【作者】 王伟；

【导师】 李锡夔；

【作者基本信息】 大连理工大学 ， 计算力学， 2010， 博士

【摘要】 高分子成型加工过程中所涉及的应力场、压力场、温度场和化学反应效应不仅决定制品的外观、形状和质量,而且对分子链结构、超分子结构和织态结构的形成和演变具有极其重要的影响。成型加工中由流动而诱发的高分子结晶及其取向可显著提高制品的力学和光学性能。但另一方面,加工过程中时常出现的不稳定流动状态,将导致挤出物表面呈鲨鱼皮状或熔体破裂、共挤出物界面不稳定、注射制品表面有虎皮纹等影响最终制品性能和外观,因而是亟需解决的产品质量问题。研究高分子材料成型加工中的流动过程,不仅对优化工艺条件、模具结构、挤出口模、机头结构,甚至对挤出机或注射成型机的螺杆等结构设计、对节约能耗、降低成本、提高产品竞争力都起着至关重要的作用。因此,对高分子黏弹性流体流动的模拟和分析具有重要的工程实际意义。一般,高分子加工过程是在三维非等温情况下进行的,并且材料在一些高应变和高应变率区域受到拉伸和剪切的双重作用,呈现复杂的流变行为和高度的非线性特征。另外,流动分析中经常遇到具有尖角的模具或口模,这些几何奇异点容易导致高分子流体产生应力奇异行为,从而诱发不稳定流动；同时,一些加工过程,例如注塑充填过程中还要考虑材料自由面或多组分界面的追踪,这些都会给数值模拟黏弹性流动带来很大的挑战。对成型加工过程中高分子流变行为的模拟研究,可为优化工艺条件、提高产品性能和更好理解高分子流体动力学提供科学依据,从而在高聚物结构—加工—产品三者之间起到桥梁作用,为高分子熔体加工的多尺度或跨尺度模拟,产品的高性能化奠定基础。本研究用基于有限增量微积分(FIC)过程的压力稳定化迭代分步算法和DEVSS/SU方法,采用近年发展的能够较好描述支化高分子熔体的本构模型(XPP模型、PTT-XPP模型、MDCPP模型以及作者提出的S-MDCPP模型)模拟了高分子加工过程中常遇到的收缩流和挤出胀大流问题,以及非等温非牛顿黏性流体注塑充填过程中熔体的流动行为等,分析了数值模拟这些工程问题所涉及的难点,提出了解决对策,为进一步发展高效、健壮的数值算法提供新的思路。同时,基于数值结果分析了挤出胀大流动中存在的不稳定流动状态,为解决类似产品质量问题提供科学依据和对策。为了能准确描述成型加工中高分子熔体复杂的流变行为,本研究系统总结和分析了非牛顿黏性本构模型和黏弹性本构模型,指出了它们的局限性和不足；同时重点考察了近年由Pom-Pom分子理论发展的一些新的本构模型,如Pom-Pom模型、XPP模型、修正的XPP模型,PTT-XPP模型和DCPP模型。从数值模拟和试验研究的文献报道看,这些新的本构模型在一定程度上体现了高分子的拓扑结构,能较好地反映真实支化高分子熔体的复杂流变行为,但尚存在一些如解的唯一性和收敛性等数值求解困难和正确再现流变学现象的缺陷。因此,本文进一步提出了一个新的能方便地在现有程序框架中实现的本构模型—S-MDCPP模型,该模型克服了现有XPP、修正的XPP、DCPP等模型的一些缺点,如解的不唯一性、过度剪切变稀行为等。该模型的预测能力通过平面4：1收缩流标准问题进行了考核,发现其具有良好的数值稳定性：并且能够捕捉在高剪切和高拉仲速率下的真实流变行为,而XPP和PTT-XPP模型只能分别较好地捕捉在高剪切或高拉伸速率下的流变行为。此外,用S-MDCPP模型模拟了支化高分子熔体的挤出胀大行为,发现口模出口附近的剪切应力和主链拉伸最大,并从大分子滑移和松弛机理上揭示了可能引起挤出不稳定流动的现象。采用被许多学者认为能较好描述支化高分子熔体流动特性的XPP模型模拟了高分子加工过程中常遇到的收缩流问题,并详细讨论了不同Weissenberg数和XPP模型中不同材料参数对收缩流场的影响,可视化地给出了不同支化程度的高分子熔体在收缩流场中的拉伸分布情况。此外,还应用PTT模型模拟了高分子熔体的挤出胀大行为,数值结果与相关文献的试验结果吻合较好,从而验证了本文所采用算法的有效性和可靠性；并进一步讨论和分析了挤出过程中可能引起不稳定流动的原因,为深刻理解挤出过程中畸形挤出物的形成机理提供了有益的帮助。最后,分别采用修正的Cross-Arrhenius模型和Moldflow二阶黏度模型描述LLDPE熔体的流变行为,模拟了该熔体在非等温情况下的注塑充填流动过程；并设计了相应的注塑短射试验。由任意的拉格朗日—欧拉(ALE)有限元方法模拟非等温情况下非牛顿黏性流体的充填结果与注塑短射试验结果比较看,发现本文采用ALE方法追踪自由面的形状和位置与试验结果比较一致。充填结束时,模拟预测的充填时间与试验结果吻合较好。此外,还给出了不同充填量时流场中的速度、压力和温度分布以及不同横截面上的水平速度和温度分布；并得到了充填结束时,熔体碰壁后的速度分布。不同横截面上的速度和温度分布与相关文献对非牛顿黏性流体非等温流动研究得出的结果一致。这些依据表明本文所采用的ALE有限元方法能准确、可靠地追踪充填过程中的自由面位置和形状,为将来把该方法拓展到三维注塑充填分析奠定了基础。更多还原

【Abstract】 The stress, pressure and temperature fields as well as the effect of chemical reaction in polymer processes not only affect the appearance, shape and quality of final products, but also have great influences on the structures of molecule chain, supermolecule, the texture structure and their evolutions. The flow-induced crystallization and its orientation in polymer processing may improve the mechanical and optical properties of products. On the other hand, the flow instabilities which often occur in polymer processing will result in the deterioration of finished products in their properties and appearance, such as the sharkskin, melt fracture, the interface instability observed in coextrusion flows, the tiger strips on the surface of injection molding products, etc. and become crucial issues to be solved in order to ensure the product qualities. The studies of polymeric flow in polymer processing are not only related to the optimizations of processing conditions, die or mould, extrusion channel, along with the structure design of screw of extruder or injection molding machine, but also play important roles in reducing the energy consuming and the cost of production, so as to improve the competition ability of production. In one word, it is of importance to perform numerical simulation and analysis of polymer viscoelastic flow in the polymer industrial practice.In general, polymer processes exhibit complex rheological behavior and strong nonlinear characteristics, they are often in three dimension non-isothermal cases and the materials undergo elongation and shear deformations in high strain and strain rate areas. It is noted that the sharp corner of die or mould can often induce stress singularity and lead to flow instabilities. In addition, to trace moving free surfaces or moving interfaces among different melted components in some polymer processes, for example the injection mould filling process, particularly for viscoelastic flows, will bring great challenges to the numerical simulations. The modeling of macromolecule rheological behavior in polymer processing will provide the scientific bases for deep understanding the dynamics of polymeric fluid flows, optimizing technological conditions and improving the qualities of the polymer products. Hence, it bridges among the structure of the polymer, processing and product quality, and establishes a sound foundation for high-performance polymer products based on micromechanically-based and multiscale numerical simulations.The pressure-stabilized iterative fractional step algorithm based on the finite increment calculus (FIC) procedure, and the discrete elastic viscous stress splitting (DEVSS) using the inconsistent streamline-upwind (SU) method are applied in the present investigation. The XPP, PTT-XPP, MDCPP models recently developed and widely used for modeling viscoelastic behaviors of polymer melts and the S-MDCPP (Single/Simplified Modified Double Convected Pom-Pom) model proposed by the author are adopted for constitutive modeling of the contraction viscoelastic flow and extrusion swell flow in the present work. In addition, the non-isothermal non-Newtonian fluid in mold filling process is investigated. The typical difficulties encountered in modeling these engineering projects are discussed and some schemes are put forward, so as to develop the efficient and robust algorithms. Furthermore, according to the numerical results, the extrusion swell flow instabilities are analyzed in order to provide the scientific bases to solve the problems of product quality.To accurately describe the complex rheological behavior of polymer melts during the processing, the constitutive models of the generalized Newtonian and viscoelastic fluids are summarized and investigated in the present work. Meanwhile, the shortcomings and limitations of these models are identified. Particularly, some new constitutive equations recently derived from the Pom-Pom molecular theory, such as the Pom-Pom model, XPP, modified XPP, PTT-XPP and DCPP models are introduced and investigated in detail. From the numerical and experimental results reported in the literature for these new models, one will find that they may reflect the actual topological structure of branched polymer and reproduce well the complex rheological behavior of realistic branched polymer melts. However, they still, more or less, suffer from the difficulties in the uniqueness and convergence of the numerical solution procedure and the defects in the correctly reproducing the rheological phenomena in the numerical simulation. Hence, a new constitutive model, S-MDCPP (Single/Simplified Modified Double Convected Pom-Pom) model, which is conveniently implemented in the framework of the existing computer codes used for the simulation is developed in this study. The S-MDCPP model eliminates some shortcomings of the existing XPP, modified XPP and DCPP models, such as the multi-solution problem, excessive shear-thinning behavior, and so forth. The capability of this model in the numerical prediction is also investigated by means of the benchmark test problem of the planar 4:1 contraction flow. It is noted that the present model demonstrates good numerical stability and is capable of capturing real rheological behaviors under both high shear and elongational rates while the XPP and PTT-XPP models can only well capture those rheological behaviors in high shear or elongational rates respectively. Additionally, the extrusion swell flow of branched polymer melts is numerically simulated by using the S-MDCPP model. It is found that the maximum shear stress and stretch of backbone occur at the places near the die exit. In addition, the extrusion instability is explained and discussed from the macromolecule slip and stress relaxation mechanisms points of view. The XPP model, which is recognized to be able to well describe the flow characters of the branched polymer melts, is adopted to numerically simulate the planar contraction flow often encountered in the polymer processing in the present study.The influences of Weissenberg number and the material parameters of the XPP model on the flow characters exhibited in the contraction flow are discussed, and the distributions of the backbone stretch of branched polymer with different end arms are visualized. Moreover, the extrusion swell behavior of the polymer melts modeled by the PTT constitutive equation is simulated and the obtained numerical results are in good agreement with the experimental ones reported in the literature. Thus, the reliability of the algorithms adopted in this investigation is validated. Furthermore, the causes of the flow instability occurred in the extrusion processing are explicated for better understanding to the mechanism of occurrence of abnormal extruded products.Finally, the linear low density polyethylene (LLDPE) melts are described by the modified Cross-Arrhenius model and the Moldflow second order model, respectively, and the non-isothermal injection mold filling flows are simulated. Additionally, the injection short shots are performed so as to verify the locations and shape of the melts front obtained by the arbitrary Lagrangian-Eulerian (ALE) finite element simulation for the non-isothermal filling process. It is shown that the predicted locations and shape of the melts front are in good agreement with the experiment, and the time spent to complete the filling and predicted by the ALE finite element method is consistent with the experimental result. Moreover, the distributions of the horizontal velocity, pressure and temperature at different filling stages as well as the distributions of the horizontal velocity and temperature at various cross sections are given, which agree well with the results reported in the literatures. The distribution of the horizontal velocity at the time when the melts front completely reaches the wall of the mould cavity, i.e. at the end of the filling, is also given. The numerical results validate the reliability, accuracy and robustness of the ALE-based finite element algorithm employed in the present work, particularly in tracing the moving free surface for the injection filling process, and provide a sound base for further development of the present work to the three dimension injection molding process.更多还原