Fiber orientation is decisive for the mechanical properties and thus for the performance of composite materials. During manufacturing, variations in material and process parameters can significantly influence the exact fiber orientation. We employ multilevel polynomial surrogates to model the propagation of uncertain material properties in the injection molding process. To ensure reliable uncertainty quantification, a key focus is deriving novel error bounds for statistical measures of a quantity of interest, computed via these surrogates. To verify these bounds, we conduct numerical experiments using the Cross-WLF viscosity model alongside the Hagen-Poiseuille flow in a rectangular channel. In particular, the impact of uncertainties in fiber length and matrix temperature on the fractional anisotropy of fiber orientation is investigated. The Folgar-Tucker equation and the improved anisotropic rotary diffusion model are used, incorporating recently established analytical solutions of these models as part of our verification. Our results demonstrate that the investigated method significantly improves upon standard Monte Carlo estimation, while also providing error guarantees. These findings offer the first step toward a reliable and practical tool for optimizing fiber-reinforced polymer manufacturing processes in the future.

翻译：纤维取向对复合材料的力学性能具有决定性影响，进而决定其整体性能。在制造过程中，材料与工艺参数的波动会显著影响纤维的精确取向。本研究采用多层多项式代理模型来模拟注射成型过程中不确定材料特性的传播。为确保可靠的不确定性量化，一个关键重点是针对通过此类代理模型计算得到的关注量统计量，推导其新颖的误差界。为验证这些误差界，我们采用Cross-WLF粘度模型结合矩形通道中的Hagen-Poiseuille流进行数值实验。特别地，研究了纤维长度和基体温度的不确定性对纤维取向分数各向异性的影响。研究中使用了Folgar-Tucker方程和改进的各向异性旋转扩散模型，并将这些模型最新建立的分析解作为验证的一部分。结果表明，所研究的方法相较于标准蒙特卡洛估计有显著改进，同时提供了误差保证。这些发现为未来开发可靠且实用的纤维增强聚合物制造工艺优化工具迈出了第一步。