### 复合材料MMB试件I-II混合型层间裂纹扩展分析

1. 1. 南京航空航天大学 机械结构力学及控制国家重点实验室, 南京 210016;
2. 南京航空航天大学 多功能轻量化材料与结构工业和信息化部重点实验室, 南京 210016;
3. 南京航空航天大学 飞行器先进设计技术国防重点学科实验室, 南京 210016
• 收稿日期:2020-05-19 修回日期:2020-06-12 发布日期:2020-06-24
• 通讯作者: 卢天健 E-mail:tjlu@nuaa.edu.cn
• 基金资助:
国家自然科学基金（51905264，11972185）；中国博士后科学基金（2019M661818，2019M650115）；江苏高校优势学科建设工程资助项目；中央高校基本科研业务费专项资金（NP2017401）

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

DENG Jian1,2, LU Tianjian1,2, YIN Qiaozhi1,3

1. 1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2. MⅡT Key Laboratory of Multifunctional Lightweight Materials and Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
3. Key Laboratory of Fundamental Science for National Defense-Advanced Design Technology of Flight Vehicle, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
• Received:2020-05-19 Revised:2020-06-12 Published:2020-06-24
• Supported by:
National Natural Science Foundation of China (51905264, 11972185); China Postdoctoral Science Foundation (2019M661818, 2019M650115); Priority Academic Program Development of Jiangsu Higher Education Institutions; the Fundamental Research Funds for the Central Universities (NP2017401)

Abstract: 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.