搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

相场法研究Fe-Cu-Mn-Al合金富Cu相析出机制

郭震 赵宇宏 孙远洋 赵宝军 田晓林 侯华

引用本文:
Citation:

相场法研究Fe-Cu-Mn-Al合金富Cu相析出机制

郭震, 赵宇宏, 孙远洋, 赵宝军, 田晓林, 侯华

Phase field study of effect of Al on Cu-rich precipitates in Fe-Cu-Mn-Al alloys

Guo Zhen, Zhao Yu-Hong, Sun Yuan-Yang, Zhao Bao-Jun, Tian Xiao-Lin, Hou Hua
PDF
HTML
导出引用
  • 基于Ginzburg-Landau理论采用连续相场法模拟了Fe-15%Cu-3%Mn-xAl(质量分数x = 1%, 3%, 5%)合金在873 K等温时效时纳米富Cu析出相沉淀机制及Al含量对富Cu相析出的阻碍效应. 通过计算成分场变量和结构序参数, 研究了富Cu析出相的形貌、颗粒密度、平均颗粒半径、生长和粗化动力学. 研究结果表明: 在时效早期阶段, 纳米富Cu相通过失稳分解机制析出, 由于原子扩散速率存在差异, 从而形成以富Cu相为核心的核壳结构. 随着时效时间延长, 富Cu相析出物结构由体心立方转变为面心立方. 其中Al和Mn原子在富Cu核外偏析形成Al/Mn簇, 可以将其视为阻碍富Cu析出相形成的缓冲层; 在沉淀过程中, 随着Al含量的增大, Al/Mn金属间相促进了缓冲层的生长, 阻碍富Cu析出相的生长和粗化.
    Low carbon steel plays an important role in many applications due to its high strength. Its high strength comes from the strengthening effect of nano-Cu-rich phase precipitates. In order to effectively adjust the microstructure of Cu-rich phase precipitates and obtain Fe-Cu-based steel with the best properties by adding different alloying elements (Mn, Al), it is necessary to understand the precipitation process of Cu particles. In this paper, based on the Ginzburg-Landau theory, the previous phase field model is modified, and the continuous phase field method is used to simulate the precipitation mechanism of nanometer Cu-rich precipitates and the inhibiting of the effect of Al content on Cu-rich precipitates of Fe-15%Cu-3%Mn-xAl (x = 1%, 3%, 5% mass fraction) alloy at 873 K isothermal aging. Combining with the free energy derived from thermodynamics database, the microstructure evolution corresponds to the real alloy system. By calculating the composition field variables and structural order parameters, the evolution of phase separation and precipitated phase morphology in aging process are simulated. Moreover, the influence law of morphology, quantity density, average particle radius, growth and coarsening of Cu-rich precipitated phase are discussed. The results show that in the early stage of aging process, the nano-Cu-rich phase precipitates through the spinodal decomposition mechanism, and is randomly distributed in the iron matrix. Furthermore, due to the difference in atomic diffusion rate, the core-shell structure with Cu-rich phase as a core is formed. With the aging time extending, the structure of Cu-rich phase precipitates changes from bcc to fcc. Because of the synergistic effect between Al and Cu, the diffusion of Cu is slowed down. Besides, with the Al and Mn atoms precipitating, Al/Mn clusters are segregated around the Cu-rich precipitates, forming the Al/Mn intermetallic core-shell structure, and gradually wrapping the Cu-rich phase uniformly. During the evolution of the precipitation stage, the Al/Mn clusters are isolated around the Cu-rich precipitation phase, forming a gradually uniform Al/Mn intermetallic phase core shell structure covering the Cu-rich phase, which is to hinder the buffer layer from forming in the precipitation stage of the reservoir. In addition, with the Al content increasing, the Al/Mn intermetallic phase promotes the growth of the buffer layer and hinders the Cu-rich precipitate phase from growing and coarsening.
      通信作者: 赵宇宏, zhaoyuhong@nuc.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 22008224, 52074246, 51774254, 51774253, 51804279, 51801189)、中央引导地方科技发展专项资金项目(批准号: YDZX20191400002796)、山西省科技重大专项(批准号: 20181101014, 20191102008, 20191102007)、山西省平台基地和人才专项(批准号: 201805D211036)、山西省科技成果转化引导专项(批准号: 201804D131039)、山西省青年科技研究基金(批准号: 201801D221152)和装备预研领域基金重点项目(批准号: 61409230407)资助的课题
      Corresponding author: Zhao Yu-Hong, zhaoyuhong@nuc.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 22008224, 52074246, 51774254, 51774253, 51804279, 51801189), the Guiding Local Science and Technology Development Projects by the Central Government, China (Grant No. YDZX20191400002796), the Science and Technology Major Project of Shanxi Province, China (Grant Nos. 20181101014, 20191102008, 20191102007), the Platform and Talent Project of Shanxi Province, China (Grant No. 201805D211036), the Transformation of Scientific and Technological Achievements Special Guide Project of Shanxi Province, China (Grant No. 201804D131039), the Youth Science and Technology Research Foundation of Shanxi Province, China (Grnat No. 201801D221152) and the Key Project of Equipment Pre-research Foundation, China (Grant No. 61409230407)
    [1]

    Zhu J M, Zhang T L, Yang Y, Liu C T 2019 Acta Mater. 166 560Google Scholar

    [2]

    Han G, Shang C J, Misra R D K, Xie Z J 2019 Physica B 569 68Google Scholar

    [3]

    Li B Y, Zhang L, Li C L, Li Q L, Chen J, Shu G G, Weng Y Q, Xu B, Hu S Y, Liu W 2018 J. Nucl. Mater. 507 59Google Scholar

    [4]

    Li B Y, Hu S Y, Li C L, Li Q L, Chen J, Shu G G, Jr C H, Weng Y Q, Xu B, Liu W 2017 Model. Simul. Mater. Sc. 25 6

    [5]

    Lv G C, Zhang H, He X F, Yang W, Su Y J 2016 Aip Adv. 6 045004Google Scholar

    [6]

    Jiao Z B, Luan J H, Miller M K, Chung Y W, Liu C T 2017 Mater. Today 20 142Google Scholar

    [7]

    Shu S P, Wells P B, Almirall N, Odette G R, Morgan D D 2018 Acta Mater. 157 298Google Scholar

    [8]

    Odette G R, Liu C L, Wirth B D 1996 MRS Online Proceedings Library Archive 439 457Google Scholar

    [9]

    Wen Y R, Hirata A, Zhang Z W, Fujita T, Liu C T, Jiang J H, Chen M W 2013 Acta Mater. 61 2133Google Scholar

    [10]

    Miller M K, Wirth B D, Odette G R 2003 Mater. Sci. Eng. A 353 133Google Scholar

    [11]

    Osamura K, Okuda H, Asano K, Furusaka M, Kishida K, Kurosawa F, Uemori R 1994 ISIJ Int. 34 346Google Scholar

    [12]

    沈琴, 王晓姣, 赵安宇, 何益锋, 方旭磊, 马佳荣, 刘文庆 2016 金属学报 52 513Google Scholar

    Shen Q, Wang X J, Zhao A Y, He Y F, Fang X L, Ma J R, Liu W Q 2016 Acta Metall. Sin. 52 513Google Scholar

    [13]

    Shen Q, Xiong X, Li T, Chen H, Cheng Y M, Liu W Q 2018 Mater. Sci. Eng. A 723 279Google Scholar

    [14]

    Vaynman S, Isheim D, Kolli R P, Bhat S P, Seidman D N, Fine M E 2008 Metall. Mater. Trans. A 39 363Google Scholar

    [15]

    Sun Y Y, Zhao Y H, Zhao B J, Yang W K, Li X L, Hou H 2019 J. Mater. Sci. 54 11263Google Scholar

    [16]

    赵宝军, 赵宇宏, 孙远洋, 杨文奎, 侯华 2019 金属学报 55 593Google Scholar

    Zhao B J, Zhao Y H, Sun Y Y, Yang W K, Hou H 2019 Acta Metall. Sin. 55 593Google Scholar

    [17]

    Wen Z Q, Zhao Y H, Hou H, Wang B, Han P D 2017 Mater. Design 114 398Google Scholar

    [18]

    Huang Z W, Zhao Y H, Hou H, Wang Z, Mu Y Q, Niu X F, Han P D 2011 Rare Metal Mat. Eng. 12 2136

    [19]

    田晓林, 赵宇宏, 田晋忠, 侯华 2018 物理学报 67 230201Google Scholar

    Tian X L, Zhao Y H, Tian J Z, Hou H 2018 Acta Phys. Sin. 67 230201Google Scholar

    [20]

    Chen L Q 2002 Annu. Rev. Mater. Res. 32 113Google Scholar

    [21]

    Zhao Y H, Tian X L, Zhao B J, Sun Y Y, Guo H J, Dong M Y, Liu H, Wang X J, Guo Z H, Umar A, Hou H 2018 Sci. Adv. Mater. 10 1793Google Scholar

    [22]

    Hou H, Zhao Y H, Zhao Y H 2009 Mater. Sci. Eng. 499 204Google Scholar

    [23]

    Kuang W W, Wang H F, Li X, Zhang J B, Zhou Q, Zhao Y H 2018 Acta Mater. 159 16Google Scholar

    [24]

    Zhao Y H, Zhang B, Hou H, Chen W P, Wang M 2019 J. Mater. Sci. Technol. 35 1044Google Scholar

    [25]

    Zhang J B, Wang H F, Kuang W W, Zhang Y C, Li S, Zhao Y H, Herlach D M 2018 Acta Mater. 148 86Google Scholar

    [26]

    Cahn J W 1961 Acta Metal. 9 795Google Scholar

    [27]

    Zhao Y H, Wang S, Zhang B, Yuan Y, Guo Q W, Hou H 2019 J. Solid State Chem. 276 232Google Scholar

    [28]

    Koyama T, Hashimoto K, Onodera H 2006 Mater. Trans. 47 2765Google Scholar

    [29]

    Koyama T, Onodera H 2005 Mater. Trans. 46 1187Google Scholar

    [30]

    Dinsdale A T 1991 Calphad 15 317Google Scholar

    [31]

    Bergner D, Khaddour Y 1993 Defect Diffus Forum 6 95

  • 图 1  时效温度873 K时Fe-15%Cu-3%Mn-1%Al合金沉淀相三维演化相场模拟 (a1)−(a4) t* = 17000; (b1)−(b4) t* = 18500; (c1)−(c4) t* = 20000; (d1)−(d4) t* = 22500

    Fig. 1.  Three-dimensional phase-field simulation of precipitation phase of Fe-15%Cu-3%Mn-1%Al alloy when aged at 873 K: (a1)−(a4) t* = 17000; (b1)−(b4) t* = 18500; (c1)−(c4) t* = 20000; (d1)−(d4) t* = 22500.

    图 2  时效温度873 K时Fe-15%Cu-3%Mn-1%Al合金中富Cu相结构序参数演化曲线

    Fig. 2.  Evolution curves of Cu-rich phase structure order parameter in Fe-15%Cu-3%Mn-1%Al alloy when aged at 873 K.

    图 3  时效温度为873 K时Fe-15%Cu-3%Mn-xAl合金三维富Cu相演化相场模拟 (a1)−(d1) x = 1%; (a2)−(d2) x = 3%; (a3)−(d3) x = 5%; (a1)−(a3) t* = 21000; (b1)−(b3) t* = 22000; (c1)−(c3) t* = 25000

    Fig. 3.  Three dimensional evolution diagrams of Cu rich phase in quaternary alloy Fe-15%Cu-3%Mn-xAl alloy aged at 873 K: (a1)−(d1) x = 1%; (a2)−(d2) x = 3%; (a3)−(d3) x = 5%; (a1)−(a3) t* = 21000; (b1)−(b3) t* = 22000; (c1)−(c3) t* = 25000.

    图 4  时效温度873 K时Fe-15%Cu-3%Mn-xAl(x = 1%, 3%, 5%)合金Gibbs自由能随时间变化曲线

    Fig. 4.  Gibbs free energy curves in Fe-15%Cu-3%Mn-xAl (x = 1%, 3%, 5%) alloy when aged at 873 K.

    图 5  时效温度873 K时Fe-15%Cu-3%Mn-xAl (x = 1%, 3%, 5%)合金中富Cu析出相颗粒密度随时间变化曲线

    Fig. 5.  Curves of Cu-rich precipitate phase particle density in Fe-15%Cu-3%Mn-xAl (x = 1%, 3%, 5%) alloy aged at 873 K.

    图 6  时效温度873 K时Fe-15%Cu-3%Mn-xAl (x = 1%, 3%, 5%)合金富Cu析出相平均颗粒半径随时间变化

    Fig. 6.  Average particle radius of Cu-rich precipitates in Fe-15%Cu-3%Mn-xAl (x = 1%, 3%, 5%) alloy aged at 873 K.

    表 1  相场模型参数表[16]

    Table 1.  Parameters used in phase field simulation[16]

    ParameterValueUnit
    $ {k}_{c}, {k}_{\eta } $${k}_{c}=5.0\times {10}^{-15}, $$ {\mathrm{J} \cdot \mathrm{m}}^{2}/{\mathrm{mol}}^{} $
    ${k}_{c}=1.0\times {10}^{-15} $
    $ {V}_{m} $$ 7.09\times {10}^{-6} $$ {\mathrm{m}}^{3}/{\mathrm{mol}}^{} $
    T$ 873 $$ \mathrm{K} $
    Y$ 214 $$ \mathrm{GPa} $
    $ {L}_{x}\times {L}_{y}\times {L}_{z} $$ 64\times 64\times 64 $$ \mathrm{n}{\mathrm{m}}^{3} $
    W$ 5.0\times {10}^{3} $$ \mathrm{J}/{\mathrm{mol}}^{} $
    $ {D}_{i}^{0, \varphi }\left(\varphi =\alpha, \gamma \right) $${D}_{\mathrm{Cu} }^{0, \alpha }=4.7\times {10}^{-5},$

    ${D}_{\mathrm{Cu} }^{0, \gamma }=4.3\times {10}^{-5} $
    $ {\mathrm{m}}^{2}/{\mathrm{s}}^{} $
    ${D}_{\mathrm{Mn} }^{0, \alpha }=1.49\times {10}^{-4}, $

    ${D}_{\mathrm{Mn} }^{0, \gamma }=1.78\times {10}^{-5} $
    ${D}_{\mathrm{Al} }^{0, \alpha}$[31]$=5.35\times {10}^{-4}, $

    $ {D}_{\mathrm{Al} }^{0, \gamma } $[31]$=2.20\times {10}^{-5} $
    $ {Q}_{i}^{0, \varphi }\left(\varphi =\alpha, \gamma \right) $${Q}_{\mathrm{Cu} }^{0, \alpha }=2.44\times {10}^{5}, $

    ${Q}_{\mathrm{Cu} }^{0, \gamma }=2.80\times {10}^{5} $
    $ \mathrm{J}/{\mathrm{mol}}^{} $
    ${Q}_{\mathrm{Mn} }^{0, \alpha }=2.63\times {10}^{5},$

    $ {Q}_{\mathrm{Mn} }^{0, \gamma }=2.64\times {10}^{5} $
    ${Q}_{\mathrm{Al} }^{0, \alpha }$[31]$=2.71\times {10}^{5}, $

    ${Q}_{\mathrm{Al} }^{0, \gamma } $[31]$=2.67\times {10}^{5} $
    注: $ {k}_{c}, {k}_{\eta } $, 梯度能量系数; $ {V}_{m} $, 摩尔体积; T, 热力学温度; Y, 平均刚度系数; $ {L}_{x}, {L}_{y}, {L}_{z} $, 沿x, y, z轴的模拟区域宽度; W, 双势阱高度; $ {D}_{i}^{0, \varphi } $, 扩散系数; $ {Q}_{i}^{0, \varphi } $, 热扩散激活能.
    下载: 导出CSV
  • [1]

    Zhu J M, Zhang T L, Yang Y, Liu C T 2019 Acta Mater. 166 560Google Scholar

    [2]

    Han G, Shang C J, Misra R D K, Xie Z J 2019 Physica B 569 68Google Scholar

    [3]

    Li B Y, Zhang L, Li C L, Li Q L, Chen J, Shu G G, Weng Y Q, Xu B, Hu S Y, Liu W 2018 J. Nucl. Mater. 507 59Google Scholar

    [4]

    Li B Y, Hu S Y, Li C L, Li Q L, Chen J, Shu G G, Jr C H, Weng Y Q, Xu B, Liu W 2017 Model. Simul. Mater. Sc. 25 6

    [5]

    Lv G C, Zhang H, He X F, Yang W, Su Y J 2016 Aip Adv. 6 045004Google Scholar

    [6]

    Jiao Z B, Luan J H, Miller M K, Chung Y W, Liu C T 2017 Mater. Today 20 142Google Scholar

    [7]

    Shu S P, Wells P B, Almirall N, Odette G R, Morgan D D 2018 Acta Mater. 157 298Google Scholar

    [8]

    Odette G R, Liu C L, Wirth B D 1996 MRS Online Proceedings Library Archive 439 457Google Scholar

    [9]

    Wen Y R, Hirata A, Zhang Z W, Fujita T, Liu C T, Jiang J H, Chen M W 2013 Acta Mater. 61 2133Google Scholar

    [10]

    Miller M K, Wirth B D, Odette G R 2003 Mater. Sci. Eng. A 353 133Google Scholar

    [11]

    Osamura K, Okuda H, Asano K, Furusaka M, Kishida K, Kurosawa F, Uemori R 1994 ISIJ Int. 34 346Google Scholar

    [12]

    沈琴, 王晓姣, 赵安宇, 何益锋, 方旭磊, 马佳荣, 刘文庆 2016 金属学报 52 513Google Scholar

    Shen Q, Wang X J, Zhao A Y, He Y F, Fang X L, Ma J R, Liu W Q 2016 Acta Metall. Sin. 52 513Google Scholar

    [13]

    Shen Q, Xiong X, Li T, Chen H, Cheng Y M, Liu W Q 2018 Mater. Sci. Eng. A 723 279Google Scholar

    [14]

    Vaynman S, Isheim D, Kolli R P, Bhat S P, Seidman D N, Fine M E 2008 Metall. Mater. Trans. A 39 363Google Scholar

    [15]

    Sun Y Y, Zhao Y H, Zhao B J, Yang W K, Li X L, Hou H 2019 J. Mater. Sci. 54 11263Google Scholar

    [16]

    赵宝军, 赵宇宏, 孙远洋, 杨文奎, 侯华 2019 金属学报 55 593Google Scholar

    Zhao B J, Zhao Y H, Sun Y Y, Yang W K, Hou H 2019 Acta Metall. Sin. 55 593Google Scholar

    [17]

    Wen Z Q, Zhao Y H, Hou H, Wang B, Han P D 2017 Mater. Design 114 398Google Scholar

    [18]

    Huang Z W, Zhao Y H, Hou H, Wang Z, Mu Y Q, Niu X F, Han P D 2011 Rare Metal Mat. Eng. 12 2136

    [19]

    田晓林, 赵宇宏, 田晋忠, 侯华 2018 物理学报 67 230201Google Scholar

    Tian X L, Zhao Y H, Tian J Z, Hou H 2018 Acta Phys. Sin. 67 230201Google Scholar

    [20]

    Chen L Q 2002 Annu. Rev. Mater. Res. 32 113Google Scholar

    [21]

    Zhao Y H, Tian X L, Zhao B J, Sun Y Y, Guo H J, Dong M Y, Liu H, Wang X J, Guo Z H, Umar A, Hou H 2018 Sci. Adv. Mater. 10 1793Google Scholar

    [22]

    Hou H, Zhao Y H, Zhao Y H 2009 Mater. Sci. Eng. 499 204Google Scholar

    [23]

    Kuang W W, Wang H F, Li X, Zhang J B, Zhou Q, Zhao Y H 2018 Acta Mater. 159 16Google Scholar

    [24]

    Zhao Y H, Zhang B, Hou H, Chen W P, Wang M 2019 J. Mater. Sci. Technol. 35 1044Google Scholar

    [25]

    Zhang J B, Wang H F, Kuang W W, Zhang Y C, Li S, Zhao Y H, Herlach D M 2018 Acta Mater. 148 86Google Scholar

    [26]

    Cahn J W 1961 Acta Metal. 9 795Google Scholar

    [27]

    Zhao Y H, Wang S, Zhang B, Yuan Y, Guo Q W, Hou H 2019 J. Solid State Chem. 276 232Google Scholar

    [28]

    Koyama T, Hashimoto K, Onodera H 2006 Mater. Trans. 47 2765Google Scholar

    [29]

    Koyama T, Onodera H 2005 Mater. Trans. 46 1187Google Scholar

    [30]

    Dinsdale A T 1991 Calphad 15 317Google Scholar

    [31]

    Bergner D, Khaddour Y 1993 Defect Diffus Forum 6 95

  • [1] 刘钟磊, 曹津铭, 王智, 赵宇宏. 相场法探究铁电体涡旋拓扑结构与准同型相界. 物理学报, 2023, 72(3): 037702. doi: 10.7498/aps.72.20221898
    [2] 王凯乐, 杨文奎, 史新成, 侯华, 赵宇宏. 相场法研究AlxCuMnNiFe高熵合金富Cu相析出机理. 物理学报, 2023, 72(7): 076102. doi: 10.7498/aps.72.20222439
    [3] 郭灿, 康晨瑞, 高莹, 张一弛, 邓英远, 马超, 徐春杰, 梁淑华. 金属基复合材料原位反应相场模型. 物理学报, 2022, 71(9): 096401. doi: 10.7498/aps.71.20211737
    [4] 蒋新安, 赵宇宏, 杨文奎, 田晓林, 侯华. 相场法研究Fe84Cu15Mn1合金富Cu相析出的内磁能作用机理. 物理学报, 2022, 71(8): 080201. doi: 10.7498/aps.71.20212087
    [5] 杨辉, 冯泽华, 王贺然, 张云鹏, 陈铮, 信天缘, 宋小蓉, 吴璐, 张静. Fe-Cr合金辐照空洞微结构演化的相场法模拟. 物理学报, 2021, 70(5): 054601. doi: 10.7498/aps.70.20201457
    [6] 王陶, 李俊杰, 王锦程. 界面润湿性及固相体积分数对颗粒粗化动力学影响的相场法研究. 物理学报, 2013, 62(10): 106402. doi: 10.7498/aps.62.106402
    [7] 张宪刚, 宗亚平, 吴艳. 相场再结晶储能释放模型与显微组织演变的模拟研究. 物理学报, 2012, 61(8): 088104. doi: 10.7498/aps.61.088104
    [8] 王雅琴, 王锦程, 李俊杰. 定向倾斜枝晶生长规律及竞争行为的相场法研究. 物理学报, 2012, 61(11): 118103. doi: 10.7498/aps.61.118103
    [9] 魏承炀, 李赛毅. 温度梯度对晶粒生长行为影响的相场模拟. 物理学报, 2011, 60(10): 100701. doi: 10.7498/aps.60.100701
    [10] 王明光, 赵宇宏, 任娟娜, 穆彦青, 王伟, 杨伟明, 李爱红, 葛洪浩, 侯华. 相场法模拟NiCu合金非等温凝固枝晶生长. 物理学报, 2011, 60(4): 040507. doi: 10.7498/aps.60.040507
    [11] 宗亚平, 王明涛, 郭巍. 再结晶和外力场下第二相析出的相场法模拟. 物理学报, 2009, 58(13): 161-S168. doi: 10.7498/aps.58.161
    [12] 龙文元, 吕冬兰, 夏春, 潘美满, 蔡启舟, 陈立亮. 强迫对流影响二元合金非等温凝固枝晶生长的相场法模拟. 物理学报, 2009, 58(11): 7802-7808. doi: 10.7498/aps.58.7802
    [13] 陈玉娟, 陈长乐. 相场法模拟对流速度对上游枝晶生长的影响. 物理学报, 2008, 57(7): 4585-4589. doi: 10.7498/aps.57.4585
    [14] 冯 力, 王智平, 路 阳, 朱昌盛. 二元合金多晶粒的枝晶生长的等温相场模型. 物理学报, 2008, 57(2): 1084-1090. doi: 10.7498/aps.57.1084
    [15] 李俊杰, 王锦程, 许 泉, 杨根仓. 外来夹杂物颗粒对枝晶生长形态影响的相场法研究. 物理学报, 2007, 56(3): 1514-1519. doi: 10.7498/aps.56.1514
    [16] 龙文元, 蔡启舟, 魏伯康, 陈立亮. 相场法模拟多元合金过冷熔体中的枝晶生长. 物理学报, 2006, 55(3): 1341-1345. doi: 10.7498/aps.55.1341
    [17] 张玉祥, 王锦程, 杨根仓, 周尧和. 相场法模拟弹性场对沉淀相变组织演化及相平衡成分的影响. 物理学报, 2006, 55(5): 2433-2438. doi: 10.7498/aps.55.2433
    [18] 杨 弘, 张清光, 陈 民. 热扰动对过冷熔体中二次枝晶生长影响的相场法模拟. 物理学报, 2005, 54(8): 3740-3744. doi: 10.7498/aps.54.3740
    [19] 李梅娥, 杨根仓, 周尧和. 二元合金高速定向凝固过程的相场法数值模拟. 物理学报, 2005, 54(1): 454-459. doi: 10.7498/aps.54.454
    [20] 龙文元, 蔡启舟, 陈立亮, 魏伯康. 二元合金等温凝固过程的相场模型. 物理学报, 2005, 54(1): 256-262. doi: 10.7498/aps.54.256
计量
  • 文章访问数:  4735
  • PDF下载量:  117
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-11-04
  • 修回日期:  2020-12-23
  • 上网日期:  2021-04-14
  • 刊出日期:  2021-04-20

/

返回文章
返回