多场耦合材料的界面力学和局部效应研究
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摘要
由于具有优良的电力耦合性能,多场耦合材料如压电材料、功能梯度压电材料和压电纤维复合材料等作为各种执行器、传感器等广泛应用于声纳发射器、水下潜艇、医学超声成像、健康检测等智能结构。对这类材料的研究具有重要的科学意义和工程应用前景。
本文首先介绍了多场耦合材料的研究背景和发展现状,指出了在界面力学、局部效应如奇异性、圣维南衰减等领域需要解决的问题。本文以多场耦合材料的界面力学和局部效应为两个主要研究内容。
对于压电纤维复合材料,本文建立了修正的剪滞模型,以压电纤维的push-out试验为例,考察了粘接界面和摩擦界面上的应力传递和电场分布特征。对于部分脱粘界面,仍然以剪滞模型为基础,用断裂力学的方法建立了纤维脱粘的能量准则,研究了材料参数、电场载荷等对能量释放率和界面应力传递及纤维电场分布的影响。此外,用势函数法和汉克尔变换,解决了压电纤维中的币形裂纹问题,并考虑了弹性涂层尺寸、材料性能对币形裂纹的影响。
对于压电材料和功能梯度压电材料,本文将它们的控制方程导入哈密顿体系或空间状态变量方程,利用分离变量法研究了压电楔和具有环向材料性能变化的功能梯度压电材料(AGPM)楔在反平面变形下的奇异性问题。数值结果表明,材料常数、楔角、材料梯度等因素对楔状体的奇异性阶次有重要的影响,因而可以利用这些因素来减小或避免应力及电场集中现象。另一方面,用类似的方法研究了压电材料和功能梯度材料在平面变形、反平面变形下的圣维南衰减问题。对于压电材料发现存在两种衰减模式,并且其衰减特征长度要远远大于弹性材料,数值算例说明,可以通过材料参数、材料梯度参数等因素来控制材料端部的衰减行为。
Due to their coupling among various fields, multi-field materials such as piezoelectric materials, functionally graded piezoelectric materials (FGPM) and piezoelectric fibre composites have been widely used as sensors and actuator in applications such as sonar projectors, under-water use, medical ultrasonic imaging applications and health monitoring systems, etc. Thus, study on these materials be of great importance scientifically and potential in engineering applications.
In this thesis, a comprehensive review on the research background and development of the multi-field materials is presented, and some problems related to interface mechanics and local effects of multi-filed coupled materils such as singularity and Sanit-Venant’s decay effect are pointed out have been systematically studied. In the following, the thesis puts emphasis on the solution process of these problems.
Based on some assumptions, a modified shear-lag model for piezoelectric fibre composites has been developed. Using the model, stress transfer and electric fields for a piezoelectric fibre composite with a fully bonded interface or frictional interface has been investigated. For a composite with partially debonded interface, a debonding criterion for the piezoelectric effect is presented utilizing a fracture mechanics approach to investigate the debonding process of piezoelectric fibre in the push-out test under combined electrical and mechanical loading within the framework of shear-lag theory. In addition, the problem of a penny-shaped crack in a piezoelectric fibre with an elastic coating embedded is investigated. By using the potential theory and Hankel transform, this problem is formulated as the solution of a system of dual integral equations which are reduced to a Fredholm integral equation of the second kind. Numerical studies are conducted to show the effect of the thickness and the elastic material properties of the coating on the fracture of piezoelectric fibre.
Finally, the singularity behaviour of electroelastic fields in a wedge with homogeneous piezoelectric materials (PM) and/or angularly graded piezoelectric material (AGPM) under anti-plane deformation is investigated based on the Hamiltonian system and/or the mixed–variable state space formulation developed in this thesis. Numerical examples demonstrate that the materials properties, wedge angle and the angular variation of the materials properties have an important influence on the singularities of the PM wedge and AGPM wedge and the material inhomogeneity degreeηcan be used to control the singularities of AGPM wedge systems. Using a similar procedure to the singularity analysis, the Saint-Venant decay effects for the PM and FGPM strip and laminate under plane deformation and anti-plane deformation have been investigate. These studies indicate that the decay rate of stress and electric fields can be determined by way of the real part of the eigenvalue with the smallest positive real part of the matrix operator. There exist two type of decay mode depended on the materials properties and the characteristic decay lengths for the piezoelectric materials under plane deformation are larger that that for elastic materials. In addition, the material inhomogeneity plays an important role in Saint-Venant end effects for FGPM laminates.
本文首先介绍了多场耦合材料的研究背景和发展现状,指出了在界面力学、局部效应如奇异性、圣维南衰减等领域需要解决的问题。本文以多场耦合材料的界面力学和局部效应为两个主要研究内容。
对于压电纤维复合材料,本文建立了修正的剪滞模型,以压电纤维的push-out试验为例,考察了粘接界面和摩擦界面上的应力传递和电场分布特征。对于部分脱粘界面,仍然以剪滞模型为基础,用断裂力学的方法建立了纤维脱粘的能量准则,研究了材料参数、电场载荷等对能量释放率和界面应力传递及纤维电场分布的影响。此外,用势函数法和汉克尔变换,解决了压电纤维中的币形裂纹问题,并考虑了弹性涂层尺寸、材料性能对币形裂纹的影响。
对于压电材料和功能梯度压电材料,本文将它们的控制方程导入哈密顿体系或空间状态变量方程,利用分离变量法研究了压电楔和具有环向材料性能变化的功能梯度压电材料(AGPM)楔在反平面变形下的奇异性问题。数值结果表明,材料常数、楔角、材料梯度等因素对楔状体的奇异性阶次有重要的影响,因而可以利用这些因素来减小或避免应力及电场集中现象。另一方面,用类似的方法研究了压电材料和功能梯度材料在平面变形、反平面变形下的圣维南衰减问题。对于压电材料发现存在两种衰减模式,并且其衰减特征长度要远远大于弹性材料,数值算例说明,可以通过材料参数、材料梯度参数等因素来控制材料端部的衰减行为。
Due to their coupling among various fields, multi-field materials such as piezoelectric materials, functionally graded piezoelectric materials (FGPM) and piezoelectric fibre composites have been widely used as sensors and actuator in applications such as sonar projectors, under-water use, medical ultrasonic imaging applications and health monitoring systems, etc. Thus, study on these materials be of great importance scientifically and potential in engineering applications.
In this thesis, a comprehensive review on the research background and development of the multi-field materials is presented, and some problems related to interface mechanics and local effects of multi-filed coupled materils such as singularity and Sanit-Venant’s decay effect are pointed out have been systematically studied. In the following, the thesis puts emphasis on the solution process of these problems.
Based on some assumptions, a modified shear-lag model for piezoelectric fibre composites has been developed. Using the model, stress transfer and electric fields for a piezoelectric fibre composite with a fully bonded interface or frictional interface has been investigated. For a composite with partially debonded interface, a debonding criterion for the piezoelectric effect is presented utilizing a fracture mechanics approach to investigate the debonding process of piezoelectric fibre in the push-out test under combined electrical and mechanical loading within the framework of shear-lag theory. In addition, the problem of a penny-shaped crack in a piezoelectric fibre with an elastic coating embedded is investigated. By using the potential theory and Hankel transform, this problem is formulated as the solution of a system of dual integral equations which are reduced to a Fredholm integral equation of the second kind. Numerical studies are conducted to show the effect of the thickness and the elastic material properties of the coating on the fracture of piezoelectric fibre.
Finally, the singularity behaviour of electroelastic fields in a wedge with homogeneous piezoelectric materials (PM) and/or angularly graded piezoelectric material (AGPM) under anti-plane deformation is investigated based on the Hamiltonian system and/or the mixed–variable state space formulation developed in this thesis. Numerical examples demonstrate that the materials properties, wedge angle and the angular variation of the materials properties have an important influence on the singularities of the PM wedge and AGPM wedge and the material inhomogeneity degreeηcan be used to control the singularities of AGPM wedge systems. Using a similar procedure to the singularity analysis, the Saint-Venant decay effects for the PM and FGPM strip and laminate under plane deformation and anti-plane deformation have been investigate. These studies indicate that the decay rate of stress and electric fields can be determined by way of the real part of the eigenvalue with the smallest positive real part of the matrix operator. There exist two type of decay mode depended on the materials properties and the characteristic decay lengths for the piezoelectric materials under plane deformation are larger that that for elastic materials. In addition, the material inhomogeneity plays an important role in Saint-Venant end effects for FGPM laminates.
引文
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