EFFECTS OF MAXWELL STRESSES ON THE MOVING CRACK IN PIEZOELECTRIC MATERIAL
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- 英文论文题名：EFFECTS OF MAXWELL STRESSES ON THE MOVING CRACK IN PIEZOELECTRIC MATERIAL
- 论文作者：Lu-qiao QI ; Yu-hao LI ; Cun-fa GAO
- 英文论文作者：Lu-qiao QI ; Yu-hao LI ; Cun-fa GAO ; State Key Laboratory of Mechanics and Control of Mechanical Structures ; Nanjing University of Aeronautics and Astronautics
- 年：2016
- 作者机构：State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics;
- 英文论文关键词：Maxwell stress ; Moving crack ; Critical velocity ; Plane problem
- 会议召开时间：2016-10-21
- 会议录名称：2016年全国压电和声波理论及器件应用研讨会论文摘要集
- 英文会议录名称：Abstract Book of 2016 Symposium on Piezoelectricity, Acoustic Waves and Device Applications
- 语种：英文
- 分类号：TB34;O346.1
- 学会代码：AGLU
- 会议名称：2016年全国压电和声波理论及器件应用研讨会
- 会议地点：中国陕西西安
- 主办单位：中国力学学会、中国声学学会、IEEE UFFC分会
- 学会名称：中国力学学会
- 页数：2
- 文件大小：79k
- 原文格式：D
- 会议级别：全国
摘要
Background, Motivation and Objective In fracture mechanics of electric dielectrics, the Maxwell stresses have great influence on electric fields of cavity with vacuum、air or liquid. Thus, the problems of Maxwell stress in piezoelectric solids have aroused great interest. In recent years, some analytical researches have been focused on the Maxwell stress, e.g., see the works of Gao et al.(2004), Mc Meeking and Landis(2005), Ricoeur and Kuna(2009), Bustamante et al.(2009), Zhang and Wang(2014), Wang(2014). However, all the above studies are for the cases of static cracks. It is well known that the moving crack properties are quite different with the static ones. Yoffe(1951) studied the tip fields of a crack moving with a constant length for all the time. She came to the conclusion that there is a critical velocity of about 0.6 times of the shear wave velocity, at which the crack tends to curve and branch out. And at lower velocities, the initial growth is expected to occur along the line of the crack. There are many analytical researches focused on the propagation crack in traditional materials, e.g., Chen, et al.(1997,1998), Gao, et al.(2001), Li and Chen(2008), Kwon and Lee(2000), Soh, et al.(2002), Chen, et al.(2013). But, to the best of my knowledge, the effects of the Maxwell stress on the moving crack in a piezoelectric solid have not been studied well. Statement of Contribution/Methods In this paper, a plane problem of a moving crack with constant velocity in piezoelectric materials is investigated systematically. The electrically semi-permeable crack boundary condition is adopted. Based on the extended Stroh formalism, the closed-form expression of electric displacement in the moving crack, the electrostatic fields and dynamic stress and dynamic electric intensity factors are obtained. Results Analytical results are presented and numerical solutions for PZT-5H material are also given graphically. The influence of Maxwell stresses and the speed of the crack and studied when the material is subject to combined mechanical and electrical loads at infinity. The influence of mediums inside the crack and surrounding the matrix at infinity is also analyzed. Discussion and Conclusions In the calculations, the velocity of the crack is less than the lowest bulk wave speed when the plane wave propagates along the x-direction in the transversely isotropic piezoelectric medium. Numerical solutions reveal that the dynamic intensity factors are related to not only the electric field, but also the velocity of the moving crack, when the Maxwell stress is considered. Furthermore, the ratio of mechanical load and electrical load has conspicuous effect on the dynamic intensity factors. The relationships among crack branching, crack velocity and Maxwell stress are revealed in the form of diagrams.
Background, Motivation and Objective In fracture mechanics of electric dielectrics, the Maxwell stresses have great influence on electric fields of cavity with vacuum、air or liquid. Thus, the problems of Maxwell stress in piezoelectric solids have aroused great interest. In recent years, some analytical researches have been focused on the Maxwell stress, e.g., see the works of Gao et al.(2004), Mc Meeking and Landis(2005), Ricoeur and Kuna(2009), Bustamante et al.(2009), Zhang and Wang(2014), Wang(2014). However, all the above studies are for the cases of static cracks. It is well known that the moving crack properties are quite different with the static ones. Yoffe(1951) studied the tip fields of a crack moving with a constant length for all the time. She came to the conclusion that there is a critical velocity of about 0.6 times of the shear wave velocity, at which the crack tends to curve and branch out. And at lower velocities, the initial growth is expected to occur along the line of the crack. There are many analytical researches focused on the propagation crack in traditional materials, e.g., Chen, et al.(1997,1998), Gao, et al.(2001), Li and Chen(2008), Kwon and Lee(2000), Soh, et al.(2002), Chen, et al.(2013). But, to the best of my knowledge, the effects of the Maxwell stress on the moving crack in a piezoelectric solid have not been studied well. Statement of Contribution/Methods In this paper, a plane problem of a moving crack with constant velocity in piezoelectric materials is investigated systematically. The electrically semi-permeable crack boundary condition is adopted. Based on the extended Stroh formalism, the closed-form expression of electric displacement in the moving crack, the electrostatic fields and dynamic stress and dynamic electric intensity factors are obtained. Results Analytical results are presented and numerical solutions for PZT-5H material are also given graphically. The influence of Maxwell stresses and the speed of the crack and studied when the material is subject to combined mechanical and electrical loads at infinity. The influence of mediums inside the crack and surrounding the matrix at infinity is also analyzed. Discussion and Conclusions In the calculations, the velocity of the crack is less than the lowest bulk wave speed when the plane wave propagates along the x-direction in the transversely isotropic piezoelectric medium. Numerical solutions reveal that the dynamic intensity factors are related to not only the electric field, but also the velocity of the moving crack, when the Maxwell stress is considered. Furthermore, the ratio of mechanical load and electrical load has conspicuous effect on the dynamic intensity factors. The relationships among crack branching, crack velocity and Maxwell stress are revealed in the form of diagrams.
Background, Motivation and Objective In fracture mechanics of electric dielectrics, the Maxwell stresses have great influence on electric fields of cavity with vacuum、air or liquid. Thus, the problems of Maxwell stress in piezoelectric solids have aroused great interest. In recent years, some analytical researches have been focused on the Maxwell stress, e.g., see the works of Gao et al.(2004), Mc Meeking and Landis(2005), Ricoeur and Kuna(2009), Bustamante et al.(2009), Zhang and Wang(2014), Wang(2014). However, all the above studies are for the cases of static cracks. It is well known that the moving crack properties are quite different with the static ones. Yoffe(1951) studied the tip fields of a crack moving with a constant length for all the time. She came to the conclusion that there is a critical velocity of about 0.6 times of the shear wave velocity, at which the crack tends to curve and branch out. And at lower velocities, the initial growth is expected to occur along the line of the crack. There are many analytical researches focused on the propagation crack in traditional materials, e.g., Chen, et al.(1997,1998), Gao, et al.(2001), Li and Chen(2008), Kwon and Lee(2000), Soh, et al.(2002), Chen, et al.(2013). But, to the best of my knowledge, the effects of the Maxwell stress on the moving crack in a piezoelectric solid have not been studied well. Statement of Contribution/Methods In this paper, a plane problem of a moving crack with constant velocity in piezoelectric materials is investigated systematically. The electrically semi-permeable crack boundary condition is adopted. Based on the extended Stroh formalism, the closed-form expression of electric displacement in the moving crack, the electrostatic fields and dynamic stress and dynamic electric intensity factors are obtained. Results Analytical results are presented and numerical solutions for PZT-5H material are also given graphically. The influence of Maxwell stresses and the speed of the crack and studied when the material is subject to combined mechanical and electrical loads at infinity. The influence of mediums inside the crack and surrounding the matrix at infinity is also analyzed. Discussion and Conclusions In the calculations, the velocity of the crack is less than the lowest bulk wave speed when the plane wave propagates along the x-direction in the transversely isotropic piezoelectric medium. Numerical solutions reveal that the dynamic intensity factors are related to not only the electric field, but also the velocity of the moving crack, when the Maxwell stress is considered. Furthermore, the ratio of mechanical load and electrical load has conspicuous effect on the dynamic intensity factors. The relationships among crack branching, crack velocity and Maxwell stress are revealed in the form of diagrams.
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