异步轧制Pb-Ca-Sn-Al合金晶界节点分形分析
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摘要
为了确定晶界节点分形维数是否存在,以低碳钢冷轧薄板标样为研究对象,在MATLAB软件平台上自行开发了晶界分形维数计算程序,采用标准分形图形-koch曲线检验了自开发分形程序的准确性,利用该程序计算了3种标准下(不同晶粒延伸度)不同晶粒度级别的金相图片晶界节点分形维数,并研究了不同工艺条件下Pb-Ca-Sn-Al合金晶界节点的分形维数.结果表明:自开发的分形计算程序准确;晶界节点的分形维数存在;不同工艺条件Pb-Ca-Sn-Al合金晶界节点的分形维数与工艺参数之间存在定量联系.在一定范围内,随着压下率、异速比、退火温度的增加,晶界节点的分形维数随之增加;随退火时间的增加,Pb-Ca-Sn-Al合金晶界节点分形维数先上升后下降;退火张力增加,晶界节点分形维数下降.
To confirm the existence of the fractal dimension of grain boundary nodes, a program for calculating the fractal dimension of grain boundary was developed on the platform of MATLAB for cold rolled low carbon steel sheet.The accuracy of this fractal program was tested by using the standard fractal graph-koch curve. The program was utilized to calculate the fractal dimensions of grain boundary under three standards. Fractal dimension of grain boundary nodes in Pb-Ca-Sn-Al alloys under different processing conditions was also investigated. The results show that there exists the fractal dimension of grain boundary nodes. And there is a quantitative relationship between the grain boundary node fractional dimensions of Pb-Ca-Sn-Al alloy and the process condition. The effect of different process parameters on the fractal dimension of Pb-Ca-Sn-Al alloy grain boundary nodes is as follows:within a certain range, the fractal dimension of the grain boundary node was increased with inceasing the reduction ratio, the isokinetic ratio, and the annealing temperature.With the increase of annealing time, the fractal dimension of grain boundary joints of Pb-Ca-Sn-Al alloy increases first and then decreases, while the fractal dimension of grain boundary joints decreases with the increase of annealing tension.
To confirm the existence of the fractal dimension of grain boundary nodes, a program for calculating the fractal dimension of grain boundary was developed on the platform of MATLAB for cold rolled low carbon steel sheet.The accuracy of this fractal program was tested by using the standard fractal graph-koch curve. The program was utilized to calculate the fractal dimensions of grain boundary under three standards. Fractal dimension of grain boundary nodes in Pb-Ca-Sn-Al alloys under different processing conditions was also investigated. The results show that there exists the fractal dimension of grain boundary nodes. And there is a quantitative relationship between the grain boundary node fractional dimensions of Pb-Ca-Sn-Al alloy and the process condition. The effect of different process parameters on the fractal dimension of Pb-Ca-Sn-Al alloy grain boundary nodes is as follows:within a certain range, the fractal dimension of the grain boundary node was increased with inceasing the reduction ratio, the isokinetic ratio, and the annealing temperature.With the increase of annealing time, the fractal dimension of grain boundary joints of Pb-Ca-Sn-Al alloy increases first and then decreases, while the fractal dimension of grain boundary joints decreases with the increase of annealing tension.
引文
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[2] 文洪杰,彭达岩.分形理论在材料研究中的应用和发展[J].钢铁研究报,2000,12(5):70-73.WEN Hongjie,PENG Dayan.Application and development of fractal theory in materials research[J].Steel research report,2000,12(5):70-73.DOI:10.3321/j.issn:1001-0963.2000.05.017
[3] 徐炜新,苏建红,谢崇津.分形理论在金相学中的应用[J].理化检验:物理分册,2008,44(7):349-353.XU Yixin,SU Jianhong,XIE Chongjing.Application of fractal theory in metallography[J]Physical and chemical inspection:Physical Volume,2008,44(7):349-353.
[4] LEHOCKEY E M,PALUMBO G ,LIN P,et al.On the relationship between grain boundary character distribution and intergranular corrosion[J].Scripta Materialia,1997,36(10):1211-1218.
[5] 郭洪民,杨湘杰,凝固微观组织的多层次模拟[J].中国有色金属学报,2004,14(6):928933.GUO Hongmin,YANG Xiangjie,Multi-level simulation of solidified microstructure[J].Chinese Journal of Nonferrous Metals,2004,14(6):928933.DOI:10.3321/j.issn:1004-0609.2004.06.009
[6] GLASS H J,WITH G D.Fractal characterization of the compaction and sintering of ferrites[J].Materials Characterization,2001,47(1):27-37.DOI:10.1016/S1011-5803(01)00148-6
[7] MANDELBROT B.How Long Is the Coast of Britain Statistical Self-Similarity and Fractional Dimension[J].Science,1967,156(3775):636.
[8] PERFECT E.Estimating soil mass fractal dimensions from water retention curves 1[J].Geoderma,1999,88(s3–4):221-231.DOI:10.1016/S0016-7061(98)
[9] HAN Z,CHEN Y,FU Y.Studying relationships between the fractal dimension of the drainage basins and some of their geomorphological characteristics[J].International Journal of Geosciences,2013,4(3):636-642.DOI:10.4236/ijg.2013.43058
[10] BISWAS M K,GHOSE T,GUHA S,et al.Fractal dimension estimation for texture images:A parallel approach[J].Pattern Recognition Letters,1998,19(3–4):309-313.DOI:10.1016/S0167-8655(98)000026
[11] KOBAYASHI S,KOBAYASHI R,WATANABE T.Control of grain boundary connectivity based on fractal analysis for improvement of intergranular corrosion resistance in SUS316L austenitic stainless steel[J].Acta Materialia,2016,102:397-405.DOI:10.1016/j.actamat.2015.08.075
[12] USOV V V,RABKINA M D,SHKATULYAK N M,et al.Fractal dimension of grain boundaries and mechanical properties of the metal of oxygen cylinders[J].Materials Science,2015,50(4):1-9.DOI:10.1007/s11003-015-9761-8
[13] 张青,李萍,薛克敏.热变形Ti-15-3合金再结晶晶粒的分形分析[J].中国有色金属学报,2007,17(7):1149-1154.ZHANG Qing,LI Ping,XUE Kemin.Fractal analysis of recrystallized grains of hot deformed Ti-15-3 alloy[J].Chinese Journal of Nonferrous Metals,2007,17(7):1149-1154.DOI:10.3321/j.issn:1004-0609.2007.07.021
[14] XU M,CHEN J,LU H,et al.Effects of residual stress and grain boundary character on creep cracking in 2.25Cr-1.6W steel[J].Materials Science & Engineering A,2016,659:188-197.DOI:10.1016/j.msea.2016.02.025
[15] KOBAYASHI S,TSUREKAWA S,WATANABE T.A new approach to grain boundary engineering for nanocrystalline materials.[J].Beilstein Journal of Nanotechnology,2016,7:1829-1849.DOI:10.3762/bjnano.7.176
[16] Z?LLNER Dana.Topology of grain microstructures in two dimensions:a comparison of grain boundary and triple junction controlled grain growth[J].Modelling & Simulation in Materials Science & Engineering,2014,22(22):25-28.DOI:10.1088/0965-0393/22/2/025028
[17] 王静,吴希俊.三叉结点对铜-铋三晶断裂行为的影响[J].物理学报,1993,42(12):1963-1967.WANG Jing,WU Xijun.Effect of trigeminal junction on the deformation behavior of Cu-Nb tricrystal[J].Journal of Physics,1993,42(12):1963-1967.
[18] 张其阳,刘国奇,杨帅明等.改进的分水岭算法在牛乳体细胞上的分割及应用[J].无线互联科技,2017(5):101-102.ZHANG Qiyang,LIU Guoqi,YANG Shuaiming,et al.Segmentation and application of improved watershed algorithm on bovine milk cells[J].Wireless Internet Technology,2017(5):101-102.DOI:10.3969/j.issn.1672-6944.2017.05.045
[19] LIM A T,HAATAJA M,CAI W,et al.Stress-driven migration of simple low-angle mixed grain boundaries[J].Acta Materialia,2012,60(3):1395-1407.DOI:10.1016/j.actamat.2011.11.032
[20] 李德超,董俊慧,陈海鹏,等.退火张力对无取向硅钢再结晶织构和磁性能的影响[J].材料导报,2017(2):92-95.LI Dechao,DONG Junhui,CHEN Haipeng,et al.Effect of annealing tension on recrystallization texture and magnetic properties of non-oriented silicon steel[J].Material Guide,2017(2):92-95.DOI:10.11896/j.issn.1005-023X.2017.02.020
[21] 李彬.张力作用下Pb-Ca-Sn-Al合金再结晶模型与组织模拟的研究[D].武汉:武汉科技大学,2015.LI Bing.Study on Recrystallization Model and Microstructure Simulation of Pb-Ca-Sn-Al Alloy under Tension[D].Wuhan:Wuhan University of Science and Technology,2015.