Piezoelektrik kompozitlerin elektromekanik özelliklerinin analizi
Analysis of electromechanical properties of piezoelectric composites
Yazar: HASAN AKSÜT
Danışman: PROF. DR. CELALETDİN ERGUN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Malzeme ve İmalat Bilim Dalı
Derece: Yüksek Lisans, 2020
Konu: Makine Mühendisliği = Mechanical Engineering
Dizin: Gözeneklilik = Porosity ; Kompozitler = Composites ; Modelleme = Modelling ; Piezoelektrik = Piezoelectric ; Sensörler = Sensors

Özet:
Sürülebilir ya da püskürtülebilir piezoelektrik kompozit boyalar sensör uygulamalarında kullanılmaktadır. Bu boyaların karakteristik özelliklerinin geliştirilebilmesi için kompozitin elektromekanik özelliklerinin bilinmesine ihtiyaç duyulur.
Piezoelektriklik ve piezoelektrik malzeme çeşitleri incelenmiştir. Bunlarla yapılabilecek polimer matrisli kompozitlerin doğrultuları ve özellikleri hakkında literatür araştırması yapılmıştır.
Piezoelektrik kompozitlerin yapısal denklemleri verilmiştir, bunlar ayrıca kolaylık amaçlı Voigt gösteriminde de yazılmıştır. Eshelby'nin elastik takviye probleminin piezoeletrik durumda dönüşeceği şekil gösterilmiştir. 
Kompozitlerin yapısal piezoelektrik modüllerinin belirlenebilmesi için ihtiyaç duyulan Eshelby tensörleri kapalı formda küresel takviye için elde edilmiştir. Mori-Tanaka, kendi içinde tutarlı yaklaşım ve Odegard yaklaşımıyla mikromekanik modeller sayesinde elektromekanik modüller analitik bir biçimde bulunmuştur.
Bu kompozitlerin seramik ve polimer dışında ayrıca boşluk da bulundurabileceği göz önüne alınarak analitik hesaplamalar her yaklaşımda 3 bileşenli bir kompozit için genişletilip ayrıca uygulanmıştır.
Basit kübik, hacim merkezli kübik, yüzey merkezli kübik ve hegzagonal sıkı paket birim kafes yapılarının parametrik tasarımları gerçekleştirilmiştir. Bu temsili hacim elemanları üzerinden sonlu elemanlar modeliyle uygun sınır koşulları yapısal denklemler vasıtasıyla bulunmuştur. Alınan sonuçlar üzerinden hesaplanan hacim ortalamaları kullanılarak kompozitin genel elektromekanik modülü elde edilmiştir.
Bir piezoelektrik kompozit sensör deney düzeneğinin sayısal modellemesi yapılmıştır. Farklı mesh büyüklüklerinde analizler gerçekleştirilmiştir. Bu modele malzeme özellikleri olarak analitik Mori-Tanaka yöntemiyle hesaplanan elektromekanik modülün özellikleri girilerek voltaj çıktısı elde edilmiştir.
Çalışmada kullanılan malzemenin özelliklerinin sabit gerilme altında ölçülerek verilmiş değerlerinin sabit birim şekil değişimi altında olacak şekle dönüşümleri yapılmıştır. Bu değerlerden seramik modülü bulunmuştur. Polimer malzemenin özelliklerinden modülü bulunmuştur. 
Mikromekanik modellerin analizlerinden elde edilmiş sonuçlar elastiklik modülü, kesme modülü, piezoelektrik katsayılar ve dielektrik katsayılar cinsinden değişen seramik hacim yüzdelerine bağlı olarak grafiklere çizdirilmiştir. YMK birim kafes yapısıyla elde edilen sonlu eleman yönteminden alınan sonuçlar karşılaştırma amacıyla çizilen grafiklere eklenmiştir.
Mikromekanik modellerin grafikleri boşluklu durum için de aynı şekilde çizdirilmiştir.
Deney düzeneği modellemesinin sonuçları ideal, boşluklu, piezo indirgenmiş ve hem piezo indirgenmiş hem boşluklu olmak üzere grafiklere aktarılmıştır. Ayrıca farklı bir mesh boyutunda ideal durum için grafik eklenmiştir.
Elde edilen tüm sonuçlar birbirleriyle karşılaştırılmıştır.

Abstract:
Various types of piezoelectric composite paints are used in sensor applications. To improve the characteristic properties of these kinds of paints, one needs to determine electromechanical properties of the composite.
History of developments of piezoelectric materials were examined. Various usages and innovations involving piezoelectricity were shown.
Piezoelectricity is the relation between the mechanical and electrical reactions of a crystal structure. Various piezoelectric materials exist, such as natural, ferroelectric and synthetic crystals. Generally, synthetic PZT is used in applications.
A comparison made between soft and hard piezo ceramics were given. It consisted of characteristic properties involving piezoelectric constants, permittivity, dielectric constants, dielectric losses, electromechanical coupling factor, electromechanical resistance, mechanical quality factor and polarization.
Four different applications of piezoelectric materials were exemplified. Those were actuators, sensors, transducers and generators.
Connection types of composites were shown. 0-3 piezo ceramic/polymer piezoelectric paints and their history of developments were summarized.
Constitutive equations of piezoelectric composites were defined. Voigt notation is explained and constitutive equations were expressed according to that notation.
Eshelby's inclusion problem was described. Piezoelectric equivalent of Eshelby tensors were obtained for a spherical inclusion.
Micromechanics models were employed to calculate the overall piezoelectic modulus of the composite. Concentration tensor is explained.
Mori-Tanaka method, self-consistent method and a method proposed by Odegard were then used to find the concentration tensor.
Calculations were made for a composite which consists of a piezoelectric ceramic and a polymer. After that concentration tensors were calculated again, this time for a composite with 3 components. The third component was assumed to be air to represent porosity which may be in the structure of the composite.
Representative volume elements were considered to carry out finite element analyses. Four different crystal unit cell structures were utilized as representative volume elements: simple cubic, body-centered cubic, face-centered cubic and hexagonal close packed.
These designs were made using parameters as lengths of the structure. By the way of fixing the diameter of the inclusion, different volume fractions were represented by different amounts of matrix material.
Maximum volume fractions for simple cubic RVE, body-centered cubic RVE, face-centered cubic RVE and hexagonal close packed RVE are 52.3, 68.0, 74.0 and 74.0 percent, respectively.
Appropriate boundary conditions to be applied to the surfaces of the RVE were obtained using constitutive equations.
Volumetric average values of stress, strain, electric displacement and electric field were acquired. Using these values, components of the overall moduli of the composite was found.
An experimental setup involving a sensor which is a piezoelectric composite layer on an aluminium plate was modelled in ANSYS. Element types were chosen to be SOLID5 for aluminium plate and SOLID45 for piezoelectric composite. Analytically calculated piezoelectric material properties obtained from Mori-Tanaka method were input to the model. Two different mesh sizes were considered. A displacement was applied to the end of the plate. Transient analysis was carried out. Output is attained as voltage values.
Manufacturing, polarization and measurement of a piezo paint were explained.
Properties of the piezoelectric ceramic (APC 856) to be used in this study was given as measurements under constant strain. These properties was transformed to the constant stress forms, for example compliance to stiffness. From there, piezoelectric modulus is found.
Piezoelectric modulus of the polymer was found from the elasticity modulus, Poisson's ratio and permittivity of acrylic.
Mori-Tanaka method showed closest agreement with the results of the finite element model for values of the elasticity modulus. Analytical models produced very high results for shear moduli compared to the finite element model.
All three piezoelectric constants were highly different for self-consistent compared to the other models over volume fractions of 20%. Mori-Tanaka method was closer to the finite element model in terms of e15 and Odegard was closer in terms of e31 and e33.
Mori-Tanaka was closest to finite element model's dielectric constants in lower volume fractions while Odegard was closest in higher volume fractions.
In the case of a porosity of 18 percent, elastic properties were affected by approximately 40 percent for Mori-Tanaka and Odegard methods while piezoelectric properties were affected by around 70 percent. Dielectric properties generally decline by about 50 percent.
Modellings were made for the case of 80% APC 856/20% acrylic (by weight). This corresponds to about 39% volume fraction as is the case for the experiment examined in this study. The composite was polarized in a field of 2.5 kV/mm in the experiment.
As shown in some studies, 15 kV/mm is the saturation value of polarization for a piezo ceramic/polymer composite. If a polarization value of 2.5 kV/mm is applied, piezoelectric activity drops 10 fold approximately. In accordance with that, constants concerning electromechanical values were adjusted when calculating the modulus of the composite. Also 18% porosity was considered.
These final material values were used in ANSYS model. Voltage output was in close agreement with the results of the experiment.
In order to get better piezoelectric response from the composite paint, higher polarization values and a better manufacturing process were recommended.