模具钢电渣重熔铸坯凝固组织形貌的分形特征
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摘要
为了更为精细化地表达及控制铸坯质量,以H13模具钢电渣重熔铸坯凝固组织为研究对象,引入分形维数对其主体形貌特征进行定量描述。结果表明,基于数盒子法计算得到的分形维数可定量表征凝固组织形貌的自相似复杂程度,其值从柱状晶向中心等轴晶先减小后增大;凝固组织分形维数可作为衡量铸坯偏析程度(偏析率大小)的指标,且分形维数越大,对应区域偏析率越小,偏析越轻;通过凝固组织分形维数、偏析率和偏析点平均面积与二次枝晶间距关系的研究发现,使用二次枝晶间距表征铸坯凝固组织形貌差异并由此反映偏析程度的方法存在局限性。
In order to describe and control the quality of casting billet more delicately, solidification macrostructure of H13 die steel electroslag remelting billet was researched based on fractal dimension calculated by box-counting method, and the overall morphology of solidification structure was described quantitatively. Meanwhile, the relationship between solidification characteristics and segregation characteristics was also studied. The results show that the fractal dimension can be used to quantitatively characterize the degree of self similarity of solidification structure, which decreases firstly and then increases from columnar grain to equiaxed grain. The fractal dimension of solidification structure can be used as an index to measure the segregation degree(segregation ratio) of the billet. The larger the fractal dimension, the smaller is the corresponding region segregation ratio and the lighter is the segregation. The relationship of the fractal dimension of solidification structure, segregation ratio and the average area of segregation point with secondary dendrite spacing was studied, respectively. Based on the results, limitations exist through using secondary dendrite spacing to describe the billet morphology difference of solidification macrostructure and to reflect the segregation extent.
In order to describe and control the quality of casting billet more delicately, solidification macrostructure of H13 die steel electroslag remelting billet was researched based on fractal dimension calculated by box-counting method, and the overall morphology of solidification structure was described quantitatively. Meanwhile, the relationship between solidification characteristics and segregation characteristics was also studied. The results show that the fractal dimension can be used to quantitatively characterize the degree of self similarity of solidification structure, which decreases firstly and then increases from columnar grain to equiaxed grain. The fractal dimension of solidification structure can be used as an index to measure the segregation degree(segregation ratio) of the billet. The larger the fractal dimension, the smaller is the corresponding region segregation ratio and the lighter is the segregation. The relationship of the fractal dimension of solidification structure, segregation ratio and the average area of segregation point with secondary dendrite spacing was studied, respectively. Based on the results, limitations exist through using secondary dendrite spacing to describe the billet morphology difference of solidification macrostructure and to reflect the segregation extent.
引文
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[13] Zhong X T,Rowenhorst D J,Beladi H,et al.The five-parameter grain boundary curvature distribution in an austenitic and ferritic steel[J].Acta Materialia,2017,123:136.
[14] Spittle J A.Columnar to equiaxed grain transition in as solidified alloys[J].International Materials Reviews,2006,51(4):247.
[15] 朱华,姬翠翠.分形理论及其应用[M].北京:科学出版社,2011.(Zhu H,Ji C C.Fractal Theory and Its Applications[M].Beijing:Science Press,2011.)
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[21] 郁伯铭,徐鹏,邹明清,等.分形多孔介质输运物理[M].北京:科学出版社,2014.(Yu B M,Xu P,Zou M Q,et al.Fractal Porous Media Transport Physics[M].Beijing:Science Press,2014.)
[22] Sugawara R,Toshihisa I,Natsume Y,et al.Prediction of dendrite morphology in Fe-base-ternary alloys and evaluation of permeability[J].Tetsu-to-Hagnané,2013,99(2):126.
[23] Ishida H,Natsume Y,Ohsasa K.Characterization of dendrite morphology for evaluating interdendritic fluidity based on phase-field simulation[J].ISIJ International,2009,49(1):37.
[24] Satou F,Esaka H,Shinozuka K.Effect of size and morphology of equiaxed grains on macroscopic segregation[J].Tetsu-to-Hagnané,2013,99(2):108.
[25] 刘俊明,周尧和,商宝禄.Al-Si共晶生长过程中Si相分析的分维特征[J].材料科学进展,1990,4(5):398.(Liu J M,Zhou Y H,Shang B L.On fractal of silicon-branching clusters for Al-Si eutectic growth[J].Materials Science Progress,1990,4(5):398.)
[26] 孙力玲,董连科,张静华,等.镍基高温合金定向凝固过程中MC型碳化物的分形分析[J].金属学报,1993,29(9):6.(Sun L L,Dong L K,Zhang J H,et al.Fractal analysis of MC in a directionally solidified nickel-base superalloy[J].Acta Metallurgica Sinica,1993,29(9):6.)
[27] 刘政,徐丽娜,余昭福,等.电磁场作用下半固态A356-La铝合金初生相形貌及分形维数的研究[J].金属学报,2016,52(6):698.(Liu Z,Xu L N,Yu Z F,et al.Research on the morphology and fractal dimension of primary phase in semisolid A356-La aluminum alloy by electromagnetic stirring [J].Acta Metallurgica Sinica,2016,52(6):689.)
[28] Yamamoto M,Narita I,Miyahara H.Fractal analysis of solidification microstructure of high carbon high alloy cast roll manufactured by centrifugal casting[J].Tetsu-to-Hagané,2013,99(2):72.
[29] Wang W,Hou Z B,Chang Y,et al.Effect of superheat on quality of central equiaxed grain zone of continuously cast bearing steel billet based on two-dimensional segregation ratio[J].Journal of Iron and Steel Research International,2018,25(1):1.
[30] 车向前,李正邦.控制电渣重熔高速钢凝固质量的研究[J].钢铁研究总院学报,1987,7(S1):37.(Che X Q,Li Z B.Study of controlling quality of high speed steel in electroslag remelting process[J].Central Iron and Steel Research Institute,1987,7(S1):37.)
[31] Beckermann C.Modelling of macrosegregation:Applications and future needs[J].International Materials Reviews,2002,47(5):243.
[32] 李正邦.电渣冶金的理论与实践[M].北京:冶金工业出版社,2011.(Li Z B.Electroslag Metallurgy Theory and Practice [M].Beijing:Metallurgical Industry Press,2011.)
[33] Mullins W W,Sekerka R F.Stability of a planar interface during solidification of a dilute binary alloy[J].Dynamics of Curved Fronts,1988,35(2):345.
[34] 李涛,陈光,林鑫,等.搅拌条件下二元合金凝固组织的形态演化[J].金属学报,2006,42(6):577.(Li T,Chen G,Lin X,et al.Morphological evolution of solidification microstructure of binary alloy under stirring[J].Acta Metallurgica Sinica,2006,42(6):577.)
[2] 常立忠,李正邦.电渣重熔过程中金属凝固的控制方法[J].炼钢,2007,23(4):56.(Chang L Z,Li Z B.Control method of metal solidification in ESR Process[J].Steel-Making,2007,23(4):56.)
[3] Flemings M C.Our understanding of macrosegregation:Past and present[J].ISIJ International,2000,40(9):838.
[4] Choudhary S K,Ganguly S.Morphology and segregation in continuously cast high carbon steel billets[J].ISIJ International,2007,47(12):1759.
[5] 侯自兵,曹江海常毅,等.基于分形维数的模具钢电渣重熔铸坯碳偏析形貌特征研究[J].金属学报,2017,53(7):769.(Hou Z B,Cao J H,Chang Y,et al.Morphology characteristics of carbon segregation in die steel billet by ESR based on fractal dimension[J].Acta Metallurgica Sinica,2017,53(7):769.)
[6] Trivedi R,Kurz W.Dendritic growth[J].International Materials Reviews,1994,39(2):4.
[7] Langer J S,Müller-Krumbhaar J.Stability effects in dendritic crystal growth[J].Journal of Crystal Growth,1977,42:11.
[8] Braun R J,Murray B T.Adaptive phase-field computations of dendritic crystal growth[J].Journal of Crystal Growth,1997,174(1/2/3/4):41.
[9] 侯自兵.高碳钢连铸方坯凝固组织致密度与宏观偏析特征及定量化模型研究[D]//北京:北京科技大学,2012.(Hou Z B.Compactness Degree of Solidification Structure and Characteristics and Quantitative Model of Macrosegregation in Continuous Casting Billet of High-Carbon Steel[D]//Beijing:Beijing University of Science and Technology,2012.)
[10] Wang W L,Luo S,Zhu M Y.Dendritic growth of high carbon iron-based alloy under constrained melt flow[J].Computational Materials Science,2014,95:136.
[11] Virginie E,Patrick T.Experimental study of dendritic growth with an external flow[J].Journal of Crystal Growth,1995,156(3):285.
[12] 赵代平,荆涛,柳百成.相场模型参数对枝晶形貌的影响[J].金属学报,2003,39(8):813.(Zhao D P,Jing T,Liu B C.Influence of phase-field parameters on the dendrite morphology[J].Acta Metallurgica Sinica,2003,39(8):813.).
[13] Zhong X T,Rowenhorst D J,Beladi H,et al.The five-parameter grain boundary curvature distribution in an austenitic and ferritic steel[J].Acta Materialia,2017,123:136.
[14] Spittle J A.Columnar to equiaxed grain transition in as solidified alloys[J].International Materials Reviews,2006,51(4):247.
[15] 朱华,姬翠翠.分形理论及其应用[M].北京:科学出版社,2011.(Zhu H,Ji C C.Fractal Theory and Its Applications[M].Beijing:Science Press,2011.)
[16] Mandelbrot B B.The Fractal Geometry of Nature[M].San Francisco:Freeman,1982.
[17] 陈颙,陈凌.分形几何学[M].北京:地震出版社,2005.(Chen Y,Chen L.Fractal Geometry[M].Beijing:Earthquake Press,2005.)
[18] 刘代俊.分形理论在化学工程中的应用[M].北京:化学工业出版社,2006.(Liu D J.Fractal Theory Applied to Chemical Industry[M].Beijing:Chemical Industry Press,2006.)
[19] 谢和平,陈志达.断口定量分析的分形几何方法[J].工程力学,1989,6(4):1.(Xie H P,Chen Z D.The method of fractal geometry for quantitative analysis of fracture surface [J].Engineering Mechanics,1989,6(4):1.)
[20] 孙力玲,董连科,张济山,等.高温合金定向凝固行为的分形分析[J].金属学报,1993,29(3):19.(Sun L L,Dong L K,Zhang J S,et al.Fractal analysis of directional solidification behavior of Ni-base superalloy[J].Acta Metallurgica Sinica,1993,29(3):19.)
[21] 郁伯铭,徐鹏,邹明清,等.分形多孔介质输运物理[M].北京:科学出版社,2014.(Yu B M,Xu P,Zou M Q,et al.Fractal Porous Media Transport Physics[M].Beijing:Science Press,2014.)
[22] Sugawara R,Toshihisa I,Natsume Y,et al.Prediction of dendrite morphology in Fe-base-ternary alloys and evaluation of permeability[J].Tetsu-to-Hagnané,2013,99(2):126.
[23] Ishida H,Natsume Y,Ohsasa K.Characterization of dendrite morphology for evaluating interdendritic fluidity based on phase-field simulation[J].ISIJ International,2009,49(1):37.
[24] Satou F,Esaka H,Shinozuka K.Effect of size and morphology of equiaxed grains on macroscopic segregation[J].Tetsu-to-Hagnané,2013,99(2):108.
[25] 刘俊明,周尧和,商宝禄.Al-Si共晶生长过程中Si相分析的分维特征[J].材料科学进展,1990,4(5):398.(Liu J M,Zhou Y H,Shang B L.On fractal of silicon-branching clusters for Al-Si eutectic growth[J].Materials Science Progress,1990,4(5):398.)
[26] 孙力玲,董连科,张静华,等.镍基高温合金定向凝固过程中MC型碳化物的分形分析[J].金属学报,1993,29(9):6.(Sun L L,Dong L K,Zhang J H,et al.Fractal analysis of MC in a directionally solidified nickel-base superalloy[J].Acta Metallurgica Sinica,1993,29(9):6.)
[27] 刘政,徐丽娜,余昭福,等.电磁场作用下半固态A356-La铝合金初生相形貌及分形维数的研究[J].金属学报,2016,52(6):698.(Liu Z,Xu L N,Yu Z F,et al.Research on the morphology and fractal dimension of primary phase in semisolid A356-La aluminum alloy by electromagnetic stirring [J].Acta Metallurgica Sinica,2016,52(6):689.)
[28] Yamamoto M,Narita I,Miyahara H.Fractal analysis of solidification microstructure of high carbon high alloy cast roll manufactured by centrifugal casting[J].Tetsu-to-Hagané,2013,99(2):72.
[29] Wang W,Hou Z B,Chang Y,et al.Effect of superheat on quality of central equiaxed grain zone of continuously cast bearing steel billet based on two-dimensional segregation ratio[J].Journal of Iron and Steel Research International,2018,25(1):1.
[30] 车向前,李正邦.控制电渣重熔高速钢凝固质量的研究[J].钢铁研究总院学报,1987,7(S1):37.(Che X Q,Li Z B.Study of controlling quality of high speed steel in electroslag remelting process[J].Central Iron and Steel Research Institute,1987,7(S1):37.)
[31] Beckermann C.Modelling of macrosegregation:Applications and future needs[J].International Materials Reviews,2002,47(5):243.
[32] 李正邦.电渣冶金的理论与实践[M].北京:冶金工业出版社,2011.(Li Z B.Electroslag Metallurgy Theory and Practice [M].Beijing:Metallurgical Industry Press,2011.)
[33] Mullins W W,Sekerka R F.Stability of a planar interface during solidification of a dilute binary alloy[J].Dynamics of Curved Fronts,1988,35(2):345.
[34] 李涛,陈光,林鑫,等.搅拌条件下二元合金凝固组织的形态演化[J].金属学报,2006,42(6):577.(Li T,Chen G,Lin X,et al.Morphological evolution of solidification microstructure of binary alloy under stirring[J].Acta Metallurgica Sinica,2006,42(6):577.)