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University of Nairobi
Department of mechanical & manufacturing Engineering
__________________________________________________________
FINAL YEAR PROJECT REPORT [FME 561/562]
PROJECT TITLE: THERMAL SHOCK AND LIFE-TME PROPERTIES OF CERAMIC MATERIALS
PROJECT CODE: JKM 03/2011
REPORT COMPILED BY: 1. NZIOKI JOSEPH NDATA F18/2007/2005 2. MOGUSU CLIVE ONTOMWA F18/1828/2006
Supervisor: Prof. J.K. Musuva
This project is submitted as a partial fulfillment of the requirement for the award of the
degree of
BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING, U.o.N. 30th May, 2011
DECLARATION
We, the undersigned, declare that this project report is of our own original work and has not been
submitted for a degree award in any other institution of higher learning or published anywhere else.
Nzioki Joseph Ndata -F18/2007/2005 Date
Mogusu Clive Ontomwa -F18/1828/2006 Date
This project has been submitted for examination with the approval of our project supervisor.
Professor J. K. Musuva Date
I
ABSTRACT
This project mainly focuses on ceramics manufactured using locally available raw clay from Murang’a (which will be referred to as Murang’a pure clay) and Nyeri (which will be referred to as Nyeri pure clay) and improving their thermo-shock resistance for high temperature applications. The study involved preparation of samples, improvement of extrusion and testing facilities and testing of the samples. Of major importance were motorizing the extruder used by previous researchers, testing the modified equipment, investigating the effect of adding silica to the thermal shock behaviour of test samples and confirming results of past research.
The extrusion machine, which is a modified meat mincer, was motorized by mounting it on a lathe machine and holding its rotating shaft in the spindle of the lathe. This utilized the lathe's motor to drive belts and by selecting the desired speed and torque, uniform, steady extrusion was achieved. Specimen holding equipment were also fabricated in the workshop using steel, including a pair of tongs and cylindrical cup-like equipment that were used during testing (shocking).
Raw clays from Nyeri and Murang'a were purified, then mixed with water to form a suspension which was sieved to remove impurities and then put out to dry in a drying bay. After significant drying (until clay was malleable), it was put in plastic bags to avoid further drying to await extrusion. Sieved sand was thoroughly kneaded into the clay in ratios of 3:1, 2:1 and 1:1. Extrusion followed using the motorized extruder to make 8 different groups of samples, each group having approximately 80 specimens. The green ceramic specimens obtained were then left to dry in cool conditions after which they were fired to 1200°C to raise their strength.
Thermal shock testing followed where specimens were heated to temperatures of 400°C, 600°C and 800°C and quenched in water at room temperature. Thermal cycling was also done by quenching specimens 10 times from 500°C to room temperature.
Three point bending tests were done on the Hounsfield Tensometer and the results obtained tabulated and analysed in calculations, graphs and charts. Using these, the average breaking strengths, weibull modulus and
II
lifetime of the ceramics were determined.Modification of the equipment used was greatly beneficial. It resulted
in well made specimens that gave comparatively consistent results. The effect of thermal shock was reduced mechanical strength. This is justified by the observed progressive reduction in strength as shocking temperatures increased. The higher the sand content, the higher the thermo-shock resistance of both clays. However, the higher the sand concentration, the lower the mechanical strength of the clay (beyond a concentration of 33% for both clays.) A compromise has to be reached between mechanical strength and thermo-shock resistance for best results. Murang'a clay has a higher thermo-shock resistance than Nyeri clay. To improve thermal shock resistance while maintaining mechanical strength, sand at a ratio of 3:1 (25% sand) was found to be best ratio at all shocking temperatures. The observed results were compared with those from past research.
It was recommended that specimen production methods be improved such that a uniform surface finish is obtained to remove variation due to differing surface texture. It was suggested that better quenching apparatus be made to reduced the time spent moving the specimens from the hot to cold environment.
III
DEDICATION
To Almighty God for the life and strength He has granted us.
To our beloved families and special friends (Naomi) for their treasured encouragement and support
IV
ACKNOWLEDGEMENT
In preparing this project, we were in contact with many people, researchers, academicians, and
practitioners. They have contributed towards our understanding and thoughts in the subject. In
particular, we wish to express our sincere appreciation to our project supervisor, Prof. J.K. Musuva, for
his encouragement, guidance, criticism and friendship. Without his continued support and interest, this
project would not have been the same as presented here.
We are also indebted to the librarians at University of Nairobi (UoN) for their assistance in supplying
the relevant literatures.
Our heartfelt gratitude goes to all the staff and technicians of the departmental workshop, especially
Mr. Njue and Mr Githome who were very helpful throughout the project.
Our sincere appreciation also extends to all the staff of Concrete Laboratory, Department of Civil and
Construction Engineering [UoN], the Kenya Industrial Research and Development Institute [KIRDI]
and the Department of Physics-Chiromo Campus [U.o.N] who provided assistance at various
occasions. Their views and tips were useful indeed. Unfortunately, it is not possible to list all of them
in this limited space.
We are grateful to all our family members and friends who encouraged us all the time to complete this
project.
To all we say thank you and God bless you.
V
ABBREVIATIONS AND NOMENCLATURES
M Maximum bending moment
I second moment of inertia
P Fracture load
m Weibull modulus
a Crack length
n Slow crack growth exponent
t Time
ΔT Thermal shock temperature range
E Elastic modulus
k Thermal conductivity
h Surface heat coefficient
Pf Failure probability
Ps Survival probability
L Span
VI
Greek alphabets used:
σ Modulus of rapture (MOR)
σf Average modulus of rapture (Av. modulus)
ν Poisson’s ratio
α Coefficient of thermal expansion
β Biot number
VII
Table of contentsOBJECTIVES .......................................................................................... 1CHAPTER 1- INTRODUCTION
1.1 Ceramics .............................................................................. 21.2 Clay ..................................................................................... 31.3 Kaolin .................................................................................. 31.4 Plasticity of clay ............................................................... 31.5 Porosity ............................................................................... 4 1.6 Shrinkage and reaction with alkali …............................. 41.7 Mixing with water................................................................ 41.8 Behaviour of clay when heated....................................... 51.9 Addition of silica................................................................. 51.10 Thermo-shock ................................................................... 5
CHAPTER 2 – BACKGROUND 2.1 Similarities ............................................................................. 72.2 Differences ............................................................................. 9
CHAPTER 3 – THEORY 3.1 Crack propagation under thermal stress ........................ 133.2 Measurement of strength .................................................. 133.3 Statistical treatment of strengths ...................................... 143.4 Determination of the Weibull's parameters ..................... 153.5 Life time of ceramics ........................................................ 163.6 Derivation of life time formulae and
determination of constant n .............................................. 16
CHAPTER 4 – MATERIALS AND EQUIPMENT 4.1 Materials required and their collection.............................. 194.2 Equipment ............................................................................. 194.3 Pictures of equipment........................................................... 204.4 Modification of equipment .................................................. 214.5 Making of specimen holders............................................... 23
CHAPTER 5 – METHODOLOGY 5.1 Preparation of the sand and clay..................................... 245.2 Mixing of the sand and clay ........................................... 245.3 Preparation of the specimens for testing ....................... 26
VIII
5.4 Thermo-shock testing............................................................ 275.5 Thermo-fatigue testing ......................................................... 27
CHAPTER 6 – RESULTS 6.1 Results from quenching once ............................................ 296.2 Weibull modulus ........................................................... 426.3 Results from shocking specimens ten times...................... 446.4 Value of ceramic constant n ............................................ 47
CHAPTER 7 – DISCUSSION7.1 Modified extruder ............................................................ 477.2 Effect of sand addition to mechanical strength …......... 477.3 Quenching / thermo-shock ................................................. 537.4 Weibull Modulus .................................................................. 567.5 Thermal fatigue ................................................................... 577.6 Lifetime of ceramic............................................................... 587.7 Possible sources of error.................................................... 60
CHAPTER 8 - CONCLUSIONS8.1 The trend of thermo-shock behavior
with variation of sand concentration ............................... 61
CHAPTER 9 - RECOMMENDATIONS9.1 Difficulties experienced ....................................................... 629.2 Recommendations................................................................. 62
LIST OF REFERENCES ..................................................................... 64
PHOTOGRAPHS .................................................................................. 65
APPENDIX ............................................................................................ 67
IX
OBJECTIVESThe projects objectives are
1. To improve the equipment used.2. To test the modified equipment. 3. To investigate and summarise the trend of thermo-shock behaviour when
sand is added to it.4. To confirm results of past research.
Page 1
CHAPTER 1 : INTRODUCTION
1.1 Ceramics The word ceramics is derived from the Greek word “keramics” meaning
potters clay. They are inorganic non-metallic materials which require use of high temperatures at some time in their manufacture. They may have a crystalline, partly crystalline or even amorphous structure.
Ceramic materials may be studied under 2 categories. i.e.a) Traditional ceramicsThese are clays that have been used over the centuries due to their widespread availability and relative ease of manufacture.They include:
1. Clay products : brick, pottery and sewer pipes.2. Abrasive products : abrasive wheels, emery cloth and sand paper, nozzles
for sand blast.3. Construction brick : concrete tile, plaster, glass.4. Glass : bottles, lab ware.5. Refractories : brick crucibles, molds, cement.6. Whitewares : dishes ,tiles plumbing, enamels.
b) Engineering ceramicsThese are ceramics used in high stress applications and are relatively simple compounds of metals or the metalloids of silicon or Boron with non metals, for example oxygen, carbon or nitrogen.Some of the oxides, carbide and nitride ceramics used include
1. Hafnium carbide (Melting point: 3900 C)˚
2. Tantalum carbide (Melting point: 3890 C)˚
3. Thorium oxide (Melting point: 3315 C)˚
4. Magnesium oxide (Melting point: 2800 C)˚
5. Zirconiom oxide (Melting point: 2600 C)˚
6. Alluminium oxide (Melting point: 2050 C)˚
7. Berrylium oxide (Melting point: 2550 C)˚
8. Silicon nitride (Melting point: 1900 C)˚
This report deals with ceramics made from the drying and firing of clay which is a traditional ceramic.
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1.2 Clay A ceramic may also be a clay that has been dried then fired. Ideal clay is a material called kaolin. In nature, kaolin rarely occurs in an entirely pure form. It is found mixed with other finely ground materials such as mica, feldspar, and quartz. This mixture is called clay.
1.3 Kaolin Kaolin is made from the decomposition of a feldspar such as Potassium feldspar. The reaction is shown below.
K2O·Al2O3·6SiO2 DECOMPOSE Al2O3·2SiO2·2H2O + K2O + SiO2 Potassium feldspar Kaolin Potassium oxide Silicon dioxide
Reaction 1.3
Feldspar is the most abundant material in crystalline rocks such as granite and gneiss. In nature, it decomposes due to reactions with humic acid in the absence of oxygen. Kaolin, which is the ideal clay, is formed. It is however mixed with other materials such as undecomposed feldspar, mica, quartz which were present at the site of formation or were introduced as the clay was moved to another location by water.
Clays can either be primary or secondary clays. Primary clays are those found near the site of formation while secondary clays are those transported by water to some other place.
1.4 Clays plasticity Addition of water to clay makes it plastic and once shaped the clay retains its
shape. This is due to the sheet-like (laminar) structure of clay. The unit clay crystals are attached to one another by valency forces in two dimensions only so continuous layers are formed one crystal unit thick. The crystals are almost completely 2D in nature. When water is added to the clay, it goes between these crystals where it forms layers that lubricate the clay. Therefore the clay can move in directions of crystal planes without losing cohesion which is maintained by the electrical forces of the ions present in the watery solution.
Drying makes clay loose water and crystals come into direct contact with one another. Just as two clean glass plates are hard to separate after they are placed one on top of another, the clay particles become hard to separate. The strength of the clay depends on the number of crystals that come into contact per unit area, and therefore on the degree of drying and size of the clay
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particles. The loss of water between the layers and the moving into contact of the crystals explains the shrinking that happens as clay dries.
The plasticity of clay depends on the percentage of kaolin present in the clay and the physical properties of the clay. Kaolins with the same chemical formulas have been found to have different plasticities. For example, kaolins of smaller particle size have higher plasticity than those with bigger particle size.
1.5 Porosity Clay particles never lie all parallel. At certain points the crystals and their
intermediate water layers are not stacked together in an orderly manner and pockets are formed where there is only point contact between the crystals. Water fills these pockets. When the clay is dried, this water evaporates and pockets filled with air are formed.
1.6 Shrinkage and reaction with an alkali Clay contracts as it looses water until the water content reaches 14%
where further contraction (without the addition of heat) stops. This is due to the holes the pores which fill up with air as the water is lost. At this stage, the clay is in a “green state”. Complete loss of water results in a white state.
Few drops of an alkali solution such as sodium silicate or alkaline sodium carbonate, have been found to turn a stiff clay paste into a liquid slip of cream-like consistency. This is because the OH- ions repel the negatively charged clay crystals and counteracts the mutual electrical attraction of the clay crystals. Further addition of the alkali turns the clay back into a stiff and sticky paste. When in slip form, the clay can be moulded.
1.7 Mixing with water Due to the small size of individual clay particles, clay remains in
suspension after being mixed thoroughly with water. Heavier particles settle. This behaviour enables clay to be separated from materials of relatively larger size with great ease. However, the clay keeps the finely ground impurities in suspension with it making these hard to remove.
Page 4
1.8 B ehavior of clay when heated Clay undergoes physical and chemical reactions as it is heated. Some of the major changes are listed below.
1. Chemically combined water is lost (almost completely) at 450°C-500°C and meta kaolin is formed Al2O3⋅2SiO2⋅2H2Os⇒ Al2O3⋅2SiO2 s 2H2Og Reaction 1.8.1
2. Between 800°C - 830°C Meta kaolin decomposes.3. Between 850°C - 910°C, Alumina is formed (AL2O3)4. Between 910°C - 975°C Sillimanite is formed.
Al2O3s SiO2 s ⇒ Al2O3⋅SiO2 s Reaction 1.8.2
5. At 975°C formation of Mullite commences. i.e.
Al2O3⋅SiO2s SiO2s ⇒ Al2O3⋅2SiO2 s Reaction 1.8.3
Clay has no definite melting point. The melting point used is that at which a cone formed of the clay under test completely collapses so that its apex leans over and touches its base. This temperature is 1770°C for kaolin.
1.9 Addition of silica Fused silica (quartz glass) has a very low thermal expansion. It is the
lowest of all known materials i.e. 0.5 x 10-6 per °C. Quartz in crystal form, on the other hand, has a very high thermal expansion. Parallel to the axis it is 8 x 10-6
per °C. and perpendicular to the axis it it 5.4 x 10-6 per °C. Consequently, if the particles are lying at random, the average expansion is about fifteen times greater than that of fused quartz. The thermal expansion of ceramics mixtures is greatly reduced when part of the sand content fuses and forms a glass rich in silica.Other impurities are lime, feldspar, magnesia, iron compounds such as iron oxide.
1.10 Thermo-shockDespite their widespread use in high temperature applications, ceramics often
fail due to thermal shock and thermal fatigue. This is the effect of thermal gradients that change rapidly with time. For example, when a heat engine or a furnace is shut off. It is the way in which some materials fail if they are exposed to sudden changes in temperature; which is a reaction to a rapid or extreme temperature fluctuation (temperature gradient).
Page 5
Basically, the temperature change creates a thermal gradient in an uneven fashion leading to uneven expansion thereby causing thermal stress in the ceramic. Failure occurs when the thermal stress exceeds the strength of the material in that mode of stressing. For example, when a ceramic material is heated suddenly from room temperature, the surface of the material attains high temperature in a very short time. The surface expands and experiences compressive stress. However, the interior of the sample still remains at low temperature (due to low thermal conductivity) and expands less than the surface. Therefore, the interior experiences tensile stress which cause failure if the stresses are greater than the yield stress of the material.
An example of thermal shock failure is when a hot glass is exposed to ice water—the result is a cracked, broken, or even shattered glass. Another is where ice cubes placed in a glass of warm water crack. The exterior surface increases in temperature much faster than the interior. As ice has a larger volume than the water that created it, the outer layer shrinks as it warms and begins to melt, whilst the interior remains largely unchanged. This rapid change in volume between different layers creates stresses in the ice that build until the force exceeds the strength of the ice, and a crack forms.
This property is one of the few grey spots in an otherwise perfect refractory material. It requires that the temperature be changed slowly whenever the ceramic is in use. This is unwanted in most industrial applications where low cost and high productivity is desired. As a result, a ceramic that will have high thermo-shock resistance and thermal fatigue life will be valuable. The thermal stresses responses to temperature depend on:
• thermal boundary conditions• geometrical boundary conditions• coefficient of thermal expansion • modulus of elasticity• thermal conductivity• strengthThis report documents the results of an attempt to improve thermo-shock
resistance. The method used is the addition of sand to the clay then firing the mixture to make a ceramic. This material lowers the coefficient of thermal expansion of the clay thus increasing thermo-shock resistance and fatigue life.
Page 6
CHAPTER 2 : BACKGROUND
Attempts to improve the thermal characteristics of ceramics have been done in the past. Different methods have been used; with that intended in this project having been experimented by B. W. Kipng'etich & P. O. Thure[10] and then by F. M. Mbithi & S. N. Florida[8]. The results they obtained have greatly aided in the present experimentation. A brief analysis of their experimentation and results was done and below are some of the observations noted.
The two groups, i.e. that of F. M. Mbithi & S. N. Florida[8] and that of Mbithi and Florida[10], attempted to improve the thermo-shock properties of clay by that addition different percentages of sand to the clay before firing. Kipng'etich and Thure[10] used a clay to sand ratio of 1:1 ,while Mbithi and Florida[8] used one of ratio of 3:1. Their results generally agreed with the theoretical data. The strength of the clay was observed to decrease with the increase in the temperature change the clay was quenched through and sand added decreased the rate of this drop in strength. Results of the two groups were however conflicting. Some of the similarities and differences are shown below. These differences led to the need to carry out conclusive experimentation.
2.1 SimilaritiesThe graphs figure 2.1.1, 2.1.2, 2.1.3 & 2.1.4, show the downward trend of the
average strength of the samples with increase in the temperature through which they were quenched. Figure 2.1.1 and Figure 2.1.1 are graphs plotted from Kipng'etich and Thure's[10] results of clay collected from Murang'a. The former is that of plain clay while the latter is that of clay mixed with sand at a ratio of 1:1.
Graph plotted using results by Kipng'tich and Thure [10] for the average MOR against temperature change for plain Nyeri clay
Figure 2.1.1
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0 400 600 800 1000
0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
16.000
18.000
20.000
Graph of average strength against temperature change for plain Nyeri clay
Temperature change
Av
era
ge
str
en
gth
(N
/mm
)
Graph plotted using results by Kipng'tich and Thure [10] for the average MOR against temperature change for plain Murang'a clay
Figure 2.1.2
The graphs figure 2.2.3 & 2.2.4, are from Mbithi and Florida's[8] results of clay collected from Nyeri. Figure 2.2.3 is plotted for plain clay while figure 2.2.4 is for clay mixed with sand at a ratio of 3:1. Similarly, the progressive decrease in the average strengths of the samples with increase in the temperature difference the clay was shocked through is observed.
Graph plotted using results by Mbithi and Florida [8] for the average MOR against temperature change for plain Nyeri clay
Figure 2.1.3
Page 8
0 400 600 800 1000 1200
0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
16.000
18.000
20.000
Graph of average strength against temperature change
Ave
rag
e s
tre
ng
th (
N/m
m)
Temperature change
0 400 600 800 1000
0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
16.000
18.000
20.000
Graph of average strength against temperature changeA
vera
ge
str
en
gth
(N
/mm
)
Temperature change
Graph plotted using results by Mbithi and Florida [8] for the average MOR against temperature change for plain Murang'a clay
Figure 2.1.4
2.2 DifferencesHowever, their results conflicted when it came to the effect of adding sand to
the clay in-spite of having used the clay from the same locations. Figure 2.2.1 and 2.2.2 show the inconsistencies.
The graphs below show the effect of adding sand to clay. Figure 2.2.1 and 2.2.2 are graphs drawn from Kipng'etich and Thure's[10] results, and the next two, Figure 2.2.1 and 2.2.2, from Mbithi and Florida's[8] results.The shape of figure 2.2.1 implies that the sand does not lower the strength of plain Nyeri clay but increases it before and during shocking. It improves the thermo-shock resistance in large temperature changes.
Graph from Kipng'etich and Thure's [10] results for the average MOR against temperature change for plain and mixed Nyeri clay
Figure 2.2.1 Page 9
0 400 600 800 1000 1200
0.000
1.000
2.000
3.000
4.000
5.000
6.000Graph of average strength against temperature change
Ave
rag
e s
tre
ng
th (
N/m
m)
Temperature change
0 400 600 800 10000.000
5.000
10.000
15.000
20.000
25.000
Graph of average MOR against shocking temperature differencefor pure clay and clay mixed with sand (Nyeri clay)
shocking temperature difference
Ave
rag
e M
OR
(M
N/m
2)
On the other hand, figure 2.2.2 implies that addition of sand lowers the average strength of plain Murang'a clay but drastically improves its thermo-shock resistance.
Graph from Kipng'etich and Thure's [10] results for the average MOR against temperature change for plain and mixed Murang'a clay
Figure 2.2.2
Figure 2.2.3 and 2.2.4 are graphs drawn from Mbithi and Florida's[8] results. Figure 2.2.3 shows that the sand lowers the strength of plain Nyeri clay but slightly increases the thermo-shock resistance in large temperature changes. From figure 2.2.4 it is observed that addition of sand lowers the average strength of plain Murang'a clay and that sand actually has a detrimental effect to the thermo-shock resistance of the clay.
These variations are believed to have originated from the experimentation being open to the influence of factors other than the variation of the sand content. These include:
1. Preliminary tests showed that the clay contained a high percentage of sand in its natural state. This sand is small enough to pass through the 1mm sieve that was used to filter the clay and go into the clay used to make the test samples. The sand therefore contained higher percentages of sand thus altered the desired ratio and the results as well.
Page 10
0 400 600 800 1000 1200
0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
16.000
18.000
Graph of average MOR against temperature changefor pure clay and clay mixed with sand (Murang'a clay)
shocking temperature difference
Av
era
ge M
OR
(M
N/m
2)
Graph from Mbithi and Florida 's [8] results for the average MOR against temperature change for plain and mixed Nyeri clay
Figure 2.2.3
Graph from Mbithi and Florida 's [8] results for the average MOR against temperature change for plain and mixed Murang'a clay
Figure 2.2.4
Page 11
0 400 600 800 1000 1200
0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
16.000
18.000
20.000
Graph of Average MOR against shocking temperature differencefor plain clay and clay mixed with sand (Nyeri clay)
Temperature change
Ave
rag
e s
tre
ng
th (
N/m
m)
0 400 600 800 1000
0.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
16.000
18.000
20.000
Graph of average MOR against temperature change for pure clay and clay mixed with sand (Murang'a clay)
Shocking temperature difference
Ave
rage
MO
R (
MN
/m2)
2. The extrusion machines were manually operated so the rate of extrusion could have affected the specimens made. They could easily have differed in strength due to different rates of extrusion. This would mean different duration spent in the machine before the required size is reached which would result in different levels of compaction.3. Their experimentation involved mixing the clays with sand from different sources. This increased the factors that could have affected the thermo-shock and thermo- fatigue properties of the clay. The results were not merely of those that would result from differing concentrations of sand but also the constituents of the sand used. To remove the effect of resulting from differing constituents in the sand, one type of sand best be used.4. Kipng'etich and Thure[10], analysis of fatigue failure involved quenching till a crack propagated to a depth of 5mm. This method is not the best to use since there may be internal cracks that can not be seen and noted. Depth of the crack is also difficult to ascertain. Mbithi and Florida[8] used a simpler method of counting the number of samples that survived quenching through progressively higher temperature differences.
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CHAPTER 3 : THEORY
3.1 Crack propagation under thermal stressThermo-shock does not necessarily lead to complete failure. Cracks may
propagate some distance and then stop as they outrun the thermal stress field or as the stress field decreases. The result is the lowering in strength of ceramics when it does not lead to complete failure. This is due to the extension of cracks until all the energy released is converted into crack surface energy.
After propagation from an imposed thermal strain that equals or slightly exceeds the critical value, the crack will be stable under subsequent imposition of somewhat larger thermal strains. As the size of the initial temperature differences increased, there is no crack propagation and no reduction in the specimen strength until a critical value is exceeded, upon which the cracks extends kinetically to a new length, giving the specimen a lower strength.
Figure 3.1.1 Graph of drop in strength with increase in shocking temperature
Exposing the surface to a subsequent, slightly greater temperature difference causes further crack propagation or further decrease in strength. If the weakened specimen is thermally shocked through a set of progressively larger temperature differences, eventually a critical value Tc is reached at which point further crackΔ propagation and strength decrease takes place.
3.2 Measurement of strengthStrength is measured using the three point bending test. The three point
bending (flexural) test is a simple test that enables values for the modulus of elasticity in bending, flexural stress, flexural strain and the
Page 13
flexural stress-strain response of a material to be obtained.This method is carried out by placing the specimen on two supports and then
loading it at the specimen's center.
Figure 3.1.1 a) Schematic diagram of b) Picture of cement block d 3-point bending test undergoing 3-point testing
Load required to cause fracture is noted and used to calculate the strength of the beam. For a circular cross section equation 3.4.2 is used.
f=PL
R3 Eq 3.4.2
Where σf : Stress in outer fibers at midpoint (MPa)
P : load at a given point on the load deflection curve (N)
L : Support span (mm) b : Width of test beam (mm)
However, the results of this testing method are sensitive to specimen and loading geometry and strain rate.
3.3 Statistical treatment of strengthA series of nominally identical ceramic specimens produce considerable scatter
when measured for strength. This results from a scatter in the size of cracks responsible for failure. This scatter results in the failure of materials below their average failure strength and the greater probability of failure of a large body in comparison to a small one. The larger specimen has greater probability of having a serious flaw in the larger volume.
Weibull statistics provide a means of describing these flaws quantitatively. It is a form of extreme value statistics dealing with the weakest link situation in which the failure of a single element causes failure of the whole specimen.
Page 14
The Weibull concept yields the material parameter m which rates the brittleness of a material based on its probability of failure when a given stress is applied to it.As m increases, the material becomes less brittle. The Weibull expression that links the probability of failure of brittle material under stress and the Weibull
modulus m is given as: Ps=1−Pf=exp [−V − u
m
] Eq 3.4.1
where Pf : Probability of failurePs : Probability of survivalV : Volume of specimen under stress.σ : Applied stressσu : Normalizing stress
3.4 Determination of the Weibull's parameters. The procedure used is the least square method. Arithmetic modification of the Weibull's distribution gives
ln ln1Ps
=lnVm ln−m ln0 Eq 3.4.2
where Ps : Probability of survivalV : Volume of specimen under stressσ : Applied stressσo : Average stress
Parameters m can then be obtained by fitting a straight line to ln ln 1PS
as
a function of ln . Then obtaining the slope and y intercept. The slope gives the value of m and the intercept allows σ0 to be calculated.
intercept=lnV –m lnσ 0
Eq 3.4.3
where V : Volume of specimen under stressσo : Average stress
The volume term is ignored for a set of measurement taken on specimens with the same volume
Page 15
3.5 Life time of ceramics It is difficult to relate the results of short-term tests to the fatigue life in practice. However, consideration of the fact that the fatigue life is approximated by the duration in which the crack length reaches a certain critical value, beyond which the growth becomes relatively rapid, may make the prediction easy. Prediction of the life can be made by application of fracture mechanics to ceramics based on sub-critical crack growth. The formulae 3.5.1 shown below can be used to calculate the life of a ceramic after a few tests are done in a laboratory.An approximated formulae,
NN'=T N '
T Nn
Eq 3.5.1
where N and N' are the lives for temperature differences ΔTN and ΔTN', respectively, and n is a material constant.
3.6 Derivation of life time formulae and determination of constant nThe rate of crack growth is dependent on a number of factors. These are temperature, the stress applied and crack length.
dadt
=Aexp −QRT
K In Eq 3.6.1
where a = crack length t = timeT = temperatureKI = stress intensity factorR = gas constantn = a material constantA = constant
and the stress intensity factor is given by
K I=Y a12 Eq 3.6.2
Substituting gives
dadt
=A exp −QRT
Y n nan2 Eq 3.6.3 Page 16
Generally, stress( ) consists of mechanical stress, σ σM and thermal stresses, σT. Thermal fatigue determines the life of ceramics therefore mechanical stress, σM can be neglected.This leaves σf which is a function of temperature difference and time. i.e.
T=T⋅f t Eq 3.6.4
the approximate temperature over the duration of substantial crack growth can be expressed as
Tr=TO⋅T Eq 3.6.5
substituting into the earlier equation then integrating gives,
a I2−n
2 −aF2−n
2 =n−2
2T nG Tr Eq 3.6.6
where aI and aF are crack lengths before and after one shock occurs
and G(Tr)= GTO⋅T =A exp−QR
TO⋅T ⋅∫0
Y n fndt Eq 3.6.7
Failure occurs when crack length a reaches a critical value ac after N cycles of. Damage accumulates with each cycle of thermal stressing by causing extension of the crack front until the material fails after N cycles.At this stage, the equation to failure is given by:
a I2−n
2 −aF2−n
2 =n−2
2⋅N⋅T nG Tr Eq 3.6.8
For materials with the same initial crack length (ai) and af, equation 3.6.8 can be simplified to:
NN'=T N '
T Nn
Eq 3.5.1
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n may be found by using the equation: fo
f= ἑoἑ
1n1 therefore 1
n−1ln ἑo
ἑ =ln o
Eq 3.6.10
where σfo and σf are failure strengths ἐfo and ἑf are cross head speeds (strain rates)
A different strain rate was achieved by changing the pulley used to couple the tensometer to the motor.
ἑo
ἑ = DD o =95.4449.72 =1.9195 Eq 3.6.11
where Do : Diameter of pulley used first D : Diameter of pulley to which belt is attached second
ln ἑoἑ =ln 1.9195=0.6521 Eq 3.6.12
1n−1
=1
0.6521ln ' =1.5335 ln o
Eq 3.6.13
n=11.5335 ln o
1.5335 ln o
Eq 3.6.14
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CHAPTER 4 : MATERIALS AND EQUIPMENT USED
4.1 Materials The materials required are pure clay and clay mixed with sand in different ratios. The ratios of clay to sand are 1:1, 2:1 and 3:1. Before these can be made, the constituents, clay and sand, have to be obtained and prepared so that foreign bodies that would alter the results of the properties under study are removed. Such materials are organic matter such as leaves and twigs, and relatively large particles like sand and rock particles. The sand was collected from Nyeri district where it is used commercially in the making of pots. Potters add the sand to clay before forming the pots in the belief that it improves the quality of the pot. The clay was obtained from two separate locations: Maragua in Murang'a district and Nyeri district.
4.2 EquipmentBelow are the equipment used
1. Drying bay2. Extrusion machine3. Sieves of 105 m and 355 m pore sizeμ μ
4. Vernier calliper and steel rule5. Weighing scales6. Tongs and specimen holders7. Brick drying bay8. Furnace9. Hounsfield Tensometer
4.3 Pictures of the equipment
Figure 4.3.1 Picture of specimen holders without and with specimensPage 19
Figure 4.3.2 Picture of long handle tongs and of the tongs holding metallic specimen holders
Figure 4.3.3 Picture of the drying bay Figure 4.3.4 Picture of the furnace used
Figure 4.3.5 Picture of the lathe machine with extruder
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Figure 4.3.6 Picture of the Lathe and extruder
Figure 4.3.7 Hounsfield Tensometer
Figure 4.3.8 Picture of the three point loading bars of the tensometer
4.4 Modification of the extrusion machineThe extrusion machine is a modified meat mincer. It has been changed
from its original purpose by removing the meat cutting blades at the end of the Page 21
screw-like plug mill and replacing the die that had many holes with one with a single hole through which the clay was extruded.
Figure 4.4.1 Diagram showing parts of the extruder
Forcing the clay through the tiny hole of the die required great force and presented difficulty in attempting to prepare a consistent clay specimens. This led to the need to improve the machine. Further modification was done and it basically involved attaching the extrusion machine to a lathe as explained below.
• The modified meat mincer had its four supporting arms bolted onto a solid plate.
• A hole was drilled through the plate.• The extruder was then placed on the lathe bed and held there using a
bolt passing through the hole on the plate to a supporting board held in the lathe bed.
• Rigid packing material was used to raise the extruder to allow its axle to be clamped by the spindle chucks of the lathe.
• The extruder's axle was clamped to lathe.• A surface plate was paced on the lathe's cross slide. On this was placed
a large perspex plate, then a glass plate. The glass plate provided a smooth surface over which the extruded clay could slide.
After this, clay could be added at the top of the extruder then, when the lathe is switched on, removed from the glass plate in a cylindrical rods shape.
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Figure 4.3.1 Diagram of extruder and specimen holding platform
4.5 Making of specimen holdersThe specimens were to be quenched at very high temperatures. Removing them from the furnace at high temperatures to drop them in water fast and safely presented great difficulty. Use of equipment that could withstand the high temperatures as well as the sudden temperature change was required. Metallic cups made from relatively thick walled cylinders were designed and made. They could comfortably hold eight specimens. A pair of metallic tongs with long handles to allow a far reach were also made to hold and remove the specimens from the furnace.
Figure 4.5.1, Picture of metallic cups and tongsPage 23
CHAPTER 5 : METHODOLOGY
5.1 Preparation of the sand and clay In its original form, the clay contained a large amount of impurities such as grass, roots, stones and even other types of soils. The clay had to be separated from these naturally occuring additives before it could be used. One distinct property of clay was used to do this: the size of clay particles. Clay particles are so small that they form a suspension with water. The suspension is so perfect that it does not settle even when given time; and it holds other foreign particles of similar size in suspension with it. The steps below were done for the Nyeri and Murang'a clay.
1. Lumps containing the clay were soaked in excess water to break down the large lumps and expose the clay to water.
2. The mixture was then stirred to form a suspension. Some time was allowed to pass so that the other large particles sunk to the bottom of the container.
3. The suspension was passed through 105 micron sieves to remove any floating bodies and large particles.
4. The suspension was poured into the drying basin made of bricks located in an isolated place. It was covered to prevent entry of foreign materials then given time to dry.
NB: As the clay dries, the space previously occupied by water empty leaving pores. These pores work to reduce the mechanical strength of the clay; thus should be discouraged. It is therefore favourable to use clay with the least amount of water that wound allow shaping.5. Once the clay had dried to the point where it was malleable but did not
stick to fingers when pressed, it was put in nylon paper bags then moved to a cool location for storage. This was done to prevent it from drying further.
The sand was sieved though 355 micron sieves then put aside to await use.
5.2 Mixing of the clay and sand Once the clay had dried to a point where it was plastic yet not sticky, it was then to be mixed with the sieved sand in different ratios. The clay to sand ratios were 3:1, 2:1 and 1:1. (By percentage of sand added, they are 25%, 33% and 50% respectively). Mixing the sand was critical since the project was based on
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the differences in the sand content. The steps below were taken to make accurate ratios:
1. The clay was used to make simple specimens of pure Nyeri and Murang'a clay. These were weighed, then left for a week to dry. They were weighed again and the percentage dry clay content calculated using the formula:
Percentagewater content=Mass of clay before dryingMass of clay after drying
×100 Eq 5.2.1
An example of the calculations done for Nyeri clay are shown below.
Table of weight of clay before and after drying for Nyeri clay
Table 4.2.1
Table of weight of clay before and after drying for Murang'a clay
Table 4.2.2
It was found that the Nyeri clay to be used contained 76.7% dry clay while Murang'a clay 74.5%.
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MASS OF NYERI CLAY
SAMPLE BEFORE DRYING AFTER DRYING1 40.30 31.00 23.08 76.922 43.30 33.30 23.09 76.913 33.00 25.30 23.33 76.674 40.60 31.20 23.15 76.855 39.10 30.00 23.27 76.736 39.50 30.30 23.29 76.717 123.08 94.50 23.22 76.788 128.31 98.20 23.47 76.539 137.14 105.00 23.44 76.56
AVERAGE 23.26 76.74
PERCENTAGE OF WATER (%)
PERCENTAGE OF CLAY (%)
MASS OF MURANG'A CLAY
SAMPLE BEFORE DRYING AFTER DRYING1 35.91 26.75 25.52 74.482 46.38 34.58 25.44 74.563 48.32 35.96 25.57 74.434 51.96 38.76 25.41 74.595 56.42 41.93 25.68 74.326 56.50 42.10 25.48 74.527 62.33 46.64 25.18 74.828 63.46 47.35 25.38 74.629 68.12 50.67 25.61 74.39
AVERAGE 25.47 74.53
PERCENTAGE OF WATER (%)
PERCENTAGE OF CLAY (%)
2. Clay to be used to make the samples was weighed and put aside. The dry clay present was calculated. For example, 4kg wet Nyeri clay contained 4×0.767=3.068kg dry clay.
3. This dry weight of clay was used to calculate the appropriate sand required to make the mixture ratios needed. For example, to make a clay to sand ratio of 3:1, clay with calculated dry content of 3kg was added to 1kg of dry sand.Water was then added to bring the mixture to the best consistency.
4. The mixtures were kneaded and stirred till even mixtures were formed. The mixtures were then put in nylon paper bags then moved to the cold room to await extrusion. (A cold room is a storage room in civil engineering highway laboratory whose temperature is intentionally kept low)
5.3 Preparation of the specimens for testing Each of the eight clay mixtures were to be shaped into cylinders using the extruder. The extrusion process involved kneading the clay then forcing it into the final shape. This mixes the clay while removing air present in the clay and forms a sturdy cylinder of clay. The constant rate of extrusion the mechanised extruder offers ensures that all the specimens undergo similar compaction and forming processes when being prepared.Clay is said to “have memory”. Once clay is moulded or forced to take a certain shape, it will go back to that shape when one attempts to make minor adjustments to it. It was therefore imperative that the specimens were extruded as straight cylinders. If bent, the clay would return to its curved shape while drying even after being straighten.The steps below were taken to make the best specimens possible.
Figure 4.2.3, Pictures showing the extrusion process.
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1. Pure clay then the three different ratios of Nyeri and Murang'a clay were extruded. Eighty test specimens each of diameter 15mm and length 150mm were extruded.
2. The specimens were moved to a cool isolated place where they could dry without interference. Care was taken to avoid their bending in any way.
3. The specimens dried slowly in a cool room to prevent nonuniform drying that would result in warping. They were rotated often to further encourage uniform drying.
4. Once dry, the specimens were fired to 500°C to make them strong enough to allow transportation to a furnace at KIRDI. The temperature was raised at intervals of 100°C, with an hour's wait between each increment.
5. Firing to 1200°C followed.
5.4 Thermo-shock testing1. specimens were heated to 400°C then dipped into water at room
temperature. 2. The above process was done for other specimens for the temperatures of
600°C and 800°C.3. The specimens were then placed in the Hounsfield Tensometer and the
three point bending test carried out to determine their strength.4. The results of the tests were taken and analysed.
5.5 Thermo-fatigue testingThis differed slightly from thermo-shock testing in that the specimens were put back into the furnace after quenching until ten cycles were reached. Eight specimens of each of the different ratios of sand to clay were quenched ten times between 500°C and room temperature and the number that failed were noted. Those that survived had their fracture strength determined using the Hounsfield Tensometer.
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