一种基于镍基高温合金成分的雀斑预测模型
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摘要
针对当前雀斑判据在合金成分上存在的不足,构建一个基于高温合金成分的雀斑预测模型并对其进行了验证。通过对合金各元素的密度溶质膨胀系数β和密度温度膨胀系数β_T的计算,定量分析其在凝固过程中对糊状区液相密度的影响。通过定义一个雀斑形成倾向因子P,量化各个元素对雀斑形成的影响大小。并在此基础上,构建一个虑及合金成分的雀斑预测模型,该模型可以预测不同组分的合金和雀斑形成之间影响规律。3种不同来源的k值(如实验值、二元合金相图和Thermo-Calc计算的平衡分配系数)被代入该模型计算,验证哪种k值能更好地预测雀斑形成。结果表明:基于二元合金相图的k值,预测结果与实验结果拟合较差,其线性拟合优度R~2最大时仅为0.4;而采用实验和Thermo-Calc的k值,拟合较好,v~2最大值分别达到0.87和0.95。最后,计算SX系列合金的P值,结果显示:单位含量的Hf元素对雀斑有最强的抑制作用,Ta元素的抑制作用次之;Al、Re元素对雀斑有较强的促进作用,W元素的促进作用次之。
Aiming at the currently shortage of the freckle criterion in the alloy constituents, a constituent-based freckle predictor for nickel-base suppalloy was modeled and verified by the experiment data. The effect of each element on the liquid density was quantitatively analyzed by calculating the solutal expansion coefficient β and the thermal expansion coefficient β_T of each element. The impact of each element was quantified by defining a freckle formation tendency factor.Based on calculations of these variables, a constituent-based freckle predictor was modeled, which can predict the influence between different alloy constituents and freckle formation. Three different equilibrium distribution coefficients k were taken into this model and verified which was the best k value to predict freckle. The results show that the fitting of the number of freckles using the k value based on binary phase diagram is poor, and the linear goodness-of-fit(R~2)maximum is only 0.4; while using the k values of experiment and Thermo-Calc the fitting is good, and the maximum R~2 reach 0.87 and 0.95, respectively. Finally, the P values were calculated for the SX alloys, and the results show that the hafnium has the strongest influence on freckle prevention, tantalum also has beneficial effects though not as pronounced as hafnium; aluminum and rhenium have the stronger promoting effect on freckles, and tungsten is the second.
Aiming at the currently shortage of the freckle criterion in the alloy constituents, a constituent-based freckle predictor for nickel-base suppalloy was modeled and verified by the experiment data. The effect of each element on the liquid density was quantitatively analyzed by calculating the solutal expansion coefficient β and the thermal expansion coefficient β_T of each element. The impact of each element was quantified by defining a freckle formation tendency factor.Based on calculations of these variables, a constituent-based freckle predictor was modeled, which can predict the influence between different alloy constituents and freckle formation. Three different equilibrium distribution coefficients k were taken into this model and verified which was the best k value to predict freckle. The results show that the fitting of the number of freckles using the k value based on binary phase diagram is poor, and the linear goodness-of-fit(R~2)maximum is only 0.4; while using the k values of experiment and Thermo-Calc the fitting is good, and the maximum R~2 reach 0.87 and 0.95, respectively. Finally, the P values were calculated for the SX alloys, and the results show that the hafnium has the strongest influence on freckle prevention, tantalum also has beneficial effects though not as pronounced as hafnium; aluminum and rhenium have the stronger promoting effect on freckles, and tungsten is the second.
引文
[1]高斯峰,刘林,胡小武,葛丙明,张军,傅恒志.镍基高温合金定向凝固过程中雀斑缺陷研究进展[J].材料科学与工程学报,2010,28(1):145-151.GAO Si-feng,LIU Lin,HU Xiao-wu,GE Bing-ming,ZHANG Jun,FU Heng-zhi.Review of freckle defects under directional solidification of nickle-based superalloys[J].Journal of Materials Science&Engineering,2010,28(1):145-151.
[2]赵新宝,刘林,杨初斌,张军,李玉龙,傅恒志.镍基单晶高温合金凝固缺陷研究进展[J].材料工程,2012(1):93-98.ZHAO Xin-bao,LIU Lin,YANG Chu-bin,ZHANG Jun,LIYu-long,FU Heng-zhi.Advance in research of casting defects of directionally solidified nickel-based single superalloys[J].Journal of Materials Engineering,2012(1):93-98.
[3]SARAZIN J R,HELLAWELL A.Channel formation in Pb-Sn,Pb-Sb,and Pb-Sn-Sb alloy ingots and comparison with the system NH4Cl-H2O[J].Metallurgical&Materials Transactions A,1988,19(19):1861-1871.
[4]TEWARI S N,SHAH R.Macrosegregation during dendritic arrayed growth of hypoeutectic Pb-Sn alloys:Influence of primary arm spacing and mushy zone length[J].Metallurgical&Materials Transactions A,1996,27(5):1353-1362.
[5]BECKERMANN C,GU J P,BOETTINGER W J.Development of a freckle predictor via,rayleigh number method for single-crystal nickel-base superalloy castings[J].Metallurgical&Materials Transactions A,2000,31(10):2545-2557.
[6]YANG W,CHANG K M,CHEN W.Freckle criteria for the upward directional solidification of alloys[J].Metallurgical&Materials Transactions A,2001,32(2):397-406.
[7]张麦仓,曹国鑫,董建新.冷却速度对GH4169合金凝固过程微观偏析及糊状区稳定性的影响[J].中国有色金属学报,2013,23(11):3107-3113.ZHANG Mai-cang,CAO Guo-xin,DONG Jian-xin.Effect of cooling rate on microsegregation behaviors and mush zone stability of GH4169 alloy during solidification process[J].The Chinese Journal of Nonferrous Metals,2013,23(11):3107-3113.
[8]POLLOCK T M,MURPHY W H.The breakdown of single-crystal solidification in high refractory nickel-base alloys[J].Metallurgical&Materials Transactions A,1996,27(4):1081-1094.
[9]LONG Z,LIU X,YANG W.Thermodynamic assessment of liquid composition change during solidification and its effect on freckle formation in superalloys[J].Materials Science&Engineering A,2004,386(1/2):254-261.
[10]王玲,蔡文静,刘林.In718合金凝固过程中偏析和二次枝晶角度对糊状区Rayleigh数的影响[J].铸造技术,2012,33(10):1191-1193.WANG Ling,CAI Wenjing,LIU Lin.Effects of segregation of Nb,Mo and orientation of secondary dendrites on Rayleigh number in mushy zone of Ni-base superalloys[J].Foundry Technology,2012,33(10):1191-1193.
[11]封少波,张楠楠,罗兴宏.偏析对DZ483镍基高温合金糊状区内液相密度的影响[J].金属学报,2012,48(5):541-546.FENG Shao-bo,ZHANG Nan-nan,LUO Xing-hong.Influence of segregation on liquid density in the mushy zone of DZ483 Ni-based superalloy[J].Acta Metallurgica Sinica,2012,48(5):541-546.
[12]TIN S,POLLOCK T M.Stabilization of thermosolutal convective instabilities in Ni-based single-crystal superalloys:Carbide precipitation and rayleigh numbers[J].Metallurgical&Materials Transactions A,2003,34(9):1953-1967.
[13]YUAN L,LEE P D.A new mechanism for freckle initiation based on microstructural level simulation[J].Acta Materialia,2012,60(12):4917-4926.
[14]AMOUYAL Y,SEIDMAN D N.The role of hafnium in the formation of misoriented defects in Ni-based superalloys:An atom-probe tomographic study[J].Acta Materialia,2011,59(9):3321-3333.
[15]IIDA T,GUTHRIE R I.The physical properties of liquid metals[M].Oxford:Clarendon Press,1988.
[16]MCDONALD R J,HUNT J D.Convective fluid motion within the interdendritic liquid of a casting[J].Metallurgical Transactions,1970,1(6):1787-1788.
[17]MAGIRL C S,INCROPERA F P.Flow and morphological conditions associated with unidirectional solidification of aqueous ammonium chloride[J].Journal of Heat Transfer,1993,115(4):1036-1043.
[18]AUBURTIN P,COCKCROFT S L,MITCHELL A.Liquid density inversions during the solidification of superalloys and their relationship to freckle formation in castings[J].Superalloys 1996,1996:443-447.
[19]MA D X,ZHOU B,BüHRIG-POLACZEK A.Investigation of freckle formation under various solidification conditions[C]//Advanced Materials Research.Trans Tech Publications,2011,278:428-433.
[20]戴永年.二元合金相图集[M].北京:科学出版社,2009.DAI Yong-nian.Binary alloy phase diagrams[M].Beijing:Science Press,2009.
[2]赵新宝,刘林,杨初斌,张军,李玉龙,傅恒志.镍基单晶高温合金凝固缺陷研究进展[J].材料工程,2012(1):93-98.ZHAO Xin-bao,LIU Lin,YANG Chu-bin,ZHANG Jun,LIYu-long,FU Heng-zhi.Advance in research of casting defects of directionally solidified nickel-based single superalloys[J].Journal of Materials Engineering,2012(1):93-98.
[3]SARAZIN J R,HELLAWELL A.Channel formation in Pb-Sn,Pb-Sb,and Pb-Sn-Sb alloy ingots and comparison with the system NH4Cl-H2O[J].Metallurgical&Materials Transactions A,1988,19(19):1861-1871.
[4]TEWARI S N,SHAH R.Macrosegregation during dendritic arrayed growth of hypoeutectic Pb-Sn alloys:Influence of primary arm spacing and mushy zone length[J].Metallurgical&Materials Transactions A,1996,27(5):1353-1362.
[5]BECKERMANN C,GU J P,BOETTINGER W J.Development of a freckle predictor via,rayleigh number method for single-crystal nickel-base superalloy castings[J].Metallurgical&Materials Transactions A,2000,31(10):2545-2557.
[6]YANG W,CHANG K M,CHEN W.Freckle criteria for the upward directional solidification of alloys[J].Metallurgical&Materials Transactions A,2001,32(2):397-406.
[7]张麦仓,曹国鑫,董建新.冷却速度对GH4169合金凝固过程微观偏析及糊状区稳定性的影响[J].中国有色金属学报,2013,23(11):3107-3113.ZHANG Mai-cang,CAO Guo-xin,DONG Jian-xin.Effect of cooling rate on microsegregation behaviors and mush zone stability of GH4169 alloy during solidification process[J].The Chinese Journal of Nonferrous Metals,2013,23(11):3107-3113.
[8]POLLOCK T M,MURPHY W H.The breakdown of single-crystal solidification in high refractory nickel-base alloys[J].Metallurgical&Materials Transactions A,1996,27(4):1081-1094.
[9]LONG Z,LIU X,YANG W.Thermodynamic assessment of liquid composition change during solidification and its effect on freckle formation in superalloys[J].Materials Science&Engineering A,2004,386(1/2):254-261.
[10]王玲,蔡文静,刘林.In718合金凝固过程中偏析和二次枝晶角度对糊状区Rayleigh数的影响[J].铸造技术,2012,33(10):1191-1193.WANG Ling,CAI Wenjing,LIU Lin.Effects of segregation of Nb,Mo and orientation of secondary dendrites on Rayleigh number in mushy zone of Ni-base superalloys[J].Foundry Technology,2012,33(10):1191-1193.
[11]封少波,张楠楠,罗兴宏.偏析对DZ483镍基高温合金糊状区内液相密度的影响[J].金属学报,2012,48(5):541-546.FENG Shao-bo,ZHANG Nan-nan,LUO Xing-hong.Influence of segregation on liquid density in the mushy zone of DZ483 Ni-based superalloy[J].Acta Metallurgica Sinica,2012,48(5):541-546.
[12]TIN S,POLLOCK T M.Stabilization of thermosolutal convective instabilities in Ni-based single-crystal superalloys:Carbide precipitation and rayleigh numbers[J].Metallurgical&Materials Transactions A,2003,34(9):1953-1967.
[13]YUAN L,LEE P D.A new mechanism for freckle initiation based on microstructural level simulation[J].Acta Materialia,2012,60(12):4917-4926.
[14]AMOUYAL Y,SEIDMAN D N.The role of hafnium in the formation of misoriented defects in Ni-based superalloys:An atom-probe tomographic study[J].Acta Materialia,2011,59(9):3321-3333.
[15]IIDA T,GUTHRIE R I.The physical properties of liquid metals[M].Oxford:Clarendon Press,1988.
[16]MCDONALD R J,HUNT J D.Convective fluid motion within the interdendritic liquid of a casting[J].Metallurgical Transactions,1970,1(6):1787-1788.
[17]MAGIRL C S,INCROPERA F P.Flow and morphological conditions associated with unidirectional solidification of aqueous ammonium chloride[J].Journal of Heat Transfer,1993,115(4):1036-1043.
[18]AUBURTIN P,COCKCROFT S L,MITCHELL A.Liquid density inversions during the solidification of superalloys and their relationship to freckle formation in castings[J].Superalloys 1996,1996:443-447.
[19]MA D X,ZHOU B,BüHRIG-POLACZEK A.Investigation of freckle formation under various solidification conditions[C]//Advanced Materials Research.Trans Tech Publications,2011,278:428-433.
[20]戴永年.二元合金相图集[M].北京:科学出版社,2009.DAI Yong-nian.Binary alloy phase diagrams[M].Beijing:Science Press,2009.