基于实验的镁合金本构模型及其在轧制数值模拟中的应用研究
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摘要
本文结合国家科技支撑计划项目（2012BAF09B01）“面向冶金行业关键装备、技术研发及示范应用子课题——镁合金深加工关键技术研究及大型成套设备研制”，以AZ31镁合金在不同温度、不同应变速率、沿不同方向条件下的拉伸和压缩应力-应变实验数据为基础，建立Arrhenius双曲正弦流变应力本构模型、含常软化因子的高温流变应力本构模型、非关联流动各向异性本构模型和拉-压不对称各向异性本构模型，通过数值模拟和轧制试验研究镁合金热轧轧板宽展和头部翘曲变形的规律，以指导镁合金厚板热轧工艺设计，控制板材成形质量。
材料的本构模型是进行轧制过程数值模拟的基础，本文综述了国内外镁合金热轧成形数值模拟技术研究成果，归纳了各向异性本构理论在金属塑性成形中的应用情况，讨论了各种常用本构模型的特点。为研究AZ31镁合金的拉伸、压缩力学性能随温度和应变速率变化的规律，进行了25℃~375℃、应变速率为0.001s-1~0.1s-1条件下镁合金轧制试件的单轴拉伸和单轴压缩试验。结果表明温度和应变速率对AZ31镁合金的流变应力有较大影响：AZ31镁合金的拉伸、压缩应力水平均随变形温度的升高和应变速率的减小而降低，25℃下AZ31镁合金的拉、压初始屈服应力差别较大，随着温度的升高这种差别逐渐减小，但两种状态下的硬化关系仍具有较大差别。通过沿轧板面内各方向和垂向的单轴拉伸和单轴压缩试验，得到了AZ31镁合金不同方向的拉、压屈服应力和塑性应变比，数据表明轧制AZ31镁合金具有较强的应力应变各向异性。
为综合考虑AZ31镁合金高温变形过程中变形温度和应变速率对流变应力的影响，利用AZ31镁合金的拉伸、压缩力学性能随温度和应变速率变化的试验数据，建立了Arrhenius双曲正弦型流变应力本构方程和含常软化因子的高温流变应力本构方程，进行了板材轧制热固耦合有限元模拟，分析了AZ31镁合金多道次热轧过程中轧板、轧辊和输送辊温度场变化的规律和轧板的翘曲变形，并通过与实际翘曲量的对比验证了热固耦合有限元方法在预测轧板翘曲变形方面的可行性。
含常软化因子的高温流变应力本构方程未考虑AZ31镁合金应力应变的各向异性，是导致模拟结果存在误差的原因之一，本文将各向异性本构模型引入镁合金板材轧制。根据AZ31镁合金沿轧板面内各方向和垂向的压缩屈服应力和压缩塑性应变比，建立了三维应力状态下的非关联流动Hill48和非关联流动Hu2005本构模型，通过与试验数据和具有18个各向异性参数的Yld2004-18p本构模型进行比较，证明了上述非关联流动本构模型能够准确地预测AZ31镁合金沿不同方向的压缩屈服应力和压缩塑性应变比。将非关联流动Hill48和非关联流动Hu2005本构模型编写了相应的用户材料子程序VUMAT，然后在Abaqus/Explicit中调用该子程序模拟了恒温下AZ31镁合金的轧制过程，预测了方形棒材的宽展变形，仿真结果与试验数据吻合较好，验证了上述非关联流动本构模型的正确性。
根据AZ31镁合金沿轧板面内各方向和垂向的拉伸、压缩屈服应力和塑性应变比，建立了三维应力状态下的CPB06ex2拉-压不对称各向异性本构模型，试验数据表明采用CPB06ex2拉-压不对称各向异性本构模型预测的镁合金方形棒材和板材的头部翘曲量与实际变形吻合较好。在此基础上，分析了上下轧辊辊速比、轧制速度、轧板与轧辊表面间的摩擦条件等因素对AZ31镁合金方形棒材头部翘曲的影响规律。论文的研究成果对改进轧制模拟的仿真精度、提高国产镁合金深加工装备板材成形质量具有重要的指导意义。
This research is supported by a sub-project under the National Key Technology R&DProgram (No.2012BAF09B01): Research on key technology of magnesium alloy furtherprocessing and development of large equipments. Different constitutive models, such asArrhenius hyperbolic sinusoidal flow stress constitutive equation, flow stress constitutiveequation with a constant strain-softening factor, anisotropic constitutive model undernon-associated flow rule and anisotropic-asymmetric constitutive model were built based onthe tension and compression stress-strain data of the AZ31magnesium alloy at varioustemperatures, different strain rates and along different directions. The deformation rule ofspread and head warping of the hot-rolled magnesium alloy sheet were analyzed bynumerical simulation and experiments to instruct the design of magnesium alloy rollingprocess and control the quality of the sheet forming.
The constitutive model of the magnesium alloy is the basis of the numerical simulationof rolling process. An overview of the relevant research achievements on the numericalsimulation technology of the magnesium alloy hot-rolling process was provided, applicationof the anisotropic constitutive theory in metal forming was summarized, features of thecommonly used constitutive model were discussed. Under the condition that the range oftemperature is25℃~375℃and strain rate changes from0.001s-1s to0.1s-1s, uniaxialtension and compressive tests were carried to study the tensile and compression mechanicalproperties of AZ31magnesium alloy at various temperatures. Results indicates thattemperature and strain rate has a great effect on the flow stress of AZ31magnesium alloy,and the difference of the initial yield stress between tension and compression stage undertemperature of25℃is large. The difference decreases as the temperature rises, but thehardening relationship between two states still has a big difference. Besides, uniaxial tensionand compression tests along each direction of the rolling field and vertical direction werecarried out to obtain anisotropy in the tensile and compressive yield stress and the plasticstrain ratio of AZ31magnesium alloy. The experimental result shows that the rolling AZ31magnesium alloy has strong stress-strain anisotropy effect.
Arrhenius hyperbolic sinusoidal flow stress constitutive equation was built to generallyconsider the effects of deformation temperature and strain rate on peak stress during theprocess of the magnesium alloy deformation at high temperatures, while the flow stressconstitutive equation with a constant strain-softening factor reflects the effects on the wholestress-strain behavior, and the simulation results of both the equations correspond well withthe experimental data. The coupled thermo-mechanical finite element method was used to analyze the temperature field of the rolled piece, the roller and the conveyor roller, thecomparison between the simulation results with the experimental warping shows thefeasibility of the coupled thermo-mechanical finite element method in predicting thewarping.
Because the anisotropic property in stress and strain of AZ31magnesium alloy was nottaken into consideration in the the flow stress constitutive equation with a constantstrain-softening factor, so the error of the simulation is unavoidable, this paper introducedthe anisotropic constitutive model in the simulation of the rolling process of magnesiumalloy. According to the compressive yield stress and the plastic strain ratio of AZ31magnesium alloy along different directions in the plane of rolled piece and the verticaldirection, the three-dimensional Hill48and Hu2005constitutive models undernon-associated flow rule were established. Compared with the experimental data and theYld2004-18p constitutive model which has18anisotropic parameters, the result shows thatthe constitutive models under non-associated flow rule could accurately predict thecompressive yield stress and plastic strain ratio of AZ31magnesium alloy at each direction.The non-associated Hill48and Hu2005constitutive models were implemented into auser-defined material subroutine (VUMAT) to simulate the rolling process of AZ31magnesium alloy at constant temperature in Abaqus/Explicit. The simulation predicted thespread of the magnesium alloy bar. The simulation result is very close to the experimentresult. Thus the accuracy of the constitutive models under non-associated flow rule isverified.
According to the tensile and compressive yield stress and plastic strain ratio alongdifferent directions in the plane of the rolled AZ31piece and the vertical direction, atension-compression asymmetric&anisotropic constitutive model of CPB06ex2under thethree-dimensional stress state was built. The result shows that the predicted head warpingwith the tension-compression asymmetric&anisotropic constitutive model of CPB06ex2matches well with the measured data. Then, the effects of speed ratio of the upper roller tothe lower roller, the rolling speed and the friction condition between the rolled sheet and theroller surface on head warping of the rolled AZ31sheet were analyzed. The achievements ofthis thesis have significant meaning in improving the precision of rolling simulation and thequality of magnesium alloy sheet metal.
材料的本构模型是进行轧制过程数值模拟的基础，本文综述了国内外镁合金热轧成形数值模拟技术研究成果，归纳了各向异性本构理论在金属塑性成形中的应用情况，讨论了各种常用本构模型的特点。为研究AZ31镁合金的拉伸、压缩力学性能随温度和应变速率变化的规律，进行了25℃~375℃、应变速率为0.001s-1~0.1s-1条件下镁合金轧制试件的单轴拉伸和单轴压缩试验。结果表明温度和应变速率对AZ31镁合金的流变应力有较大影响：AZ31镁合金的拉伸、压缩应力水平均随变形温度的升高和应变速率的减小而降低，25℃下AZ31镁合金的拉、压初始屈服应力差别较大，随着温度的升高这种差别逐渐减小，但两种状态下的硬化关系仍具有较大差别。通过沿轧板面内各方向和垂向的单轴拉伸和单轴压缩试验，得到了AZ31镁合金不同方向的拉、压屈服应力和塑性应变比，数据表明轧制AZ31镁合金具有较强的应力应变各向异性。
为综合考虑AZ31镁合金高温变形过程中变形温度和应变速率对流变应力的影响，利用AZ31镁合金的拉伸、压缩力学性能随温度和应变速率变化的试验数据，建立了Arrhenius双曲正弦型流变应力本构方程和含常软化因子的高温流变应力本构方程，进行了板材轧制热固耦合有限元模拟，分析了AZ31镁合金多道次热轧过程中轧板、轧辊和输送辊温度场变化的规律和轧板的翘曲变形，并通过与实际翘曲量的对比验证了热固耦合有限元方法在预测轧板翘曲变形方面的可行性。
含常软化因子的高温流变应力本构方程未考虑AZ31镁合金应力应变的各向异性，是导致模拟结果存在误差的原因之一，本文将各向异性本构模型引入镁合金板材轧制。根据AZ31镁合金沿轧板面内各方向和垂向的压缩屈服应力和压缩塑性应变比，建立了三维应力状态下的非关联流动Hill48和非关联流动Hu2005本构模型，通过与试验数据和具有18个各向异性参数的Yld2004-18p本构模型进行比较，证明了上述非关联流动本构模型能够准确地预测AZ31镁合金沿不同方向的压缩屈服应力和压缩塑性应变比。将非关联流动Hill48和非关联流动Hu2005本构模型编写了相应的用户材料子程序VUMAT，然后在Abaqus/Explicit中调用该子程序模拟了恒温下AZ31镁合金的轧制过程，预测了方形棒材的宽展变形，仿真结果与试验数据吻合较好，验证了上述非关联流动本构模型的正确性。
根据AZ31镁合金沿轧板面内各方向和垂向的拉伸、压缩屈服应力和塑性应变比，建立了三维应力状态下的CPB06ex2拉-压不对称各向异性本构模型，试验数据表明采用CPB06ex2拉-压不对称各向异性本构模型预测的镁合金方形棒材和板材的头部翘曲量与实际变形吻合较好。在此基础上，分析了上下轧辊辊速比、轧制速度、轧板与轧辊表面间的摩擦条件等因素对AZ31镁合金方形棒材头部翘曲的影响规律。论文的研究成果对改进轧制模拟的仿真精度、提高国产镁合金深加工装备板材成形质量具有重要的指导意义。
This research is supported by a sub-project under the National Key Technology R&DProgram (No.2012BAF09B01): Research on key technology of magnesium alloy furtherprocessing and development of large equipments. Different constitutive models, such asArrhenius hyperbolic sinusoidal flow stress constitutive equation, flow stress constitutiveequation with a constant strain-softening factor, anisotropic constitutive model undernon-associated flow rule and anisotropic-asymmetric constitutive model were built based onthe tension and compression stress-strain data of the AZ31magnesium alloy at varioustemperatures, different strain rates and along different directions. The deformation rule ofspread and head warping of the hot-rolled magnesium alloy sheet were analyzed bynumerical simulation and experiments to instruct the design of magnesium alloy rollingprocess and control the quality of the sheet forming.
The constitutive model of the magnesium alloy is the basis of the numerical simulationof rolling process. An overview of the relevant research achievements on the numericalsimulation technology of the magnesium alloy hot-rolling process was provided, applicationof the anisotropic constitutive theory in metal forming was summarized, features of thecommonly used constitutive model were discussed. Under the condition that the range oftemperature is25℃~375℃and strain rate changes from0.001s-1s to0.1s-1s, uniaxialtension and compressive tests were carried to study the tensile and compression mechanicalproperties of AZ31magnesium alloy at various temperatures. Results indicates thattemperature and strain rate has a great effect on the flow stress of AZ31magnesium alloy,and the difference of the initial yield stress between tension and compression stage undertemperature of25℃is large. The difference decreases as the temperature rises, but thehardening relationship between two states still has a big difference. Besides, uniaxial tensionand compression tests along each direction of the rolling field and vertical direction werecarried out to obtain anisotropy in the tensile and compressive yield stress and the plasticstrain ratio of AZ31magnesium alloy. The experimental result shows that the rolling AZ31magnesium alloy has strong stress-strain anisotropy effect.
Arrhenius hyperbolic sinusoidal flow stress constitutive equation was built to generallyconsider the effects of deformation temperature and strain rate on peak stress during theprocess of the magnesium alloy deformation at high temperatures, while the flow stressconstitutive equation with a constant strain-softening factor reflects the effects on the wholestress-strain behavior, and the simulation results of both the equations correspond well withthe experimental data. The coupled thermo-mechanical finite element method was used to analyze the temperature field of the rolled piece, the roller and the conveyor roller, thecomparison between the simulation results with the experimental warping shows thefeasibility of the coupled thermo-mechanical finite element method in predicting thewarping.
Because the anisotropic property in stress and strain of AZ31magnesium alloy was nottaken into consideration in the the flow stress constitutive equation with a constantstrain-softening factor, so the error of the simulation is unavoidable, this paper introducedthe anisotropic constitutive model in the simulation of the rolling process of magnesiumalloy. According to the compressive yield stress and the plastic strain ratio of AZ31magnesium alloy along different directions in the plane of rolled piece and the verticaldirection, the three-dimensional Hill48and Hu2005constitutive models undernon-associated flow rule were established. Compared with the experimental data and theYld2004-18p constitutive model which has18anisotropic parameters, the result shows thatthe constitutive models under non-associated flow rule could accurately predict thecompressive yield stress and plastic strain ratio of AZ31magnesium alloy at each direction.The non-associated Hill48and Hu2005constitutive models were implemented into auser-defined material subroutine (VUMAT) to simulate the rolling process of AZ31magnesium alloy at constant temperature in Abaqus/Explicit. The simulation predicted thespread of the magnesium alloy bar. The simulation result is very close to the experimentresult. Thus the accuracy of the constitutive models under non-associated flow rule isverified.
According to the tensile and compressive yield stress and plastic strain ratio alongdifferent directions in the plane of the rolled AZ31piece and the vertical direction, atension-compression asymmetric&anisotropic constitutive model of CPB06ex2under thethree-dimensional stress state was built. The result shows that the predicted head warpingwith the tension-compression asymmetric&anisotropic constitutive model of CPB06ex2matches well with the measured data. Then, the effects of speed ratio of the upper roller tothe lower roller, the rolling speed and the friction condition between the rolled sheet and theroller surface on head warping of the rolled AZ31sheet were analyzed. The achievements ofthis thesis have significant meaning in improving the precision of rolling simulation and thequality of magnesium alloy sheet metal.
引文
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