The present paper proposes a new analytical model for predicting the effective stiffness of composite laminates with fiber breaks and transverse cracks. The model is based on continuum damage mechanics and the classical laminate theory. We derived damage variables describing stiffness reduction due to fiber breaks and its maximum value during ultimate tensile failure from the global load-sharing model. Furthermore, a simplified analytical model is presented for obtaining two damage variables for a cracked ply subjected to transverse tensile loading or in-plane shear loading. This model was developed assuming that the displacement field of the longitudinal direction can be expressed in the form of a quadric function by loosening the boundary condition for the governing differential equation. For verifying the developed model, the elastic constants of damaged composite laminates were predicted for cross-ply and angle-ply laminates and compared with the finite element analysis results. As for the appropriate expression of the effective elastic stiffness matrix of the damaged ply, we verified four types of effective compliance/stiffness matrices including the Murakami, Yoshimura, Li, and Maimí models. We found the Maimí model to be the most appropriate among these four models. Moreover, we successfully simplified the expressions for damage variables in the complicated infinite series obtained in our previous study. We also proved that this could contribute toward improving the accuracy of our analysis. After verifying the present model, the stress–strain response and failure strength of carbon- or glass-fiber-reinforced plastic cross-ply laminates were predicted using Maimí’s compliance model and the simplified damage variables.

中文翻译：

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使用连续损伤力学确定聚合物基复合材料层压板的有效刚度和力学行为的分析模型

本文提出了一种新的分析模型，用于预测具有纤维断裂和横向裂纹的复合材料层压板的有效刚度。该模型基于连续介质损伤力学和经典层压板理论。我们从全局负载共享模型中导出了描述由于纤维断裂引起的刚度降低及其在极限拉伸破坏期间的最大值的损伤变量。此外，还提出了一个简化的分析模型，用于获得受到横向拉伸载荷或面内剪切载荷的裂纹层的两个损伤变量。该模型的开发假设纵向位移场可以通过放松控制微分方程的边界条件以二次函数的形式表示。为了验证开发的模型，预测了交叉层和角层层压板受损复合层压板的弹性常数，并与有限元分析结果进行了比较。对于损坏层有效弹性刚度矩阵的适当表达，我们验证了四种类型的有效柔度/刚度矩阵，包括 Murakami、Yoshimura、Li 和 Maimí 模型。我们发现 Maimí 模型是这四种模型中最合适的。此外，我们成功地简化了先前研究中获得的复杂无限级数中损伤变量的表达式。我们还证明，这有助于提高我们分析的准确性。验证当前模型后，