板材粘弹塑性软模成形有限元—无网格法耦合模型与模拟
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摘要
板材粘性介质压力成形与刚性模成形和气、液软模成形的不同之处在于成形过程中板材与软模之间具有明显的耦合变形特征，软模性能对板材变形有较大的影响，这种板材变形与软模体积变形之间的耦合变形解析求解很困难，借助于数值分析的手段对其进行研究是十分必要的。由于成形过程中软模变形量较大，使用有限元法容易出现网格畸变，软模体积变形网格重划既困难又影响计算精度。本文针对板材半固态粘性介质和固态聚氨酯软模成形提出了板材粘弹塑性软模成形有限元-无网格法耦合分析方法，对粘性介质粘弹塑性本构模型、板材有限元分析与软模无网格法分析之间的接触摩擦处理、粘性介质与板材间的粘附应力模型等进行了研究，编制了相应的耦合分析程序，对板材软模成形过程进行了数值模拟，并通过试验验证了模型和程序的有效性。
首先，提出采用有限元法和无网格法相耦合的方法分析板材软模成形过程，即板材弹塑性变形采用有限元法进行分析，软模体积变形采用无网格Galerkin法进行分析，两种方法相结合，可以充分发挥两种算法各自的优势。推导了板材弹塑性、半固态粘性介质软模粘弹塑性和固态软模超弹性本构方程，进而建立了基于更新拉格朗日列式的板材软模成形过程有限元-无网格法耦合分析列式，并通过计算实例对上述模型进行了验证。
其次，由于板材软模成形过程不仅存在板材与刚性凹模之间的接触，还包含了软模与板材这两种耦合变形体之间的接触，这也是板材软模成形数值模拟有别于传统刚性模冲压成形数值模拟的重要特征。分别针对板材与凹模之间的滑动摩擦，半固态粘性介质与板材之间的粘附作用以及固态软模与板材之间的接触摩擦建立相应模型，重点研究了板材与软模这两种不同类型离散方式的耦合变形体之间的界面接触处理方法。在多变形体耦合变形分析中采用静力显式算法避免了隐式算法中的多重迭代收敛问题，保证每一加载步长内变形体的变形和接触状态保持稳定，进而给出增量过程中板材和软模的应力和应变增量计算过程。
再次，对半固态粘性介质的粘弹塑性本构模型进行了研究。利用动态剪切流变仪对六种不同分子量（550000g/mol、600000g/mol、650000g/mol、700000g/mol、800000g/mol和900000g/mol）的粘性介质分别进行了振荡、蠕变回复和剪切粘度实验，得到了不同分子量粘性介质粘弹塑性本构模型的材料参数，建立了粘性介质分子量与粘弹塑性模型材料参数之间的关系式，为粘性介质在成形过程中变形行为的分析提供了依据。
最后，采用开发的板材粘弹塑性软模成形过程有限元-无网格法耦合分析程序对板材弹性软模胀形、聚氨酯超弹性软模胀以及不同分子量的粘性介质压力胀形形过程进行了数值模拟。通过板材弹性软模胀形的数值模拟，研究了有限元-无网格法耦合分析程序在处理软模体积大变形上的优势；选用1Cr18Ni9Ti不锈钢板材对聚氨酯软模胀形进行数值模拟，分析了板材固态聚氨酯软模胀形过程中不同胀形高度下板材的应变分布、壁厚分布规律，与试验结果进行对比验证了所开发的程序的可靠性。使用不同粘度的粘性介质对工业纯铝Al1060板材进行了粘性介质压力胀形数值模拟和试验研究，分析粘性介质压力胀形过程中不同粘度的粘性介质对于板材构形、应力应变分布、壁厚减薄等的影响，数值模拟和实验结果表明高粘度的粘性介质可以使应变最大值位置发生转移，提高了板材壁厚分布的均匀性。对圆锥形零件粘性介质压力成形过程的数值模拟和试验结果进行了对比，二者具有较好的吻合性。
Viscous pressure forming (VPF) is different from sheet rigid-die forming andgaseous or hydro forming process. Not only because of the coupled deformationcharacteristics between sheet metal and flexible-die in the forming process, but also theinfluence of flexible die’s properties on the formability of sheet metal. This coupleddeformation is difficult to solved analytically, it is necessary to utilize numerical analysismethod to make an in-depth study. Due to the large deformation of flexible-die in theforming process, it often leads to a mesh distortion when finite element method is used,remeshing for bulk forming of flexible-die is difficult and will affect the calculationaccuracy. In this paper, a coupled finite element and meshless method was proposed toanalyse viscous pressure forming and sheet metal polyurethane rubber forming. The keytechniques such as the visco-elasto-plastic constitutive model of viscous medium,frictional contact treatment between sheet metal and flexible-die and adhesive stressmodel between viscous medium and sheet metal were also studied. Based on the abovetheories, a coupled analysis program was developed to forecast sheet metal flexible-dieforming numerically. The validity of the model and forecast program was verifiedthrough experimental research.
First of all, a new numerical analysis method which coupled finite elementmethod and meshless method was proposed to analyse sheet visco-elasto-plasticflexible-die forming process. In this method, the elastoplastic deformation of sheetmetal was analyzed with finite element method and the bulk deformation of flexible-die was analyzed with element-free Galerkin method, it can make full use of theirrespective advantages of these two algorithms. The elasto-plastic constitutiveequation of sheet metal, visco-elasto-plastic constitutive equation of semisolidviscous medium and hyperelastic constitutive equation of solid polyurethane rubberwere given firstly. Then a coupled FEM-EFGM formulation of sheet flexible-dieforming process was established based on updated Lagrangian formulation, and itsvalidity was verified through numerical examples.
Secondly, it contains not only contact between sheet metal and die, but also contactbetween two coupled deformation bodies (flexible-die and sheet metal) in sheet flexible-die forming process, which is an important difference with rigid-die forming process.According to the sliding friction between the sheet metal and die, adhesive stressbetween semisolid viscous medium and sheet metal and frictional contact between solidflexibile-die and sheet, corresponding numerical models were established respectively.The interface contact treatment between sheet metal and flexible was a key problem because of different discrete ways of these two coupled deformation bodies. A staticexplicit algorithm was adopted to solve multi-body coupled deformation problems, thesize of the time step was controlled to keep the material state and contact state stable ineach loading step which can aviod the disadvantage of misconverged iteration in a static-implicit algorithm. The calculation of stress and strain increment of sheet metal andflexible-die in incremental process were also illustrated.
Thirdly, visco-elasto-plastic constitutive model of semi-solid viscous medium werestudied. Viscous mediums with six different molecular weights (550000g/mol,600000g/mol,650000g/mol,700000g/mol,800000g/mol, and900000g/mol) wereseparately carried on oscillation, creep-recovery and shear viscosity experiments byusing dynamic shear rheometer (DSR). Through analyzing the results of the experiment,visco-elasto-plastic constitutive model parameters of viscous mediums with differentmolecular weights were obtained. Furthermore, a relationship between molecular weightof different viscous mediums and visco-elasto-plastic constitutive model parameters wasestablished, it can provide a guide for analysing the deformation behavior of viscousmediums in viscous pressure forming process.
Finally, by using the coupled FEM-EFGM analysis program, sheet elastic flexible-die bulging, sheet polyurethane rubber bulging and viscous pressure bulging process withdifferent molecular weights were forecasted numerically. Viscous pressure bulgingprocesses of Al1060sheet with different viscosity viscous mediums were forecastednumerically and experimentally. The advantages of coupled FEM-EFGM program indealing with large bulk deformation were investigated through forecasting sheet elasticflexible-die bulging numerically. By forecasting1Cr18Ni9Ti stainless steel sheetpolyurethane rubber bulging process, the strain and wall-thickness distribution of bulgingparts were analyzed at different dome heights. Compared with experimental results, thevalidity of the coupled FEM-EFGM forecast program was obtained. The influence ofviscosity on the configuration, stress, strain distribution and thickness reduction ratio ofbulging parts were investigated in detail. Both the numerical forcast analysis and theexperimental result showed that high viscosity viscous medium can change the maximumstrain location and make a more uniform wall-thickness distribution. Viscous pressureforming processes of conical part were also forecasted by the coupled FEM-EFGMprogram, the experimental results and numerical ones were in good agreement.
首先，提出采用有限元法和无网格法相耦合的方法分析板材软模成形过程，即板材弹塑性变形采用有限元法进行分析，软模体积变形采用无网格Galerkin法进行分析，两种方法相结合，可以充分发挥两种算法各自的优势。推导了板材弹塑性、半固态粘性介质软模粘弹塑性和固态软模超弹性本构方程，进而建立了基于更新拉格朗日列式的板材软模成形过程有限元-无网格法耦合分析列式，并通过计算实例对上述模型进行了验证。
其次，由于板材软模成形过程不仅存在板材与刚性凹模之间的接触，还包含了软模与板材这两种耦合变形体之间的接触，这也是板材软模成形数值模拟有别于传统刚性模冲压成形数值模拟的重要特征。分别针对板材与凹模之间的滑动摩擦，半固态粘性介质与板材之间的粘附作用以及固态软模与板材之间的接触摩擦建立相应模型，重点研究了板材与软模这两种不同类型离散方式的耦合变形体之间的界面接触处理方法。在多变形体耦合变形分析中采用静力显式算法避免了隐式算法中的多重迭代收敛问题，保证每一加载步长内变形体的变形和接触状态保持稳定，进而给出增量过程中板材和软模的应力和应变增量计算过程。
再次，对半固态粘性介质的粘弹塑性本构模型进行了研究。利用动态剪切流变仪对六种不同分子量（550000g/mol、600000g/mol、650000g/mol、700000g/mol、800000g/mol和900000g/mol）的粘性介质分别进行了振荡、蠕变回复和剪切粘度实验，得到了不同分子量粘性介质粘弹塑性本构模型的材料参数，建立了粘性介质分子量与粘弹塑性模型材料参数之间的关系式，为粘性介质在成形过程中变形行为的分析提供了依据。
最后，采用开发的板材粘弹塑性软模成形过程有限元-无网格法耦合分析程序对板材弹性软模胀形、聚氨酯超弹性软模胀以及不同分子量的粘性介质压力胀形形过程进行了数值模拟。通过板材弹性软模胀形的数值模拟，研究了有限元-无网格法耦合分析程序在处理软模体积大变形上的优势；选用1Cr18Ni9Ti不锈钢板材对聚氨酯软模胀形进行数值模拟，分析了板材固态聚氨酯软模胀形过程中不同胀形高度下板材的应变分布、壁厚分布规律，与试验结果进行对比验证了所开发的程序的可靠性。使用不同粘度的粘性介质对工业纯铝Al1060板材进行了粘性介质压力胀形数值模拟和试验研究，分析粘性介质压力胀形过程中不同粘度的粘性介质对于板材构形、应力应变分布、壁厚减薄等的影响，数值模拟和实验结果表明高粘度的粘性介质可以使应变最大值位置发生转移，提高了板材壁厚分布的均匀性。对圆锥形零件粘性介质压力成形过程的数值模拟和试验结果进行了对比，二者具有较好的吻合性。
Viscous pressure forming (VPF) is different from sheet rigid-die forming andgaseous or hydro forming process. Not only because of the coupled deformationcharacteristics between sheet metal and flexible-die in the forming process, but also theinfluence of flexible die’s properties on the formability of sheet metal. This coupleddeformation is difficult to solved analytically, it is necessary to utilize numerical analysismethod to make an in-depth study. Due to the large deformation of flexible-die in theforming process, it often leads to a mesh distortion when finite element method is used,remeshing for bulk forming of flexible-die is difficult and will affect the calculationaccuracy. In this paper, a coupled finite element and meshless method was proposed toanalyse viscous pressure forming and sheet metal polyurethane rubber forming. The keytechniques such as the visco-elasto-plastic constitutive model of viscous medium,frictional contact treatment between sheet metal and flexible-die and adhesive stressmodel between viscous medium and sheet metal were also studied. Based on the abovetheories, a coupled analysis program was developed to forecast sheet metal flexible-dieforming numerically. The validity of the model and forecast program was verifiedthrough experimental research.
First of all, a new numerical analysis method which coupled finite elementmethod and meshless method was proposed to analyse sheet visco-elasto-plasticflexible-die forming process. In this method, the elastoplastic deformation of sheetmetal was analyzed with finite element method and the bulk deformation of flexible-die was analyzed with element-free Galerkin method, it can make full use of theirrespective advantages of these two algorithms. The elasto-plastic constitutiveequation of sheet metal, visco-elasto-plastic constitutive equation of semisolidviscous medium and hyperelastic constitutive equation of solid polyurethane rubberwere given firstly. Then a coupled FEM-EFGM formulation of sheet flexible-dieforming process was established based on updated Lagrangian formulation, and itsvalidity was verified through numerical examples.
Secondly, it contains not only contact between sheet metal and die, but also contactbetween two coupled deformation bodies (flexible-die and sheet metal) in sheet flexible-die forming process, which is an important difference with rigid-die forming process.According to the sliding friction between the sheet metal and die, adhesive stressbetween semisolid viscous medium and sheet metal and frictional contact between solidflexibile-die and sheet, corresponding numerical models were established respectively.The interface contact treatment between sheet metal and flexible was a key problem because of different discrete ways of these two coupled deformation bodies. A staticexplicit algorithm was adopted to solve multi-body coupled deformation problems, thesize of the time step was controlled to keep the material state and contact state stable ineach loading step which can aviod the disadvantage of misconverged iteration in a static-implicit algorithm. The calculation of stress and strain increment of sheet metal andflexible-die in incremental process were also illustrated.
Thirdly, visco-elasto-plastic constitutive model of semi-solid viscous medium werestudied. Viscous mediums with six different molecular weights (550000g/mol,600000g/mol,650000g/mol,700000g/mol,800000g/mol, and900000g/mol) wereseparately carried on oscillation, creep-recovery and shear viscosity experiments byusing dynamic shear rheometer (DSR). Through analyzing the results of the experiment,visco-elasto-plastic constitutive model parameters of viscous mediums with differentmolecular weights were obtained. Furthermore, a relationship between molecular weightof different viscous mediums and visco-elasto-plastic constitutive model parameters wasestablished, it can provide a guide for analysing the deformation behavior of viscousmediums in viscous pressure forming process.
Finally, by using the coupled FEM-EFGM analysis program, sheet elastic flexible-die bulging, sheet polyurethane rubber bulging and viscous pressure bulging process withdifferent molecular weights were forecasted numerically. Viscous pressure bulgingprocesses of Al1060sheet with different viscosity viscous mediums were forecastednumerically and experimentally. The advantages of coupled FEM-EFGM program indealing with large bulk deformation were investigated through forecasting sheet elasticflexible-die bulging numerically. By forecasting1Cr18Ni9Ti stainless steel sheetpolyurethane rubber bulging process, the strain and wall-thickness distribution of bulgingparts were analyzed at different dome heights. Compared with experimental results, thevalidity of the coupled FEM-EFGM forecast program was obtained. The influence ofviscosity on the configuration, stress, strain distribution and thickness reduction ratio ofbulging parts were investigated in detail. Both the numerical forcast analysis and theexperimental result showed that high viscosity viscous medium can change the maximumstrain location and make a more uniform wall-thickness distribution. Viscous pressureforming processes of conical part were also forecasted by the coupled FEM-EFGMprogram, the experimental results and numerical ones were in good agreement.
引文
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