粘弹性聚合物熔体注射成型模型化理论与数值模拟研究
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摘要
注射成型是聚合物的主要成型加工方法之一，成型过程中聚合物要经历熔体流动和固化等非等温、非平衡过程，由于聚合物的粘弹性，流动过程中建立的剪切应力、法向应力和大弹性形变在固化过程中不能完全松弛，在制品中形成残余应力和取向，对制品的机械和光学性能有着重要影响。为构造能够描述注射成型中聚合物所受热机历史与微观形态结构变化的物理和数学模型，预测残余应力和取向的变化及形成规律，本文对粘弹性聚合物熔体注射成型的模型化理论和数值模拟方法进行了研究，主要工作如下：
1．根据连续介质力学的基本概念和非平衡不可逆热力学基本理论，推导出可描述粘弹性流体大弹性形变、非等温和可压缩流动的Leonov本构模型，重点对不同条件下的Leonov模型进行了分析，建立了适用于不同情况的Leonov模型，并给出了确定模型参数的方法。
2．基于不同温度下松弛时间谱可以通过水平和垂直移动进行叠加的假设，建立了一种由动态流变数据计算水平活化能及垂直活化能，通过对动态流变曲线进行水平、垂直移动生成动态流变主曲线的方法，较采用经典时温叠加(只进行水平移动)生成主曲线的方法具有更广泛的适用性。
3．采用循环平均假设，忽略模壁温度的周期变化，将模具的传热简化为三维稳态热传导问题，考虑到注射模的结构特点(型腔为狭缝面，冷却孔细长)，建立了注射模三维温度场的边界积分方程及数值求解方法，开发出注射模三维温度场边界元计算软件。
4．建立了求解粘弹性聚合物熔体在薄壁型腔中充模／保压过程的数学模型，实现了注射成型过程中流动应力和分子取向建立及松弛过程的数值模拟，研究了熔体温度、模具温度和注射速率等工艺条件对分子冻结取向的影响，取得了与实验相符的结果。
本文研究工作得到国家“863”计划项目(2002AA336120)“基于模拟仿真的聚合物成型加工—微观结构演化—制品质量控制的研究”资助。
Injection molding is one of the most widely employed method of polymer processing. The flow of polymer melts in a cold cavity is a typical example of an unsteady, non-isothermal flow of viscoelastic fluids. Every particle in the material experiences a complex thermo-mechanic history which is important since the viscoelastic nature of the polymer results in development of shear stress and normal stress and large elastic deformation during flow with subsequent incomplete relaxation during the cooling stage. The resultant residual stresses, which determine the orientation in the final molded part, the orientation is important since it influences the mechanical and optical performance of the molded part. Because of the complexity of the process, numerical simulation is essential to understand the mechanism behind orientation. The objective of this thesis is to develop a numerical simulation model for the buildup and relaxation of stresses and molecular orientation in injection molding process of amorphous polymer. The following works have been finished:
1. In terms of continuum mechanics and nonequilibrium irreversible thermodynamics theories, compressible Leonov constitutive model is derived to describe large recoverable elastic strain development in non-isothermal flow of compressible viscoelastic melts. It is tempting to specify the model and then compare it to basic rheological tests in the hope that such a model will yield a good description of the nonlinear viscoelasticity of polymer melts. This sort of preliminary attempt was made for steady and small-amplitude oscillatory shear flow and stress relaxation following cessation of steady shear flow.
2. A unified method for handing the temperature dependent of both dynamic and steady rheological data is presented. Based on assumption that relaxation spectra derived from data at different temperature can be made to superimpose by vertical and horizontal shifts, vertical and horizontal activation energies are estimated independently from dynamic rheological data, then using the estimated activation energies, shift the raw data to reference temperature for extracting the temperature dependence.
3. An efficient numerical simulation has been developed for predicting 3D temperature profile of injection mold. In the simulation, the fluctuating component of mold wall temperature is considered to be negligibly small and mold heat transfer is reduced as three-dimensional static heat conduction; heat transfer within the molded-part is treated as transient one-dimensional heat
conduction. An modified three-dimensional boundary element method is used for solving cyclic-averaged temperature of the mold containing complex and thin cavity and circular cooling channels.
4. To simulate buildup and relaxation of flow-induced stresses and molecular orientation in injection molding process, A mathematical model is derived that describes the unsteady and non-isothermal flow of viscoelastic polymer melts in the thin wall mold cavity on the base of thin film approximation. By means of numerical simulation, the results are given in terms of residual stresses and associated birefringence in the molded part, as influenced by the processing conditions. The result indicates that, for a given polymer, the main factors affecting residual stresses and associated birefringence are flow rate and melt temperature.
This work is supported by the project of Research on the Polymer Processing volution of Micro structureart Quality Control Eased on Numerical Simulation, supported by The National High Technology Research and Development Program (863 Program,2002AA336120).
1．根据连续介质力学的基本概念和非平衡不可逆热力学基本理论，推导出可描述粘弹性流体大弹性形变、非等温和可压缩流动的Leonov本构模型，重点对不同条件下的Leonov模型进行了分析，建立了适用于不同情况的Leonov模型，并给出了确定模型参数的方法。
2．基于不同温度下松弛时间谱可以通过水平和垂直移动进行叠加的假设，建立了一种由动态流变数据计算水平活化能及垂直活化能，通过对动态流变曲线进行水平、垂直移动生成动态流变主曲线的方法，较采用经典时温叠加(只进行水平移动)生成主曲线的方法具有更广泛的适用性。
3．采用循环平均假设，忽略模壁温度的周期变化，将模具的传热简化为三维稳态热传导问题，考虑到注射模的结构特点(型腔为狭缝面，冷却孔细长)，建立了注射模三维温度场的边界积分方程及数值求解方法，开发出注射模三维温度场边界元计算软件。
4．建立了求解粘弹性聚合物熔体在薄壁型腔中充模／保压过程的数学模型，实现了注射成型过程中流动应力和分子取向建立及松弛过程的数值模拟，研究了熔体温度、模具温度和注射速率等工艺条件对分子冻结取向的影响，取得了与实验相符的结果。
本文研究工作得到国家“863”计划项目(2002AA336120)“基于模拟仿真的聚合物成型加工—微观结构演化—制品质量控制的研究”资助。
Injection molding is one of the most widely employed method of polymer processing. The flow of polymer melts in a cold cavity is a typical example of an unsteady, non-isothermal flow of viscoelastic fluids. Every particle in the material experiences a complex thermo-mechanic history which is important since the viscoelastic nature of the polymer results in development of shear stress and normal stress and large elastic deformation during flow with subsequent incomplete relaxation during the cooling stage. The resultant residual stresses, which determine the orientation in the final molded part, the orientation is important since it influences the mechanical and optical performance of the molded part. Because of the complexity of the process, numerical simulation is essential to understand the mechanism behind orientation. The objective of this thesis is to develop a numerical simulation model for the buildup and relaxation of stresses and molecular orientation in injection molding process of amorphous polymer. The following works have been finished:
1. In terms of continuum mechanics and nonequilibrium irreversible thermodynamics theories, compressible Leonov constitutive model is derived to describe large recoverable elastic strain development in non-isothermal flow of compressible viscoelastic melts. It is tempting to specify the model and then compare it to basic rheological tests in the hope that such a model will yield a good description of the nonlinear viscoelasticity of polymer melts. This sort of preliminary attempt was made for steady and small-amplitude oscillatory shear flow and stress relaxation following cessation of steady shear flow.
2. A unified method for handing the temperature dependent of both dynamic and steady rheological data is presented. Based on assumption that relaxation spectra derived from data at different temperature can be made to superimpose by vertical and horizontal shifts, vertical and horizontal activation energies are estimated independently from dynamic rheological data, then using the estimated activation energies, shift the raw data to reference temperature for extracting the temperature dependence.
3. An efficient numerical simulation has been developed for predicting 3D temperature profile of injection mold. In the simulation, the fluctuating component of mold wall temperature is considered to be negligibly small and mold heat transfer is reduced as three-dimensional static heat conduction; heat transfer within the molded-part is treated as transient one-dimensional heat
conduction. An modified three-dimensional boundary element method is used for solving cyclic-averaged temperature of the mold containing complex and thin cavity and circular cooling channels.
4. To simulate buildup and relaxation of flow-induced stresses and molecular orientation in injection molding process, A mathematical model is derived that describes the unsteady and non-isothermal flow of viscoelastic polymer melts in the thin wall mold cavity on the base of thin film approximation. By means of numerical simulation, the results are given in terms of residual stresses and associated birefringence in the molded part, as influenced by the processing conditions. The result indicates that, for a given polymer, the main factors affecting residual stresses and associated birefringence are flow rate and melt temperature.
This work is supported by the project of Research on the Polymer Processing volution of Micro structureart Quality Control Eased on Numerical Simulation, supported by The National High Technology Research and Development Program (863 Program,2002AA336120).
引文
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128．吴子牛，计算流体力学基本原理，科学出版社，北京，2001
129．瞿金平，胡汉杰，聚合物成型原理及成型技术，化学工业出版社，北京，2001
130．冯康等，数值计算方法，国防工业出版社，北京，1978