镁合金板带热轧热力耦合有限元仿真分析
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摘要
镁合金板材在航空、航天、汽车,3C产业等领域有着广泛的应用,其制造技术已经成为当前镁合金研发的重点。镁合金板材一般采用轧制成形的方法生产。准确计算和匹配轧制过程各项工艺参数,可以提高镁合金板带的成型效率和质量。板带热轧过程中,存在着几何、材料特性、边界条件等复杂多变量非线性及相互影响的问题,给研究带来很大的困难。近年来随着计算技术以及模拟软件的日益成熟和完善,将热力耦合分析方法引入软件程序中使应用板材热轧方面问题的分析成为可能。
镁合金板带热轧过程中,精确地计算轧件内部的温度场和应力场分布是制定轧制工艺参数的关键,而在加工过程中,温度场与应力场是互相耦合的,温度场的结果直接影响应力场计算的准确性。为了分析该过程,本文采用大型非线性有限元商用软件MSC.Marc,根据实验设备参数,建立弹塑性有限元模型。利用热力耦合分析方法,模拟了AZ31镁合金的轧制过程。研究发现:
1.基于非线性有限元法基本原理,综合轧件在大变形过程中的应力应变规律,建立了用于描述大变形工件在参考系中位置的两类有限元方程,发现更新的拉格朗日描述方程较总的拉格朗日描述方程更具有普遍适用性,故本文中模型分析参数的设定选用更新的拉格朗日描述法。
2.基于传热方程和大变形弹塑性理论,结合轧件轧制过程中的力平衡方程和能量平衡方程,建立了热力耦合数学模型。得出了在每个时间增量步启动时,用当前的位移增量修正域V和边界S,在时间增量步内交替间增量步内交替迭代力平衡和能量平衡的求解规律,综合比较几种求解方法得出完全的Newton- Raphson方法迭代求解最好,收敛判据则选择位移检查收敛。
3.根据AZ31镁合金高温变形的本构方程,使用Marc软件的接口,采用FORTRAN语言编写了流变应力子程序。得到了AZ31镁合金高温流变应力变化规律的材料模型。
4.模拟了镁合金板带热轧过程中的轧制力和轧制力矩,与实验结果比较,验证了模型的正确性。同时发现二维模型模拟结果比三维模拟结果计算更精确,更节约大量的计算时间和计算资源。
5.基于三维和二维模型,模拟了板带热轧过程中的温度场、变形速率、等效塑性应力场和等效塑性应变等情况,较为全面、系统地分析了这些参量沿着轧件各个方向的分布规律。温度梯度在接触面附近较大,远离接触面的区域较小。轧制变形区域内变形速率数值大小的分布与理论方程描述情况一致。等效塑性应力场沿着轧件厚度方向的分布规律与应变理论相同;沿宽度方向,中心处的应力较小,大小分布较为均匀,边部的应力情况较为复杂。沿厚度方向,等效塑性应变从表面到中心逐渐减小;沿宽度方向,从中心到边部应变逐渐增大。
6.研究了不同工艺参数的改变对轧制力、温度场以及宽展的影响。发现轧制力受压下率和初始温度变化的影响较为明显,轧制力随压下率增大而变大,随初始温度升高而减小。高温轧制时,不同的轧制速度对应着轧件不同变形抗力,轧制速度越大,变形抗力也越大,材料就越难以屈服,轧制力越大。轧制力随摩擦系数的变大而增大,增大的幅度较小。对于宽展,随着压下率增大,宽展量也在增大。当B1=L,B2>L时,在[B1,B2]范围内,宽展量随着板宽的增大而变小。其他条件不变的情况下,随着轧辊半径的增大,宽展量也在增大;同样随着摩擦系数的增加,宽展增加。
Magnesium alloy strips and sheets are being widely used in aviation、aerospace、automotive industry、3C and many other fields. the research on making-technology of which has been the focus in whole word. Generally the alloy strips and sheets are produced by rolling method. If we could accurately calculate and match every technics parameter in the rolling process the deforming efficiency and quality of the sheets will be greatly improved. The strip hot rolling process is a complex problem that many variables interact each other, and also a nonlinear analysis which includes material nonlinear analysis, geometrical nonlinear Analysis、contactile nonlinear analysis and the like, both of them bring great hardship to the research. In recent years, with extensive application of simulation software and the increasing maturity of calculation technology,the thermo-mechanical coupled method has been introduced into software program to apply it to analyse the problem of sheet hot rolling .
In magnesium alloy strip hot rolling process, it is important to accurately calculate Distribution of temperature field and stress field in strip for designing rolling technology parameters. In fact, during the process temperature field and Stress field influence each other. In order to study and analysis this process, elastic-plastic finite element model was developed based on experiment equipment technology by MSC. Marc software. All process of magnesium alloy AZ31 sheet hot rolling are simulated by choosing the advanced thermo-mechanical coupled method. The simulated result detailed analysis was made too. The main contents are as following:
1. Based on the basic principle of nonlinear finite element method, comprehensively considering the Similarity of stress and strain distribution in large deformation of rolling piece process, finite element equations that is used to describe the position of large deformable body position in reference system, was established. Finding out that Updated Lagrangian description of equation is more general than Total Lagrangian description, Therefore, the updated Lagrangian description method is used for this set of model parameters
2. Based on heat transfer equation and theories of elastic-plastic large deformation, considering mechanical equilibrium equations and energy balance equation, a thermo-mechanical coupled mathematics model was established. Obtained at beginning of each time step, obtain the current displacement increment amendments domain V and boundary S, and the Solution Principles between the incremental steps within Force balance and Energy balance. Comprehensive comparison of several methods for solving was made, proved the Newton-Raphson to be best, and a method best convergence criterion chosen to check convergence of the displacement.
3. According to constitutive equation of magnesium alloy AZ31 at high temperature, relying on interface program provided by Marc, using FORTRAN language to compile subroutine of the flow stress, for secondary development to the software. Magnesium alloy AZ31 of material models with change law of high-temperature flow stress is obtained.
4. The rolling force and torque in rolling process was simulated. Compared with the experiment results the simulation was almost the same as the experiment results, and verified its accuracy. Also found that two-dimensional model simulation results was more accurate than calculation of three-dimensional simulation results ,and it saved a lot of computing time and computing resources.
5. Based on 3-D and 2-D model, temperature field, temperature gradient, equivalent plastic strain, equivalent plastic strain rate and equivalent plastic stress field in rolling process were simulated. The distribution law of these parameters along the thickness and width, on the surface and in the core, was systematically and Comprehensively analysed. Overall temperature gradient near contact surface area is larger, but away from the area the result is smaller. deformation rate distribution at rolling region is consistent with the theoretical equations. Equivalent plastic stress distribution law along the thickness direction in according to rolling theory; along the width direction, the stress is smaller and more uniform distribution at center, the stress situation at edge is more complicated. Along the thickness direction, from surface to center the equivalent plastic strain is decreasing gradually; along the width direction, from center to edge strain increasing.
6. The effect of different technological parameters on rolling force, temperature field and Spread was studied. the Similarity of rolling force, temperature field and spread under different operating conditions was summarized. The result indicate that initial temperature and reduction rate have obvious influence on rolling force. As the reduction rate largen, the rolling fore is increasing. At high temperature rolling times, different rolling speed corresponds to a deformation resistance, following rolling speed increasing, the rolling force is becoming bigger, at the same time deformation resistance of material is harder. With friction coefficient increasing rolling force is becoming bigger, but the range is small. To spread, following reduction rate increasing, the spread is increasing. When B1= L, B2=.L, and between [B1,B2] interval, with plate width increasing the spread is becoming bigger. Under other conditions remain unchanged, with roller radius the spread also becomes big, and there is similar law between the spread and friction coefficient.
镁合金板带热轧过程中,精确地计算轧件内部的温度场和应力场分布是制定轧制工艺参数的关键,而在加工过程中,温度场与应力场是互相耦合的,温度场的结果直接影响应力场计算的准确性。为了分析该过程,本文采用大型非线性有限元商用软件MSC.Marc,根据实验设备参数,建立弹塑性有限元模型。利用热力耦合分析方法,模拟了AZ31镁合金的轧制过程。研究发现:
1.基于非线性有限元法基本原理,综合轧件在大变形过程中的应力应变规律,建立了用于描述大变形工件在参考系中位置的两类有限元方程,发现更新的拉格朗日描述方程较总的拉格朗日描述方程更具有普遍适用性,故本文中模型分析参数的设定选用更新的拉格朗日描述法。
2.基于传热方程和大变形弹塑性理论,结合轧件轧制过程中的力平衡方程和能量平衡方程,建立了热力耦合数学模型。得出了在每个时间增量步启动时,用当前的位移增量修正域V和边界S,在时间增量步内交替间增量步内交替迭代力平衡和能量平衡的求解规律,综合比较几种求解方法得出完全的Newton- Raphson方法迭代求解最好,收敛判据则选择位移检查收敛。
3.根据AZ31镁合金高温变形的本构方程,使用Marc软件的接口,采用FORTRAN语言编写了流变应力子程序。得到了AZ31镁合金高温流变应力变化规律的材料模型。
4.模拟了镁合金板带热轧过程中的轧制力和轧制力矩,与实验结果比较,验证了模型的正确性。同时发现二维模型模拟结果比三维模拟结果计算更精确,更节约大量的计算时间和计算资源。
5.基于三维和二维模型,模拟了板带热轧过程中的温度场、变形速率、等效塑性应力场和等效塑性应变等情况,较为全面、系统地分析了这些参量沿着轧件各个方向的分布规律。温度梯度在接触面附近较大,远离接触面的区域较小。轧制变形区域内变形速率数值大小的分布与理论方程描述情况一致。等效塑性应力场沿着轧件厚度方向的分布规律与应变理论相同;沿宽度方向,中心处的应力较小,大小分布较为均匀,边部的应力情况较为复杂。沿厚度方向,等效塑性应变从表面到中心逐渐减小;沿宽度方向,从中心到边部应变逐渐增大。
6.研究了不同工艺参数的改变对轧制力、温度场以及宽展的影响。发现轧制力受压下率和初始温度变化的影响较为明显,轧制力随压下率增大而变大,随初始温度升高而减小。高温轧制时,不同的轧制速度对应着轧件不同变形抗力,轧制速度越大,变形抗力也越大,材料就越难以屈服,轧制力越大。轧制力随摩擦系数的变大而增大,增大的幅度较小。对于宽展,随着压下率增大,宽展量也在增大。当B1=L,B2>L时,在[B1,B2]范围内,宽展量随着板宽的增大而变小。其他条件不变的情况下,随着轧辊半径的增大,宽展量也在增大;同样随着摩擦系数的增加,宽展增加。
Magnesium alloy strips and sheets are being widely used in aviation、aerospace、automotive industry、3C and many other fields. the research on making-technology of which has been the focus in whole word. Generally the alloy strips and sheets are produced by rolling method. If we could accurately calculate and match every technics parameter in the rolling process the deforming efficiency and quality of the sheets will be greatly improved. The strip hot rolling process is a complex problem that many variables interact each other, and also a nonlinear analysis which includes material nonlinear analysis, geometrical nonlinear Analysis、contactile nonlinear analysis and the like, both of them bring great hardship to the research. In recent years, with extensive application of simulation software and the increasing maturity of calculation technology,the thermo-mechanical coupled method has been introduced into software program to apply it to analyse the problem of sheet hot rolling .
In magnesium alloy strip hot rolling process, it is important to accurately calculate Distribution of temperature field and stress field in strip for designing rolling technology parameters. In fact, during the process temperature field and Stress field influence each other. In order to study and analysis this process, elastic-plastic finite element model was developed based on experiment equipment technology by MSC. Marc software. All process of magnesium alloy AZ31 sheet hot rolling are simulated by choosing the advanced thermo-mechanical coupled method. The simulated result detailed analysis was made too. The main contents are as following:
1. Based on the basic principle of nonlinear finite element method, comprehensively considering the Similarity of stress and strain distribution in large deformation of rolling piece process, finite element equations that is used to describe the position of large deformable body position in reference system, was established. Finding out that Updated Lagrangian description of equation is more general than Total Lagrangian description, Therefore, the updated Lagrangian description method is used for this set of model parameters
2. Based on heat transfer equation and theories of elastic-plastic large deformation, considering mechanical equilibrium equations and energy balance equation, a thermo-mechanical coupled mathematics model was established. Obtained at beginning of each time step, obtain the current displacement increment amendments domain V and boundary S, and the Solution Principles between the incremental steps within Force balance and Energy balance. Comprehensive comparison of several methods for solving was made, proved the Newton-Raphson to be best, and a method best convergence criterion chosen to check convergence of the displacement.
3. According to constitutive equation of magnesium alloy AZ31 at high temperature, relying on interface program provided by Marc, using FORTRAN language to compile subroutine of the flow stress, for secondary development to the software. Magnesium alloy AZ31 of material models with change law of high-temperature flow stress is obtained.
4. The rolling force and torque in rolling process was simulated. Compared with the experiment results the simulation was almost the same as the experiment results, and verified its accuracy. Also found that two-dimensional model simulation results was more accurate than calculation of three-dimensional simulation results ,and it saved a lot of computing time and computing resources.
5. Based on 3-D and 2-D model, temperature field, temperature gradient, equivalent plastic strain, equivalent plastic strain rate and equivalent plastic stress field in rolling process were simulated. The distribution law of these parameters along the thickness and width, on the surface and in the core, was systematically and Comprehensively analysed. Overall temperature gradient near contact surface area is larger, but away from the area the result is smaller. deformation rate distribution at rolling region is consistent with the theoretical equations. Equivalent plastic stress distribution law along the thickness direction in according to rolling theory; along the width direction, the stress is smaller and more uniform distribution at center, the stress situation at edge is more complicated. Along the thickness direction, from surface to center the equivalent plastic strain is decreasing gradually; along the width direction, from center to edge strain increasing.
6. The effect of different technological parameters on rolling force, temperature field and Spread was studied. the Similarity of rolling force, temperature field and spread under different operating conditions was summarized. The result indicate that initial temperature and reduction rate have obvious influence on rolling force. As the reduction rate largen, the rolling fore is increasing. At high temperature rolling times, different rolling speed corresponds to a deformation resistance, following rolling speed increasing, the rolling force is becoming bigger, at the same time deformation resistance of material is harder. With friction coefficient increasing rolling force is becoming bigger, but the range is small. To spread, following reduction rate increasing, the spread is increasing. When B1= L, B2=.L, and between [B1,B2] interval, with plate width increasing the spread is becoming bigger. Under other conditions remain unchanged, with roller radius the spread also becomes big, and there is similar law between the spread and friction coefficient.
引文
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