Modelling and Investigation of the Dynamic Behavior of a Penny-Shaped Interface Crack in Piezoelectric Bimaterials

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Yani Zhang, Junlin Li, Di Liu, Xiufeng Xie
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Abstract

In this section, the dynamic propagation behavior of a penny-shaped interface crack in piezoelectric bimaterials is analyzed. The objective of this paper is to use the boundary conditions of the penny-shaped interface crack to study the dynamic propagation of the crack under the action of load, so as to provide some valuable implications for the fracture mechanics of the piezoelectric bimaterials and simulate the interface crack between piezoelectric bimaterials, it is necessary to establish a suitable model and give appropriate boundary conditions according to the actual situation. The elastic displacement and potential equations are constructed according to the structural characteristics of the circular crack. In the case of a given displacement or stress, the Laplace transform and Hankel transform are used to simplify the problem into an integral equation with unknown functions. According to the boundary conditions, the corresponding unknowns are obtained, and the closed solution is derived. The results show that the fracture toughness of a penny-shaped interface crack in piezoelectric bimaterials is related to the thickness of the material, the impact time, the material characteristics, and the electric field. At the same time, it can be found that different materials have different roles in the crack propagation, so it is very important to study the crack opening displacement (COD) intensity factor of the crack for safety design.
压电双材料中竹篙形界面裂缝的动态行为建模与研究
本节分析了压电双材料中一分钱形界面裂纹的动态扩展行为。本文的目的是利用一分钱形界面裂纹的边界条件研究裂纹在载荷作用下的动态扩展,从而为压电双材料的断裂力学提供一些有价值的启示,模拟压电双材料之间的界面裂纹,需要根据实际情况建立合适的模型并给出合适的边界条件。根据圆形裂缝的结构特征构建弹性位移和位势方程。在给定位移或应力的情况下,利用拉普拉斯变换和汉克尔变换将问题简化为带未知函数的积分方程。根据边界条件,得到相应的未知数,并推导出闭合解。结果表明,压电双材料中的一分钱形界面裂纹的断裂韧性与材料厚度、冲击时间、材料特性和电场有关。同时,可以发现不同材料在裂纹扩展中的作用不同,因此研究裂纹的开裂位移(COD)强度因子对于安全设计非常重要。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Advances in Mathematical Physics
Advances in Mathematical Physics 数学-应用数学
CiteScore
2.40
自引率
8.30%
发文量
151
审稿时长
>12 weeks
期刊介绍: Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.
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