Heterojen malzemelerin termal gerilme analizi

Thermal stress analysis of heterogeneous materials

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Tez No: 917969
Yazar: TUĞBA KURU
Danışmanlar: DOÇ. DR. OSMAN BULUT
Tez Türü: Doktora
Konular: İnşaat Mühendisliği, Civil Engineering
Anahtar Kelimeler: Belirtilmemiş.
Yıl: 2025
Dil: Türkçe
Üniversite: İstanbul Teknik Üniversitesi
Enstitü: Lisansüstü Eğitim Enstitüsü
Ana Bilim Dalı: İnşaat Mühendisliği Ana Bilim Dalı
Bilim Dalı: Yapı Mühendisliği Bilim Dalı
Sayfa Sayısı: 189

Özet

Bir çok mühendislik alanında çeşitli avantajlar ve ilerlemeler sunması nedeniyle heterojen malzemelerin bir sınıfı olan fonksiyonel derecelenmiş malzemeler (FDM) 'in uygulama alanları ve teknikleri büyük önem taşımaktadır. Literatürde mevcut sayısal ve analitik çalışmaları doğrulamak ve bu alanda katkıda bulunmak için fonksiyonel derecelendirilmiş malzemelerin termal gerilme analizleri deneysel yöntemlerle gerçekleştirilmelidir. Uzun vadeli yapısal tasarım için fonksiyonel derecelenmiş malzemelerde oluşabilecek kusur veya oyuklar civarında gerilme konsantrasyonları ile termal gerilme dağılımları araştırılmıştır. Bu çalışmada, sabit sıcaklık değişimi etkisindeki kompozit plakta termal gerilmelerin analizi yapılmıştır. Bunun için teknik literatürde bulunan bilgiler tartışılarak gereken analizler ile yeni çıkarımlar yapılmıştır. Çalışma kapsamında günümüzde pek çok alanda kullanılan tabakalı kompozit ve fonksiyonel derecelendirilmiş plaklar ele alınmıştır. İlk olarak, yalnızca termal genleşme katsayıları farklı olan malzemelerden imal edilmiş kompozit plaklar ele alınmış ve termal gerilme dağılımını anlamak için deneysel ve sayısal modeller geliştirilmiştir. Deney modelleri literatürde karşılaşılan farklı oyuk tipi ve geometrilerini içeren iki katmanlı plak modelleri ve üç katmanlı plak modelini içermektedir. Deney yönteminde termal genleşmenin mekanik modellenmesi yöntemi ile üç boyutlu fotoelastisite kullanılmıştır. Deneysel ve sayısal analizi doğrulamak için literatürde homojen plak için önerilen temel termoelastisite yöntemleri, ele alınan problemlere uygulanarak analitik çözüm türetilmiştir. Türetilen analitik ifadeler ele alınan modellere uygulandığında deneyden elde edilen sonuçlarla uyumlu sonuçlar elde edilmiştir. Ayrıca deneylerden oyuk ucu yarıçapı ile gerilme yığılması değişimine ait sonuçlar elde edilmiştir. Oyuk ucundaki gerilme yığılmasının, iki katmanlı bir kompozit plağa ara katman eklendiğinde azaldığı gösterilmiştir. Fonksiyonel derecelendirilmiş malzeme (FDM) ile yapılan kaplama uygulamalarına ait termal gerilme analizi için deney modeli geliştirilmiştir. Bunun için termal genleşme katsayısı iki farklı fonksiyona göre değişen FDM ile kaplanmış plak modelleri oluşturulmuştur. Bu durumlara ait optimum derecelendirme fonksiyonuna ait bazı çıkarımlar yapılmıştır. İkinci olarak kalınlığı doğrultusunda ısıl genleşme katsayısı ve elastisite modülünün sürekli bir fonksiyonla değiştiği heterojen plakta termal gerilme analizi yapılmıştır. Bu tür problemler için literatürde önerilen analitik çözümdeki bazı eksiklikler belirlenmiştir. Literatürde şeritlerde termal gerilme analizi için önerilmiş“Şekil Değiştirmelerin Bastırılması Yöntemi (Strain Suppression Method)”ele alınan plak problemi için uygulanmış ve deneylerle uyumlu sonuçlar elde edilmiştir. Bu tür problemler için farklı malzemelerden imal edilmiş plak modelleri kullanılmıştır. Sayısal model kullanılarak kompozit plakta katman sayısı, katman kalınlığı, derecelendirme fonksiyonu, kompozitteki malzemelerin elastisite modüllerinin oranı parametreleri çalışılmıştır. Ayrıca kompozit ile kaplanmış plakta kompozit özellikleri de parametre olarak seçilmiştir. Deney modelleri katmanlarındaki malzeme özellikleri adım değişimi, modellerdeki malzeme katsayılarının sürekli veya çok katmanlı (>2) adım değişimi için bir referans noktası olarak kullanılmıştır. Yapılan analizler sonucunda elastisite modülünün değişiminin çeşitli tabakalı kompozit ve FDM için gerilme dağılımlarına ve gerilme konsantrasyonunun değişimine etkileri gösterilmiştir. Dört katmanlı deneysel model, katmanlı bir kaplamanın sonucu olarak termal gerilme dağılımlarındaki farkları göstermiştir. Elastisite modülünün değişimi açısından malzeme derecelendirmesini optimize etmek için ampirik bir formül türetilmiştir. Bu formül, kompozit plakalardaki malzemelerin veya kompozit malzeme ile kaplanmış plakalardaki kaplamaların derecelendirmelerinin, doğrulanmış analitik ve sayısal modellerle optimize edilebilmesini sağlamaktadır.

Özet (Çeviri)

Functionally graded materials (FGMs), a class of heterogeneous materials, are of great importance in application areas and techniques due to the various advantages and advances they offer in many engineering fields. Functionally graded materials are generally produced by changing their properties from ceramic to metal with a continuous function. Properties such as modulus of elasticity, Poisson's ratio, and coefficient of thermal expansion are changed depending on the functions. Layered composites, which are a class of composite materials, are also produced by changing the volumetric ratio in this way. In applying functionally graded materials, the gradation mentioned in the material properties is also created by combining a certain number of layers. The targeted functional gradation in the material can be represented by selecting a sufficient number of layers. In various industries such as defense, chemistry, and aerospace, the analysis of thermal stresses caused by high-temperature differences in composite materials and functionally graded materials is of great importance in terms of the design and sustainability of these materials. Studies in the literature have shown that appropriate grading reduces stress variations and stress concentrations caused by changes in material properties and geometrical discontinuities, respectively. Thermal stress concentrations may occur in the joint surfaces of materials and in the cavities and cracks that form in the materials over time. All these defects and stress accumulations that occur can reduce the performance of the material and prevent it from working with the desired features. Therefore, the analysis of thermal stress distributions is of great importance for the correct determination of the life of the structure and the determination of safe resistance limits in the structure. To verify the existing numerical and analytical studies in the literature and contribute to this field, the thermal stress of functionally graded materials should be properly performed using experimental methods. Stress concentrations and thermal stress distributions in the vicinity of defects or cavities that may occur in functionally graded materials were investigated for long-term structural design. In this study, the analysis of thermal stresses in a free plate under the effect of a constant temperature change was directed to the study by examining the studies presented in the literature and drawing some discussions and conclusions. Layered composites and functionally graded plates used in many areas today were considered. The study was carried out on two basic problems where functional gradation in the material is provided with only the thermal expansion coefficient and the material gradation is provided with both thermal expansion and the modulus of elasticity changes. In experimental studies, the three-dimensional photoelasticity method was used. The photoelasticity method is based on David Brewster's discovery of the birefringence property of light by observing the color fringe beams formed under the effect of tension in glass plates under polarized light. It is suggested that in some engineering applications, using glass models or materials like polymers suitable for optical examination with birefringence under light would allow the measurement of stresses under loading of the structures. In this study, many polymer-based materials were obtained and their mechanical and thermal properties were determined. Single/Dual (S/D) cantilever beam tests were performed in DMA Q800 (Dynamic Mechanical Analyzer) device to determine the glass transition temperature and viscoelastic temperature values of the samples. Tension tests were also performed in DMA to determine the elasticity modulus ($E$) values. When materials are heated, their thermal expansion coefficients also change. Force-controlled tests were performed using the tension clamp in the DMA device to determine the expansion coefficients of the supplied materials. The tests were conducted by selecting the force-controlled stress deformation method in the DMA device. The temperature was increased to 180 °C with a regime of 2 °C/min and kept at this temperature for 5 minutes. The aim here is to calculate the thermal expansion coefficients by reading the length changes and thermal expansion values under the effect of temperature without applying any load to the sample placed in the tension head and by using the known temperature values. For S/D tests, the test procedure was applied in multifrequency strain-temperature ramp-frequency sweep stages. Amplitude (amplitude), frequency (f), and soak time were 15 µm, 1 Hz, and 5 minutes respectively. The temperature value was increased to 190 °C starting from 35 °C with a 3 °C/minute increase. Furthermore, force controlled test method and stress-strain graphs were selected in film tension tests. The temperature was increased to 155 °C in 30 minutes and the test was performed by increasing the temperature to 18 N with a change of 0.5 N/min. The mechanical modeling method of thermal expansion in photothermoelasticity has been used in experimental studies. The mechanical modeling method refers to the mechanical creation of deformations caused by the desired temperature difference on a material suitable for photoelastic examination. In this method, the element manufactured from the material on which the model will be created is slowly heated in a certain heating regime in a furnace suitable for photoelastic examination until the viscoelastic temperature strain is reached. The viscoelastic temperature is the temperature at which the material behaves linearly elastic, as it does at room temperature. At this temperature, the material is subjected to mechanical loading that will create the deformation determined by the temperature. By applying the analogy of the equality of deformations in photoelasticity, the thermal expansions that will occur in the case of applying a constant temperature change to an element made of different materials in photoelasticity experiments can be practically modeled mechanically by applying a different temperature change to an element made of the same material. First, experimental and numerical models were developed to understand the thermal stress distribution in a functionally graded plate where only the thermal expansion coefficient is graded. The experimental models include three different two-layer plates and three-layer plates with different cavity types and geometries found in the literature. In order to verify the experimental and numerical analysis, an analytical solution is derived to obtain the thermal stress distributions in a free plate under the effect of constant temperature change. Three two-layer models can be considered as a bimetal prototype model. The effects of the radius of the cavity and the distance between the cavity tip and the interface on the stress distribution and stress concentration factor $K_C$ were observed. The three-layer composite model consisting of three layers with three different thermal expansion values in the same range as the bimetal models was investigated to determine the effects of changing the thermal expansion coefficient. The analytical solution and experimental models derived in this study were used to validate the numerical model proposed to investigate the effect of the change in the modulus of elasticity and the coefficient of thermal expansion on the thermal stress distribution. The finite element model is created as half of the unit-thickness section in the experimental model due to symmetry. This section is defined with the symmetry condition at the inner boundaries in the ABAQUS finite element analysis program. There is no stress and displacement on the outer surfaces of the model. The material is defined as linear and elastic with the values taken from the experimental model. The finite element mesh is created using the ABAQUS finite element package algorithm with quadrilateral CAX4R (4-node bilinear axisymmetric quadrilateral) elements with a mesh size of 0.2. The mesh is improved due to geometric changes around the cavity. Experimental results were compared with the results of analytical solutions and finite element models. Since the finite element analysis results agree very well with other methods in the relevant areas, further analysis has been performed using this method to understand the behavior of the plate with only a functionally graded coefficient of thermal expansion. As the compatibility of the numerical method with the experimental method and derived analytical expressions is shown, the distributions of thermal stresses are obtained with the change of stress concentration at the cavity tip, the tip radius, and the distance from the cavity tip to the joint surface. It is shown that the stresses at the cavity tip decrease when an intermediate layer is added to a two-layer composite plate. An analysis of a particular substrate coated with a material whose coefficient of thermal expansion is graded according to two different functions is performed, and it is suggested that the optimal gradation should be between parabolic and linear functions. The previous model and solutions in which only the thermal expansion coefficient is graded are further developed and the problem of thermal expansion coefficients and elastic modulus values that change with a particular gradation in the direction of plate thickness was investigated. In particular, for the case where the material properties change with a certain function in the plate and for the case where the same modeling is done in the form of layered composites, the equations of thermal stresses in the free plate under the influence of temperature, which can be applied, were derived by the“Strain Suppression Method”. To verify the analytical formulation derived here and to understand the thermal stress concentration in functionally graded and laminated composite plates, experimental models based on three-dimensional photoelasticity were investigated. To understand the effects of the number of layers, the thickness of a layer, the grading function, especially the ratio of elasticity moduli and the coating, the models were replicated via the verified finite element analyses. The stepwise change of material properties in the layers of the experimental models was used as a reference point for the continuous or multi-layer (>2) stepwise change of material coefficients in the models. As a result of the analyses, the effects of the change in elastic modulus on the stress distributions and the change in stress concentration were shown for different laminated and continuous gradation cases. The four-layer experimental model showed the differences in thermal stress distributions as a result of a layered coating. An experimental formula was derived to optimize the material gradation concerning the change in the modulus of elasticity. The results obtained make it possible to optimize and enable the gradations of the materials in the plate or the plate coating using validated analytical and numerical models.

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