全淬透圆柱件淬火应力的有限元模拟及实验验证
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摘要
利用温度场、组织场和应力场相互耦合的数学模型对直径60 mm的40CrNiMo水淬圆棒的淬火应力进行研究。结果表明,有限元模拟的淬火应力及其分布与XRD测量结果相符,论证了所运用的温度场、组织场和应力场相互耦合的数学模型(包括建立的相变塑性函数)的正确性。通过计算机模拟分离了淬火马氏体钢中的热应力和组织应力,揭示了不同直径淬透圆棒试样的应力分布规律及其起因以及不同淬火介质对淬火应力的影响规律。
Quenching is one of the most important heat-treatment processes for improving the mechanical properties of steel components in manufacture industry. The quenching stress is a source of cracking, which is frequently detrimental to steel properties. Therefore, the investigation of quenching stress is very important for the control of distortion, cracking and residual stress distributions of components. In the study of quenching stress, the measurement of stress distribution is necessary to the stress analysis and design of quenching process. However, in most cases, the cracking of a quenched component is caused by transient stress during quenching, while experiment can only measures the final internal stress(residual stress), rather than transient stress. As a result, the measurement of residual stress associated with finite element simulation(FES) has been a mainstream direction in the investigation of quenching stress. In this work, a full through-hardened 40 CrNiMo cylinder with 60 mm diameter was water-quenched, and cooling curves at three positions along the radius of cylinder were measured. Then,an optimized heat transfer coefficient as a function of surface temperature was obtained by fitting with the measured cooling curves using the trial and error method. Based on an exponent-modified(Ex-Modified)normalized function describing transformation plasticity kinetics proposed, the thermo-elasto-plastic constitutive equations were deduced.The commercial finite element software,Abaqus/Standard,was used to solve the coupled temperature field,microstructure field and stress(strain)field.The results indicate that the quenching stress and its distribution predicted by FES is well consistent with those measured by XRD,which verified that the models employed in coupling of thermal field,phase transformation field and stress field including transformation plasticity function proposed are correct.Meanwhile,the features of residual stress distribution were revealed that compressive stress exists in the core and surface of cylinder and the maximum tensile stress exists at subsurface.The separated calculation of thermal stress and phase transformation stress by FES reveals the origin of residual stress distribution feature in quenched cylinders,that is,the relative higher phase transformation compressive stress and lower tensile thermal stress at the core of cylinder make the residual stress to be compressive,while at the surface of cylinder the compressive stress is predominantly from thermal stress,because it is much larger than the tensile stress caused by phase transformation stress.The tangential residual stress distributions in cylinders with several diameters from 3 mm to 100 mm were predicted by FES,and the results indicate that when diameter is less than 5 mm,the tensile stress at the surface increases with increasing diameter until to5 mm,then decreases with increasing diameter to 20 mm,finally the tensile stress becomes compressive stress.Besides,with the increase of diameter,maximum tensile stress shifts from the surface to the location of 0.6 radius.The effects of different quenching media on quenching stress were also investigated by FES.The results demonstrated that although there is compressive stress at surface of cylinder quenched in water or salt solution,the maximum stress locates the subsurface,meaning that cracking easily occurs at the subsurface,which is consistent with cracking in practical components.This work is helpful for the analysis of cracking from quenching stress in components with different sizes and under different quenching media.
Quenching is one of the most important heat-treatment processes for improving the mechanical properties of steel components in manufacture industry. The quenching stress is a source of cracking, which is frequently detrimental to steel properties. Therefore, the investigation of quenching stress is very important for the control of distortion, cracking and residual stress distributions of components. In the study of quenching stress, the measurement of stress distribution is necessary to the stress analysis and design of quenching process. However, in most cases, the cracking of a quenched component is caused by transient stress during quenching, while experiment can only measures the final internal stress(residual stress), rather than transient stress. As a result, the measurement of residual stress associated with finite element simulation(FES) has been a mainstream direction in the investigation of quenching stress. In this work, a full through-hardened 40 CrNiMo cylinder with 60 mm diameter was water-quenched, and cooling curves at three positions along the radius of cylinder were measured. Then,an optimized heat transfer coefficient as a function of surface temperature was obtained by fitting with the measured cooling curves using the trial and error method. Based on an exponent-modified(Ex-Modified)normalized function describing transformation plasticity kinetics proposed, the thermo-elasto-plastic constitutive equations were deduced.The commercial finite element software,Abaqus/Standard,was used to solve the coupled temperature field,microstructure field and stress(strain)field.The results indicate that the quenching stress and its distribution predicted by FES is well consistent with those measured by XRD,which verified that the models employed in coupling of thermal field,phase transformation field and stress field including transformation plasticity function proposed are correct.Meanwhile,the features of residual stress distribution were revealed that compressive stress exists in the core and surface of cylinder and the maximum tensile stress exists at subsurface.The separated calculation of thermal stress and phase transformation stress by FES reveals the origin of residual stress distribution feature in quenched cylinders,that is,the relative higher phase transformation compressive stress and lower tensile thermal stress at the core of cylinder make the residual stress to be compressive,while at the surface of cylinder the compressive stress is predominantly from thermal stress,because it is much larger than the tensile stress caused by phase transformation stress.The tangential residual stress distributions in cylinders with several diameters from 3 mm to 100 mm were predicted by FES,and the results indicate that when diameter is less than 5 mm,the tensile stress at the surface increases with increasing diameter until to5 mm,then decreases with increasing diameter to 20 mm,finally the tensile stress becomes compressive stress.Besides,with the increase of diameter,maximum tensile stress shifts from the surface to the location of 0.6 radius.The effects of different quenching media on quenching stress were also investigated by FES.The results demonstrated that although there is compressive stress at surface of cylinder quenched in water or salt solution,the maximum stress locates the subsurface,meaning that cracking easily occurs at the subsurface,which is consistent with cracking in practical components.This work is helpful for the analysis of cracking from quenching stress in components with different sizes and under different quenching media.
引文
[1]Totten G,Howes M,Inoue T.Handbook of Residual Stress and Deformation of Steel[M].Materials Park,OH,USA:ASM International,2002:249
[2]Kang D T,Zhang H.A study of distributive law of thermal residual stresses in a large high-tempered shaft[J].Trans.Met.Heat Treat.,1983,4(2):61(康大韬,张海.调质大轴中残余应力沿工件截面分布规律的研究[J].金属热处理学报,1983,4(2):61)
[3]Kang D T,Nan Y.A study of transformation stresses in cylindrical parts[J].Trans.Met.Heat Treat.,1985,6(1):33(康大韬,南云.柱形件中残余组织应力的研究[J].金属热处理学报,1985,6(1):33)
[4]Zhang H.Measurement and research of hardening residual stress of heavy forging[J].Met.Phys.Exam.Test.,2001,(3):26(张海.大锻件淬火残余应力的测定及研究[J].物理测试,2001,(3):26)
[5]Wang K F,Chandrasekar S,Yang H T Y.Experimental and computational study of the quenching of carbon steel[J].J.Manuf.Sci.Eng.,1997,119:257
[6]Chen N L,Zuo X W,Xu J,et al.Research and application of digital timed quenching process and equipment[J].Heat Treat.Met.,2009,34(3):37(陈乃录,左训伟,徐骏等.数字化控时淬火冷却工艺及设备的研究与应用[J].金属热处理,2009,34(3):37)
[7]Inoue T,Nagaki S,Kishino T,et al.Description of transformation kinetics,heat conduction and elastic-plastic stress in the course of quenching and tempering of some steels[J].Ing.Arch.,1981,50:315
[8]Denis S,Sj?str?m S,Simon A.Coupled temperature,stress,phase transformation calculation model numerical illustration of the internal stresses evolution during cooling of a eutectoid carbon steel cylinder[J].Metall.Trans.,1987,18A:1203
[9]Rohde J,Jeppsson A.Literature review of heat treatment simulations with respect to phase transformation,residual stresses and distortion[J].Scand.J.Metall.,2000,29:47
[10]?im?ir C,Gür C H.3D FEM simulation of steel quenching and investigation of the effect of asymmetric geometry on residual stress distribution[J].J.Mater.Process.Technol.,2008,207:211
[11]Arimoto K,Lambert D,Lee K,et al.Prediction of quench cracking by computer simulation[A].Proceedings of the 19th ASM Heat Treating Society Conference on Including Steel Heat Treating in the New Millennium[C].Cincinnati:ASM International,1999:435
[12]Jung M,Kang M,Lee Y K.Finite-element simulation of quenching incorporating improved transformation kinetics in a plain medium-carbon steel[J].Acta Mater.,2012,60:525
[13]Lee S J,Lee Y K.Finite element simulation of quench distortion in a low-alloy steel incorporating transformation kinetics[J].Acta Mater.,2008,56:1482
[14]Ariza E A,Martorano M A,de Lima N B,et al.Numerical simulation with thorough experimental validation to predict the build-up of residual stresses during quenching of carbon and low-alloy steels[J].ISIJ Int.,2014,54:1396
[15]Yao X,Zhu L H,Li M V.A fully coupled material constitutive model for steel quench analysis[J].Int.J.Microstruct.Mater.Prop.,2010,5:501
[16]Yamanaka S,Sakanoue T,Yoshii T,et al.Transformation plasticitythe effect on metallo-thermo-mechanical simulation of carburized quenching process[J].J.Shanghai Jiaotong Univ.,2000,E-5(1):185
[17]Denis S.Considering stress-phase transformation interactions in the calculation of heat treatment residual stresses[J].J.Phys.IV,1996,6(C1):159
[18]Taleb L,Cavallo N,Waeckel F.Experimental analysis of transformation plasticity[J].Int.J.Plast.,2001,17:1
[19]Liu Y,Qin S W,Hao Q G,et al.Finite element simulation and experimental verification of internal stress of quenched AISI 4140cylinders[J].Metall.Mater.Trans.,2017,48A:1402
[20]Ferguson B L,Li Z,Freborg A M.Modeling heat treatment of steel parts[J].Comp.Mater.Sci.,2005,34:274
[21]Ju D Y,Mukai R,Sakamaki T.Development and application of computer simulation code COSMAP on induction heat treatment process[J].Int.Heat Treat.Surf.Eng.,2011,5:65
[22]Fischer F D,Sun Q P,Tanaka K.Transformation-induced plasticity(TRIP)[J].Appl.Mech.Rev.,1996,49:317
[23]Fischer F D,Reisner G,Werner E,et al.A new view on transformation induced plasticity(TRIP)[J].Int.J.Plast.,2000,16:723
[24]Xu Z Y.Effect of stress on bainitic transformation in steel[J].Acta Metall.Sin.,2004,40:113(徐祖耀.应力对钢中贝氏体相变的影响[J].金属学报,2004,40:113)
[25]Sun S Y,Dai Y K.Analytic Atlas of Heat Treatment Cracking[M].Dalian:Dalian Publishing House,2002:20(孙盛玉,戴雅康.热处理裂纹分析图谱[M].大连:大连出版社,2002:20)
[26]Isomura R,Sat?H.On quench-cracking phenomena as viewed from the aspect of quenching stresses[J].J.Jpn.Inst.Met.,1961,25:360
[27]European Standard.DS/EN15305 Non-destructive testing-test method for residual stress analysis by X-ray diffraction[S].2008
[28]Yuan F R,Wu S L.Measurement and Calculation of Residual Stress[M].Changsha:Hunan University Press,1987:212(袁发荣,伍尚礼.残余应力测试与计算[M].长沙:湖南大学出版社,1987:212)
[29]Leblond J B,Mottet G,Devaux J,et al.Mathematical models of anisothermal phase transformations in steels,and predicted plastic behaviour[J].Mater.Sci.Technol.,1985,1:815
[30]Bejan A,Kraus A D.Heat Transfer Handbook[M].New Jersey:John Wiley&Sons,Inc.,2003:165
[31]Janzen I P.Modeling of heat treating processes for transmission gears[D].Worcester:Worcester Polytechnic Institute,2009
[32]Arimoto K,Li G,Arvind A,et al.The modeling of heat treating process[A].Proceedings of the 18th Heat Treating Conference[C].Rosemont:ASM International,1998:23
[33]Koistinen D P,Marburger R E.A general equation prescribing the extent of the austenite-martensite transformation in pure iron-carbon alloys and plain carbon steels[J].Acta Metall.,1959,7:59
[34]Sourmail T,Garcia-Mateo C.Critical assessment of models for predicting the Mstemperature of steels[J].Comp.Mater.Sci.,2005,34:323
[35]van Bohemen S M C,Sietsma J.Effect of composition on kinetics of athermal martensite formation in plain carbon steels[J].Mater.Sci.Technol.,2009,25:1009
[36]Fanfoni M,Tomellini M.The Johnson-Mehl-Avrami-Kohnogorov model:a brief review[J].Nouv.Cim.,1998,20D:1171
[37]Scheil E.Anlaufzeit der Austenitumwandlung[J].Arch.Eisenhuttenwes.,1935,12:565
[38]Cheng H M,Fan J,Wang H G.Estimation of the mechanical properties of a 42Cr Mo steel cylinder with phase transformation during quenching[J].J.Mater.Process.Technol.,1997,63:568
[39]Nagasaka Y,Brimacombe J K,Hawbolt E B,et al.Mathematical model of phase transformations and elastoplastic stress in the water spray quenching of steel bars[J].Metall.Trans.,1993,24A:795
[40]Liu C C,Yao K F,Xu X J,et al.Models for transformation plasticity in loaded steels subjected to bainitic and martensitic transformation[J].Mater.Sci.Technol.,2001,17:983
[41]Yu H S.Plasticity and Geotechnics[M].US:Springer,2006:23
[42]Leblond J B,Mottet G,Devaux J C.A theoretical and numerical approach to the plastic behaviour of steels during phase transformations-II.Study of classical plasticity for ideal-plastic phases[J].J.Mech.Phys.Solids,1986,34:411
[43]Arimoto K,Yamanaka S,Narazaki M,et al.Explanation of the origin of quench distortion and residual stress in specimens using computer simulation[J].Int.J.Microstruct.Mater.Prop.,2009,4:168
[44]Lambert D,Wu W T,Arimoto K,et al.Finite element analysis of internal stresses in quenched steel cylinders[A].Proceedings of the 19th ASM Heat Treating Society Conference on Including Steel Heat Treating in the New Millennium[C].Cincinnati:ASM International,1999:425
[45]Yonetani S,translated by Zhu J P,Shao H M.Generation and Tackle of Residual Stress[M].Beijing:China Machine Press,1983:127(米谷茂著,朱荆璞,邵会孟译.残余应力的产生和对策[M].北京:机械工业出版社,1983:127)
[2]Kang D T,Zhang H.A study of distributive law of thermal residual stresses in a large high-tempered shaft[J].Trans.Met.Heat Treat.,1983,4(2):61(康大韬,张海.调质大轴中残余应力沿工件截面分布规律的研究[J].金属热处理学报,1983,4(2):61)
[3]Kang D T,Nan Y.A study of transformation stresses in cylindrical parts[J].Trans.Met.Heat Treat.,1985,6(1):33(康大韬,南云.柱形件中残余组织应力的研究[J].金属热处理学报,1985,6(1):33)
[4]Zhang H.Measurement and research of hardening residual stress of heavy forging[J].Met.Phys.Exam.Test.,2001,(3):26(张海.大锻件淬火残余应力的测定及研究[J].物理测试,2001,(3):26)
[5]Wang K F,Chandrasekar S,Yang H T Y.Experimental and computational study of the quenching of carbon steel[J].J.Manuf.Sci.Eng.,1997,119:257
[6]Chen N L,Zuo X W,Xu J,et al.Research and application of digital timed quenching process and equipment[J].Heat Treat.Met.,2009,34(3):37(陈乃录,左训伟,徐骏等.数字化控时淬火冷却工艺及设备的研究与应用[J].金属热处理,2009,34(3):37)
[7]Inoue T,Nagaki S,Kishino T,et al.Description of transformation kinetics,heat conduction and elastic-plastic stress in the course of quenching and tempering of some steels[J].Ing.Arch.,1981,50:315
[8]Denis S,Sj?str?m S,Simon A.Coupled temperature,stress,phase transformation calculation model numerical illustration of the internal stresses evolution during cooling of a eutectoid carbon steel cylinder[J].Metall.Trans.,1987,18A:1203
[9]Rohde J,Jeppsson A.Literature review of heat treatment simulations with respect to phase transformation,residual stresses and distortion[J].Scand.J.Metall.,2000,29:47
[10]?im?ir C,Gür C H.3D FEM simulation of steel quenching and investigation of the effect of asymmetric geometry on residual stress distribution[J].J.Mater.Process.Technol.,2008,207:211
[11]Arimoto K,Lambert D,Lee K,et al.Prediction of quench cracking by computer simulation[A].Proceedings of the 19th ASM Heat Treating Society Conference on Including Steel Heat Treating in the New Millennium[C].Cincinnati:ASM International,1999:435
[12]Jung M,Kang M,Lee Y K.Finite-element simulation of quenching incorporating improved transformation kinetics in a plain medium-carbon steel[J].Acta Mater.,2012,60:525
[13]Lee S J,Lee Y K.Finite element simulation of quench distortion in a low-alloy steel incorporating transformation kinetics[J].Acta Mater.,2008,56:1482
[14]Ariza E A,Martorano M A,de Lima N B,et al.Numerical simulation with thorough experimental validation to predict the build-up of residual stresses during quenching of carbon and low-alloy steels[J].ISIJ Int.,2014,54:1396
[15]Yao X,Zhu L H,Li M V.A fully coupled material constitutive model for steel quench analysis[J].Int.J.Microstruct.Mater.Prop.,2010,5:501
[16]Yamanaka S,Sakanoue T,Yoshii T,et al.Transformation plasticitythe effect on metallo-thermo-mechanical simulation of carburized quenching process[J].J.Shanghai Jiaotong Univ.,2000,E-5(1):185
[17]Denis S.Considering stress-phase transformation interactions in the calculation of heat treatment residual stresses[J].J.Phys.IV,1996,6(C1):159
[18]Taleb L,Cavallo N,Waeckel F.Experimental analysis of transformation plasticity[J].Int.J.Plast.,2001,17:1
[19]Liu Y,Qin S W,Hao Q G,et al.Finite element simulation and experimental verification of internal stress of quenched AISI 4140cylinders[J].Metall.Mater.Trans.,2017,48A:1402
[20]Ferguson B L,Li Z,Freborg A M.Modeling heat treatment of steel parts[J].Comp.Mater.Sci.,2005,34:274
[21]Ju D Y,Mukai R,Sakamaki T.Development and application of computer simulation code COSMAP on induction heat treatment process[J].Int.Heat Treat.Surf.Eng.,2011,5:65
[22]Fischer F D,Sun Q P,Tanaka K.Transformation-induced plasticity(TRIP)[J].Appl.Mech.Rev.,1996,49:317
[23]Fischer F D,Reisner G,Werner E,et al.A new view on transformation induced plasticity(TRIP)[J].Int.J.Plast.,2000,16:723
[24]Xu Z Y.Effect of stress on bainitic transformation in steel[J].Acta Metall.Sin.,2004,40:113(徐祖耀.应力对钢中贝氏体相变的影响[J].金属学报,2004,40:113)
[25]Sun S Y,Dai Y K.Analytic Atlas of Heat Treatment Cracking[M].Dalian:Dalian Publishing House,2002:20(孙盛玉,戴雅康.热处理裂纹分析图谱[M].大连:大连出版社,2002:20)
[26]Isomura R,Sat?H.On quench-cracking phenomena as viewed from the aspect of quenching stresses[J].J.Jpn.Inst.Met.,1961,25:360
[27]European Standard.DS/EN15305 Non-destructive testing-test method for residual stress analysis by X-ray diffraction[S].2008
[28]Yuan F R,Wu S L.Measurement and Calculation of Residual Stress[M].Changsha:Hunan University Press,1987:212(袁发荣,伍尚礼.残余应力测试与计算[M].长沙:湖南大学出版社,1987:212)
[29]Leblond J B,Mottet G,Devaux J,et al.Mathematical models of anisothermal phase transformations in steels,and predicted plastic behaviour[J].Mater.Sci.Technol.,1985,1:815
[30]Bejan A,Kraus A D.Heat Transfer Handbook[M].New Jersey:John Wiley&Sons,Inc.,2003:165
[31]Janzen I P.Modeling of heat treating processes for transmission gears[D].Worcester:Worcester Polytechnic Institute,2009
[32]Arimoto K,Li G,Arvind A,et al.The modeling of heat treating process[A].Proceedings of the 18th Heat Treating Conference[C].Rosemont:ASM International,1998:23
[33]Koistinen D P,Marburger R E.A general equation prescribing the extent of the austenite-martensite transformation in pure iron-carbon alloys and plain carbon steels[J].Acta Metall.,1959,7:59
[34]Sourmail T,Garcia-Mateo C.Critical assessment of models for predicting the Mstemperature of steels[J].Comp.Mater.Sci.,2005,34:323
[35]van Bohemen S M C,Sietsma J.Effect of composition on kinetics of athermal martensite formation in plain carbon steels[J].Mater.Sci.Technol.,2009,25:1009
[36]Fanfoni M,Tomellini M.The Johnson-Mehl-Avrami-Kohnogorov model:a brief review[J].Nouv.Cim.,1998,20D:1171
[37]Scheil E.Anlaufzeit der Austenitumwandlung[J].Arch.Eisenhuttenwes.,1935,12:565
[38]Cheng H M,Fan J,Wang H G.Estimation of the mechanical properties of a 42Cr Mo steel cylinder with phase transformation during quenching[J].J.Mater.Process.Technol.,1997,63:568
[39]Nagasaka Y,Brimacombe J K,Hawbolt E B,et al.Mathematical model of phase transformations and elastoplastic stress in the water spray quenching of steel bars[J].Metall.Trans.,1993,24A:795
[40]Liu C C,Yao K F,Xu X J,et al.Models for transformation plasticity in loaded steels subjected to bainitic and martensitic transformation[J].Mater.Sci.Technol.,2001,17:983
[41]Yu H S.Plasticity and Geotechnics[M].US:Springer,2006:23
[42]Leblond J B,Mottet G,Devaux J C.A theoretical and numerical approach to the plastic behaviour of steels during phase transformations-II.Study of classical plasticity for ideal-plastic phases[J].J.Mech.Phys.Solids,1986,34:411
[43]Arimoto K,Yamanaka S,Narazaki M,et al.Explanation of the origin of quench distortion and residual stress in specimens using computer simulation[J].Int.J.Microstruct.Mater.Prop.,2009,4:168
[44]Lambert D,Wu W T,Arimoto K,et al.Finite element analysis of internal stresses in quenched steel cylinders[A].Proceedings of the 19th ASM Heat Treating Society Conference on Including Steel Heat Treating in the New Millennium[C].Cincinnati:ASM International,1999:425
[45]Yonetani S,translated by Zhu J P,Shao H M.Generation and Tackle of Residual Stress[M].Beijing:China Machine Press,1983:127(米谷茂著,朱荆璞,邵会孟译.残余应力的产生和对策[M].北京:机械工业出版社,1983:127)