利用相场法研究了第二相颗粒体积分数对多晶体系晶粒粗化标度律的影响. 结果表明:随着第二相颗粒体积分数增加, 晶粒生长阻力增大,晶粒平均半径Ra随时间t的演化关系偏离t=ARam+B非线性关系,且动力学指数m随第二相颗粒体积分数增加而增大.在晶粒粗化阶段,无论第二相颗粒是否存在, 及第二相颗粒体积分数的大小, 系统均满足标度律.随着第二相颗粒体积分数增加, 系统结构因子曲线的峰值逐渐降低,且当波矢k值增大到某一值后, 系统结构因子曲线基本重合;随着第二相颗粒体积分数增加, 系统标度函数峰值降低, 峰宽变宽. 在较大的k值情况下,同一k值对应的标度函数值随第二相颗粒体积分数的增加而增大.由结构因子和标度函数可知, 第二相颗粒体积分数增加, 晶粒间的相互作用减弱,晶粒粗化过程中的尺寸均匀性将更好.

关键词 相场方法粗化动力学结构函数标度律    
Abstract

The kinetic scaling of the grain coarsening in the polycrystalline system containing the dispersive second-phase particles were studied by phase field method. The obtained results showed that the increase in the volume fraction of second--phase particles enhanced the growth resistance of grain, resulting in the remarkable deviation of the relationship between the average grain radius Ra and the time t from the non-linear relationship t=ARam+B. The kinetic exponent m also increased with the increasing volume fraction of second-phase particles. No matter whether the second-phase particles existed or not in the system studied, the scaling rule had been satisfied at the late stage of grain coarsening. The increase in the volume fraction of the second-phase particles would cause the decrease in the peak value of structure factor profile. When the value of the wave vector k increased to a certain value, the structure factor curve of the studied system was essentially coincident. With the increase in the volume fraction of second-phase particles, The peak values of scaling function decreased and the peak width became wider. According to structure factor and scaling function, it was known that with the increase in the volume fraction of second-phase particles, the interaction among grains weakens and the grain size would become more uniform during the grain coarsening.

Key wordsphase field method    coarsening kinetics    structure function    scaling rule
收稿日期: 2013-04-07     
基金资助:

国家重点基础研究发展计划项目201B631206, 以及国家自然科学基金项目50931004, 51071164和50671102资助

作者简介: 赵彦, 男, 1981年生, 博士

[1] Fan D, Chen L Q.  Acta Mater, 1997; 45: 611

[2] Zhang H L, Tian J L, Hu X Y, Gao Y J.  Guangxi Sci, 2009; 16: 297
 (张海林, 田军龙, 胡项英, 高英俊. 广西科学, 2009; 16: 297)
[3] Tikare V, Holm E A, Fan D, Chen L Q.  Acta Mater, 1999; 47: 363
[4] Moelans N, Blanpain B, Wollants P.  Acta Mater, 2005; 53: 1771
[5] Fan D, Chen L Q.  Acta Mater, 1997; 45: 3297
[6] Hu S Y, Chen L Q.  Acta Mater, 2001; 49: 1879
[7] Zhu J Z, Wang T, Ardell A J, Zhou S H, Liu Z K, Chen L Q.  Acta Mater, 2004; 52: 2837
[8] Li D Y, Chen L Q.  Scr Mater, 1997; 37: 1271
[9] Palmer M A, Glicksman M E, Rajan K.  Scr Mater, 2003; 48: 1173
[10] Hillert M, Sundman B.  Acta Metall, 1976; 24: 731
[11] Jahazi M, Jonas J J.  Mater Sci Eng, 2002; A335: 49
[12] Xu T, Song S.  Acta Metall, 1989; 37: 2499
[13] Joel L L, Marro J, Kalos M H.  Acta Metall, 1982; 30: 297
[14] Fan D, Chen L Q, Chen S P.  Mater Sci Eng, 1997; A238: 78
[15] Ostwald W.  Lehrbuch der Allgemeinen Chemie. Vol.2, Germany: Leipzig Press, 1896: 1
[16] Kobayashi K, Blinc K K, Cevc R P, Share M.  Phys Rev, 1967; 159: 411
[17] Rogers T M, Elder K R, Rashmi C D.  Phys Rev, 1988; 37B: 9638
[18] Seigert M, Rao M.  Phys Rev Lett, 1993; 70: 1956
[19] Allen S M, Cahn J W.  Acta Metall, 1979; 27: 1085
[20] Gao Y J, Zhang H L, Jin X, Huang C G, Luo Z R.  Acta Metall Sin, 2009; 45: 1190
 (高英俊, 张海林, 金星, 黄创高, 罗志荣. 金属学报, 2009; 45: 1190)
[21] Gill F X, Rodrringer D T, Krill III C E.  Acta Mater, 2003; 51: 2743
[22] Fltham P.  Acta Metall, 1957; 5: 97
[23] Jones G R, Jackson M, O'Grady K.  J Magn Magn Mater, 1999; 193: 75
[24] Liftshitz I M, Slyozov V V.  J Phys Chem Solids, 1961; 19: 35
[25] Hillert M.  Acta Metall, 1965; 13: 227
[26] Wang K G, Ding X, Chang K, Chen L Q.  J Appl Phys, 2010; 107: 061801
[27] Ohnogi H, Shiwa Y.  Phys Rev, 2011; 84E: 011611
[28] Brumberger H.  Modern Aspects of Small--Angle Scattering. Dordrecht:Kluwer Academic Publishers, 1995: 57
[29] Lebedev V, Didebko V, Lapin A, Konoplev K.  J Appl Crystal, 2003; 36: 629
[30] Amitabha C, Ra\ul T T, James D G.  Phys Rev, 1993; 47E: 3025
[31] Joel L L, Marro J, Kalos M H.  Acta Metall, 1982; 30: 297
[32] Fratzl P, Lebowitz J L.  Acta Metall, 1989; 37: 3245
[33] Liu J M, Wu Z C, Liu Z G.  Acta Phys Sin, 1997; 46: 1146
 (刘俊明, 吴状春, 刘治国. 物理学报, 1997; 46: 1146)
[34] Li Y S, Chen Z, Wang Y X, Lu Y L, Zhang J J.  Prog Nat Sci, 2005; 16: 604
 (李永胜, 陈铮, 王永欣, 卢艳丽, 张建军. 自然科学进展, 2005; 16: 604)
[35] Fratzl P, Lebowitz J L, Penrose O, Amar J.  Phys Rev, 1991; 44B: 4794
[36] Tokuyama M, Enomoto Y, Kawasaki K.  Physica, 1987; 143A: 183
[37] Anderson M P, Srolovitz D J, Grest G S, Sahni P S.  Acta Metall, 1984; 32: 783
[38] Chen L Q.  Annu Rev Mater Res, 2002; 32: 113
[39] Weaire D, Kermode J P.  Philos Mag, 1983; 48B: 245
[40] Huang F, Di H S, Wang G S.  Acta Phys Sin, 2009; 58: 313
 (黄锋, 邸洪双, 王广山. 物理学报, 2009; 58: 313)
[41] Chen L Q, Yang W.  Phys Rev, 1994; 50B: 15752
[42] Burke J, Turnbull D.  Prog Met Phys, 1952; 3: 220
[43] Amitabha C, Raul T, James D G.  Phys Rev, 1993; 47E: 3025
[1] 刘续希, 柳文波, 李博岩, 贺新福, 杨朝曦, 恽迪. 辐照条件下Fe-Cu合金中富Cu析出相的临界形核尺寸和最小能量路径的弦方法计算[J]. 金属学报, 2022, 58(7): 943-955.
[2] 王晨充,张弛,杨志刚,苏杰,翁宇庆. 高Co-Ni二次硬化钢的设计准则与时效工艺分析[J]. 金属学报, 2017, 53(2): 175-182.
[3] 周广钊,王永欣,陈铮. 相场法模拟弹性应变能对Ti-Al-Nb合金 α2→ O相变粗化动力学的影响[J]. 金属学报, 2012, 48(4): 485-491.
[4] 周广钊 王永欣 陈铮. 相场法模拟不同形状的硬质颗粒对两相晶粒长大的影响[J]. 金属学报, 2012, 48(2): 227-234.
[5] 张玉妥; 庞维诚 . 用相场方法模拟纯物质等轴枝晶生长[J]. 金属学报, 2000, 36(6): 589-591 .
[6] 刘俊明;刘治国;吴状春. 非规则共晶定向凝固结构的标度律[J]. 金属学报, 1993, 29(3): 11-18.