复合材料MMB试件I-II混合型层间裂纹扩展分析

基于经典层合板理论及双线性黏聚区本构关系，建立了含一般分层裂纹层合板的理论模型，对I-Ⅱ混合型弯曲（MMB）断裂试件进行了裂纹扩展理论分析。提出了一种I-Ⅱ混合型断裂叠加模型，引入I型裂纹分量的刚体转动位移，同时考虑了裂纹长度超过试件半长后中部载荷分量对裂纹扩展的闭合效应，并根据黏聚区力学响应，分段获得了位移函数通解。结合叠加模型的边界条件与连续性条件，分析了MMB试件的裂纹扩展过程，求解获得了载荷-位移曲线。通过与梁模型预测以及试验结果进行对比，验证了本文模型对I-Ⅱ混合型裂纹扩展预测的有效性和准确性，并讨论了初始断裂模式混合比及闭合效应对裂纹扩展过程的影响。结果表明：初始Ⅱ型裂纹比重较大时，中部载荷的闭合效应更为明显，可能出现I型裂纹完全闭合的情况；裂纹扩展过程中，当裂纹长度小于试件半长时，断裂混合比基本保持常数；当裂纹扩展超过试件半长后，闭合效应明显，混合裂纹形式逐渐向单一型断裂模式退化。

Analysis on I-II mixed interlaminar crack propagation of composite MMB specimens

A theoretical model of general delamination cracked laminates is established based on the classical laminate theory and the bilinear cohesive zone model. The crack propagation in Mixed-Mode Bending (MMB) specimen is studied considering both I and Ⅱ mode cracks. A crack superposition model of I and Ⅱ mode cracks is proposed, followed by the introduction of the rigid body rotational displacement of the mode I crack component. The closing effect of the central load component on the mode I crack propagation is also considered in the MMB tests. According to the mechanical responses in the cohesive zone, a piecewise general solution to the displacement functions is obtained considering that the crack could be larger than half of the specimen length. Combining the boundary and continuity conditions of the superposition model, we analyzes the crack propagation process in the MMB test, obtaining the load-displacement curves. Comparison with both predictions of the beam model and the existing test results verifies the effectiveness and accuracy of the proposed model for I-Ⅱ mixed mode crack propagation. The model is further applied to the discussion of the effect of mode mixity ratios and the closing effect. The results show that the closing effect is more intensive when the initial mixity of the mode Ⅱ crack is relatively larger, which can lead to the closure of the mode I crack. During crack propagation, the mode mixity ratio remains essentially constant when the crack length is smaller than half of the specimen length. Conversely, as the crack length exceeds half of the specimen length, the crack mode gradually degenerates to a single mode fracture with a relatively large initial mode mixity ratio due to the closing effect.