The cross-section of an injection-molded plate of foamed long glass fiber reinforced polypropylene was analyzed using scanning electron microscopy. The distribution of the glass fiber orientations and the microcellular structure in the thickness direction were also studied. A multilayer representative volume element was constructed based on the fiber orientation tensors and the cell distribution. Nested and two-step homogenization methods based on the Mori–Tanaka and Voigt models were used to homogenize each layer of the representative volume element. Finally, classic laminate theory was used to obtain the effective elastic modulus of the material. The computed elastic moduli of the single-layer and multilayer representative volume element models with different loading directions predicted by the homogenization and finite element methods were compared with the experimental results. We found that the constructed multilayer representative volume element model can predict the elastic moduli of the foamed glass fiber reinforced polypropylene effectively and that the predicted results were accurate and stable.

中文翻译：

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泡沫长玻纤增强聚丙烯的有效弹性模量：实验与计算

使用扫描电子显微镜分析了泡沫长玻璃纤维增​​强聚丙烯的注射成型板的横截面。还研究了玻璃纤维取向的分布和厚度方向的微孔结构。基于纤维取向张量和单元分布构建了多层代表性体积单元。基于 Mori-Tanaka 和 Voigt 模型的嵌套和两步均质化方法用于均质化代表性体积元素的每一层。最后，使用经典的层压理论来获得材料的有效弹性模量。通过均质化和有限元方法预测的具有不同加载方向的单层和多层代表性体积元模型的计算弹性模量与实验结果进行了比较。我们发现构建的多层代表性体积元模型可以有效地预测泡沫玻璃纤维增​​强聚丙烯的弹性模量，并且预测结果准确稳定。