考虑变温效应的压电陶瓷及结构断裂力学模型与实验

The studies of fracture physics and mechanics mechanism for piezoelectric solids can be used to propose an important basis for the reliability analysis and designs of piezoelectric devices.The main objective is to reveal the crack growth and micro or meso physical mechanism for fracture mechanics of piezoelectric solids under applied thermo-electro-mechanical loadings. The fracture mechanics models and experiments of piezoelectric ceramics and their structures are studied by considering the temperature-change effects in the present project. 1) A medium-crack model is applied to simulate the real crack full of a medium. Based on Fourier and Non-Fourier thermal transformation theory, the stress distributions near crack tips are investigated under thermo-electro-mechanical loadings for pizoelectric ceramics with a typical elastic and plastic crack. The effects of applied loadings, physical properties of crack interior and the thermal relaxation on the fracture criteria such as the thermal stress intensity factor and J-integral are made. 2) A model for modelling the metallic electrode with a finite thickness and thermal plastic deformation is made in a multilayered structure of piezoelectric ceramics and electrode. The thermoelectroelastic field near the electrode tip is addressed under thermo-electro-mechanical loadings. The obtained results are compared with those by using the rigid and soft electrode models with no thickness. 3) To simulate the roughness of a prograting crack face, the fractal crack model is given by using the exmpermental observations. The influences of piezoelectric ceramic grain sizes on the crack growth are dealt with. 4) To fill a medium into a crack in the poled and non-poled PZT specimens,the effects of the medium of crack interior and temperature change on the crack grwoth of piezo-ceramics are studied.

压电材料断裂的物理力学机制研究能够为压电器件的可靠性分析与设计提供重要理论基础，旨在揭示热力电等荷载下的裂纹扩展规律和微细观物理机制。 本项目研究考虑变温效应的压电陶瓷及结构断裂力学模型与实验：1）基于刻画裂纹内部介质影响的裂纹模型，并采用Fourier或非Fourier热传导定律，研究热电力荷载下压电陶瓷的弹塑性裂纹问题，揭示力电荷载、裂纹内部介质物理特性和热松弛因子等对热应力强度因子或J积分的影响。2）建立更符合压电陶瓷-电极结构中电极实际状态的有厚度热塑性模型，将其用于研究电极端部的热电弹性场，并与采用无厚度刚性或柔性电极模型所获得的结果进行比较分析。3）模拟压电陶瓷中裂纹扩展面的粗糙性，通过实验观察法建立分形裂纹模型，并由此研究晶粒大小对热力作用下裂纹扩展的影响。4）通过给极化或非极化压电陶瓷的裂纹内部填充多种介质，实验研究裂纹内部介质的物理特性和温度变化对裂纹扩展行为的影响。

压电陶瓷的力电耦合效应为传感器等器件制作和应用提供了物理基础. 研究压电陶瓷的断裂力学问题旨在为压电器件的可靠性分析与设计提供一定的物理力学机制. 本项目主要就热应力作用下的电弹性体断裂力学问题及其求解方法开展研究，取得的一些主要成果如下：.1)基于热介质裂纹面边界条件，分析了压电材料I型裂纹诱导的热电弹性场，研究结果表明，外加力电荷载影响介质裂纹尖端热应力场，绝热和热全渗透型裂纹模型为其特例。进一步研究了磁电热弹性体的I型裂纹，获得了裂纹尖端场的封闭解。.2)提出了压电材料裂纹桥接模型，获得了桥接晶粒承载的电弹性场的封闭解。分析了裂纹桥接对裂纹扩展的影响，结果表明，外加电场荷载对裂纹扩展影响的不同实验结果可以通过裂纹桥接模型进行解释。.3)提出了新的热介质裂纹模型，扩展了已有的热介质裂纹模型，分析表明，新的热介质裂纹模型更能模拟实际热荷载下的裂纹情形。该模型可以进一步推广应用到热电弹性体和热磁电弹性体相关断裂问题研究。.4)提出了裂纹问题导出的带连续核和弱奇异核Fredholm积分方程数值求解新方法，构造了新的数值解并进行了收敛性和误差分析。