三明治结构Ⅰ型断裂行为的研究

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	三明治结构Ⅰ型断裂行为的研究
英文题名	Research on Mode Ⅰ Fracture Behavior of Sandwich Structure
	张凡凡
导师	刘小明
	2020-05-25
学位授予单位	中国科学院大学
学位授予地点	北京
学位类别	硕士
学位专业	固体力学
关键词	三明治结构，中间层厚度，解析模型，能量释放率，界面应力
摘要	因其具有较高的比强度和较大的比刚度等优点，三明治结构经常作为载荷传递和连接元件，广泛应用于航空航天、材料表征和柔性电子等领域。研究I型断裂模式是研究三明治结构断裂行为的简单有效方法之一，因此众多学者研究了I型断裂模式下三明治结构的断裂行为。前人研究发现，中间层厚度、模量比和裂纹初始长度等参数都对三明治结构的断裂行为有很大影响，但对中间层厚度较大的情况关注较少。随着大型船舰等的发展，中间层厚度较大的三明治结构需求变多。因此为了更好地应用三明治结构及更深入地了解其断裂行为和特点，本文基于理论建模和有限元模拟，系统地研究了三明治结构I型断裂行为。主要研究结果如下：（1）基于改良弹性地基理论模型，同时考虑到中间层厚度对三明治结构I型断裂的影响，建立了三明治结构I型断裂的理论模型。中间层厚度的影响主要分为两部分：中间层剪切力的影响及中间层厚度增加带来的结构刚度增加的影响。将两个模型进行对比，可以发现中间层厚度、模量比和无量纲裂纹初始长度中任一变量的增大都会造成中间层剪切力对能量释放率影响的增大。中间层厚度的增大或模量比的减小都会造成结构刚度对能量释放率影响的增大，而无量纲裂纹初始长度的变化不会对其造成影响。（2）通过结合围道积分后处理的有限元方法，建立了求解能量释放率的三明治结构I型断裂模型，讨论了各参数对三明治结构能量释放率的影响。并将理论模型与有限元模型进行了对比，当无量纲中间层厚度取最大值2的时候，改良弹性地基理论模型与有限元结果的相对误差为83%，而新理论模型与有限元结果的相对误差仅为5%，新理论模型与有限元结果更为吻合。这一结论可以说明新理论模型适用范围更广。（3）利用新理论模型，以常见的金属作上下层（即非中间层），假定结构的断裂韧性为常数，讨论了各参数对临界载荷的影响。可以发现，随着无量纲中间层厚度的增大，临界载荷先减小后增大。随着模量比增大和裂纹初始长度的减小，临界载荷增大。将这一结论应用到工程中时，只要选择模量小的非中间层，就可以用较小的载荷使结构达到其断裂韧性而破坏。（4）利用新理论模型和有限元模拟研究了三明治结构的界面应力。可以发现不同接头形状会造成在内凹临界点出现应力集中现象。新理论模型和有限元模拟的界面应力结果有一定差距。考虑到理论模型无法表征裂尖奇异性，将理论模型与裂尖奇异性造成的界面应力进行叠加，并与有限元结果进行比较，发现吻合的较好。
英文摘要	Because of its advantages such as high specific strength and large specific stiffness, sandwich structures are often used as load transfer and connection elements, and are widely used in aerospace, material characterization, and flexible electronics. Studying the mode I fracture mode is one of the simple and effective methods to study the fracture behavior of the sandwich structure. Therefore, many scholars have studied the fracture behavior of the sandwich structure under the mode I fracture mode. Previous studies have found that the thickness of the intermediate layer, modulus ratio, and initial crack length have a great influence on the fracture behavior of the sandwich structure, but less attention is paid to the case where the thickness of the intermediate layer is large. With the development of large ships, the demand for sandwich structures with thicker middle layers has increased. Therefore, in order to better apply the sandwich structure and gain a deeper understanding of its fracture behavior and characteristics, based on theoretical modeling and finite element simulation, this paper systematically studied the mode I fracture behavior of the sandwich structure. The main findings are as follows: (1) Based on the improved elastic foundation theoretical model, and taking into account the influence of the thickness of the intermediate layer on the mode I fracture of the sandwich structure, a theoretical model of mode I fracture of the sandwich structure is established. The influence of the thickness of the middle layer is mainly divided into two parts: the influence of the shear force of the middle layer and the effect of the increase of the structural rigidity caused by the increase of the thickness of the middle layer. Comparing the two models, it can be found that the increase of any variable in the thickness of the intermediate layer, the modulus ratio and the initial length of the dimensionless crack will increase the influence of the shear force of the intermediate layer on the energy release rate. the increase of the thickness of the middle layer or the decrease of the modulus ratio will increase the influence of structural stiffness on the energy release rate, while the change of the initial length of the dimensionless crack will not affect it. (2) By combining the post-processing finite element method of the channel, a sandwich structure mode I fracture model for solving the energy release rate is established, and the effects of various parameters on the energy release rate of the sandwich structure are discussed. The theoretical model is compared with the finite element model. When the thickness of the dimensionless middle layer reaches the maximum value of 2, the absolute error between the theoretical model of the improved elastic foundation and the finite element results is 83%, while the absolute error between the new theoretical model and the finite element results is only 5%. The new theoretical model is more consistent with the finite element results.This conclusion can explain that the new theoretical model is more applicable. (3) Using the new theoretical model, the upper and lower layers (that is, the non-middle layers) are made of common metals.Assuming that the fracture toughness of the structure is constant, the influence of various parameters on the critical load is discussed.It can be found that as the thickness of the dimensionless intermediate layer increases, the critical load decreases first and then increases. As the modulus ratio increases and the initial crack length decreases, the critical load increases. When this conclusion is applied to engineering, as long as the non-intermediate layer with small modulus is selected, the structure can reach its fracture toughness and fail with small load. (4) The interfacial stress of the sandwich structure was studied by a new theoretical model and finite element simulation. It can be found that different joint shapes will cause stress concentration in the concave critical point.There is a gap between the interface stress results of the new theoretical model and the finite element simulation. Considering that the theoretical model cannot characterize the singularity of the crack tip, the interface stress caused by the singularity of the crack and the theoretical model is superimposed and compared with the results of the finite element, and it is found that the agreement is good.
索取号	Mas2020-010
语种	中文
文献类型	学位论文
条目标识符	http://dspace.imech.ac.cn/handle/311007/81916
专题	非线性力学国家重点实验室
推荐引用方式 GB/T 7714	张凡凡. 三明治结构Ⅰ型断裂行为的研究[D]. 北京. 中国科学院大学,2020.

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