高速注射纤维增强聚合物取向和相形态的建模-模拟及机理分析

Fiber-reinforced polymer plays a very important role in the development of technology and industry. Exploring the formation mechanism, quantitative description and control technique of its orientation and phase morphology is a frontier of manufacturing industry. This project aims at the modeling, simulation and mechanism analysis of the orientation and phase morphology of fiber-reinforced polymer during high speed injection. First, for the orientation, we will solve the problems of how to track the front interface of the melt accurately and how to model the orientational motions of mesoscopic fiber and microscopic macromolecules. Through solving these problems, a multi-scale model for predicting orientations will be established by coupling the macroscopic injection, mesoscopic fiber orientation and microscopic macromolecules orientation. Because of the strong convection, high elasticity, including moving interface and multi-scale coupling properties of the multi-scale model, we will research on the stabilization technology, high resolution scheme and efficient solving strategy in proposing numerical method for the model. Based on simulation results, the possible rule and mechanism of the predicted orientation will be investigated. Second, for the phase morphology, we will analysize the effects of orientation on crystal nucleation and growth, give the corresponding quantitative description, and establish a phase transition model upon orientation based on phase -field method by deducing the proper initial boundary conditions and model parameters. For dealing with huge amount of calculation, an efficient numerical method for the phase transition model will be proposed. Then, the influence rule and mechanism of orientation on phase transition will be investigated. Through the researches of this project, a complete set of theoretical analysis model and numerical simulation method will be provided, which will advance the cognition on orientation and phase transition of fiber-reinforced polymer during high speed injection.

纤维增强聚合物材料对科技和工业的发展有着十分重要的作用。探索其取向和相形态的形成机理、定量描述和控制技术是加工工业发展的前沿。本项目研究高速注射中纤维增强聚合物取向和相形态的理论建模、数值计算及机理分析。取向方面：解决熔体前沿界面的准确追踪、介观纤维和微观大分子的取向建模，构建宏观充填流动和微介观取向耦合的多尺度模型；针对模型强对流、高弹性、包含运动界面和多尺度耦合等特点，研究数值求解的稳定化技术、高分辨率格式和高效求解方案，实现取向预测并分析潜在规律及机理。相形态方面：分析取向对晶体成核和生长的影响，给出定量数学描述，并基于相场方法，推导相应的初边值条件及模型参数，建立取向基础上的相形态演化模型；面对巨大计算量，提出高效的模型求解方法，探索取向对相形态的影响规律及机理。通过研究，将提供一套完整的理论分析模型和数值模拟方法，推进对高速注射纤维增强聚合物取向结构和相形态演化规律和机理的认识。

纤维增强聚合物在加工中形成的取向结构和相形态对材料的使用性能具有决定性影响。本项目采用数值模拟手段，研究了高速注射成型中纤维增强聚合物的取向结构和相形态演化，解决了模拟中涉及的一系列模型和算法问题。主要研究结果有：1）针对纤维增强聚合物的取向结构建模，采用Jerry轨道模型描述介观纤维取向，FENE-P哑铃模型描述微观大分子取向，基于level-set的气-液两相流模型描述充填流动，建立了高速注射过程中纤维增强聚合物取向结构演化的数学模型；为获得准确的纤维曳力计算式，建立了一套颗粒流模拟的三维LBM并行求解算法，得到了新的曳力关联式，并通过动态粗颗粒化大大提高了曳力的计算效率。2）针对取向结构的数值模拟，采用分裂格式将粘弹两相一体化模型解耦为若干子方程，发挥FEM和DG两种方法的各自优势，实现了较高Wi数下粘弹流动问题的稳定、高效求解；结合半拉格朗日方法和无网格方法，提出了强对流问题求解的SL-EFG方法，在大时间步长下获得了稳定的数值结果。3）针对取向结构上的相形态演化建模，以分子的最优取向和拉伸量为桥梁，建立了取向基础上的晶体成核模型；考虑到取向结构会导致晶体的各向异性生长，推导了新的各向异性界面能函数，得到了取向结构上的相形态演化模型；采用粗颗粒化的分子动力学方法探索了粗糙晶体表面对流体的微观结构、流变学性质和动力学行为的影响。4）针对相形态演化的数值模拟，基于凸分裂、IEQ、SAV等发展了多种具有二阶精度的无条件能量稳定数值格式，并给出了理论证明和数值算例验证；利用泰勒公式的局部逼近特性，提出了一种移动泰勒多项式逼近方法，降低了相场方程求解中高阶导数的逼近难度；最后，通过分解简化，分阶段实现了高速注射纤维增强聚合物取向和相形态演化的初步数值模拟。通过本项目研究，提供了一套理论分析模型和数值模拟方法，可用于高速注射纤维增强聚合物取向结构和相形态演化的定性分析，揭示一些演化规律，具有一定的实用价值。