TWO-DIMENSIONAL AND NUMERICAL ANALYSIS OF … · International Interdisciplinary Journal of Scientific Research Vol. 1 No. 2 November, 2014 29 TWO-DIMENSIONAL AND NUMERICAL ANALYSIS

International Interdisciplinary Journal of Scientific Research Vol. 1 No. 2 November, 2014

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TWO-DIMENSIONAL AND NUMERICAL ANALYSIS OF

SIALON-BASED CUTTING TIPS THERMAL CONDUCTIVITY

BY USING SEM IMAGES

Battal DOĞAN* and Nur ÇEKEL**

* Department of Mechanical Engineering, Faculty of Engineering, Kirikkale University,

Kirikkale, 71450 Turkey Email: [email protected]

**Ministry of Transport Maritime Affairs and Communications Ankara, Turkey,

Email: [email protected]

ABSTRACT

In this study, two-dimensional and numerical solution of sialon-based cutting tips’thermal conductivity was

done by using SEM images. Finite element solutions were repeated for different area ratios and node

amounts. Area ratios and node amounts changed according to the structure of finite element model. While

sintering the materials, grain boundary phase called as “interphase” occurred beside the main phase

structure.This structure was made out in the electron microscope (SEM) images of material and in the

models of numerical analysis. While doing the numerical analysis, effective thermal conductivity was

computed by a finite material based program (Ansys) depending on knowing the conductivity of main phase

and interphase by considering SEM images as a two-dimensional surface. The calculations were given as

comparative to the analytical and experimental results. When the results are compared, it is proved that

thermal conductivity of cutting tips or the similar materials with two-phase structures can be set down by

numerical calculations beside their analytical and experimental measurements.

Keywords: Thermal Conductivity, Sialon, Cutting Tip, SEM

International Interdisciplinary Journal of Scientific Research ISSN: 2200-9833 www.iijsr.org

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Nomenclatures

A Area (m2)

L Length (m)

k Thermal Conductivity (W/m.K)

ke Effective Thermal Conductivity (W/m.K)

kf Thermal Conductivity of Main Phase Material (W/m.K)

km Thermal Conductivity of Inter Phase Material (W/m.K)

φ Volumetric Rate

T Temperature (K,0C)

kx,ky Thermal Conductivity depend on dimension (W/m.K)

α Thermal Diffusivity Coefficient (m2/s)

ρ Density (kg/m3)

q Heat Flux (W/m2)

γ Enlargement Element (Enlargement ratio/50.000)

q Thermal Power (W)

c Specific Heat (J/kg.K)

v Volume (m3)

(x,y) Coordinate axis

1. INTRODUCTION

Today the cutting speed for the cutters used in manufacturing has constituted high temperatures between the

cutter and the rake face. This situation features the usage of materials including good mechanical

characteristics on high temperatures. When the resistance of enduring to high temperatures is considered,

ceramics have shown better performance. Ceramic cutting tips with high rigidity characteristic can protect

their rigidity on high temperatures and don’t react with the work piece. Their endurance life to high cutting

speeds is high. α Sialon ceramics have shown high rigidity, high fracture toughness, high resistance, high

chemical resistance and high wear resistance. As sialon ceramics can be used without lubricant in contact

with the metallic pieces and are durable on high temperatures, they are indispensable on corrosive

environments in manufacturing industry.

The studies based on Rayleigh and Maxwell’s [1] researches for determining the thermal conductivity of

composites has revealed a lot of models until now. A lot of analytical, experimental and numerical studies

were made on this subject [2,3]. The studies in literature are usually experimental and were used for

determining the thermal conductivity of the materials [4,5,6]. The chemical behaviours and internal

structures of composites and especially advanced engineering ceramics in high temperatures were searched

by using scanning electron microscope [7]. The changes occurring in chemical structure and the structural

problems were searched [13,15]. Numerical solutions were made by using finite difference method for some

materials [16,26].

In this study, the thermal conductivity was calculated analytically, numerically and experimentally and the

results were compared. SEM images obtained by electron microscope were modelled by a program based on

finite element, two different materials were identified for main phase and interphase and the thermal

conductivity value was used differently. As a result, effective thermal conductivity was calculated for the

whole composite. The thermal change of main phase material was considered in numerical solutions.


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In the numerical study, constant surface heat was used with the help of SEM images, and effective thermal

value was found by calculating the heat flux in the boundaries. The thermal conductivity was calculated two

dimensional depending on the temperature, but in the literature, two dimensional analyses depending on the

temperature weren’t observed.

The experimental studies were made by using the Laser flash technology in laboratory. Specific heat,

intensity and thermal diffusion coefficients of the samples were calculated and thermal conductivity was

identified by using (k=α.ρ.c) formula.

Analytical studies were made for comparing the numerical results. These analytical solutions were made by

the empirical terms used in literature. The areal ratios of solution surface from SEM images were identified,

and the analytical solutions were compared on the same geometry.

2. MATERIALS AND METHOD

The solutions can be made by considering the systems where the temperature and energy transfer is the

function of only one position coordinate. However, in industry and practice, the complex geometry in the

composites and the definition type of boundary conditions make essential the usage of two or three-position

coordinates. So, in this study, two dimensional solutions for Sialon based ceramic cutting tips were made.

When two dimensional solutions of the material were made, the boundary conditions in Figure 1 were used.

The aim of solving any thermal conductivity problem is to determine the heat flux and temperature

distribution. Heat flux is calculated on solution surface where constant surface temperature boundary

condition is used. The thermal conductivity can be found for (x) and (y) lines by using the heat fluxes.

Effective thermal conductivity depending on the line (kx,ky) has different values. The reason of this is the

change of thermal conductivity depending on the line.

T (0,y) = Ty1 T (x,0) = Ty3

T (Lx,y) = Ty2 T (x,Ly) = Ty4

The surface was cauterized with suitable acids for clearer SEM images. The images of main phase and

interphase materials are diverged with lines in the Ansys programme. The areas formed by using these lines

were shown in Figure 2. These areas can be thought as two different composite with different physical

characteristic. The thermal conductivity of these areas and the change functions of them depending on the

temperature are identified. So, it is the thermal conductivity problem in two dimensional steady regimes.

The numerical solution can be done under the given boundary conditions.

The size of elements or lines forming the areas determines the number of nodal used for the solution. The

number of node must be on a level that doesn’t negatively affect the numerical solution on small areas

especially on interphase areas. It is clear that the fluid solution of elements will be made more correctly in

the inner regions out of the boundaries of interphase forming a resistance to thermal conductivity. Solution

surface can be seen in Figure3.

3. THEORY

In the study, as numerical solutions were made for the situations where the thermal conductivity changed

with temperature, this change was given on Table 1. These values were measured in laboratory


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environments for Sialon material. Average thermal conductivity value is taken as 10.765W/m.K for the

situation where the thermal conductivity didn’t change. While making both solutions, the value of interphase

thermal conductivity was taken as 0.65W/mK. The interphase material is a glassy structure composed during

the combination of elements in cutting tip. The change of thermal conductivity and heat couldn’t be

identified in the studies in literature and laboratory environment. If the volumetric ratio of interphase in

ceramic cutting tips is low, grain size on thermal conductivity, thermal conductivity of main phase and

structural errors gain importance.

The surface temperatures were identified as respectively 298K,373K,473K,...,1273K by considering that the

temperature differences weren’t low than 100 K in both lines. The isotherms under these temperatures were

given in Figure 4 and temperature gradients were given in Figure 5. When the Figure 5 was examined, the

relationship between node number on solution surface and effective thermal conductivity coefficient can be

determined. (γ) is identified as growth factor for making it understand easily. (γ=1) is for 50000 growth rate,

(γ=0.6) is for 30000 growth rate and (γ=0.5) is for 25000 growth rate.

It is known that effective thermal conductivity of composites is changed depending on the directions.

Surface boundary condition on the other direction is used for determining the conductivity in one

dimensional heat transfer. While two dimensional solutions were made, constant surface heat boundary

condition on two directions was identified. The thermal conductivity for different magnifications was given

in Table 2 and Table 3. While the calculations in the Tables were made;

1. When the thermal conductivity of phase material changed with the temperature, values in Table 1 were

observed. When the thermal conductivity of phase material became constant, 10.765W/mK value was

obtained. In both situations, operation was made by using 0.65W/mK value as the thermal conductivity of

interphase material.

2. The node count was identified by doing mesh in Ansys programme.

3. T1=298 K, T2= 1273K, T3=298K and T4=1273 K values were taken as boundary conditions.

4. Heat flux values on x=0, x=Lx, y=0 and y=Ly surfaces were calculated from the programme.

5. q Differencex = (qx=0) - (qx=Lx) and qdifference,y = (qy=0) - (qy=Ly) flux differences were calculated.

6. (kx) and (ky) were calculated from q��,� = k�.∆�

� andq��,� = k�.

∆�

��equations.

While determining the effective thermal conductivity of composites in the study, the calculations were made

considering two-dimensional heat transfer. When it was considered that the thermal conductivity of main

phase material didn’t change parallel to heat, Figure 6 and Figure 7 were obtained; when the thermal

conductivity of main phase material changed parallel to heat, Figure 8 and Figure 9 were obtained. In both

situations, when the node count passed a certain value, effective thermal conductivity of the composite

didn’t change.

Effective thermal conductivity didn’t change after node count passed a certain value and became asymptote

in one value. So, the increase of node count is very important on effective thermal conductivity solutions.

For numerical solutions, the situation that main phase thermal characteristic of thermal conductivity

changed, and the hypothesis that main phase thermal characteristic was constant were used. The relationship

between node count and magnification ratios is an important parameter in solutions and it corresponds to

finite element magnitude. Increasing the node counts considering the whole geometry causes much element

formation on big areas and a parallel rise on interphase areas. For solving this, interphase and main phase


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areas can be divided into different elements and then these areas can be integrated again; as a result it means

less node and better results. In this study, considering the magnification ratios, this method wasn’t used. This

deficiency is tried to remove by using high element count.

4. RESULTS

When the effective thermal conductivity as an internal structure in Sialon based cutting tips is examined, the

effect of interphase element can be understood more clearly. When the amount of interphase with low

thermal conductivity value decreases, effective thermal conductivity increases according to the mixture rule.

main phase / interphase ↑ conductivity ↑

However, when the interphase amount decreases, effective thermal conductivity doesn’t increase in expected

proportion. The reason of this is the grain size magnitude effect of main phase element which is denser

volumetrically. When the grain sizes of main phase reduced, effective thermal conductivity will be

decreased. The reason of this is that the effect of main phase with increasing grain size to effective thermal

conductivity will be more.

Grain size ↑ diffusivity ↓

In Figure 12 and 13, the comparison of experimental calculations with results in (x) and (y) directions in

different magnitude ratios are given when the thermal conductivity of main phase element changes with

temperature. When one and two dimensional solutions are examined, it is observed that if magnitude ratio

decreases numerical results approach to experimental ones. If both (x) and (y) directions are considered, the

solutions with 25000 magnitude ratio become the most optimal numerical solution. The less magnitude

ratios are, the more realistic areas belonging to main phase and interphase will be. However, when the area

count increases, the solution in drawing and analysis programmes will be difficult.

When numerical modelling was made for composite, different mesh was made in Ansys programme and

solutions were made on different element count. After the element count passed the value of 50000,

effective thermal conductivity coefficient didn’t change.

The results taken from two dimensional numerical solutions were given in Figure 14. After determining (kx)

and (ky) values on numerical calculations, effective thermal conductivity wascalculated from Equation 1.

When the magnitude value was 0.6 as a result of numerical calculations, the values were found approximate

to the experimental results.

(ke)2 = (kx)

2 + (ky)2 (1)

5. CONCLUSIONS

Two-dimensional and numerical solution of sialon based cutting tips’thermal conductivity has been done by

using SEM images. This structure has been made out in the electron microscope (SEM) images of material

and in the models of numerical analysis. While doing numerical analysis, effective thermal conductivity has

been computed by a finite material based program (Ansys) depending on knowing the conductivity of main

phase and interphase by considering the SEM images as a two-dimensional surface. The calculations were

given as comparative to the analytical and experimental results. When the results are compared, it is proved

that thermal conductivity of cutting tips or the similar materials with two phase structures can be set down


34

by numerical calculations beside their analytical and experimental measurements.According to the technique

used in the industry, cutting tips are produced first and then thermal conductivity measurements are carried

out. In this study, first modelling and calculation of tips’ thermal conductivity and then producing the cutting

tipsare aimed.

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[11] ZenotchkineMisha, Kim Joo-Sun.(2002).Effect of Seeding on the Microstructure and Mechanical

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[12] Yamada R., IgawaN., Taguchi T., JitsukawaS.(2002). Highly Thermal Conductive, Sintered SiC fiber-

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[16] Karl Dr B., Torsten P.(2005). Jurgen S.Silicon nitride based ceramics for boundary application.

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[17] Basu B., Vleugels J., Klain M., Biest Van Der.(2005). Friction and Wear Behavior of SiAlON Ceramics

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[18] Pakdemirli M., Şahin A.Z. (2006). A similarity Solution of Fin Equation with Variable Thermal

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[19] HongmeiGu, Hunt John F. (2007). Two-Dimensional Finite Element Heat Transfer Model of

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[20] Kurama S. (2008). The Effect of Processing on the SiAlON transformation during cycling heat

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TABLES

Table 1. Thechange of thermalconductivityandtemperatureforanaphasematerial[2].

Temperature(K) 298 373 473 573 673 773 873 973 1073 1273

k (W/m.K) 21.26 15.48 13.75 12.41 11.15 10.26 9.66 8.95 8.14 6.87

Table 2. Boundaryconditionsandresultsfortwodimensional (x) line.

Magnification

ratio

Nodec

ount

Lx

(mm)

Ly

(mm)

T1=T3

(K)

T2=T4

(K)

∆T

(K)

qfx

(W/mm2)

kx

(W/m.K)

25000 91761 421.31 294.66 298 K 1273 K 975 K 22.21x10-3 9.6

30000 90931 626.24 434.93 298 K 1273 K 975 K 11.36x10-3 7.3

50000 91650 1342.02 918.48 298 K 1273 K 975 K 7.99x10-3 11

Table 3. Boundaryconditionsandresultsfortwodimensional (y) line.

Magnificationr

atio

Nodeco

unt

Lx

(mm)

Ly

(mm)

T1=T3

(K)

T2=T4

(K)

∆T

(K)

qfy

(W/mm2)

ky

(W/m.K)

25000 91761 421.31 294.66 298 K 1273 K 975 K 19.5x 10-3 5.92

30000 90931 626.24 434.93 298 K 1273 K 975 K 12.5.x10-3 5.6

50000 91650 1342.02 918.48 298 K 1273 K 975 K 7.21x 10-3 6.8

International Interdisciplinary Journal o

FIGURES

Figure 1:Two-dimensionalmodeling of S

Figure 2: Theareasformed in Ansysprogr

x

y

qx

qy

Ty1

Ty3

Ty4 qy+dy

Ly

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f SEM image.

gramme

Ty2

qx+dx

Lx

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Figure 3: Image of nodalpoints.

Figure 4:Thetemperaturedistributionresu

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sultsfortwodimensionalsolutions.

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Figure 5: Thetemperaturegradientsforthesolution in twodimensionalvariablecharacteristic.

Figure 6:The change of effective thermal conductivity on constant (x) direction.


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Figure 7: The change of effective thermal conductivity on constant (y) direction.

Figure 8: Thechange of effectivethermalconductivity on variable (x) direction.


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Figure. 9: The change of effective thermal conductivity on variable (y) direction.

Figure. 10. The change of effective thermal conductivity on two dimensional (x) direction.


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Figure. 11. The change of effective thermal conductivity on two dimensional (y) direction.

Figure. 12: Thecomparison of results on twodimensional (x) directionwithvariablecharacteristic.


Figure. 13: The comparison of results on

Figure 14:Thecomparison of twodimensi

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on two dimensional (y) direction with variable cha

nsionalresults.

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haracteristic.

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TWO-DIMENSIONAL AND NUMERICAL ANALYSIS OF … · International Interdisciplinary Journal of Scientific Research Vol. 1 No. 2 November, 2014 29 TWO-DIMENSIONAL AND NUMERICAL ANALYSIS