Master's Thesis of Mechanical Engineering-Applied Design
Abstract
In many applications, graphene (monolayer or multilayer) is used in the polymer matrix as a composite. In this research, ideal graphene with a hexagonal bond shape between atoms, located in a polymer matrix, with different boundary conditions, including stiff and simple, under biaxial external compressive loading and thermal loading is investigated. This composite is considered in the form of a stack.
For modeling, first displacements are estimated using the third order shear deformation theory and the polymer matrix will be modeled using two Winkler and Pasternak models. Using the strain-inertia gradient theory, the dynamic equilibrium equations are obtained and the equations are solved using the improved differential quadratic method. The temperature distribution on the surface of the structure is assumed to be linear with respect to the length and width of the plate, and in the form of a wide load. The natural frequencies and the shape of the corresponding modes are calculated depending on the system parameters at different temperatures, and the effect of parameters such as Winkler and Pasternak coefficients, strain-inertia gradient parameters and also the number of grid points are investigated. From the very high natural frequencies obtained in this research, the high hardness of the system can be concluded. rtl;">1-1-1 History:
In graphite[2] (another allotrope of carbon), each of the tetravalent carbon atoms is connected to three other carbon atoms with three covalent bonds and forms an extensive network. This layer itself is placed on completely similar layers and in this way, the fourth valence electron also forms a van der Waals bond that is weaker than covalency. For this reason, graphite layers easily slide on top of each other and can be used in the tip of a pencil. Graphene is a material in which there is only one of these graphite layers, and in other words, the fourth bonded electron of carbon remains as a free electron.
Although Philip Wallace[3] wrote about graphene[4] for the first time in 1947, and since then many efforts have been made to make it, but the Mermin-Wanger theorem[5] existed in statistical mechanics and quantum field theory. He considered making a two-dimensional material impossible and unstable. However, in 2004, Andre Geim[6] and Konstantin Novoself[7] from the University of Manchester managed to make this substance and showed that the Mermin-Wanger theorem cannot be completely correct. The 2010 Nobel Prize in Physics was also awarded to these two scientists for the construction of two-dimensional materials.
1-1-2 Introduction:
Graphene is a two-dimensional structure of a single layer of carbon honeycomb network. In graphene, each carbon atom is bonded to three other carbon atoms. These three links are in the same plane and the angles between them are equal to 120?. In this case, the carbon atoms are placed in a position that creates a network of regular hexagons
Of course, this is the most ideal state of a graphene sheet. In some cases, the shape of this sheet changes in such a way that pentagons and heptagons are also created in it.
Graphene has become a unique material due to its extraordinary properties in electrical and thermal conductivity, high density and mobility of charge carriers, optical conductivity [1] and mechanical properties [2]. Due to these extraordinary properties, this new solid state system is considered as a very suitable candidate for replacing silicon in the next generation of photonic and electronic components, and thus it has attracted little attention in fundamental and applied research. The length of the carbon-carbon bond in graphene is about 0.142 nm.
The basic structure for making carbon nanostructures is a single layer of graphene, which, if placed on top of each other, forms a three-dimensional mass of graphite.
The underlying structure for making carbon nanostructures is a single layer of graphene, which if placed on top of each other, form a three-dimensional mass of graphite, and the interaction between these sheets is van der Waals type with a distance between the sheets of 0.335 nm. If the graphite sheet is twisted around the axis, it forms a quasi-one-dimensional carbon nanotube, and if it is twisted spherically, it forms a quasi-zero-dimensional fluorine. Graphene layers from 5 to 10 layers are called thin layer graphene and between 20 to 30 layers are called multilayer graphene, thick graphene or thin graphite nanocrystals. Pure single-layer graphene shows quasi-metallic properties [3].
1-1-3 Graphene manufacturing methods
Today, many different methods are used to manufacture graphene, the most common of which are mechanical exfoliation, chemical exfoliation, chemical synthesis, and chemical vapor deposition [1]. Some other methods such as carbon nanotube splitting [4] and microwave manufacturing [5] have also been used recently. An overview of graphene fabrication methods is given below:
bottom-up (from carbon atom to graphene sheet)
thermal cleavage
chemical vapor deposition [6]
plasma
Abstract
The Stone Age, the Bronze Age, the Iron Age. Every global epoch in the history of mankind is characterized by materials used in it. In 2004 a new era in material science was opened: the era of graphene or, more generally, of two-dimensional materials. Graphene is the one-atom thin layer of sp2-bonded carbon atoms arranged in a honeycomb lattice. It possesses the unique physical properties: graphene is the strongest and the most stretchable material known, has the record thermal conductivity and the very high intrinsic mobility and is completely impermeable. The charge carriers in graphene are the massless Dirac fermions and its unique electronic structure leads to a number of interesting physical effects, such as the minimal electrical conductivity, anomalous quantum Hall effect, Klein tunneling, the universal optical conductivity and the strong nonlinear electromagnetic response. Graphene offers and promises a lot of different applications, including conductive ink, terahertz transistors, ultrafast photodetectors, bendable touch screens, strain tensors and many others.
In many applications, graphene (single or multi layered) is used within a polymer matrix in composite form. In this research, an ideal graphene with hexagonal bonds between its atoms, located in the polymer matrix, under biaxial external pressure and thermal loading is investigated. The composite is single layer and different boundary conditions including clamped and simply supported are considered.
For modeling of the problem, firstly displacements are estimated using the third order shear deformation theory and Winkler and Pasternak models are used to model polymer matrix. Then, dynamic equilibrium equations are obtained using the Strain-Inertia Gradient theory and solved using Generalized Differential Quadrature (GDQ) method. The temperature distribution is assumed to be linearly distributed in terms of the length and width of the structure. Natural frequencies and corresponding mode shapes which are depending on the system parameters are calculated at different temperatures, and the effect of parameters such as coefficients of Winkler and Pasternak, Strain-Inertia Gradient parameters and the number of lattice points, are obtained. The high hardness of the system is the result of very high natural frequencies obtained in this study.