含纤聚合物充模过程的多尺度数学模型研究与过程模拟

发布时间：2018-12-11 11:15

【摘要】：含纤聚合物基复合材料制品具有广泛的应用与发展空间,但是目前人们对于含纤聚合物基复合材料的研究还不完善。首先,大部分研究集中在成品制件的力学性能测试上,且多是采用实验方法,对于含纤聚合物基复合材料成型过程的数值模拟研究不多。其次,充模过程是注塑成型的主要阶段,伴随相当复杂的物理过程,即固化、体积收缩及可能的结晶过程。目前虽有文献建立了聚合物熔体充填过程的数学模型并进行了数值模拟,但是对于含纤聚合物基复合材料的充模过程,都忽略了相变的产生。再次,高分子材料的性能与注塑成型过程中聚合物的微观结构关系密切,然而研究者大多只注意注塑成型过程中熔体及纤维的宏观行为,很少研究注塑成型过程中熔体及纤维的微观行为。迄今为止,还没有一个全面而准确的描述带有相变充填过程的多尺度数学模型。本文从数学建模的角度出发,建立了带有相变的含纤聚合物基复合材料充模过程的多尺度数学模型,并采用相应的数值方法进行求解,成功地模拟了黏弹性熔体以及含纤黏弹性熔体在成型过程中壁面附近的凝固现象及型腔内熔接线的形成,并对熔体充模流动过程中的一些流体动力学、热力学问题、纤维运动和取向、应力变化以及微观分子链构象信息等进行了研究,得到了与实验定性一致的计算结果。本文的主要工作如下:1、基于相场模型建立了一种新的Level Set方法做为本文充填过程中追踪运动界面的方法,并给出了相应的高精度求解格式。与传统的Level Set方法相比,该方法将Level Set方程与重新初始化方程合并成一个方程,在极大地减少计算量的同时,可以更准确地追踪运动界面。2、提出了一个对型腔内熔体和气体都适用的修正的焓模型来描述充模过程中的相变,进而建立了黏(弹)性流体在充模过程中带有相变的气-液两相宏观模型。采用基于同位网格的有限体积法对控制方程进行离散并求解,并通过非等温平板收缩流、液滴下落、溃坝等基准问题验证了模型及算法的有效性。3、建立了带有相变的含纤聚合物基复合材料充模的宏观(流动)-介观(纤维)模型,并采用基于同位网格的有限体积法对该模型进行离散并求解,成功模拟了含纤聚合物基复合材料的充填过程。对充填过程中各物理量的变化、凝固现象、纤维取向等问题进行了研究,得到了与实验定性一致的结果。4、建立了带有相变的含纤聚合物基复合材料充模过程的宏观(流动)-介观(纤维)-微观(分子链)多尺度模型。宏观流动的物理特性由Navier-Stokes方程描述,介观尺度的纤维运动用牛顿运动定理来描述,微观分子链的信息用Brown构型场方法来获得。采用基于同位网格的有限体积法对模型进行离散并求解,成功模拟了含纤聚合物基复合材料的充填过程,得到了宏观物理特性、介观纤维取向与微观分子链构象等信息。
[Abstract]:Fiber-containing polymer matrix composites have a wide range of applications and development space, but the research of fiber-containing polymer-based composites is not perfect. First of all, most of the research focused on the mechanical properties of the finished parts, and most of the experimental methods are used, and there are few numerical simulation studies on the molding process of polymer matrix composites containing fiber. Secondly, the filling process is the main stage of injection molding, accompanied by quite complex physical processes, that is, solidification, volume shrinkage and possible crystallization process. Although some literatures have established the mathematical model of polymer melt filling process and carried out numerical simulation, but for the filling process of polymer matrix composites containing fiber, the generation of phase transition has been neglected. Thirdly, the properties of polymer materials are closely related to the microstructure of polymer during injection molding. However, most researchers only pay attention to the macroscopic behavior of melt and fiber during injection molding. The microscopic behavior of melt and fiber during injection molding is seldom studied. Up to now, there is no comprehensive and accurate multi-scale mathematical model with phase change filling process. In this paper, from the point of view of mathematical modeling, a multi-scale mathematical model of the filling process of fiber polymer matrix composites with phase transition is established, and the corresponding numerical method is used to solve the model. The solidification phenomena near the wall and the formation of weld lines in the cavity during the molding process of the viscoelastic melt and the fibrillar viscoelastic melt are successfully simulated, and some hydrodynamic and thermodynamic problems during the filling process of the melt are discussed. The motion and orientation of the fiber, the stress change and the conformation information of the micro molecular chain were studied, and the calculated results were in agreement with the experimental results qualitatively. The main work of this paper is as follows: 1. Based on the phase field model, a new Level Set method is established as a method to track the moving interface in the filling process, and the corresponding high precision solution scheme is given. Compared with the traditional Level Set method, this method combines the Level Set equation and the reinitialization equation into one equation, which can greatly reduce the computational cost and track the motion interface more accurately. A modified enthalpy model suitable for both melt and gas in the cavity is proposed to describe the phase transition during the filling process, and a gas-liquid two-phase macroscopic model with phase transition in the filling process of the viscous (elastic) fluid is established. The control equation is discretized and solved by the finite volume method based on the same grid. The validity of the model and the algorithm is verified by the datum problems such as non-isothermal plate shrinkage flow, drop and dam-break. A macroscopic (flow) mesoscopic (fiber) model for the filling of fiber polymer matrix composites with phase transition is established. The model is discretized and solved by using the finite volume method based on the in-situ grid. The filling process of polymer matrix composites containing fiber was successfully simulated. The changes of physical quantities, solidification phenomena and fiber orientation during filling are studied. The results are consistent with the experimental results. A macroscopic (flow)-mesoscopic (fiber)-microcosmic (molecular chain) multi-scale model for the filling process of fiber containing polymer matrix composites with phase transition was established. The physical properties of macroscopic flow are described by Navier-Stokes equation, the mesoscopic fiber motion is described by Newton's motion theorem, and the information of micro molecular chain is obtained by Brown configuration field method. The model was discretized and solved by using the finite volume method based on the same grid. The filling process of polymer matrix composites containing fiber was successfully simulated. The information of macroscopic physical properties, mesoscopic fiber orientation and micro molecular chain conformation were obtained.
【学位授予单位】：太原科技大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TQ317;TB33

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