Stress analysis, estimation of behavior and elastic properties of carbon nanotubes under tensile loading

Master's Thesis

Mechanical Engineering - Applied Design

Abstract

In recent years, most of the research has been focused on compressive and combined loading in order to investigate the buckling of nanotube structures, and for this purpose, the work done on tensile loading is very limited. Since the results of compressive and tensile loading in carbon nanotubes are completely different (due to the effect on repulsive and attractive interactions in these structures, which are of different nature and amount), so the research works on these structures are still under the optimal tensile load of the researchers and are still being investigated.

Linear and high-order approximations as well as software modeling using Lamps specialized software show that the changes in the elastic modulus are inversely proportional to the changes in diameter or index of nanotubes, and with the increase in diameter and decrease in the effect of curvature, the elastic modulus of nanotubes also decreases. Also, the stress-strain diagrams are similar to the diagrams of brittle materials, with the difference that the percentage of elongation and maximum stress are observed in them. The mechanical behavior of nanotubes has been simulated in software modeling up to the breaking point of the first link in these structures, and the difference in stress and strain values ??between software modeling and analytical method charts is caused by the effects of environmental factors such as temperature and pressure, intrastructural instabilities in the non-linear region, and the effect of length parameters, strain rate, etc. which is consistent with reality and logical.

Introduction

After the first practical experiment in 1991 by Ijima [1] on carbon nanotubes, most of the attention was drawn towards these materials and the estimation of their different properties. Very high mechanical properties against low weight, excellent electrical and thermal properties, are among the unique properties that have turned carbon nanotubes into unique structures in today's world and the focus of all kinds of engineering sciences, especially mechanical engineering. Analyzing the structural mechanics of these materials and estimating their mechanical properties using different methods and ideas has always been the focus of researchers. The general results show that mechanically, carbon nanotubes have a tensile strength of about 20 times that of steel with the highest tensile strength in nature, as well as the modulus of elasticity (Young's modulus) at the terapascal limit (TPa). Of course, these extraordinary properties also have a clear scientific justification, and that is due to the very strong SP2 hybrid carbon-carbon bond in this structure, which is also the strongest type of bond in nature. A person named Kian 2 [2] recently reported that adding only 1% by weight of carbon nanotubes increases the tensile strength of polystyrene composite films by 25%. In estimating the properties of carbon nanotubes, many researchers have used continuous medium models, especially the skin sheet model, which matches well with the geometric structure of nanotubes. Although these theories also have limitations, they have shown good results compared to the results of practical and laboratory work, and they are easier to use than other methods. In general, it is very difficult and expensive to measure the properties of carbon nanotubes practically and in a laboratory at nanoscale.

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Iijima

Qian

Of course, in recent years a very powerful tool has been used to estimate and check the mechanical properties of nanotubes with very high accuracy. It is known that the simulation is called molecular dynamics method 1. This method is a suitable tool to get rid of the difficulties of the experimental method and confirm the results obtained by analytical theories. The researches conducted on carbon nanotubes are numerous and diverse due to their extraordinary reported properties. Different people have always tried to achieve more accurate results with new theories and simpler methods.Based on this, characteristics such as Young's modulus, Poisson's ratio, stress-strain relationships and their values, maximum stress, failure strain, etc. It has always been considered by researchers. The first test to measure the modulus of elasticity in multi-walled carbon nanotubes resulted in the value of 1.8 ± 0.9 TPa [3], and then Wang [4] reported a slightly lower value of 1.28 ± 0.59 TPa. Yu 3 [5] found the tensile strength and Young's modulus of single-walled carbon nanotubes in the range of 11-63 GPa and 0.27-0.95 TPa, respectively. Krishnan 4 [6] also measured the elastic modulus of single-walled carbon nanotubes in the diameter range of 1.5-1 nm for 27 nanotubes at about 1.25 TPa. Low 5 [8, 7] and Lier 6 [9] have also obtained the Young's modulus 0.97 and 1 TPa with the experimental force constant models 7 and basic principles calculations 8. All the above results even considering their error show that the mechanical properties of carbon nanotubes are very high. rtl;">Krishnan

Lu

Lier

Emperical force constant model

ab initio

Srivastava

Among the other works done, we can mention the research of Sri Vastava 9 [10] for carbon nanotubes (0 and 8) using the molecular dynamics method indicated that this structure can be compressed up to 12% and under such an elastic limit, the stress is in the range of 110-125 GPa. In recent years, most of the researches have been focused on compressive and combined loading in order to investigate the buckling of nanotubes structure, and for this purpose, the works done on tensile loading are very limited. Since the results of compressive and tensile loading in carbon nanotubes are completely different (due to the effect on repulsive and attractive interactions in these structures, which are of different nature and amount), therefore, research works on these structures under the optimal tensile load of the researchers are still being investigated.

let's pay In terms of structure, carbon nanotubes are generally divided into two general categories, which are single-walled carbon nanotubes 1 and multi-walled carbon nanotubes 2. A single-walled carbon nanotube can schematically be the result of bending a graphite sheet and turning it into a cylindrical tube, and a multi-walled carbon nanotube is a collection of single-walled carbon nanotubes that are aligned and centered inside each other. The direction of bending and bending of the graphite sheet is defined by a vector called Chiral 3 or Ch(n,m). Figure 1-1 represents this vector in the nanotube structure. Using this vector, you can define all kinds of atomic structure arrangements.

Abstract:

In this research first we have estimated elastic modulus of zigzag and armchair single walled carbon nanotubes (SWCNTs) under uniaxial tension using a new combined method and then verify obtained results from analytical method with results of other analytical and experimental works. Results shown when diameter or indices of SWCNTs increases the young modulus of SWCNTs decreases and in the same diameter the modulus of an armchair SWCNT is more than a zigzag SWCNT. materials.

In last chapter using a computer modeling we modeled armchair SWCNT (10,10) and zigzag SWCNT (17,0) based on suitable boundary condition with LAMPS software and applying axial tensile loading and checking strain energy in small strains, elastic modulus and stress-strain diagrams of both of zigzag and armchair SWCNTs obtained.