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1. Determine the effect of Marangoni convection on mixing of molten glasses
2. Predict the extent of mechanical degradation of polymers

Introduction to Nanocomposites

Nanocomposites refer to multiphase solid materials where one of the phases of the material has either one or two or even three of its dimensions being very small at less than 100 nanometers. Nanomaterials also refer to materials whose structure has distances in the nanoscale between the individual phases that comprise of the material. The nanoscale implies that the dimensions of the building blocks utilized in the design and development of nanomaterials is in the nanometer range for purposes of improving their mechanical and physical properties. Choosing nanocomposite materials whose nanostructures have distance of around 100 nm ensures that the flexibility of the particles is reinforced, and also that the dislocation movement of the nanoscale phase matrix thus achieving higher material strengths (Kašiarová, et al., 2009).

Microstructurally, the materials depict exceptionally high levels of surface to volume ratio of the non-scale phase thus guaranteeing a higher degree of reinforcement. It also results into a high aspect ratio, as the nanoscale material can be made of materials with different structures ranging from particles to yield nanoparticles, sheets or even fibers that yield nanotubes. Due to the dimensions of the nanoscale phase, the surface area of the interface of the reinforcement and the matrix of the composite is greater in magnitude in these materials than the other materials and this yields higher amounts of strength of the material. In addition, since the surface area of reinforcement in nanomaterials is exceptionally high, there is very little impact that the nanoscale phase reinforcement material affects the physical and mechanical properties of the entire material (Kašiarová, et al., 2009). Instead, the nanoparticles incorporates into the matrix may facilitate the electrical and thermal properties of the material, as well as the mechanical parameters of resistance to damage and wear, as well as stiffness and strength. The nanoscale phase of the nanomaterial is incorporated into the matrix phase during the manufacturing and processing stages where the nanoscale phase material is literally dispersed into the matrix phase. The quantity of the nanoscale phase material dispersed into the matrix phase is determined through its mass fraction, which is defined as the percentage of the nanoscale phase in the matrix by weight (Biasini and Bellosi, 2008). The arrangement of this nanoscale phase and its orientation within the matrix is also important in the determination of the thermal conductivity of the nanomaterial.

The aim of this study was to conduct a microstructural analysis and strength estimation of nanomaterials and Silicon nitride/Silicon carbide nanomaterials were considered. These materials continue to receive immense levels of attention in the industrial and academic worlds due to the mechanical properties that the two materials demonstrate in high temperature conditions. The material is known to demonstrate low toughness and resistance to fracture, thus requiring it to be reinforced using a nanoscale reinforcement matrix that will improve these mechanical properties of the new material (Biasini and Bellosi, 2008).

The nanocomposite will be developing by incorporating Silicon Nitrite nanoscale particles into a Silica Carbide matrix to develop a material with a high fracture toughness for resisting damage and wear, as well as high mechanical strength in different thermal conditions. The study will implement the use of finite element analysis methods in order to simulate the preparation of the  nanomaterial and to conduct a microstructural analysis and thus estimate the strength of the material.

Microstructural Analysis and Strength Estimation of Nanomaterials

As ceramic nanomaterial continue to find increasing industrial applications in industrial sectors  such as electronics, automotive, aerospace, consumer products development, medical, and military uses among others, the need  to improve their structural and mechanical properties is also greatly increased. These ceramic materials that are generally classified into nitrides, carbides, borides, oxides and oxy-nitrides present a broad variety in the in their properties and thus impacting their applicability in industry for different purposes. Some of the important physical, mechanical, and even structural properties that affect the application of the material in industry include the high temperature stability of the material, as well as its fracture toughness, brittleness, stiffness and strength (Greil, Petzow, and Tanaka, 2007, 21). Ceramic materials however demonstrate very low levels of fracture toughness and thus it limits the structural properties that make the material applicable in some industry sectors. Fracture toughness can be described as the resistance a material shows towards failing after the initiation of weak points and a crack has already occurred. When a material has a high level of fracture toughness, the material therefore demonstrates an ability to remain durable regardless of the possibility of the occurrence of failure on the material. Thus enhancing the mechanical properties of ceramic materials through improving their structures to form strong nanocomposites can be effective in improving the applicability of such material in industry.

An example of a ceramic material which can be converted into a nanomaterial is Silica Carbide (SiC) which is widely applied in the engineering field due to is high level of strength, a resistance to corrosion and creep as well as its high temperature performance characteristics. This material demonstrates a high level of yield strength and hardness levels of 9GPa and 2800/mm2 respectively, yet has a low fracture toughness level of 4.6MPa (Hermann, et al. 2008). This is due to the fact that the material contains strong covalent bonds between the silicon and carbide atoms, yet ionic bonds form up the microstructure of the material. These ionic bonds determine the mechanical and physical properties of SiC. Thus any improvement on the microstructure of this material will result in an improvement of the toughness of this material.  

After the development of a crack, any loading conditions that have an impact on the surface having the crack risk the occurrence of failure for the material. Loading conditions that continue to occur on the material could easily result in a continuation of the development of the crack to failure r fracture, resulting in the failure of the entire structure of the material. Since ceramic materials have a mechanical property of high brittleness, the material is hardly ever able to resist the development of the crack when lines of weakness due to loading action occur on the material. As such, ceramic materials also experience low toughness and thus the applicability of the material in industry is highly limited by the low levels of fracture toughness (Balázsi, et al. 2003).

Researchers from different parts of the world have contributed to the development of new methods that can be used to improve the fracture toughness of ceramic materials. Several methodologies have been proposed as a  result of the contribution of these researchers, namely bridging the crack, blunting it, or even relaxing the field of strain on the area of the material that is affected by a crack. The first procedure details the process of blunting the crack such that it follows a predetermined cause of failure to encourage the possibility of repairing the structure. Bridging a crack in ceramics would entail the incorporation of new material to bridge the crack and ease all the loading tension felt on the area to discourage the progression of the crack (Greil, Petzow and Tanaka, 2007). Finally the method of easing and relaxing the field of strain on the affected area on the material would entail an identification of the strains that contribute to the progression of the crack. In easing the strains felt in that area, the strain conditions are able to redistribute themselves in order to reduce and even permanently stop the progression of a crack, paving way for the implementations of other interventions to prevent the impact of the crack.

Finite Element Analysis Methods in Simulating Preparation of Nanomaterial

When considering the ceramics-based on the material known as silicon carbide (SiC) different forms of modelling can be incorporated in order to devise workable solutions about the deformation and toughness improvement of ceramic materials. These methodologies utilize both atomic and technological modelling solutions through enriching silicon carbide ceramic materials with nanodiamond composites, carbon nanoparticles as well as the development of nanoscale tubes or films where some of the silicon atoms are replaced by carbon atoms. These new additions into the structure of the ceramic material are able to improve the toughness and strength of the material through considerations of atomic level structural linkages and even through the study of simulated materials (Hirano and Niihara, 2015, 251). The method allows for the alteration of the structure of the material to incorporate alternating layers of brittle and ductile materials which has an impact of increasing the strength and toughness of the material. As such the strength and toughness of the SiC material can be improved by changing the structure of the material to incorporate alternating layers of brittle and ductile material through the preparation of a  nanomaterial. This can be achieved through the doping of Yttrium with SiC sample with Carbon.

With modelling and simulation, complex simulations of different improved software systems that allow the analysis and assessment of the properties of the modelled material are simulated. The simulation is able to demonstrate the microstructural conditions of the newly modelled composite. This allows for the system to model and simulate the bonding and atomic structure of the material thus enabling more changes to be done in order to optimize mechanical and structural properties of the modelled material for its intended purpose or goal. This allows the design of the material to be done to completion by considering all possible factors influencing the proposed design (Hirano and Niihara, 2015). As such the designer or developer of the material has an opportunity to test that efficiency and the accuracy of the material design before any actual material manufacturing is commenced on.

To improve the toughness and brittleness of Silicon nitride, nanoparticles of silicon carbide can be incorporated to make a Si3N4-SiC nanomaterial. Since both of the materials to be incorporated into this study are ceramic material, they demonstrate good mechanical and structural properties at high temperatures. It is also worth noting that the mechanical properties of the two materials differ considerably since for instance Silicon Nitride has a comparatively good fracture strength while the Carbide demonstrates high toughness and strength. This is due to the fact that Si3N4 has as intergranular glassy phase separated by the granular separations of the material which softens in high heat conditions to cause the intergranular boundary to slide against the other layers and thus a low strength and toughness level (Nangrejo, Bao, and Edirisinghe, 2000). Thus the development of a  nanomaterial where the nanometer sized particles of SiC will be dispersed within the guarantee the improvement of the fracture toughness of the nanomaterial Si3N4 matrix. Addition of the SiC to the Si3N4 reduces the properties of the glassy phase of the nitride, such as the percentage amount of this glassy phase, as well as the crystallization behavior and viscosity of the phase thus reducing its property of low strength and toughness in the nanomaterial.

Improving Structural and Mechanical Properties of Ceramic Materials

In addition, simulation studies indicate that an amorphous interfacial area between the two materials is formed during the preparation of the nanomaterial, and this has an impact of the interface being a site of crack nucleation. This results in an improvement of the fracture toughness and the strength of the material through a non-diffusional technique of reducing the size of the grains (Kašiarová, et al. 2009). This in turn hinders action of plastic flow on the intergranular boundary of the glass phase to hinder the growth of cracks into failure or fractures.

 as a nanomaterial can be generated through a number of methods ranging from polymer pyrolysis, carbon deposition, and even powder mixing, depending on the preparation conditions. The most common method of preparing the nanomaterial is through the in-situ method of nitridizing a powder of Silicon Carbide (SiC) to generate . In this method, the SiC is taken to be nanoscale reinforcement phase while the Silicon nitrideis taken to be the in situ matrix. The nanomaterials are achieved through the process of dispersing the nanoparticles of SiC within the grains of the matrix or even the grain boundaries of that matrix. After the dispersion of the reinforcement particles into the matrix material, a process known as hot pressing the precursor powders of SiC-N to form an amorphous interface between the nanoparticles and the matrix (Wan, Duan, Mukherjee, 2015, 12). This in turn results into an improvement in the fracture toughness of the matrix which can be maintained to a temperature of 1200°C.

The dispersion of the SiC nanoparticles has a positive impact on the mechanical properties and even the microstructure of the nanomaterials, and this positive trend can be maintained even at high temperatures. The powder mixtures considered for the preparation of a  nanocomposite taken through a high pressure treatment to facilitate the distribution of the nanoscale phase material in homogeneity into the powder mixture. This method allows for the ratio of the two ingredients to be controlled and thus monitoring the kinetics of the reaction. This method also allows for the utilization of cheap materials thus allowing for an analysis of the microstructure and the mechanical properties of the nanomaterials to be conducted (Wan, et al., 2006). While the nanocommposites demonstrate mechanical drawbacks such as brittleness and a low tolerance to flaws and cracks on the material, thus demonstrating a low reliability in their different applications. Other important aspects that both the nanocomposites of silicon carbide and silicon nitride demonstrate include the high resistance levels to oxidation as well as the creep behavior demonstrated by the materials. Thus making a nanocomposite seeks to improve the mechanical properties of the material at high temperatures and thus their reliability to their application for use and the lifetime use of the material for its intended purpose (Nangrejo, Bao, Edirisinghe, 2000).

Incorporating the nanoparticles of SiC as the reinforcement phase into a Si3N4 ceramic matrix is achieved through the processes of high pressure treatment known as hot-pressing with hindered densification. Hot pressing increases the relative density of the material with the increasing degree of SiC nanoparticles and then eventually begins to decrease with the increase in the amount of SiC nanoparticles due to the tendency of the nanoparticles to inhibit the densification of the entire composite nanomaterial.  The  nanomaterial with the best mechanical properties are derived by utilization of Carbon and Silica (SiC) which are cheap being dispersed into the Si3N4 ceramic matrix (Kašiarová, et al. 2009). The chemical reaction for the production of the  nanocomposite begins with the combination of carbon with a pure powder of SiC to formulate silicon nitride (Si3N4 ).

Silica Carbide as a Nanomaterial

Silicon carbide is then added at this stage without any sintering aids and then the mixture was uniaxially compacted into Silicon nitride through the process of nitridition. This stage is further optimized through the variation of the nitridition temperatures. After the new nanomaterial has been collected, an X-Ray diffraction analysis will be conducted in order to establish the crystalline phases of the sample. Hot pressing increases the relative density of the material with the increasing degree of SiC nanoparticles and then eventually begins to decrease with the increase in the amount of SiC nanoparticles due to the tendency of the nanoparticles to inhibit the densification of the entire composite nanomaterial.  The fracture can thus be evaluated by the identifying the fracture strength of the material. As the content of SiC nanoparticles continues to increase they suppress and limit the transportation of mass on the grain boundary of the matrix thus retarding the rate at which α grains are transformed to grains (Rendtel et al 2008).

Some of the mechanical processes that will be analyzed in this study will include the fracture strength of the nanomaterial, the micro hardness of the material, and creep. The microstructure of a  nanomaterial is done using Electron Microscopy techniques and using X-Ray Diffraction techniques. Electron Microscopy techniques include the use of two types of electron microscopes known as the scanning and transmission electron microscopes also known as SEM and TEM. For microstructural analysis, experimental method are performed through the characterization of the nanocomposite using the sections of the Scanning Electron Microscope that are either etched with plasma or those  that are polished. The diameter of the material being analyzed is first estimated before X-Ray diffraction methodologies are used to identify the phase components of the nanomaterial. The hardness of the material was measured using a Vickers’ indentation device at a given load. The Young’s modulus was also measures using the same indentor a different technique referred to as depth sensing. The strength of the material can also be determined using four point flexure tests. Notch beams were also utilized for the determination of the fracture tension of the nanomaterial through the chamfering of the edges of the sample material to prevent the tensile failures emanating from the edges of the specimen. The creep of the nanomaterial was also measured by placing it in the creep machine where the loading system. The strain of the material is also taken to be the creep strain of the material and used to compute the rate of creep of the nanomaterial. The oxidation patterns of the materials were also measured in the process of heating and cooling the material and then an XRD. X-Ray microanalysis was also conducted on the specimen. The bulk density of the specimen was also measured through the technique known as Archimedes immersion where the specimen is inserted in a toluene solution (Lindley and Godfrey, 2011). The analytical computations can be computed using the formulae below:

For the 5MPa loading characteristics, deformation of the reinforcement material can be computed following the impact of tension and compression. 

Enhancing Mechanical Properties of Ceramic Materials through Nanocomposites

While the deformation of the entire composite after the reinforcement phase has been included and dispersed on the matrix can be computed following the impact of tension and compression. 

Where L is  the length

F is the force exterted

A is the surface area of force exertion

E is the Young’s Modulus and

 is the maximum amount of tension or compressive stresses 

The microstructural simulations have been conducted using the ANSYS software by estimating the fracture toughness of the simulated the  nanomaterial. The details obtained can be used to optimize the fracture toughness of the material through modeling the material’s failure when there is already a crack on the material. This is achieved through varying the thickness of the material. The microstructure of the material was analyzed through finite element analysis software known as ANSYS.  In the ANSYS simulation, the  nanomaterial was geometrically modelled in order to analyze the compressive and tensile loads that a specimen of the material experiences. The layers of the model of the composite were modelled as SHELL181 which ids the most suitable model for the Analysis of the nanocomposite and thick shell structures and materials (Weinmann, Zern, and Aldinger, 2001). The material modelled was assigned four nodes for all the vertices of the specimen modelled and also each of the nodes assumed to have 6 dof (degrees of freedom). These allowed the specimen to be sampled in the x, y and z-directions. The option of degenerate triangular was selected when modelling the incorporation of the filler element of the composite. The model of SHELL 181 allowed for the strain and stress simulations to be conducted on the specimen, as well as an analysis of linear and nonlinear applications of the stress and strain curves.

The simulation involves the geometric modelling of the Silicon Nitrite matrix phase where the Silicon Carbide reinforcement phase of the composite is simulated to be reinforced on in order to form a  nanomaterial. The stiffness and loading conditions are thus accounted for in this simulation and the stiffness parameter is related to the factors that affect the distribution of pressures and stresses on the modelled simulation. This model also guarantees that the accuracy of the obtained results and recommendations is as a result of the shear deformation of the different loading to cause deformation (Poorteman, et al. 2003). The measures of the stress and strain obtained in this simulation forms the foundation of the formulation of this system using kinematic aspects that promote the impact of strains. The results of the simulation were compared with the results obtained from past literature on the experimental analysis of the same material. The parameters that can be compared include the aspects such as strain, stress, deformation, and even the value of the Young’s Modulus of the material for different conditions of loading. The dimensions of the specimen being simulated were 256.73*312.36*2000nm and was reinforced with a reinforcement phase whose dimensions were 120*60*20nm. To obtain a  nanomaterial composite meshed model, the element size of 1.5 nanometers was utilized in order to obtain nanotube materials with a structure that is similar to a honeycomb (Choi, Heness, and Ben-Nissan, 2018). The model was then analyzed in both the plane and longitudinal axes then tested for the tensile and compressive behavior of the material at different loading values ranging from 5-15MPa. The value of the poison’s ratio was selected at 0.33 for both axes while the Young’s Modulus for the horizontal and longitudinal planes was 13GPa and 7.5 GPa respectively.

Limitations of Ceramic Materials

After the ANSYS application was opened and a new work was began the simulation process began with the identification of the molecular models that were to be simulated by the system. The unit cells of the materials being modelled in this report were Silicon nitride (Si3N4) and silicon carbide nanoparticles (SiC). The values of the lattice constants that had been proposed in the literature review section of the report were selected and then incorporated into the simulation.

The layers of the analysis that would be simulated in this exercise were also selected and the structure of the material modelled with regard to the geometry of the material. The ANSYS version used for this simulation was version 16.1 Release. The unit system for the values that would be keyed in was then set to the metric system, and the units for measuring angles, totational velocity and temperature were set to degrees, rad/s and Celsius respectively. 

The dimensions of the model as proposed in the preliminary stages of the report were also keyed in to guarantee that the simulated model had the same parameters as the materials that were going to be put through experimental analysis methods. Another model obtained from the progress so far was used to simulate the material application condition in ANSYS. The geometry of the product was set to be fully defined solid body. The dimensions of the product that were used include a length dimension 0.0025673, a width (y-length)of 0.0031236 m and finally a height (length z) of 0.2m The volume of the figure was simulated  to 0.00011058m3 and a mass of 0.0066351kg. It was simulated to have 1263 nodes and 160 elements. The model was also chosen to be simulated using the Cartesian system of orientation

The simulation conditions were then chosen such that the temperature and loading conditions were keyed in and fitted into the model. In the first simulation, the models simulated are primarily equilibrated to ensure that the values for a stress free or ideal condition situation is modelled. Loading simulations allowed to ensure that the simulated data is able to yield a stress-strain curve that will be used to extrapolate and derive the other required parameters. Due to its capabilities in stress distribution simulations, the ANSYS software was best equipped to simulate the required results and data given that the orientation of the model was in the manner that it is required. 

To simulate the deformation levels of the simulated model, the modelling of the mechanical properties of the materials was then conducted. The model was first simulated in stress-free conditions and then the application of the loads commenced. The system was  then able to derive a stress strain curve from the loading conditions that were simulated on the model. 

The simulation of the model of equivalent deformation was obtained after applying the strain along the y axes of the model and then the data obtained was plotted against the expected location of the atoms of the model. The maximum value of deformation according to the simulation was 0.038844nm while the minimum amount is 0.00nm.

To estimate the equivalent von misses stress felt by the model during the simulation, tge average data obtained from the strain curve obtained in the above process is developed into the amount of engineering virial loading conditions that is used in the determination of the stresses the material will feel as well as the impact of the strains applied on the material using the von misses criterion in engineering. The equivalent von misses stress for this simulation was found to be a maximum of 4. 6296 MPa while the minimum stress is 2.5616 MPa.   

Findings of microstructural analyses conducted using scanning electron microscopes are able to depict the distribution of the grains of the matrix grains made up of the particles as well as the other grains that have a fine equi-axial structure. The intergranular phases of the matrix which are known to be glassy are also depicted in the SEM image and can be easily identified as the phases that reflect a brightness around the grains of the matrix. The size of a grain of the matrix has a diameter of about 150nm if it is within a  nanomaterial with a SiC reinforcement of 1% by weight and the number reduces to about 135nm if the composite has a SiC reinforcement of 5% by weight. The microstructure thus can be said to continue becoming finer and finer as more SiC nanoparticles are incorporated into the composite (Niihara, Izaki, and Kawakami, 2010). This is because the nanoparticles will have an impact of reducing the rate at which grains can continue to grow in the matrix and thus limiting the action of plastic flow on the intergranular boundary of the glass phase to hinder the growth of cracks into failure or fractures. 

For the sample, the X-Ray diffraction test results depicted the following result. 

The crystalline phases identified were the hexagonal phase of as well as the two orthorhombic crystalline phases namely  and . The intergranular glassy phase of the was stabilized in the process through its interaction with the nanoparticles in order to establish the orthorhombic structures of Yttrium desilicates as it is a  refractory material. The diffraction test was able to establish that the Silicon Nitride ( was only able to be converted into of  silicon nitride grains as no were depicted by the XRD. The test was also able to e stablish that the pattern of diffraction for the   nanomaterial with a SiC reinforcement of 5% by weight revealed only grains in a cubic structure (Tiang, Li, and Dong, 2009, 2549).

Mechanical properties that were measured in the experimental process under room temeprature  were summarized the table below

Material

Hardness

Young’s Modulus

Fracture Toughness

Strength

Composite (1%)

14.46 GPa

288 GPa

4.56MPa

790 MPa

Composite (5%)

16.34 GPa

320 GPa

3.75MPa

680MPa

A summary of the mechanical properties of the materials through experimentation analysis

The Young’s modulus of the composite is less than that of the nanoscale reinforcing phase due to the impact of a higher degree of deformation experienced as a result of the interface adhesion between the reinforcing particles and the matrix phase. This is because the particles if the SiC were both harder  and stiffer  and the matrix was softer on the matrix. The values of the fractured toughness recorded is higher for the nanocomposite with a bigger mass fraction of reinforcement particles (SiC) to imply that this specimen more fine grains and that the nanomaterial’s aspect ratio is lower than that of its counterpart. Any decreases in the Young’s modulus of the simulation that is dependent on load variations may be explained with the commencement of failure through the development of weak points or the initiation of cracks (Pezzotti and Sakai, 2010). The nanomaterial specimen with a higher mass fraction of the SiC reinforcement phase causes defects while analyzing the fractionation of the nanomaterial leading to a low flexural strength in this material. During sintering, the material also undergoes a process that leads to the production of SiC particles that result in any technical analysis inconsistencies that may be noted on the product.

High Temperature Mechanical Properties

In high temperature conditions, the mechanical properties of the  nanomaterial that ought to be considered include the creep rates and resistances as well as the oxidation behavior of the material. For instance, the graph below demonstrates the creep resistances of the modelled nanomaterials which presented different mass fractions of the SiC nanoparticles. The creep resistance of the material with the higher mass fraction of the nanoparticles was found to be higher in comparison to the nanomaterial with a lower weight of the SiC nanomaterial. The creep rate also demonstrates the behavior (Giorgi, at al.2016)

A graph depicting the behavior of creep rate in relation to temperatures at different stresses.

The activation energy (Qc) can also be computed as an inverse function of the temperature need for the material. This value was estimated to be at approximately 350lJ/mol for the two nanocomposite materials created. The plots of graphs of strain rates against stress for varying temperature ranges were found to provide stress components ranging from 0.8-1.3 for the nanomaterial with the higher nanoparticle content while it was 0.8-1.2 for that with the smallest content of SiC. This implies that the two materials exhibit a similar creep mechanism, as the nanoparticles of SiC incorporated into the matrix only has an ability of impacting only the processes that facilitate deformation within a material (Rendtel, et al.  2008)

Considering the oxidization behaviors of the material, the individual materials formed different oxidized layers after being exposed to the same oxidization conditions. For the  nanomaterial with a nanoparticle composition of 5%, the products of oxidation that developed on the surface of the material include a mixture of  and . Oxidation products also form within the silicon Carbide layer of the composite which can be structurally defines as fine globular crystals and needle-like structures  composed of . This is depicted in the images that are attached below (Park, Kim, amd Niihara). 

While the oxidation products realized on the two specimen had the same chemical composition, it depicts a varying morphology of the oxides that had been formed. This is  due to the impact of the elongated  crystals of  which occur to be smaller than the globular particles. This yields a lower aspect ratio in the  nanomaterial with 1% weight SiC than the one with 5% SiC. Higher exposure levels at the surface also result in the formation of a larger quantity of oxidation products. The distribution of Yttrium in the layer is responsible for the difference in morphology of the formed oxides. This is due to the fact that the yttrium oxides in the  nanomaterial with 1% weight SiC tend to collect on the surface and on the interface beween the material bulk and the oxide layer (Dusza, Saigalik, and Steen, 2009). This implies that the material will be covered by the oxides  on the surface in comparison with the amount of oxides that forms within the material layers. This also implies that any high temperature impact on the material might have resulted in many fine cracks on the material as a result of thermal stresses felt by the material  while heating it up to oxidize allowing for the material to diffuse  the oxides to  the surface of the material during its oxidation process.

The values obtained compare very well with the analytical data computed using the experimental results collected from the literature of other studies conducted before this one. Differences between the analytical values obtained in the experimental analyses of the studies that have been conducted before this finite element analysis simulation using ANSYS are minimal and similar. The simulation was able to yield depictions of the predicted deformations of the material under different loading conditions ranging from 5, 10 and 15MPa. The simulation was also used to predict the stress and strain conditions of the material under different loading conditions for both tensile and compressive loading conditions. (Riedel, Strecker, and Petzow, 2009)

The deformation of the simulation for both the tensile loading situations were modelled and the results were found to range from 0.042nm to 0.092nm for the reinforcing phase while it ranged from 0.19nm to 0.59nm across loading values between 5 , 10, and 15 MPa respectively. On the other hand, the deformation levels obtained for the three loading conditions of 5, 10, and 15 MPa in compressive loading were 0.63, 0.64, and 0.64 nm for the nanoscale reinforcing phase while it was 0.19, 0.39, and 0.58nm for the matrix phase of the nanomaterial. The von-misses strains obtained were also modelled for the tensile loading conditions and varied from 26, 54, and 59 MPa and 19.77, 40.1, and 60.2MPa for the loading conditions at 5, 10 and 15 MPa respectively. This was a different case in the compressing loading conditions where the values for the nanoscale material were 143, 145, and 165 MPa while they were 20, 40.1, 59.9 MPa for the entire nanomaterial. The strain values of the simulation were also obtained from the software values for different loading conditions and are detailed in Table 1 below which also details the values of the Young’s modulus for the reinforcement and the matrix of the composite.

The data was used to plot graphs of the load against deformation for both the tensile and compressive loading conditions which demonstrate the loading effectiveness of the materials under different loading condition. The deformation of the entire composite is depicted to reduce while that of  the nanoscale reinforcement composite is expected to increase since the response of the material increases due to a higher deformation of the matrix than the reinforcement. The results however depict that the loading and deformation vary linearly due to the Newtonian behavior of the materials. With regard to stress and strain curves strain also depicts a linear variation with strain for both the matrix phase and the reinforcement phase of the nanomaterial. The linearity is however only depicted for certain loading levels and then a surge in the strain properties of the materials is demonstrated. This could be explained by the consideration that the sudden increase in the strain is brought about by the initiation of a crack which eventually develops into cracks and then the failure of the material (Tomar, 2008). Any differences noted in the stress-strain relationship of the materials can be further propagated by the impact of strain hardening.

The results obtained from conducting this study demonstrated that an increase in the amount of the Silicon Carbide nanomaterials were incorporated in the Silicon nitride matrix results in a declination of the transformation of the grains into their counterparts as well as the growth of the grains of the matrix (). This results in an increase in the amount of equiaxed grains of the matrix. This in turn results to an inhibition of the strength and toughness of the material in the long-term, although it will result in an increase of the toughness and strength of the nanomaterial at first (Sawaguchi, Toda, and Niihara, 2011). The relative density of the composite materials may also depict an improvement during the hot-processing stage. This changes as more nanoparticles are being added into the product resulting in an inhibition of the densification of the particles into the matrix. The maximum values of these three parameters were noted at the 25% mark.

This differs slightly for the highest value of fracture tension or strength that was noted at 5% mass fraction of the SiC nanoparticles dispersion into the matrix of the product. Beyond the 10% marked the fracture toughness will begin to show a decrease in the strength and toughness of the material. This decrease in the fracture toughness can be linked to the tendency of the material to inhibit the growth of grains of the longer and larger () due to the increase of the dispersions of the SiC (Kim, et al. 2009). Finally the mechanical properties of the material especially in high temperature conditions improved when the process of SiC dispersion was commenced due to the effect of the SiC nanoparticles to reduce the sliding of the intergranular grain boundaries of the silicon nitride matrix as the SiC particles enter granular boundary space of the matrix.

Conclusion and Recommendations 

Finite Element Analysis using ANSYS allows for a simulation of the stress and strain conditions of the nanomaterial in order to estimate the strength of the material. Microstructure analysis was also conducted in order to expand on the microstructural characteristics of the material thus explaining the mechanical properties of Silicon Nitride and Silicon Carbide nanomaterial. The values obtained were compared to the analytical results from computing values obtained in previous literature on study conducted on this topic for both compressive and tensional loading conditions.

The  nanomaterial that was simulated using ANSYS in this report was found to have the ability to efficiently withstand both the tensile and compressive loading they experience in their application before they encounter any failure or fracture (Turan and Knowles, 2005). This ability was able to increase with the increase in the number of nanoparticles being simulated, and then begins to show a decline even as more SiC nanoparticles continue to be added on to the composite. This behavior of  the relative density of the material increasing with the increasing degree of SiC nanoparticles and then eventually begins to decrease with the increase in the amount of SiC nanoparticles can be attributed to the tendency of the nanoparticles to inhibit the densification of the entire composite nanomaterial during the period of producing the nanomaterial. Further, as the content of SiC nanoparticles continues to increase they suppress and limit the transportation of mass on the grain boundary of the matrix thus retarding the rate at which α grains are transformed to grains. This implies that the dispersion of the nanoscale reinforcement phase fits the matrix phase in the best possible way, as it encourages the nanoscale reinforcement material to obediently respond to the mechanical and physical properties of the macro material (the matrix phase).

The analysis of   nanomaterial with varying amounts of SiC nanoparticle allowed for a microstructural analysis of the material in different conditions. The analysis helped to identify the impact of nanoparticles on the mechanical properties of the material that determine its strength and applicability in industry (Wan et al., 2006). Specifically, the impact of the SiC nanoparticles into the silicon nitride is an increase in the Young’s modulus of the nanomaterial as well as the hardness of the material. Other aspects that have been brought out in this study include the fact that a higher mass  fraction of the SiC  nanoparticles result in reduced strength characteristics of the material that contribute to technical  processes that are not satisfactory. This is because a high weightage of the SiC nanoparticles in a nanomaterial will bring about a higher level of creep resistance. This in turn changes the chemical compositions and reactions of the intergranular glassy phase of the  thus acting as an obstacle that limits the grain boundary sliding of the material thus affecting the deformation rates of the material. The limitation of the sliding of the grain boundary also prevents the additives from migrating homogeneously into the matrix affecting the physical properties of the material. This is also of extreme importance because it guarantees that the material is able to resist oxidation behavior and thus guaranteeing the durability of the material (Niihara, Izaki, and Kawakami, 2012). Addition fracture can thus be evaluated by the identifying the fracture strength of the material through the consideration of experimental methods.

Ceramic materials pose plenty of potential for usability in the industries as it could be applicable in high temperature, high corrosion and even high mechanical strength conditions. While the material demonstrates high strength and high stiffness qualities, it is greatly limited by the brittleness and the low fracture toughness qualities that limit the materials applicability in industry. This property is due to the impact of effect of the type of bonding witnessed in this type of materials as it has directional covalent  and ionic bonds that limit the deformation capabilities of the material and hence any dislocations on the structure of the material. This in turn maintains its fracture toughness and brittleness at an all-time low. Increasing the toughness and brittleness of the material would require that all the other beneficial properties of the metal like its strength and its stiffness are not compromised in the process. This thus guarantees the improvement of ceramic materials in order for them to be applied in many areas in the field of engineering for  different technical applications in fields  such as electronics, automotive, aerospace, consumer products development, medical, and military uses among others (Choi, Heness, Ben-Nissan, 2018). This is due to the fact that this intervention results in the eradication of the of the low fracture toughness properties in order to maximize on the exceptional properties of high stiffness and high strength even in thermally stressed conditions.

The use of the ANSYS software to simulate the microstructural characteristics of the material was important in ensuring that a new ceramic material with different properties that are favorable to the industry is successfully simulated. This will go a long way in making ceramic materials with desired mechanical and structural properties available to the markets as well as in optimizing the physical and mechanical properties of the material in order to address the problems of the future concerning the material. In the past the use of ceramic materials was limited to pottery although the material continues to acquire new demand as its properties continue to be ameliorated for better suitability in the industry. The material presents outstanding capabilities such as the capability to withstand high temperatures and demonstrate high strengths, resistance to damage and wear, strength, and stiffness, among other properties. Specifically, ceramics are largely utilized as a structural material as it is both strong and stiff (Dusza, et al. 2005). Ceramic material also demonstrates the property of being lightweight in comparison to other materials that are widely used in structural work like steel. The materials also costs less than other popularly preferred materials used in the structural field. 

References 

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