水泥基压电复合材料的模拟与优化设计
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摘要
水泥基压电复合材料是将压电陶瓷(PZT)按照不同的分布形式和陶瓷体积分数分布于水泥石基体中而制备成的新型材料。由于水泥基压电复合材料因压电陶瓷可以被极化而具有压电效应,使得水泥基压电复合材料在既克服传统纯陶瓷材料与混凝土相容性差等缺点的同时,又保持压电材料的优点,从而可以用于混凝土结构的健康监测中。研究水泥基压电复合材料的有效性能,对水泥基压电复合材料基于性能需求的设计、优化,以及水泥基压电传感器在实际工程中的应用具有十分重要的意义。本文重点研究不同类型的水泥基压电复合材料的性能预测理论模型,通过试验验证模型的合理性,并进行模型的数值讨论与分析,最后提出设计优化的建议。主要研究内容如下：
(1)根据水泥材料作为基体容易出现与PZT夹杂粘结界面不牢固的事实,提出了合理的压电材料的广义弹簧界面模型,推导了广义弹簧模型参数与压电材料界面层(相)的的数学关系。基于夹杂的广义本征应变问题,建立了细观力学中压电材料的修正广义Eshelby张量,定量给出了修正广义Eshelby张量与经典压电材料广义Eshelby张量的关系。提出了两种修正的广义Eshelby张量的具体数值算法,并对影响修正广义Eshelby张量的界面参数进行了讨论。
(2)基于压电材料的修正的广义Eshelby张量,建立了夹杂与基体为非完美界面时的三维细观力学框架,给出修正的稀疏法、修正的Mori-Tanaka法、修正的微分法以及修正的自洽法模型的统一表达式,提出采用修正的细观力学模型预测PZT与基体为非完美界面时的压电复合材料的有效性能。通过理论预测值与文献中试验值的对比分析,初步界定了经典细观力学方法的适用范围。
(3)根据以往0-3型水泥基压电复合材料有效性能试验中出现的PZT颗粒粒径效应及PZT夹杂与水泥基体的扫描电镜结果,建立了PZT与水泥基体为非完美界面时,基于PZT颗粒平均半径的0-3型水泥基压电复合材料有效性能理论预测模型；与试验进行比较,验证了模型的可靠性；从原理上阐释了0-3型水泥基压电复合材料的有效性能产生PZT粒径效应的机制,在于水泥基体与PZT颗粒之间存在非完美界面,非完美界面对复合材料有效性能的影响随夹杂颗粒的体表比大小而变化；通过理论与试验的对比分析,提出了0-3型水泥基压电复合材料的优化设计建议。
(4)基于2-2型水泥基压电复合材料为单方向上的准周期性结构,采用宏细观相结合的多尺度模型,预测压电复合材料有效性能；试验研究了2-2型水泥基压电复合材料的有效性能,并与理论预测结果进行比对,验证了理论模型的可靠性。结果表明,通过调整压电功能相的体积分数可使2-2型水泥基压电复合材料的静水压电应变系数dhEff高于压电功能相的静水压电应变系数dhEff;结合理论与试验提出了2-2型水泥基压电复合材料的优化设计建议。
(5)依据1-3型水泥基压电复合材料为双方向上的准周期性结构,压电功能增强相的横截面为方形(或矩形)等特点,采用以多尺度模型为基础的“二次均匀法”预测了1-3型压电复合材料的有效性能；试验研究了1-3型水泥基压电复合材料的有效性能,并与理论预测结果进行比对,验证了模型的可靠性。结果表明,当采用合适的压电功能相的体积分数时,可使1-3型水泥基压电复合材料的静水压电应变系数dhEff达到最优；结合理论与试验提出了1-3型水泥基压电复合材料的优化设计建议。
本研究基于但不局限于水泥基压电智能复合材料,可进一步拓展到更为广义的智能复合材料(如树脂基压电复合材料等),为包括水泥基压电复合材料在内的智能复合材料的设计与工程应用提供理论基础与科学依据。
Cement-based piezoelectric composites fabricated by cement matrix and piezoelectric ceramic phase in different mixing rules and volume fraction are new kinds of materials. Cement-based piezoelectric composites have very sensitive transduction properties as well as good compatibilities with the most popular construction materials (cement and concrete) used in civil engineering. They have received much research attention in the recent decades and have appeared to be a novel kind of electromechanical transducer materials in structural health monitoring (SHM). The studying of overall properties of PZT-cement composites is crucial to the design, optimization and practical engineering application of transducer. In this dissertation, theoretical predicting models of effective properties for PZT-cement composites in different types were focused. Experiments on cement-based composites with different types were carried out to verify theoretical models. After numerical discussions, some considerable suggestions were made on the optimal design of cement-based piezoelectric composites. This dissertation was organized as follows:
(1) Based on the fact that the bonding between cement and PZT is not always good, a general spring-type interface model was proposed and the relation between spring-type interface parameters and interphase material was obtained. The Eshelby problem was formulated for a piezoelectric ellipsoidal inclusion embedded in an infinite piezoelectric matrix when the interfacial bonding between them is imperfect. The modified piezoelectric Eshelby tensor was derived via the classical piezoelectric Eshelby tensor. The averaged piezoelectric Eshelby tensor was calculated by using two methods. Numerical results were presented and discussed for a simple spring-type interface model.
(2) By incorporating the spring-type imperfect interface model and using the modified Eshelby tensor for piezoelectricity, this dissertation have successfully further developed and extended four micromechanics models such as modified dilute method, modified Mori-Tanaka method, modified differential scheme and modified self-consistence method to predict the effective properties of piezoelectric composites containing imperfect interfaces. By comparing the calculated results with the published experimental data, application scopes of classical methods were discussed.
(3) Based on the fact that the effective properties of PZT-cement composites containing particles show size-dependence and the SEM result of cement-based composites, a micromechanics model was adopted to calculate the effective properties of composites. The adopted model can take the imperfect interfaces into account and the theoretically estimated results are in good agreement with the experimental observations. In fact, the results are quite perspicuous on the account of the fact that, there are imperfect interfaces in the composite and its influence on the effective properties increase with the decreasing surface-to-volume ratio of PZT particles. Some suggestions for the design and optimization of0-3type cement-based piezoelectric composites were furthergiven.
(4) For the unidirectional periodic characteristic of2-2type cement-based piezoelectric composites, asymptotic homogenization method with macro-and micro-scale was formulated to calculate the effective properties of cement-based piezoelectric composite. Some experiments about2-2type cement-based piezoelectric composites were done to verify this model. It is shown that by manipulating the volume fraction of PZT, hydrostatic piezoelectric constant dhEff of composites can be higher, than dhEff of the constituents.
(5) For the characteristic of1-3type cement-based piezoelectric composites with two periodic directions, double homogenization method was adopted to calculate the effective properties of these kinds of periodic structures. Some properties of1-3type cement-based piezoelectric composite were measured. Comparisons between the experimental data and predicted values indicate the correctness of the model. Moreover, numerical discussions and experiments show that one should choose proper volume fraction of constituents to obtain the best performance of the1-3type cement-based piezoelectric, composites.
This research focused on the cement-based piezoelectric composites but was not limited to these kinds of composites. Proposed models can be extended to broader range such as polymer based piezoelectric composites, piezomagnetic composites, and so on. This study is useful for the design and engineering application of intelligent composites.
(1)根据水泥材料作为基体容易出现与PZT夹杂粘结界面不牢固的事实,提出了合理的压电材料的广义弹簧界面模型,推导了广义弹簧模型参数与压电材料界面层(相)的的数学关系。基于夹杂的广义本征应变问题,建立了细观力学中压电材料的修正广义Eshelby张量,定量给出了修正广义Eshelby张量与经典压电材料广义Eshelby张量的关系。提出了两种修正的广义Eshelby张量的具体数值算法,并对影响修正广义Eshelby张量的界面参数进行了讨论。
(2)基于压电材料的修正的广义Eshelby张量,建立了夹杂与基体为非完美界面时的三维细观力学框架,给出修正的稀疏法、修正的Mori-Tanaka法、修正的微分法以及修正的自洽法模型的统一表达式,提出采用修正的细观力学模型预测PZT与基体为非完美界面时的压电复合材料的有效性能。通过理论预测值与文献中试验值的对比分析,初步界定了经典细观力学方法的适用范围。
(3)根据以往0-3型水泥基压电复合材料有效性能试验中出现的PZT颗粒粒径效应及PZT夹杂与水泥基体的扫描电镜结果,建立了PZT与水泥基体为非完美界面时,基于PZT颗粒平均半径的0-3型水泥基压电复合材料有效性能理论预测模型；与试验进行比较,验证了模型的可靠性；从原理上阐释了0-3型水泥基压电复合材料的有效性能产生PZT粒径效应的机制,在于水泥基体与PZT颗粒之间存在非完美界面,非完美界面对复合材料有效性能的影响随夹杂颗粒的体表比大小而变化；通过理论与试验的对比分析,提出了0-3型水泥基压电复合材料的优化设计建议。
(4)基于2-2型水泥基压电复合材料为单方向上的准周期性结构,采用宏细观相结合的多尺度模型,预测压电复合材料有效性能；试验研究了2-2型水泥基压电复合材料的有效性能,并与理论预测结果进行比对,验证了理论模型的可靠性。结果表明,通过调整压电功能相的体积分数可使2-2型水泥基压电复合材料的静水压电应变系数dhEff高于压电功能相的静水压电应变系数dhEff;结合理论与试验提出了2-2型水泥基压电复合材料的优化设计建议。
(5)依据1-3型水泥基压电复合材料为双方向上的准周期性结构,压电功能增强相的横截面为方形(或矩形)等特点,采用以多尺度模型为基础的“二次均匀法”预测了1-3型压电复合材料的有效性能；试验研究了1-3型水泥基压电复合材料的有效性能,并与理论预测结果进行比对,验证了模型的可靠性。结果表明,当采用合适的压电功能相的体积分数时,可使1-3型水泥基压电复合材料的静水压电应变系数dhEff达到最优；结合理论与试验提出了1-3型水泥基压电复合材料的优化设计建议。
本研究基于但不局限于水泥基压电智能复合材料,可进一步拓展到更为广义的智能复合材料(如树脂基压电复合材料等),为包括水泥基压电复合材料在内的智能复合材料的设计与工程应用提供理论基础与科学依据。
Cement-based piezoelectric composites fabricated by cement matrix and piezoelectric ceramic phase in different mixing rules and volume fraction are new kinds of materials. Cement-based piezoelectric composites have very sensitive transduction properties as well as good compatibilities with the most popular construction materials (cement and concrete) used in civil engineering. They have received much research attention in the recent decades and have appeared to be a novel kind of electromechanical transducer materials in structural health monitoring (SHM). The studying of overall properties of PZT-cement composites is crucial to the design, optimization and practical engineering application of transducer. In this dissertation, theoretical predicting models of effective properties for PZT-cement composites in different types were focused. Experiments on cement-based composites with different types were carried out to verify theoretical models. After numerical discussions, some considerable suggestions were made on the optimal design of cement-based piezoelectric composites. This dissertation was organized as follows:
(1) Based on the fact that the bonding between cement and PZT is not always good, a general spring-type interface model was proposed and the relation between spring-type interface parameters and interphase material was obtained. The Eshelby problem was formulated for a piezoelectric ellipsoidal inclusion embedded in an infinite piezoelectric matrix when the interfacial bonding between them is imperfect. The modified piezoelectric Eshelby tensor was derived via the classical piezoelectric Eshelby tensor. The averaged piezoelectric Eshelby tensor was calculated by using two methods. Numerical results were presented and discussed for a simple spring-type interface model.
(2) By incorporating the spring-type imperfect interface model and using the modified Eshelby tensor for piezoelectricity, this dissertation have successfully further developed and extended four micromechanics models such as modified dilute method, modified Mori-Tanaka method, modified differential scheme and modified self-consistence method to predict the effective properties of piezoelectric composites containing imperfect interfaces. By comparing the calculated results with the published experimental data, application scopes of classical methods were discussed.
(3) Based on the fact that the effective properties of PZT-cement composites containing particles show size-dependence and the SEM result of cement-based composites, a micromechanics model was adopted to calculate the effective properties of composites. The adopted model can take the imperfect interfaces into account and the theoretically estimated results are in good agreement with the experimental observations. In fact, the results are quite perspicuous on the account of the fact that, there are imperfect interfaces in the composite and its influence on the effective properties increase with the decreasing surface-to-volume ratio of PZT particles. Some suggestions for the design and optimization of0-3type cement-based piezoelectric composites were furthergiven.
(4) For the unidirectional periodic characteristic of2-2type cement-based piezoelectric composites, asymptotic homogenization method with macro-and micro-scale was formulated to calculate the effective properties of cement-based piezoelectric composite. Some experiments about2-2type cement-based piezoelectric composites were done to verify this model. It is shown that by manipulating the volume fraction of PZT, hydrostatic piezoelectric constant dhEff of composites can be higher, than dhEff of the constituents.
(5) For the characteristic of1-3type cement-based piezoelectric composites with two periodic directions, double homogenization method was adopted to calculate the effective properties of these kinds of periodic structures. Some properties of1-3type cement-based piezoelectric composite were measured. Comparisons between the experimental data and predicted values indicate the correctness of the model. Moreover, numerical discussions and experiments show that one should choose proper volume fraction of constituents to obtain the best performance of the1-3type cement-based piezoelectric, composites.
This research focused on the cement-based piezoelectric composites but was not limited to these kinds of composites. Proposed models can be extended to broader range such as polymer based piezoelectric composites, piezomagnetic composites, and so on. This study is useful for the design and engineering application of intelligent composites.
引文
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