基于DEFORM-3D平台1Cr13板材热轧数值模拟研究
摘要
在分析了国内外板材轧制数值模拟发展及现状的基础上,通过有限元法对轧制过程进行了数值模拟,以探求轧制过程中的规律,为合理制定工艺参数,优化工艺结构提供技术支持和理论依据。
本论文研究的主要内容有:
(1)通过1Cr13高温拉伸试验研究400℃、500℃、600℃、650℃、700℃温度点下的屈服强度,抗拉强度等基本力学性能。利用试验得出的400℃、700℃温度点下的应力应变数据,在DEFORM-3D平台上对其它温度点进行拉伸试验数值模拟。结果直观地显示了各阶段应力应变分布及试样的变形过程,仿真屈服强度、最大抗拉强度等与试验实测值吻合较好,随着有限元软件的不断发展,数值模拟有望成为拉伸试验的另一手段。利用该数值模型外推得到了900℃、1000℃、1100℃的应力应变曲线,从而为本构模型的建立奠定基础。为该材料轧制模型的建立提供必要的力学性能数据,以便热轧模拟能够更精确的进行。
(2)对1Cr13材料进行热轧数值分析,用云图直观地反映出轧制各个阶段应力应变分布情况,并通过多组试验对影响轧制压力的参数如轧制温度、轧辊转速、压下量、轧板厚度进行了分析,得到了轧制温度、轧辊转速、压下量、轧板厚度对轧制压力的影响规律。
(3)将模拟轧制压力值与西姆斯热轧轧制力公式计算出的理论值进行比较,两者的变化趋势一致,但有一定的误差存在,对误差存在的原因进行了分析。
(4)通过对影响轧板应变程度的参数如:压下率、宽高比(B/H)、轧制温度、轧制转速等进行研究,得到了轧制应变渗透到中心层的临界值,并分析了压下率、宽高比(B/H)、轧制温度、轧制转速对应变以及板材侧形的影响规律。用点跟踪法对不同厚度层上的应变进行跟踪,分析了在厚度层上应变分布规律。
(5)对热轧温度场和应力应变场进行了耦合数值模拟,分传送阶段、轧制进行阶段、喷水冷却阶段、返温阶段进行热轧模拟,得到了各个阶段轧板温度场的分布规律、应力应变场分布规律。研究了典型节点温度随时间的变化规律,分析了耦合应力应变场的变化规律,与非耦合应力应变场的变化规律进行比较,在厚度方向的最大应变从外表面转移到了次表面。并分析了轧制初始温度与轧制转速变化对轧制压力的影响规律,初始轧制温度以及轧辊转速对轧制温度场的影响规律。
Based on the analysis of the development and present situation of the numerical simulation of the plate rolling process both home and abroad, a FEM model of the rolling process are created. On the premise of being tested the reliability, the models are used for simulating the rolling process, and for searching some regularities of the rolling process, as a result, some problems can't be solved by industry experiments can be solved in this way conveniently, some technical and theoretical supports for the optimization of technology can be provided.
The main contents of the subject as following:
The tensile properties of 1Cr13 was studied by high temperature tensile tests on 400℃、500℃、600℃、650℃、700℃. It provides the necessary mechanical properties data for hot rolling. Based on the experimental data of 400℃、700℃, the tensile tests of 1Cr13 on other temperatures such as 900℃、1000℃、1100℃were simulated on DEFORM-3D. It showed the distribution of stress and strain at various stages and the deformation process of the sample intuitively. Meanwhile, the results of simulation were verified by the experiments. It was the foundation for the establishment of the rolling model. Numerical simulation is expected to become another means of tensile test with the development of the FEA Software.
Rolling model was established, and the factors that affected the rolling resistance were studied. Based on the numerical simulation, the relationship of rolling temperature, roller speed, volume reduction, rolling plate thickness and rolling resistance was studied. Then comparison of the simulated rolling results and the calculated results with Sims rolling pressure formula was studied, and the error of them was analyzed. The metal was flowing at the length direction and breadth direction when the hot rolling was going. So the strain on the two directions was altered. The effect of rolling temperature, rotation rate, volume reduction and the ratio of rolling plate breadth and thickness on the strain was studied. The critical data of the volume reduction and the ratio of the breadth and thickness which affected the strain depth were analyzed.
Taking use of the model of the rolling process, the change of the rolled piece temperature field was simulated. The temperature field distribution, stress field distribution and strain field distribution of rolling plate on various stages was studied.
As the development of FEM software, the simulation result will be more accurate. It can optimize the technique of hot rolling and provide the technical support.
本论文研究的主要内容有:
(1)通过1Cr13高温拉伸试验研究400℃、500℃、600℃、650℃、700℃温度点下的屈服强度,抗拉强度等基本力学性能。利用试验得出的400℃、700℃温度点下的应力应变数据,在DEFORM-3D平台上对其它温度点进行拉伸试验数值模拟。结果直观地显示了各阶段应力应变分布及试样的变形过程,仿真屈服强度、最大抗拉强度等与试验实测值吻合较好,随着有限元软件的不断发展,数值模拟有望成为拉伸试验的另一手段。利用该数值模型外推得到了900℃、1000℃、1100℃的应力应变曲线,从而为本构模型的建立奠定基础。为该材料轧制模型的建立提供必要的力学性能数据,以便热轧模拟能够更精确的进行。
(2)对1Cr13材料进行热轧数值分析,用云图直观地反映出轧制各个阶段应力应变分布情况,并通过多组试验对影响轧制压力的参数如轧制温度、轧辊转速、压下量、轧板厚度进行了分析,得到了轧制温度、轧辊转速、压下量、轧板厚度对轧制压力的影响规律。
(3)将模拟轧制压力值与西姆斯热轧轧制力公式计算出的理论值进行比较,两者的变化趋势一致,但有一定的误差存在,对误差存在的原因进行了分析。
(4)通过对影响轧板应变程度的参数如:压下率、宽高比(B/H)、轧制温度、轧制转速等进行研究,得到了轧制应变渗透到中心层的临界值,并分析了压下率、宽高比(B/H)、轧制温度、轧制转速对应变以及板材侧形的影响规律。用点跟踪法对不同厚度层上的应变进行跟踪,分析了在厚度层上应变分布规律。
(5)对热轧温度场和应力应变场进行了耦合数值模拟,分传送阶段、轧制进行阶段、喷水冷却阶段、返温阶段进行热轧模拟,得到了各个阶段轧板温度场的分布规律、应力应变场分布规律。研究了典型节点温度随时间的变化规律,分析了耦合应力应变场的变化规律,与非耦合应力应变场的变化规律进行比较,在厚度方向的最大应变从外表面转移到了次表面。并分析了轧制初始温度与轧制转速变化对轧制压力的影响规律,初始轧制温度以及轧辊转速对轧制温度场的影响规律。
Based on the analysis of the development and present situation of the numerical simulation of the plate rolling process both home and abroad, a FEM model of the rolling process are created. On the premise of being tested the reliability, the models are used for simulating the rolling process, and for searching some regularities of the rolling process, as a result, some problems can't be solved by industry experiments can be solved in this way conveniently, some technical and theoretical supports for the optimization of technology can be provided.
The main contents of the subject as following:
The tensile properties of 1Cr13 was studied by high temperature tensile tests on 400℃、500℃、600℃、650℃、700℃. It provides the necessary mechanical properties data for hot rolling. Based on the experimental data of 400℃、700℃, the tensile tests of 1Cr13 on other temperatures such as 900℃、1000℃、1100℃were simulated on DEFORM-3D. It showed the distribution of stress and strain at various stages and the deformation process of the sample intuitively. Meanwhile, the results of simulation were verified by the experiments. It was the foundation for the establishment of the rolling model. Numerical simulation is expected to become another means of tensile test with the development of the FEA Software.
Rolling model was established, and the factors that affected the rolling resistance were studied. Based on the numerical simulation, the relationship of rolling temperature, roller speed, volume reduction, rolling plate thickness and rolling resistance was studied. Then comparison of the simulated rolling results and the calculated results with Sims rolling pressure formula was studied, and the error of them was analyzed. The metal was flowing at the length direction and breadth direction when the hot rolling was going. So the strain on the two directions was altered. The effect of rolling temperature, rotation rate, volume reduction and the ratio of rolling plate breadth and thickness on the strain was studied. The critical data of the volume reduction and the ratio of the breadth and thickness which affected the strain depth were analyzed.
Taking use of the model of the rolling process, the change of the rolled piece temperature field was simulated. The temperature field distribution, stress field distribution and strain field distribution of rolling plate on various stages was studied.
As the development of FEM software, the simulation result will be more accurate. It can optimize the technique of hot rolling and provide the technical support.
引文
[1]Guo.J.Li,S.Kobayashi.Rigid-Plastic finite element analysis of plane strain rolling.J.Eng.Ind.,1982,104:55-64
[2]Lee S M,Shin W,Shivpui R.Investigation of Two Square-to-Round Multipass Rolling Sequences by the Slab-Finite Element Method.Int.J.Mach.Tools Manufact.1992,32(3):315-320
[3]Shivpuri R,Shin W.A Methodology for Roll Pass Optimization for Multipass Rolling Shape.Int.J.Mach.Tools Manufact,1992,32(5):671-67
[4]SkIN C G,PARK H D,HWANG S M.Prediction of three dimensional strip temperature through the entire finishing mill in hot strip rolling by finite element method.ISIJ International,2002,42:629-635
[5]Komori K.Rigid-plastic finite element method for analysis of three-dimensional rolling that requires small memory capacity.International Journal of Mechanical Science,1998,40:479-491
[6]Komori K,Koumura K.Simulation of deformation and temperature in multi-pass H-shape rolling.Journal of materials processing technology,2000,105:24-31
[7]Jiang Z Y,Tieu A K.A simulation of three-dimensional metal rolling processes by rigid-plastic finite element method.Journal of materials processing echnology,2001,112:144-151
[8]Jiang Z Y,Tieu A K,Zhang X M,ET al.Finite element simulation of cold rolling of thin strip.Journal of Materials Processing Technology,2003,140:542-547
[9]Jiang Z Y,Tieu A K.A 3-D finite element method analysis of cold rolling of thin strip with friction variation.Tribology International,2004,37:185-191
[10]Jiang Z Y,Hu W P,Zhang X M,et al.Coupled deformation and temperature analysis of strip rolling with a local perturbation of deformation using a 3D rigid-plastic FEM.Scandinavian Journal of Metallurgy 2004,33:29-38
[11]Lee Y,Kim H J,Hwang S W.Analytic model for the prediction of mean effective strain in rod rolling process.Journal of materials processing technology,2001,114:129-13
[12]Yanagimoto J,Kiuchi M,Inoue Y.Characterization of Wire and Rod Rolling with Front and Back Tensions by Three-Dimensional Rigid-Plastic Finite ElementMethod.Proceedings of 4th ICTP,1993:754-757
[13]Yanagimoto J,Kiuchi M.Three-Dimensional Rigid-Plastic FE Simulation System for Shape Rolling with Inter-Stand Remeshing.Poceedings of International Conference for Metal Forming Process Simulation in Industry,1994:219-23
[14]Chandra S,Dixit U S.A rigid-plastic finite element analysis of temper rolling Process.Journal of Materials Processing Technology,2004,152:9-16
[15]李世芸,张曙红,张代明,双金属复合带材轧制过程有限元模拟,中国有色金属学报 2001,11(6):1078-108
[16]刘相华,刚塑性有限元及其在轧制中的应用,北京:冶金工业出版社,1994
[17]徐建中,熊尚武,刘相华等,异型扁坯轧制过程的刚塑性有限元分析,东北大学学报(自然科学版),2000,21(2):199-202
[18]Xiong Shangwu,J.M.C.Rodrigues,P.A.F.Martins.Simulation of plane strain rolling through a combined element free Galerkin-boundary element approach.Journal of Materials Processing Technology,2005,159:214-223
[19]徐新平,王均安,硅钢片轧制过程的有限元数值模拟,上海金属,2005,27(4):30-33
[20]刘才,张乐乐,赵永和,刚塑性有限元法对双金属轧制结合面的模拟研究,燕山大学学报,1998,22(3):189-191
[21]李学通,杜凤山,王敏婷等,板材调宽轧制头部形状控制有限元分析,中国机械工程,2005,16(8):712-715
[22]李学通,杜凤山,孙登月等,热轧带钢粗轧区轧制宽展模型的研究,钥铁,2005.40(6):44-47
[23]李学通,杜风山,王敏婷,中厚板轧制多参量耦合的数值模拟(Ⅱ),上海金属,2006,28(1);43-47
[24]肖宏,张国民,PC轧机轧制过程耦合数值模拟研究,工程力学,2005,22(3):216-219
[25]Galantucci L M,Tricarico L.Thermo-mechanical simulation of a rolling process with an FEM approach.Journal of Materials Processing Technology,1999,92-93:494-501
[26]Gadala M S,Wang J.Elasto-plastic finite element simulation of rolling and compression between wedge-shape dies.Journal of Materials Processing Technology 2000,97:132-147
[27]Iankov R.Finite element simulation of profile rolling of wire.Journal of Materials Processing Technology 2003,142:355-61
[28]Richelsen A B,Tvergaard Y.3D Analysis of cold rolling using a constitutive model for interface friction.International Journal of Mechanical Science,2004,46:653-671
[29]Wisselink H H,Huetink J.3D FEM simulation of stationary metal forming processes with applications to slitting and rolling.Journal of Materials Technology,2004,148:328-341
[30]Boman R,Ponthot J P.Finite element simulation of lubricated contact in rolling using the arbitrary Lagrangian-Eulerian formulation.Comput.Methods Appl.Mech.Engrg,2004,193:4323-4353
[31]Lau A C W,Shivpuri R,Chou P C.An explicit time integratio elastic-plastic finite element algorithm for analysis of high speed rolling.International Journal of Mechanical Science,1989,31:483-497
[32]Nilsson A.FE simulations of camber in hot strip rolling.Journal of Material Processing Technology,1998,80-81:325-329
[33]Fukumura M,Fuji kaka M,Fujita F,et al.Elasto-plastic finite element simulation of flat rolling process by dynamic explicit method.Processing of the 7″ International Conference on Steel Rolling,Chiba Japan,1998:260-265
[34]Song J L,Dowson A L,Jacobs M H,et al.Coupled thermo-mechanical finite-element modeling of hot ring rolling process.Journal of Materials Processing Technology,2002,121:332-340
[35]Pauskar P M,Sawamiphakdi K,Jin D Q.Static Implicit vs.Dynamic Explicit Finite Element Analysis for Ring Rolling Process Modeling.NUMIFORM 2004,412-417
[36]SUN C G,PARK H D,HWANG S M.Prediction of three dimensional strip temperatures through the entire finishing mill in hot strip rolling by finite element method.ISIJ International,2002,42:629-635
[37]N.Bontcheva,G.Petzov.Total simulation model of the thermo-mechanical process in shape rolling of steel rods.Computational Materials Science,2005,34:377-388
[38]Tudbal A,Brown S G R.Practical finite element heat transfer modelling for hot rolling of steels.Ironmaking steelmaking,2006,33(1):61-66
[39]康永林,宋仁伯,任学平等,变形参数对半固态轧制影响规律的有限元模拟,塑性工程学报,2002,9(3):66-70
[40]Lin Z C,Lin V H.Analysis of the variation of the cold-rolling characteristics of rolling force,strip shape,stress and temperature,for a three-dimensional strip.Journal of Materials Processing Technology,1995,54:326-340
[41]许秀梅,张文志,波纹轨腰钢轨轧制的数值模拟与实验研究,中国机械工程,2005,16(12);1103-1106
[42]戴晓光,五道次孔型轧制40Cr大圆钢有限元模拟分析,重型机械,2006,1:34-3
[43]张鹏,鹿守理,高永生,板带轧制过程温度场有限元模拟及影响因素分析(Ⅰ),北京科技大学学报,1997,19(5):471-475
[44]阎军,鹿守理,简单断面型钢轧制温度场的三维有限元模拟,华东冶金学院学报,2000,17(2):95-97
[45]李茂,DEFORM和Marc平台下棒线材热连轧过程的数值模拟,2006,1-25
[46]孙卫华,王国栋,吴国良,带钢热轧过程中轧件横断面上温度场的解析,山东冶金,1999,16(5):30-3
[47]李立新,汪凌云,周家林,中板精轧阶段温度场的有限元分析,武汉科技大学学报(自然科学版),2002,25(2):124-125
[48]兰勇军,陈祥永,黄成江带钢热轧过程中温度演变的数值模拟和实验研究,金属学报,2001,37(1):99-103
[49]湛利华,李晓谦,基于ANSYS的快速铸轧过程温度场数值模拟重型机械,2005,2:39-4
[50]洪慧平,康永林,冯长桃,箱形孔型合金钢稳态轧制的温度场有限元模拟特殊钢,2002,23(2):11-13
[51]曲蒙,金南国,金贤玉。早龄期混凝土单轴拉伸试验的数值模拟[J].结构工程师,2005,21(6):50-55.
[52]张志远.延性金属圆柱棒的拉伸断裂数值模拟[J].塑性工程报.2004,11(3):11-14.
[53]胡振东,孙庆平.超弹性形状记忆合金管单向拉伸试验的数值模拟[J].力学季刊.2005,26(3):389-392.
[54]李传民.金属成形有限元分析实例指导教程[M].北京:机械工业出版社,2007.
[55]谢水生.金属塑性成形工艺的有限元数值模拟[M].北京:Metallurgical Industry Press,1994.
[56]王瑁成,邵敏.有限单元法基本原理和数值方法.北京:清华大学出版社.1998.
[57]周朝辉,曹海桥等.DEFORM有限元分析系统软件及其应用[J].热加工工艺.2003,4:51-52.
[58]林新波.DEFORM-2D和DEFORM-3D CAE软件在模拟金属塑性变形过程中的应用[J].模具技术.2000,3:75-80.
[59]张玉华,朱希玲.彩涂板压型过程有限元模拟[J],钢铁,2003,38(11):36-39.
[2]Lee S M,Shin W,Shivpui R.Investigation of Two Square-to-Round Multipass Rolling Sequences by the Slab-Finite Element Method.Int.J.Mach.Tools Manufact.1992,32(3):315-320
[3]Shivpuri R,Shin W.A Methodology for Roll Pass Optimization for Multipass Rolling Shape.Int.J.Mach.Tools Manufact,1992,32(5):671-67
[4]SkIN C G,PARK H D,HWANG S M.Prediction of three dimensional strip temperature through the entire finishing mill in hot strip rolling by finite element method.ISIJ International,2002,42:629-635
[5]Komori K.Rigid-plastic finite element method for analysis of three-dimensional rolling that requires small memory capacity.International Journal of Mechanical Science,1998,40:479-491
[6]Komori K,Koumura K.Simulation of deformation and temperature in multi-pass H-shape rolling.Journal of materials processing technology,2000,105:24-31
[7]Jiang Z Y,Tieu A K.A simulation of three-dimensional metal rolling processes by rigid-plastic finite element method.Journal of materials processing echnology,2001,112:144-151
[8]Jiang Z Y,Tieu A K,Zhang X M,ET al.Finite element simulation of cold rolling of thin strip.Journal of Materials Processing Technology,2003,140:542-547
[9]Jiang Z Y,Tieu A K.A 3-D finite element method analysis of cold rolling of thin strip with friction variation.Tribology International,2004,37:185-191
[10]Jiang Z Y,Hu W P,Zhang X M,et al.Coupled deformation and temperature analysis of strip rolling with a local perturbation of deformation using a 3D rigid-plastic FEM.Scandinavian Journal of Metallurgy 2004,33:29-38
[11]Lee Y,Kim H J,Hwang S W.Analytic model for the prediction of mean effective strain in rod rolling process.Journal of materials processing technology,2001,114:129-13
[12]Yanagimoto J,Kiuchi M,Inoue Y.Characterization of Wire and Rod Rolling with Front and Back Tensions by Three-Dimensional Rigid-Plastic Finite ElementMethod.Proceedings of 4th ICTP,1993:754-757
[13]Yanagimoto J,Kiuchi M.Three-Dimensional Rigid-Plastic FE Simulation System for Shape Rolling with Inter-Stand Remeshing.Poceedings of International Conference for Metal Forming Process Simulation in Industry,1994:219-23
[14]Chandra S,Dixit U S.A rigid-plastic finite element analysis of temper rolling Process.Journal of Materials Processing Technology,2004,152:9-16
[15]李世芸,张曙红,张代明,双金属复合带材轧制过程有限元模拟,中国有色金属学报 2001,11(6):1078-108
[16]刘相华,刚塑性有限元及其在轧制中的应用,北京:冶金工业出版社,1994
[17]徐建中,熊尚武,刘相华等,异型扁坯轧制过程的刚塑性有限元分析,东北大学学报(自然科学版),2000,21(2):199-202
[18]Xiong Shangwu,J.M.C.Rodrigues,P.A.F.Martins.Simulation of plane strain rolling through a combined element free Galerkin-boundary element approach.Journal of Materials Processing Technology,2005,159:214-223
[19]徐新平,王均安,硅钢片轧制过程的有限元数值模拟,上海金属,2005,27(4):30-33
[20]刘才,张乐乐,赵永和,刚塑性有限元法对双金属轧制结合面的模拟研究,燕山大学学报,1998,22(3):189-191
[21]李学通,杜凤山,王敏婷等,板材调宽轧制头部形状控制有限元分析,中国机械工程,2005,16(8):712-715
[22]李学通,杜凤山,孙登月等,热轧带钢粗轧区轧制宽展模型的研究,钥铁,2005.40(6):44-47
[23]李学通,杜风山,王敏婷,中厚板轧制多参量耦合的数值模拟(Ⅱ),上海金属,2006,28(1);43-47
[24]肖宏,张国民,PC轧机轧制过程耦合数值模拟研究,工程力学,2005,22(3):216-219
[25]Galantucci L M,Tricarico L.Thermo-mechanical simulation of a rolling process with an FEM approach.Journal of Materials Processing Technology,1999,92-93:494-501
[26]Gadala M S,Wang J.Elasto-plastic finite element simulation of rolling and compression between wedge-shape dies.Journal of Materials Processing Technology 2000,97:132-147
[27]Iankov R.Finite element simulation of profile rolling of wire.Journal of Materials Processing Technology 2003,142:355-61
[28]Richelsen A B,Tvergaard Y.3D Analysis of cold rolling using a constitutive model for interface friction.International Journal of Mechanical Science,2004,46:653-671
[29]Wisselink H H,Huetink J.3D FEM simulation of stationary metal forming processes with applications to slitting and rolling.Journal of Materials Technology,2004,148:328-341
[30]Boman R,Ponthot J P.Finite element simulation of lubricated contact in rolling using the arbitrary Lagrangian-Eulerian formulation.Comput.Methods Appl.Mech.Engrg,2004,193:4323-4353
[31]Lau A C W,Shivpuri R,Chou P C.An explicit time integratio elastic-plastic finite element algorithm for analysis of high speed rolling.International Journal of Mechanical Science,1989,31:483-497
[32]Nilsson A.FE simulations of camber in hot strip rolling.Journal of Material Processing Technology,1998,80-81:325-329
[33]Fukumura M,Fuji kaka M,Fujita F,et al.Elasto-plastic finite element simulation of flat rolling process by dynamic explicit method.Processing of the 7″ International Conference on Steel Rolling,Chiba Japan,1998:260-265
[34]Song J L,Dowson A L,Jacobs M H,et al.Coupled thermo-mechanical finite-element modeling of hot ring rolling process.Journal of Materials Processing Technology,2002,121:332-340
[35]Pauskar P M,Sawamiphakdi K,Jin D Q.Static Implicit vs.Dynamic Explicit Finite Element Analysis for Ring Rolling Process Modeling.NUMIFORM 2004,412-417
[36]SUN C G,PARK H D,HWANG S M.Prediction of three dimensional strip temperatures through the entire finishing mill in hot strip rolling by finite element method.ISIJ International,2002,42:629-635
[37]N.Bontcheva,G.Petzov.Total simulation model of the thermo-mechanical process in shape rolling of steel rods.Computational Materials Science,2005,34:377-388
[38]Tudbal A,Brown S G R.Practical finite element heat transfer modelling for hot rolling of steels.Ironmaking steelmaking,2006,33(1):61-66
[39]康永林,宋仁伯,任学平等,变形参数对半固态轧制影响规律的有限元模拟,塑性工程学报,2002,9(3):66-70
[40]Lin Z C,Lin V H.Analysis of the variation of the cold-rolling characteristics of rolling force,strip shape,stress and temperature,for a three-dimensional strip.Journal of Materials Processing Technology,1995,54:326-340
[41]许秀梅,张文志,波纹轨腰钢轨轧制的数值模拟与实验研究,中国机械工程,2005,16(12);1103-1106
[42]戴晓光,五道次孔型轧制40Cr大圆钢有限元模拟分析,重型机械,2006,1:34-3
[43]张鹏,鹿守理,高永生,板带轧制过程温度场有限元模拟及影响因素分析(Ⅰ),北京科技大学学报,1997,19(5):471-475
[44]阎军,鹿守理,简单断面型钢轧制温度场的三维有限元模拟,华东冶金学院学报,2000,17(2):95-97
[45]李茂,DEFORM和Marc平台下棒线材热连轧过程的数值模拟,2006,1-25
[46]孙卫华,王国栋,吴国良,带钢热轧过程中轧件横断面上温度场的解析,山东冶金,1999,16(5):30-3
[47]李立新,汪凌云,周家林,中板精轧阶段温度场的有限元分析,武汉科技大学学报(自然科学版),2002,25(2):124-125
[48]兰勇军,陈祥永,黄成江带钢热轧过程中温度演变的数值模拟和实验研究,金属学报,2001,37(1):99-103
[49]湛利华,李晓谦,基于ANSYS的快速铸轧过程温度场数值模拟重型机械,2005,2:39-4
[50]洪慧平,康永林,冯长桃,箱形孔型合金钢稳态轧制的温度场有限元模拟特殊钢,2002,23(2):11-13
[51]曲蒙,金南国,金贤玉。早龄期混凝土单轴拉伸试验的数值模拟[J].结构工程师,2005,21(6):50-55.
[52]张志远.延性金属圆柱棒的拉伸断裂数值模拟[J].塑性工程报.2004,11(3):11-14.
[53]胡振东,孙庆平.超弹性形状记忆合金管单向拉伸试验的数值模拟[J].力学季刊.2005,26(3):389-392.
[54]李传民.金属成形有限元分析实例指导教程[M].北京:机械工业出版社,2007.
[55]谢水生.金属塑性成形工艺的有限元数值模拟[M].北京:Metallurgical Industry Press,1994.
[56]王瑁成,邵敏.有限单元法基本原理和数值方法.北京:清华大学出版社.1998.
[57]周朝辉,曹海桥等.DEFORM有限元分析系统软件及其应用[J].热加工工艺.2003,4:51-52.
[58]林新波.DEFORM-2D和DEFORM-3D CAE软件在模拟金属塑性变形过程中的应用[J].模具技术.2000,3:75-80.
[59]张玉华,朱希玲.彩涂板压型过程有限元模拟[J],钢铁,2003,38(11):36-39.