Purpose

The orientation behavior of fiber is of great significance in improving the performance of fiber-reinforced polymer products. Generally, the Folgar–Tucker equation can accurately describe the variation of orientation vector of fiber, whereas the stability of numerical algorithms was the major challenge. This paper aims to propose an accurate, stable algorithm to solve the Folgar–Tucker equation for the fiber orientation behavior.

Design/methodology/approach

First, the mismatch problem between the strain rate and the pressure field was solved by using the integral transformation method. Then, an accurate, stable algorithm to solve the Folgar–Tucker equation based on the invariant-based optimal fitting method was proposed. The equation was discretized by finite element/finite difference method, and the Lagrange multiplier method was applied to ensure stability.

Findings

The proposed algorithm is proven to accurately and steadily coincide with the experimental results for different cases, including the fiber orientation behaviors under combined flow field, rectangular sheet, three-dimensional computed tomography imaging of tensile specimen and box cases.

Originality/value

The fiber orientation behavior during the injection molding can be accurately predicted, which plays a significant role in determining the mechanical properties of products.

中文翻译：

---

纤维取向行为的实验研究和建模研究

目的

纤维的取向行为对提高纤维增强聚合物产品的性能具有重要意义。通常，Folgar-Tucker 方程可以准确地描述纤维取向向量的变化，而数值算法的稳定性是主要挑战。本文旨在提出一种准确、稳定的算法来求解纤维取向行为的 Folgar-Tucker 方程。

设计/方法/方法

首先，利用积分变换方法解决了应变率与压力场的不匹配问题。然后，提出了一种基于不变量的最优拟合方法来求解Folgar-Tucker方程的准确、稳定的算法。方程采用有限元/有限差分法离散，并采用拉格朗日乘子法保证稳定性。

发现

该算法被证明与不同情况下的实验结果准确、稳定地吻合，包括组合流场下的纤维取向行为、矩形片、拉伸试样的三维计算机断层扫描成像和箱体情况。

原创性/价值

可以准确预测注塑过程中的纤维取向行为，这对决定产品的机械性能起着重要作用。