Existence of undulating fill and warp yarns in woven composite laminae introduces complex unit cell geometries and multi-scale interactions among the constituents. Due to these, the failure process involves various meso-scale constituent-level failure modes under complex loading scenarios such as ballistic impact. This can be challenging to model via conventional macro-scale damage tensor-based models. This challenge is tackled here via the adaptation of the previously developed multi-scale microplane triad model to ballistic impact of woven composites. The model can resolve meso-scale constituent level details (including yarn undulations) and predict not only the elastic constants of a woven lamina but also its fracturing behavior. In the present adaptation, only two damage laws are formulated, one for the fibers and one for the matrix. This enables the model to embody the correct values of the intralaminar mode I and II fracture energies of the woven lamina. The model is calibrated using constituent and lamina level test data, and then used to predict the ballistic impact behavior of a single plain-woven lamina under a wide range of projectile impact velocities. The model is demonstrated to predict very well the projectile residual (rebound and exit) velocities, the energy dissipation, the major failure modes of the lamina and the corresponding extent of damage, as well as the ballistic limit and deformation cone wave propagation speeds. The model’s simple, conceptually clear architecture, and computational efficiency represent a major advantage compared to existing damage tensor-based models. The model is also extended to multi-layer thick section woven laminate impact, where the analyses consider both intralaminar and interlaminar failures. The predictions are found to be comparable to those from MAT162, a commercially available material model in LS-Dyna, with much better computational efficiency. Via detailed sensitivity studies, it is demonstrated that the mode I and II intralaminar fracture energies of the lamina are a crucial model input, necessary for accurate predictions of ballistic impact. Not knowing these can introduce significant uncertainty and therefore, their characterization is an absolute must. Finally, the optimal meshing considerations as well as the advantages and limitations of the microplane triad model are discussed.

中文翻译：

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使用具有细观尺度损伤机制的微平面三元组模型对编织复合材料进行弹道冲击建模

编织复合材料层中波动的纬纱和经纱的存在引入了复杂的晶胞几何形状和成分之间的多尺度相互作用。因此，失效过程涉及弹道冲击等复杂载荷场景下的各种细观成分级失效模式。通过传统的基于宏观损伤张量的模型来建模可能具有挑战性。这里通过将先前开发的多尺度微平面三元组模型适应编织复合材料的弹道冲击来解决这一挑战。该模型可以解析细观尺度的成分水平细节（包括纱线波动），不仅可以预测编织层的弹性常数，还可以预测其断裂行为。在本修改中，仅制定了两种损伤定律，一种针对纤维，另一种针对基质。这使得模型能够体现编织层的层内模式 I 和 II 断裂能的正确值。该模型使用成分和层板水平测试数据进行校准，然后用于预测单个平纹编织层板在各种弹丸冲击速度下的弹道冲击行为。该模型被证明可以很好地预测弹丸残余（反弹和退出）速度、能量耗散、薄层的主要失效模式和相应的损坏程度，以及弹道极限和变形锥波传播速度。与现有的基于损伤张量的模型相比，该模型的简单、概念清晰的架构和计算效率是一个主要优势。该模型还扩展到多层厚截面编织层压件冲击，其中分析考虑层内和层间失效。结果发现，这些预测与 LS-Dyna 中的商用材料模型 MAT162 的预测相当，计算效率更高。通过详细的敏感性研究，证明了层板的 I 型和 II 型层内断裂能是关键的模型输入，对于准确预测弹道冲击是必需的。不了解这些可能会带来很大的不确定性，因此，绝对必须对它们进行表征。最后，讨论了最佳网格划分考虑因素以及微平面三元组模型的优点和局限性。