UNIVERSITY OF NAIROBI
SCHOOL OF ENGINEERING
DEPARTMENT OF MECHANICAL AND MANUFACTURING
ENGINEERING
FINAL YEAR PROJECT REPORT
[FME 561 &562]
PROJECT TITLE:
THERMAL SHOCK MEASUREMENT AND LIFETIME
PREDICTION OF CERAMIC MATERIALS
PROJECT CODE: JKM 03/2012
SUPERVISOR: PROF J.K MUSUVA
COMPILED BY:
CHERONO SHEILAH-F18/1893/2007
MOSIRIA DICKSON BWANA-F18/1865/2007
In partial fulfillment of the Degree of Bachelor of Science in Mechanical Engineering
May 2012
i
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DECLARATION:
We, the undersigned, declare that this project is of our original work and has not been
submitted for a degree award in any other institution of higher learning or published
anywhere else.
________________________________________________________________________
CHERONO SHEILAH-F18/1893/2007
DATE
________________________________________________________________________
MOSIRIA DICKSON BWANA-F18/1865/2007
DATE
This project has been submitted for examination with the approval of our project
supervisor
________________________________________________________________________
PROF.J.K. MUSUVA
DATE
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DEDICATION
To Almighty God for the life and strength he has granted us.
To our beloved families for their love and support throughout the project.
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ACKNOWLEDGEMENTS
First, we thank the Almighty God for guiding and giving us strength, peace of mind and grace
that has brought us this far.
During the preparation of this project, we came across many people who have been instrumental
in helping us complete this project. We would like to extend our sincere gratitude to them and
truly appreciate them for their untiring support.
However, in an elite category that demands mentioning are the following persons:
Our project supervisor, Prof.J.K Musuva- we are very grateful for the encouragement, guidance,
criticism, concerned assistance, patience and friendship that he gave us from the beginning of the
project to its successful completion.
We would like to thank The Chairman’s office (Dept. of Mechanical &Manufacturing
Engineering) for the earnest help you granted us that paved way to different industries and
institutions.
Our sincere appreciation also extends to all the staff of Concrete Laboratory, Department of Civil
and Construction Engineering (U.o.N), Kenya Industrial Research and Development Institute
(KIRDI), Ministry of Environment and Mineral Resources who provided assistance at various
occasions.
Our appreciation also goes to all the staff and technicians of the departmental workshop,
especially Mr. Githome and Mr. Njue for their keen support and innovativeness throughout.
Our special thanks to our dear friend and classmate, Felix Olala Aringo for his tireless support
and encouragement throughout the project.
We are grateful to all our family members and friends who supported us all the time to the
completion of this project.
To all we say thank you and God bless you.
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LIST OF SYMBOLS USED
ΔT
Thermal shock temperature range
a
crack length
D
diameter of the specimen
E
elastic modulus
I
second moment of area
K
stress intensity factor
k
thermal conductivity
Kc
critical stress intensity factor
KIc
plane strain fracture toughness
L
span
M
bending moment
m
Weibull modulus
F
fracture load
Pf
probability of failure of the specimen
Ps
probability of survival of the specimen
R
radius of the specimen
T
time
Y
geometric constant
σ
Modulus of Rapture
σf
Average Modulus of Rapture
σt
Thermal stress
σST
Tensile strength
α
Coefficient of thermal expansion
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ABSTRACT
There have been numerous efforts to increase the local content of furnaces and domestic
charcoal stoves (jikos); hence the choice of appropriate refractory material for lining of
locally manufactured furnaces and stoves has remained a major concern. This project
investigates the choice of appropriate local refractory material for the lining of laboratory
electric resistance furnaces and domestic charcoal stoves. It mainly focuses on refractory
ceramics manufactured using locally available raw clay from Nyeri and Murang’a. The
main objective was to determine the thermal shock and lifetime properties of refractory
ceramics and its improvements by addition of sand and alumina in different proportions.
The study involved collection of raw materials, preparation of the samples, assembling of
the extrusion machine, making and testing of the specimens and comparing the results
with previous researches.
The plain Nyeri and Murang’a clay were soaked in water overnight, mixed, sieved to
remove impurities and then put out in the drying bay to dry. After drying the clay was
milled into powder form. Sand was also sieved to remove impurities. Plain Nyeri and
Muranga’a clays, mixtures of the clays with sand and alumina in different proportions
were weighed and mixed thoroughly in powder form. Then controlled amount of water
was added to them and kneaded thoroughly into moldable state. Extrusion followed using
motorized extruder to make 15 different groups of samples, each group having
approximately 30 specimens. The specimens obtained were left to dry in controlled
conditions for about 4 to 5 days after which they were fired to 1000°C to raise their
strength. The shocking procedure was done where the specimens were heated to a certain
temperature say 400°C then dipped into a water bath at room temperature (23.5°C).
Thermal fatigue testing was also done by taking the specimens back to the furnace after
quenching until five and ten cycles were reached. The fracture load of the specimens was
then measured using a three point Hounsfield tensometer, from which the strengths
(modulus of rapture) and weibull modulus were calculated.
Analysis from the graphs and tables of average breaking stress showed Plain clay from
Murang’a was found to be stronger than that from Nyeri before any quenching/ shocking
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was done (unshocked specimens). Generally, from discussions and conclusions it was
found that the various percentage mixtures of Murang’a clay and alumina had the highest
percentage reduction of strength on average thus the least resistant to thermal shock. On
the other hand, the various percentage mixtures of Nyeri clay and sand had the least
percentage reduction of strength and thus most resistant to thermal shock. From our
results it was therefore found that, mixture of 20% alumina-80% Murang’a was the least
resistant to thermal shock, while 20% alumina-80% Nyeri clay was most resistant to
thermal shock. From the analysis and conclusions, recommendations for further
development of this project were proposed.
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PROJECT OBJECTIVES
1. To determine how the addition of alumina and sand affect the strength and thermal shock
properties of the refractory ceramic clay.
2. To investigate the choice of appropriate local refractory material for the lining of
laboratory electric resistance furnace and domestic charcoal stoves.
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Table of Contents
CHAPTER 1:
INTRODUCTION ................................................................................................................ 1
1.1 CERAMICS.......................................................................................................................................... 1
1.2 NATURE OF CERAMICS....................................................................................................................... 1
1.3 CLASSIFICATION OF CERAMICS........................................................................................................... 1
1.3.1 GLASSES. ..................................................................................................................................... 1
1.3.2 CLAY AND CLAY PRODUCTS ......................................................................................................... 1
1.3.3 REFRACTORIES ............................................................................................................................ 2
1.3.4 ABRASSIVES ................................................................................................................................ 2
1.3.5 CEMENTS .................................................................................................................................... 2
1.3.5 ADVANCED CERAMICS ................................................................................................................ 2
1.4 PROPERTIES OF MODERN AND TRADITIONAL CERAMICS THAT MAKE THEM SUITABLE FOR
ENGINEERING APPLICATIONS .................................................................................................................. 3
CHAPTER 2: BACKGROUND ..................................................................................................................... 5
2.1 ANALYSIS OF THE RESULTS FROM PREVIOUS REPORTS....................................................................... 5
2.1.1 RESULTS FROM SONGOK AND SURESH ........................................................................................ 5
2.1.2 RESULTS FROM NZIOKI AND MOGUSU ........................................................................................ 9
2.1.3 COMBINED RESULTS FOR AVERAGE STRENGTH AGAINST % SAND FOR SONGOK & SURESH AND
NZIOKI & MOGUSU FOR NYERI CLAY UNSHOCKED ............................................................................. 10
2.2 OBSERVATIONS................................................................................................................................ 10
2.2.1 SONGOK AND SURESH .............................................................................................................. 10
2.2.2 NZIOKI AND MOGUSU ............................................................................................................... 10
CHAPTER 3: THEORY .............................................................................................................................. 11
3.1 THERMAL STRESSES AND TEMPERATURE GRADIENTS ...................................................................... 11
3.2 THERMAL SHOCK AND THERMAL SHOCK RESISTANCE ...................................................................... 12
3.2.1 Examples of thermal shock failure include:................................................................................ 13
3.2.2 Prevention of thermal shock ..................................................................................................... 13
3.3 MEASUREMENT OF THERMAL SHOCK RESISTANCE .......................................................................... 14
3.3.1 Ultrasonic Method .................................................................................................................... 14
3.3.2 Hasselmann method ................................................................................................................. 14
3.3.3 FLEXURE TEST (BENDING).......................................................................................................... 15
3.4 MODULUS OF RUPTURE (
) ........................................................................................................... 17
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3.5 FRACTURE TOUGHNESS ................................................................................................................... 18
3.6 POROSITY ........................................................................................................................................ 18
3.7 THE STATISTICS OF STRENGTH AND THE WEIBULL DISTRIBUTION .................................................... 19
CHAPTER 4: MATERIALS AND APPARATUS ............................................................................................. 20
CHAPTER 5: METHODOLOGY ................................................................................................................. 21
5.1 PREPARATION OF CLAY, SILICA AND ALUMINA................................................................................. 22
5.2 MIXING OF CLAY WITH SAND AND ALUMINA ................................................................................... 22
5.2.1 PROPORTIONS OF RAW MATERIALS .......................................................................................... 22
5.2.2 QUANTITY OF RAW MATERIALS REQUIRED ............................................................................... 23
5.3 EXTRUSION, DRYING AND FIRING..................................................................................................... 24
5.4 THERMAL SHOCKING AND THERMAL FATIGUE TESTING ................................................................... 25
5.5 FLEXURE TEST .................................................................................................................................. 25
CHAPTER 6- RESULTS AND ANALYSIS ..................................................................................................... 25
6.1 TABLES AND GRAPHS ....................................................................................................................... 51
6.2 NYERI CLAY ...................................................................................................................................... 51
6.2.1 GRAPHS OF STRENGTH AGAINST SHOCKING TEMPERATURE-NYERI CLAY .............................. 54
6.3 MURANG’A CLAY GRAPHS................................................................................................................ 55
6.3.1 GRAPHS OF AVERAGE STRENGTH AGAINST SHOCKING TEMPERATURE-MURANG’A CLAY .......... 59
6.4 COMBINED RESULTS OF PREVIOUS RESEARCHERS AND OURS .......................................................... 60
6.5 PERCENTAGE REDUCTION OF STRENGTH AFTER 10 SHOCKS ............................................................ 62
6.6 COMPARISON OF RESULTS WITH THOSE OF PREVIOUS RESEARCHERS ............................................. 63
6.6.1 AVERAGE STRENGTH OF UNSHOCKED SPECIMEN- CHERONO &MOSIRIA ................................... 63
6.6.2 RESULTS FOR AVERAGE STRENGTH AGAINST % SILICA FROM NZIOKI & MOGUSU ..................... 64
6.6.3 RESULTS FOR AVERAGE STRENGTH AGAINST % ALUMINA FROM SONGOK AND SURESH ...... Error!
Bookmark not defined.
6.7 ACTUAL PERCENTAGES OF SILICA AND ALUMINA IN THE MIXTURES ................................................ 66
CHAPTER 7: DISCUSSION OF THE RESULTS .................................................. Error! Bookmark not defined.
7.1 VARIATION OF AVERAGE FLEXURE STRENGTH WITH ADDITION OF SAND AND ALUMINA ................. 68
7.2 Effect of sand addition to clay .......................................................................................................... 68
7.3 Effect of alumina addition to clay..................................................................................................... 70
7.4 VARIATION OF AVERAGE STRENGTH WITH QUENCHING/ THERMAL SHOCKING ............................... 70
7.5 WEIBULL MODULUS......................................................................................................................... 72
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7.6 COMPARISON OF THE RESULTS WITH PREVIOUS RESEARCHERS ....................................................... 72
7.7 ASSUMPTIONS ................................................................................................................................. 73
CHAPTER 8: CONCLUSIONS .................................................................................................................... 74
8.1 Average strength ............................................................................................................................. 74
8.2 Thermal shock resistance ................................................................................................................. 74
8.3 Weibull modulus.............................................................................................................................. 74
8.4 APPLICATION TO INDUSTRIES .......................................................................................................... 75
CHAPTER 9: CHALLENGES AND RECOMMENDATIONS ............................................................................ 76
9.1 CHALLENGES.................................................................................................................................... 76
9.2 RECOMMENDATIONS ...................................................................................................................... 76
LIST OF REFERENCES .............................................................................................................................. 77
APPENDIX .............................................................................................................................................. 78
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CHAPTER 1:
INTRODUCTION
1.1 CERAMICS
Broadly speaking ceramics are compounds between metals and non-metals. They are crystalline
solids composed of metallic and non-metallic materials {1}. The term' Ceramics’ comes from a
Greek word keramikos which means "burnt off” indicating that desirable properties are achieved
through a high-temperature heat treatment process called firing {2}.
1.2 NATURE OF CERAMICS
They are inorganic materials; that is, they do not contain carbon and are derived from mineral
sources. They are formed by the action of heat and subsequent cooling. Ceramics are of crystal
structures made of metallic ions and the bonding in ceramics can either be partially or
completely ionic. Originally ceramics were clay-based materials, consisting primarily of forms
of silicon, aluminum and oxygen. {3}.
1.3 CLASSIFICATION OF CERAMICS
Ceramics may be classified into six groups: glasses, clay products, refractories, abrasives,
cements and advanced ceramics. The first three are broadly termed traditional ceramics since
they have been used for centuries {1}.
1.3.1 GLASSES.
They are generally non-crystalline silicates containing other oxides like CaO (lime), Na2O
(soda), K2O, and AL2O. The distinguishing characteristic is their transparency {1}. Glass is used
in a load-bearing capacity in car windows, containers, diving bells and vacuum equipment. All
important glasses are based on silica (SiO3) {2}.
1.3.2 CLAY AND CLAY PRODUCTS
These are naturally occurring inorganic materials that are essentially the weathered remains of
various types of rocks. Clay is used as the raw material since it is abundant and is relatively
cheap. The common properties of clay are: Plastic when moist, become rigid when dried but
regain their plasticity when rewetted and when fired they become mechanically strong, hard and
permanently non-plastic. Clays can be molded, extruded, turned or curved {4}. The common
clay minerals are kaolinite (Al2O3.2SiO2.2H2O) and montmorillonite (Al2O3.4SiOnH2O) {2}.
Important engineering material clay-products include: bricks, tiles, porcelain, stoneware and
various chemical ware.
1
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1.3.3 REFRACTORIES
These are special materials of construction capable of withstanding high temperatures at various
industrial processes and operations .The traditional ceramic group are products of sintered clay,
consisting of crystals in a glassy matrix. These materials find use in ovens, kilns, furnaces,
melting pots, in welding and cutting and as engine parts.
Commercial refractories are complex solid bodies consisting of high melting oxides or a
combination of such oxides of elements of silicon, aluminium, calcium, and zirconium with
small elements of other impurities present {3}.
Insulating refractories have high porosity and low thermal conductivity in order to reduce the
rate of heat flow and thus maximizing the heat conservation within the furnace. These
refractories are produced from; China clay, asbestos, glass wool, mica, bubble alumina, saw dust
etc {7}*.
1.3.4 ABRASSIVES
The common abrasive materials are SiC and AL2O3 (alumina). They are used to grind other
materials. The main requirement here is high hardness, resistance, toughness and high
temperature stability {2}.
1.3.5 CEMENTS
They are used in construction on an enormous scale, equaled only by steel, brick and wood.
Cement is a mixture of a combination of lime (CaO), silica (SiO2) and alumina (Al2O3), which
sets when mixed with water. They include Portland cement, plaster of Paris and lime {1}.
1.3.5 ADVANCED CERAMICS
Due to recent development in material technology, new or advanced ceramics have been
developed. The 'new’ or 'advanced’ ceramics when used as engineering materials possess some
properties which are superior to metal-based systems. These properties include; high resistance
to abrasion, chemical inertness, high mechanical speeds (as tools), light weight and good strength
at elevated temperatures. Advanced ceramics include oxides such as Alumina and Zirconia,
carbides, borides, nitrides, silicides, combinations of oxides and non-oxides and other similar
compounds which are being developed. They are used in applications such as automobile, sports
and machine tool industries. Most are actually synthetic ceramics that are produced from fine,
poor powders using new technology that involves microwaves, electron beams and polymer
chemistry {3}.
*(http://pubs.rsc.org/en/content/articlelanding).
2
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1.4 PROPERTIES OF MODERN AND TRADITIONAL CERAMICS THAT
MAKE THEM SUITABLE FOR ENGINEERING APPLICATIONS
High melting point
Ceramics have high melting point. This is because of their strong primary bonding (ionic and
covalent) between constituent atoms. For this reason ceramics such as magnesia and alumina
which have melting points of 2800°C and 2040°C respectively make excellent refractory
materials for lining high temperature furnaces, boilers, crucibles and support for hot wires.
Alumina is used for tips of lathe tools {5}.
Low thermal conductivity
Most ceramics have very low value of thermal conductivity. It is because there are no free
electrons in such materials. Hence ceramics are generally good thermal insulators. Alumina is
used for spark plugs insulators. These articles have to withstand varied fluctuations of
temperature and pressure, the maximum being about 850°C and 6Mpa and voltage of up to
1200V. They also maintain gas tight joints with the metal conductor and the base {5}.
Hardness
Most ceramics are intrinsically hard, (ionic or covalent bonds present) an enormous lattice
resistance to the motion of dislocation. Examples of hard ceramics include: Corundum (Al2O3),
silicon carbide, diamond and cubic boron nitride. Methods used to measure hardness include;
Rockwell hardness test, Brinell hardness test, Vickers, Knoop hardness and Shore {4}.The best
method for measuring hardness in ceramics is the Vickers test. This hardness is utilized for use
in high-performance applications, such as industrial cutting tools for milling and grinding metals,
pump components, seal rings, ballistic vests and ball bearings {7}.
Chemical inertness
The chemical inertness of ceramic is finding many uses in the medical field where contacts with
body fluids are less of a problem than with most other metals. Recent advancement in ceramics
has resulted in bioceramics, such as dental implants and synthetic bones. Dentistry has advanced
with ceramic teeth that can be matched with the patient’s natural ones. Glasses are resistant to
many acids, solvents and other chemicals thus make them suitable to be used in laboratories for
chemical mixing and reactions {7}.
3
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Wear resistance
Ceramics play a major role in the machine tool industry. Their wear resistance makes them
valuable as coatings for cutting tools, surgical instruments, punches and dies. Together their
thermal and mechanical stability allows them to retain their smooth, accurate cutting surfaces
longer than metals do. Coated cutting tools and inserts each designed to serve a special function
can run productively at faster cutting speeds and at faster feed rates than can any metal alloy tool
in the machining of hard steels, super alloys and ceramics.
Brittle fracture and strength
This is characterized by low plastic deformation and low energy absorption before breaking. The
fracture toughness of ceramics is low which limits their use. The design strength of a ceramic is
determined by its low fracture toughness and by the lengths of the micro cracks it contains.
=
П
………………. (1)
Where;
ST = Tensile strength
am = length of a surface crack or half of the length of an internal crack
K1C = fracture toughness.
From the equation above there are two ways of improving the strength of ceramics; decreasing
am and increasing KIC by alloying or by making a ceramic into a composite.
Young’s modulus
Young’s modulus is a measure of the stiffness of an elastic material and is a quantity used to
characterize materials. Ceramics have a well defined Young’s modulus. Ceramic modulus is
generally greater than that of metals. The densities of ceramics are low and thus the specific
modulus (E/ ) is attractively high, this is one reason ceramics are used in composites since their
presence raises the specific stiffness of the composite enormously {2}.
4
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CHAPTER 2: BACKGROUND
Attempts to improve the thermal shock characteristics of refractory ceramics have been done in
the past. Different methods have been used, with that intended in this project having been
experimented by Songok J.K & Suresh P.J and then by Nzioki J.N & Mogusu C.O. The results
they obtained have greatly aided in the present experimentation. A brief analysis of their
experimentation and analysis was done and below are some of the observations noted.
Both groups i.e. Songok J.K & Suresh P.J and by Nzioki N.J & Mogusu C.O attempted to
improve the thermal shock properties of clay by the addition of different percentages of sand and
alumina. Songok and Suresh used a silica to clay ratio and alumina to clay ratio of 3:2 (60%40%), 7:3 (70%-30%) and 4:1 (80%-20%) in both cases while Mogusu and Nzioki used a silica
to clay ratio of 1:3 (25%-75%), 0.33:0.67 (33%-67%) and1:1 (50%-50%).
2.1 ANALYSIS OF THE RESULTS FROM PREVIOUS REPORTS.
2.1.1 RESULTS FROM SONGOK AND SURESH
AVERAGE STRENGTH AGAINST NUMBER OF SHOCKS FOR 60% SILICA-40%
CLAY
No. of Shocks Unshocked
0
7.580
10
20
30
400 °C
7.580
6.307
6.483
6.630
Average Strength,
600 °C
7.580
3.280
2.944
3.15
f
800 °C
7.580
2.088
2.120
2.117
1000 °C
7.580
1.8273
Average Strength (Mpa)
Average Strength against Number of Shocks
for 60% Silica and 40% clay
8
7
6
5
4
3
2
1
0
400 ͦc
600 ͦc
800 ͦc
1000 ͦc
0
10
20
No. of Shocks
30
40
5
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AVERAGE STRENGTH AGAINST NUMBER OF SHOCKS FOR 70% SILICA-30%
CLAY
No. of Shocks
0
10
20
30
Average Strength, σf
Unshocked
400 °C
3.309
3.309
3.129
3.677
3.376
600 °C
3.309
3.389
3.144
2.891
800 °C
3.309
0.824
0.577
0.767
Aerage Strength (Mpa)
Average Strength against Number of Shocks for
70% silica-30% clay
4
3.5
3
2.5
2
1.5
1
0.5
0
400°C
600°C
800°C
0
10
20
No. of Shocks
30
40
AVERAGE STRENGTH AGAINST NUMBER OF SHOCKS FOR 80% SILICA-20%
CLAY
No. of Shocks
0
10
20
30
Average Strength, σf
Unshocked
400 °C
6.078
6.078
4.333
4.425
4.630
600 °C
6.078
3.421
2.666
2.566
800 °C
6.078
2.134
1.292
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Average Srength (Mpa)
Average Strength Against No. of Shocks for 80%
Silica and 20% Clay
7
6
5
4
400°C
3
600°C
2
800°C
1
0
0
10
20
30
40
No. of Shocks
AVERAGE STRENGTH AGAINST NUMBER OF SHOCKS FOR 60% ALUMINA-40%
CLAY
No. of Shocks
0
10
20
30
Average Strength, σf
Unshocked
400 °C
15.957
15.957
10.260
11.065
9.973
600 °C
15.957
6.886
7.781
6.889
800 °C
15.957
5.516
4.304
2.499
Average Strength (Mpa)
Average Strength against No. of Shocks for 60%
Alumina and 40% Clay
20
15
10
400oC
5
600OC
0
800OC
0
5
10
15
20
25
30
35
No. of Shocks
7
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AVERAGE STRENGTH AGAINST NUMBER OF SHOCKS FOR 70% ALUMINA AND
30% CLAY
Average Strength,
No. of Shocks
Unshocked
400 °C
0
10
20
30
9.131
f
600 °C
9.131
4.134
4.037
4.536
800 °C
9.131
4.322
3.956
3.611
9.131
1.642
1.548
Average Strength (Mpa)
Average Strength against Number of Shocks for
70% Alumina and 30% Clay
10
8
6
4
400 ͦc
2
600 ͦc
0
800 ͦc
0
5
10
15
20
25
30
35
No. of Shocks
AVERAGE STRENGTH AGAINST NUMBER OF SHOCKS FOR 80% ALUMINA-20%
CLAY
No. of Shocks
0
10
20
30
Average Strength (Mpa)
unshocked
400°C
23.179
23.179
13.300
12.102
13.716
600°C
23.179
9.127
11,111
10.590
800°C
23.179
2.134
1.884
8
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Average Srength
(Mpa)
Average Strength Against No. of Shocks for 80%
Alumina and 20% Clay
25
20
15
10
400 °C
5
600 °C
0
800 °C
0
10
20
30
40
No. of Shocks
2.1.2 RESULTS FROM NZIOKI AND MOGUSU
AVERAGE STRENGTH AGAINST % SAND FOR NYERI CLAY
% SAND
Unshocked
10 Shocks at 500°C
Plain Clay
25
7.219
11.440
0.00
6.658
33
7.749
5.047
50
5.036
7.725
Average Srength (Mpa)
Average Srength Against Percentage Sand for Nyeri clay
14
12
10
8
6
4
2
0
Unshocked
10 Shocks at 500°C
0
10
20
30
40
50
60
% Sand
9
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2.1.3 COMBINED RESULTS FOR AVERAGE STRENGTH AGAINST %
SAND FOR SONGOK & SURESH AND NZIOKI & MOGUSU FOR NYERI
CLAY UNSHOCKED
% SAND
0
25
33
50
60
70
80
AVERAGE STRENGTH (Mpa)
7.219
11.440
7.749
5.036
7.5798
6.7721
6.084
Average
Strength(Mpa)
Average Strength Against % Sand for Nyeri Clay
15
10
5
0
0
20
40
60
80
100
% Sand
2.2 OBSERVATIONS
2.2.1 SONGOK AND SURESH



Strength is observed to reduce with increase in the silica content
Strength decreases as the number of shocks increase and as well as the shocking
temperature is increased.
Strength increases with increase in the alumina content
2.2.2 NZIOKI AND MOGUSU


When silica was added to clay, it caused an increase in strength up to 25% of silica then
decreases as the silica content increase beyond 25%.
The strength decreases with increase in the number of shocks and with increase of the
shocking temperature
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CHAPTER 3: THEORY
3.1 THERMAL STRESSES AND TEMPERATURE GRADIENTS
Thermal stresses are stresses due to temperature gradients. These stresses can be comprised of
tensile stress, which is stress arising from forces acting in opposite directions tending to pull a
material apart, and compressive stress, which is stress arising from forces acting in opposite
directions tending to push a material together. These stresses, cyclic in nature, can lead to fatigue
failure of the materials. {6}.
The resultant thermal stresses in a body are determined by the temperature distribution and the
material constants; Young’s Modulus (E), coefficient of expansion ( ) which are usually
assumed to be temperature dependent. Temperature gradients are developed within a body on
heating or cooling. On heating, the expansion of the surface layers causes compression which is
balanced by tensile stresses in the center of the body. On cooling, however, contraction of the
outer layer causes tensile stresses on the surface. Furthermore shear stresses may be induced on
the surface. The shear stresses are equal on heating or cooling and may become bending stresses
when the temperature distribution within the body is not uniform {4}
In a one dimensional plate thermal stress is given by;
σ =E ∆T………. (2)
In a two dimensional plate thermal stress is given by;
∆
σ =
………. (3)
In a three dimensional plate thermal stress is given by;
σ =
∆
………… (4)
Where;
E = elastic modulus
= linear coefficient of thermal expansion
∆T = Temperature drop
t = Thermal stress
= Poisson ratio {5}
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3.2 THERMAL SHOCK AND THERMAL SHOCK RESISTANCE
Thermal shock is the cracking as a result of a rapid temperature change. It involves the buildup
of thermal stress in a material as a result of exposure to a temperature difference between the
surface and the interior of a material. Fracture caused by sudden temperature change is a
problem in ceramics {2}.Thermal conductivity and thermal expansion are the major factors
affecting thermal shock resistance of materials particularly brittle materials like ceramics and
glasses. The size of the body is another factor affecting thermal shock resistance. {4}.
The thermal stresses responsible for the response to temperature stress depend on: geometrical
boundary conditions, thermal boundary conditions, physical parameters, such as
coefficient of thermal expansion
modulus of elasticity
E
thermal conductivity
k
Fracture strength of material
b
The magnitude of temperature
∆T {9}
change
Estimates for thermal shock resistance are done using Thermal Shock Resistance parameter, R.
This can be defined as the temperature change required to give fracture.
σ
R=
……… (5)
For very high heat transfer rates, the thermal shock resistance can be estimated by:
R=
σ
α
……..... (6)
For low and moderate heat transfer rates thermal shock is given by:
R=
α
………. (7)
The heat transfer rates can be determined by the Biot modulus.
=
…………. (8)
Where;
rm = half the thickness of the plate or the radius of a cylinder according to the shape
of the body
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h
k
= heat transfer coefficient
= thermal conductivity
From the above parameters (R and
shock resistance {4}
) we can optimize properties that we require for thermal
3.2.1 Examples of thermal shock failure include:



Splashing cold water on incandescent bulbs that have been running. The glass shutter
as a result of thermal shock.
Hard rocks can be broken by fire-setting, which involves heating the rock face with
wood fire and then quenching in cold water.
Ice cubes placed in a glass of water crack by thermal shock as the exterior
temperature is increased than the interior {7}*
3.2.2 Prevention of thermal shock






Lowering the temperature gradients and differential stresses. This is done by slow
heating or cooling of materials according to a specific schedule like firing of
ceramics, or cooling of furnaces constructed of refractories, are performed at a
specified schedule with due consideration of thermal shock resistance of the material.
Using materials with a low value of coefficient of thermal expansion. Examples are
Pyrex glass, fused silica, cordierite, Ceramics, Special porcelain and Pyroceram.
Cermets were developed for the purpose of improving the ductility of brittle materials
by combining them with ductile metals. At the same time the thermal conductivity
has been improved.
Use of small units to build large structures. The small units are each highly resistant
to thermal shock. For example the small blocks cemented lightly together for a rocket
nozzle liner or held together mechanically by a wired mesh are used to improve the
thermal shock resistance of the whole unit. Many ceramic wares are manufactured
only in a limited size in order to minimize the possibility of introducing thermal
stresses during cooling.
Reducing the heat transfer coefficient by application of surface coating, which
provide thermal insulation and also protect the material from a deleterious
atmosphere.
Introduction of an initial stress that counteracts the effect of thermal stress. This
procedure is called prestressing and is common for applications in the manufacture of
prestressed ceramics.
*(http://en.wikipedia.org/wiki/Thermal_shock)
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3.3 MEASUREMENT OF THERMAL SHOCK RESISTANCE
3.3.1 Ultrasonic Method
Ultrasonic testing method is used for non-destructive quantification of thermal shock damage in
refractory materials. When refractory materials are subjected to the industrial thermal cycles
crack nucleation and propagation occurs resulting in loss of strength and material degradation.
The formation of cracks decreases the velocity of ultrasonic pulses travelling in the refractory
because it depends on the density and elastic properties of the material. Therefore measuring
either of these properties can directly monitor the development of thermal shock damage level.
Young's modulus of representative samples is calculated using measured values of ultrasonic
velocities obtained by ultrasonic pulse velocity technique {7}*
3.3.2 Hasselmann method



A specimen is heated to a specified temperature and then quenched from temperature TO
to a temperature TU. The specimen cools rapidly by temperature ∆T= (TU-TO) which is
the temperature before and after cooling.
After quenching the flexural strength of the quenched material is measured by standard
flexure (bending) test.
Test results are plotted on the graph of strength versus ∆T. The graph below shows the
sample of the graph suggested by Hasselmann.
*(http://www.sciencedirect.com/science)
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Figure 1: The strength of thermally shocked bending samples according to
Hasselman


Up to a temperature difference of
Tc the strength does not alter. The strength then
drops sharply within a narrow range,
T. Up to
Tc’ this reduced strength then
remains constant, falling away again at higher temperature differences.
This value of ∆T is a parameter indicating thermal shock resistance of the material.
3.3.3 FLEXURE TEST (BENDING)
Preparing specimens from brittle materials, such as ceramics is difficult because of the problems
involved in shaping and machining them to proper dimensions. Furthermore, because of their
sensitivity to surface defects and notches, clamping brittle materials for testing is difficult. Also,
improper alignment of the test specimen may result in non uniform stress distribution along the
cross-section of the specimen. A commonly used test method for brittle materials is the bend or
flexure test. {9}
This test is done using Tensometer. The flexure test method measures behavior of materials
subjected to simple beam loading. Maximum stress and maximum strain are calculated for
increments of load. Results are plotted in stress-strain diagram. Flexural strength is defined as the
maximum stress in the outermost fiber. This is calculated at the surface of the specimen on the
convex or tension side. Flexural modulus is calculated from the slope of the stress versus
deflection curve. If the curve has no linear region, a secant line is fitted to the curve to determine
slope. A flexure test produces tensile stress in the convex side of the specimen and compression
stress in the concave side. This creates an area of shear stress along the midline. To ensure the
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primary failure comes from tensile or compression stress the shear stress must be minimized.
This is done by controlling the span (S) to depth (d) ratio; the length of the outer span divided by
the height (depth) of the specimen. For most materials S/d=16 is acceptable. Some materials
require S/d=32 to 64 to keep the shear stress low enough.
There are two test types; 3-point bending and 4-point bending. In a 3-point test the area of
uniform stress is quite small and concentrated under the center loading point. In a 4-point test,
the area of uniform stress exists between the inner span loading points (typically half the outer
span length). When a 3-point flexure test is done on a brittle material like ceramic or concrete it
is often called modulus of rupture (MOR).
The main advantage of a three point flexural test is the ease of the specimen preparation and
testing. However, this method has also some disadvantages: the results of the testing method are
sensitive to specimen and loading geometry and strain rate. {7}*
In a four point the area and volume under peak stress or near peak stress is higher than in a three
point bend testing hence the probability of a large flaw in a four point bend test being exposed to
a high stress is increased. Thus, the bend strength measured in a four point is lower than that
measured using a three point bend test. {8}
*(http://www.instron.us/wa/applications/test_types/flexure/default.aspx?ref=http://search.softoni
c.com/CT3031607/tb_v1)
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3.4 MODULUS OF RUPTURE (σ )
This is the stress of the extreme fiber of a specimen at its failure in the Flexure Test and can be
calculated using the flexure stress formula:
σ =
………… (9)
For specimen having a circular cross section, using the 3-point Flexure test;
y=R
M=
I=
Where;
M = bending moment
I = moment of inertia
y = distance from the neutral axis to the outer surface
σ = fracture strength of material
F = fracture load
L = span
R= specimen radius
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Therefore;
σ
=
………. (10)
3.5 FRACTURE TOUGHNESS
This is a material property that indicates its susceptibility to the spread of a crack. This is
characterized by low plastic deformation and low energy absorption before breaking. The
fracture toughness of ceramics is low which limits their use. The design strength of a ceramic is
determined by its low fracture toughness and by the lengths of the micro cracks it contains.
=
П
………… (11)
Where;
σST = Tensile strength
am = length of a surface crack or half of the length of an internal crack
K1C = fracture toughness.
From the equation above there are two ways of improving the strength of ceramics; decreasing
am and increasing KIC by allowing or by making a ceramic into a composite.
3.6 POROSITY
A fired ceramic product shows porosity to a variable degree; porosity is a measure of the
volumes of all pores present in a material. The pores may be open or closed. Accordingly two
types of porosity can be distinguished; apparent porosity and true porosity. Apparent porosity is
expressed as a percentage of the volume of the open pores with respect to the exterior volume of
the material under consideration.
%P
=
100 ……….. (12)
Where;
P = the apparent porosity
D = Weight of dry solid
S = Weight of the suspended solid in water after having been soaked in water so that
all open pores in the body are completely filled with water
W = Weight of the soaked body determined by weighing the soaked specimen from
which excess water has been removed by dabbing with a damp cloth.
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3.7 THE STATISTICS OF STRENGTH AND THE WEIBULL DISTRIBUTION
For a given ceramic material the distribution of crack size, shape, and orientation differs from
sample to sample. It is therefore inherent in the strength of ceramics that there is a statistical
variation in strength. There is no single “tensile strength” but there is a certain, definable,
probability that a given sample will have at a given strength. A large sample will fail at a lower
stress than a small one, on average, because it is more likely that it will contain one of the larger
flaws. So there is a volume dependence of the strength.
A Swedish engineer, Weibull, invented the statistical method of determining the strength of
brittle (ceramic) materials. The Weibull distribution function is given by:
Ps (V0) = exp {-( )m}…….. (13)
Where
Ps (V0) = Survival probability of the specimen
= Actual failure stress of the specimen
σ Stress level below which there is zero probability of failure.
m = Weibull modulus.
The constant m tells us how rapidly the strength falls as we approach σ . The lower the value of
m, the greater the variability of strength.
Taking natural logs in equation (13) gives
ln {
} = ( )m ……… (14)
And taking logs again gives
ln {ln (
Thus a plot of ln {ln (
) }= m ln ( ) …… (15)
)} against ln ( ) is a straight line of slope m. The probability that
one sample surviving a stress
is Ps (V0). The probability that a batch of n such samples all
n
survives the stress is {P s (V0)} . If these n samples were stuck together to give a single sample
of volume V =nV0 then its survival probability would still be {Ps (V0)} n. Thus:
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Ps (V) = {Ps (V0)} n = {Ps (V0)} V/ V0 …………. (16)
This is equivalent to
ln Ps (V) =
ln Ps (V0)………………. (17)
Rearranging equation (17) gives
Ps (V) = exp {
ln Ps (V0)}…………. (18)
Equation (13) can be rewritten as
ln Ps (V0) = - ( )m……………………… (19)
If we insert this result in equation (18) we get
Ps (V) = exp {−
( )m
OR
ln Ps (V) = -
( ) m ……..................(20) {3}
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CHAPTER 4: MATERIALS AND APPARATUS
The following major equipment and materials were used
1. Clay
2. Silica
3. Alumina
4. Extrusion machine
5. Drying bay
6. Electric furnace
7. Sieves
8. Electronic weighing machine
9. Hounsfield Tensometer
10. Vernier calipers and steel rule
11. Tongs and specimen holders
12. Lubricating oil
13. Surface plate
14. Specimen racks
15. Sprit level
16. Water basins
Fig 4.1: Extrusion machine
Fig 4.2: Hounsfield Tensometer
Fig 4.3: Rack
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CHAPTER 5: METHODOLOGY
5.1 PREPARATION OF CLAY, SILICA AND ALUMINA.
The raw clay from Nyeri and Murang’a was soaked in water for one day to break the large lumps
and the mixture stirred to form a suspension. The suspension was passed through a sieve of
250µm aperture size to remove any floating bodies and large particles. The suspension was
poured into drying basin in an isolated place to dry. Once dry, the clay was transported to KIRDI
for milling into powder form.
The sand was obtained from Murang’a. It was sieved through a sieve of 250µm aperture size to
remove large particles and to allow for ease of mixing. The alumina was provided by KIRDI in
powder form.
5.2 MIXING OF CLAY WITH SAND AND ALUMINA
5.2.1 PROPORTIONS OF RAW MATERIALS
The sieved clay was mixed with sand and alumina in various percentages as shown below:
1. MURANG’A CLAY+SAND MIXTURE
Plain Murang’a clay
20% sand +80% clay
30% sand + 70% clay
40% sand + 60 % clay
2. MURANG’A CLAY + ALUMINA MIXTURE
20% alumina +80 % clay
30% alumina+ 70% clay
40% alumina + 60 % clay
3. NYERI CLAY+SAND MIXTURE
Plain Nyeri clay
15% sand + 85% clay
55% sand + 45% clay
65% sand + 35% clay
85% sand + 15% clay
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4. NYERI CLAY+ALUMINA MIXTURE
20% alumina +80 % clay
30% alumina+ 70% clay
40% alumina + 60 % clay
5.2.2 QUANTITY OF RAW MATERIALS REQUIRED
The dimension of each specimen was 15mm (0.59 ") diameter and 72.6 mm (3") length. The
volume (V) of each specimen was calculated as shown;
V =
П
……… (21)
Where,
V =Volume
D=Diameter
L=Length
Hence the volume of each specimen was determined to be:
V = (П/4)*(0.01272) *0.0762
V=9.653 *10 -6m3
The mass of each specimen was calculated as shown;
M = V*
Where,
M=Mass
= Density
V = Volume
For the case of Alumina + clay, we used the density of Alumina which is 3700Kg/m3 since it is
much higher than that of clay. This enabled us to obtain an over estimate of the mass thus
operating in the safe region.
M = 9.653 *10 -6 * 3700
M = 0.0357 Kg
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Hence the mass of each specimen could be approximated as 0.050 kg. For 30 specimens we
needed a total mass of;
Total mass = 0.050 * 30 = 1.5 kg
The total mass of 30 specimens used was overestimated to 2kg.
20% Alumina+ 80% Clay
20
∗ 2 = 0.4 kg of Alumina
100
80
∗ 2 = 1.6 kg of Clay
100
30% Alumina+ 70% Clay
30
∗ 2 = 0.6 kg of Alumina
100
70
∗ 2 = 1.4kg of Clay
100
40% Alumina+ 60% Clay
40
∗ 2 = 0.8kg of Alumina
100
60
∗ 2 = 0.6kg of Clay
100
The above masses were carefully weighed in an electronic balance and the mixtures made.
A similar process of calculation was repeated for the sand category with the density of sand
taken to be 2700 kg/m3.
Plain Nyeri and Muranga’a clays, mixtures of the clays with sand and alumina in different
proportions were weighed and mixed thoroughly in powder form. Then controlled amount of
water was added to them and kneaded thoroughly into moldable state. Extrusion followed using
motorized extruder to make 15 different groups of samples, each group having approximately 30
specimens.
5.3 EXTRUSION, DRYING AND FIRING.
The extrusion was done using a modified meat mincing machine which was run by a lathe
machine in the mechanical workshop. Long cylindrical specimens were extruded and received on
the surface plate. The specimens were sectioned to 76.3mm length specimens and rolled into a
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drying surface. Four hundred and fifty specimen of diameter 15mm and length 76.3mm were
obtained. The specimens dried slowly in a cool room to avoid non uniform drying that could lead
to warping. Four to five days were allowed for the specimens to dry and then put into the
furnace for firing. Firing was done in a controlled manner to avoid rapid drying which could lead
to breakage. The firing was done from 100˚to 1000˚ with an hour’s wait between each increment.
The specimens were left in the furnace to cool slowly to room temperature with the door closed
to avoid rapid cooling which could lead to shocking.
5.4 THERMAL SHOCKING AND THERMAL FATIGUE TESTING
The specimens were heated to known temperatures from say 400⁰C then dipped into a water bath
at room temperature (23.5⁰C). The process was repeated for other specimens for the
temperatures of 500⁰C, 600⁰C and 800⁰C.
Thermal fatigue differed slightly from thermal shock testing in that specimens were put back into
the furnace after quenching until five and ten cycles were reached.
5.5 FLEXURE TEST
This was done using a Hounsfield Tensometer in the Mechanical and Manufacturing Engineering
strength of materials laboratory. The three point technique was employed where the test
specimen was supported at the ends and the load applied at the centre. The applied load was
increased, bending the specimen until fracture. The load at fracture F, the distance between the
supports points L, the specimen diameter D, were taken for each specimen for computation of
the flexural strength.
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CHAPTER SIX: RESULTS AND ANALYSIS
RESULTS FOR UNSHOCKED SPECIMENS-MURANG’A CLAY MIXED WITH SAND
UNSHOCKED
SPECIMEN
PLAIN
MURANG'A
NO.
FRACTURE
LOAD (N)
SPAN
(L)
(mm)
DIAMETER
(mm)
Ln{Ln(1/[1-Pf])}
38.4
12.7
30.548
0.1
0.029
-2.250
2
630
38.4
12.62
30.646
0.3
0.032
-1.031
3
570
38.4
12.7
27.207
0.5
-0.087
-0.367
4
620
38.4
12.66
29.875
0.7
0.007
0.186
5
640
38.4
12.76
30.119
0.9
0.015
0.834
Weibull
Modulu
s
5.69
29.679
1
540
38.4
12.7
25.775
0.071
-0.082
-2.602
2
600
38.4
12.8
27.973
0.214
-0.001
-1.422
3
610
38.4
12.2
32.845
0.357
0.160
-0.817
4
570
38.4
12.46
28.810
0.500
0.029
-0.367
5
570
38.4
12.66
27.466
0.643
-0.019
0.029
6
560
38.4
12.82
25.986
0.786
-0.074
0.432
7
570
38.4
12.72
27.079
0.929
-0.033
0.970
0.04
27.990
1
510
38.4
12.8
23.777
0.1
-0.016
-2.250
2
500
38.4
12.76
23.531
0.3
-0.026
-1.031
3
510
38.4
12.7
24.343
0.5
0.008
-0.367
4
530
38.4
12.7
25.298
0.7
0.046
0.186
5
500
38.4
12.7
23.866
0.9
-0.012
0.834
AVERAGE MOR
40% SAND 60%CLAY
MURANG'A
Ln(σ/σf)
640
AVERAGE MOR
30% SAND -70%
CLAY
MURANG'A
Probability
of
Failure(Pf)
1
AVERAGE MOR
20% SAND 80% CLAY
MURANG'A
MOR
(Mpa)
17.75
24.163
1
440
38.4
12.36
22.783
0.1
-0.050
-2.250
2
440
38.4
12.2
23.691
0.3
-0.010
-1.031
3
440
38.4
12.22
23.575
0.5
-0.015
-0.367
4
470
38.4
12
26.593
0.7
0.105
0.186
5
430
38.4
12.22
23.039
0.9
-0.038
0.834
AVERAGE MOR
23.936
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7.25
RESULTS FOR SPECIMENS SHOCKED ONCE FROM 400⁰C TO ROOM
TEMPERATURE FOR THE MIXTURE OF MURANG’A CLAY AND SAND
PLAIN
MURANG,A
NO.
FRACTURE
LOAD(N)
SPAN
(L)
(mm)
DIAMETER
(mm)
MOR
(Mpa
38.4
12.56
20.725
0.1
-0.135
-2.250
2
480
38.4
12.74
22.696
0.3
-0.044
-1.031
3
660
38.4
12.7
31.503
0.5
0.284
-0.367
4
470
38.4
12.52
23.415
0.7
-0.013
0.186
5
420
38.4
12.66
20.238
0.9
-0.159
0.834
Weibull
Modulus
0.6
23.715
1
440
38.4
12.7
21.002
0.1
-0.015
-2.250
2
400
38.4
12.7
19.093
0.3
-0.110
-1.031
3
480
38.4
12.72
22.803
0.5
0.067
-0.367
4
460
38.4
12.7
21.956
0.7
0.029
0.186
5
460
38.4
12.74
21.750
0.9
0.020
0.834
7.23
21.321
1
450
38.4
12.84
20.784
0.08
0.071
-2.442
2
440
38.4
13
19.581
0.25
0.011
-1.246
3
470
38.4
12.96
21.110
0.42
0.087
-0.618
4
410
38.4
12.7
19.570
0.58
0.011
-0.133
5
410
38.4
12.8
19.115
0.75
-0.013
0.327
6
340
38.4
12.76
16.001
0.92
-0.191
0.910
AVERAGE MOR
40% SAND 60%CLAY
MURANG'A
Ln{Ln(1/[1-Pf])}
420
AVERAGE MOR
30% SAND 70% CLAY
MURANG'A
Ln(σ/σf)
1
AVERAGE MOR
20% SAND 80%CLAY
MURANG'A
Probability
of
Failure(Pf)
8.8
19.360
1
440
38.4
13.38
17.960
0.1
0.999
-2.250
2
400
38.4
13.04
17.638
0.3
0.981
-1.031
3
410
38.4
13.2
17.429
0.5
0.969
-0.367
4
430
38.4
13.1
18.701
0.7
1.040
0.186
5
430
38.4
13.22
18.197
0.9
1.012
0.834
AVERAGE MOR
17.985
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16.88
RESULTS FOR SPECIMENS SHOCKED ONCE FROM 600⁰C TO ROOM TEMPERATURE FOR THE
MIXTURE OF MURANG’A CLAY AND SAND
NO.
PLAIN
MURANG'A
FRACTURE
LOAD(N)
SPAN(L)
(mm)
DIAMETER
(mm)
Ln(σ/σf)
Ln{Ln(1/[1-Pf])}
330
38.4
12.6
16.129
0.1
0.092
-2.250
2
270
38.4
12.74
12.766
0.3
-0.141
-1.031
3
310
38.4
12.7
14.797
0.5
0.006
-0.367
4
280
38.4
12.7
13.365
0.7
-0.096
0.186
5
350
38.4
12.76
16.471
0.9
0.113
0.834
20% SAND 80%CLAY
MURANG'A
40% SAND 60%CLAY
MURANG'A
Probability
of
Failure(Pf)
1
AVERAGE MOR
30% SAND 70%CLAY
MURANG'A
MOR
(Mpa)
Weibull
Modulus
0.1
14.706
1
380
38.4
12.8
17.716
0.1
0.098
-2.250
2
290
38.4
12.76
13.648
0.3
-0.163
-1.031
3
360
38.4
12.68
17.265
0.5
0.072
-0.367
4
390
38.4
12.84
18.013
0.7
0.115
0.186
5
290
38.4
AVERAGE
MOR
12.76
13.648
0.9
-0.163
0.834
2.67
16.058
1
340
38.4
12.8
15.851
0.08
0.059
-2.442
2
330
38.4
12.9
15.030
0.25
0.006
-1.246
3
330
38.4
12.74
15.603
0.42
0.043
-0.618
4
280
38.4
12.9
12.753
0.58
-0.158
-0.133
5
370
38.4
12.7
17.661
0.75
0.167
0.327
6
270
38.4
AVERAGE
MOR
12.74
12.766
0.92
-0.157
0.910
14.94
3.22
1
290
38.4
13.06
12.729
0.1
0.033
-2.250
2
250
38.4
13.52
9.891
0.3
-0.219
-1.031
3
310
38.4
13.12
13.421
0.5
0.086
-0.367
4
300
38.4
13.06
13.168
0.7
0.067
0.186
5
290
38.4
AVERAGE
MOR
13.2
12.328
0.9
0.001
0.834
12.307
28
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1.92
RESULTS FOR SPECIMENS SHOCKED ONCE FROM 800⁰C TO ROOM TEMPERATURE FOR THE
MIXTURE OF MURANG’A CLAY AND SAND.
NO. FRACTURE
LOAD (N)
PLAIN
MURANG'A
SPAN (L)
(mm)
MOR
(Mpa)
Probability
of
Failure(Pf)
12.6 10.264
0.1
-0.148
-2.250
0.3
0.5
0.7
0.9
0.003
-0.038
0.121
0.042
-1.031
-0.367
0.186
0.834
DIAMETER
(mm)
1
210
38.4
2
3
4
5
250
240
280
260
38.4
38.4
38.4
38.4
AVERAGE
MOR
12.7
12.7
12.68
12.7
11.933
11.456
13.428
12.410
Ln(σ/σf) Ln{Ln(1/
[1-Pf])}
Weibull
Modulus
9.86
11.898
20% SAND 80%
CLAY
MURANG'A
1
2
3
4
5
260
38.4
210
38.4
280
38.4
210
38.4
230
38.4
AVERAGE MOR
12.56
12.76
13.1
12.6
12.8
12.830
9.883
12.178
10.264
10.723
11.175
0.1
0.3
0.5
0.7
0.9
0.138
-0.123
0.086
-0.085
-0.041
-2.250
-1.031
-0.367
0.186
0.834
5.54
30% SAND 70%
CLAY
MURANG'A
1
2
3
250
280
190
38.4
38.4
38.4
12.68 11.989
12.96 12.576
12.8 8.858
0.08
0.25
0.42
0.278
0.326
-0.025
-2.442
-1.246
-0.618
1.83
4
240
38.4
12.76 11.295
0.58
0.218
-0.133
5
6
180
260
38.4
38.4
12.66 8.673
12.7 12.410
0.75
0.92
-0.046
0.312
0.327
0.910
0.1
0.3
0.5
0.7
0.9
0.018
-0.040
0.141
-0.108
-0.029
-2.250
-1.031
-0.367
0.186
0.834
AVERAGE MOR
40% SAND 60%
CLAY
MURANG'A
1
2
3
4
5
9.085
200
38.4
210
38.4
220
38.4
170
38.4
190
38.4
AVERAGE MOR
13.22
13.7
13.1
13.06
13.2
8.464
7.985
9.568
7.462
8.077
8.311
29
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3.05
RESULTS FOR SPECIMENS SHOCKED FIVE TIMES FROM 500⁰C TO ROOM TEMPERATURE FOR
THE MIXTURE OF MURANG’A CLAY AND SAND.
NO. FRACTURE
LOAD (N)
PLAIN
MURANG'A
CLAY
DIAMETER
(mm)
MOR
(Mpa)
Probability
of
Failure(Pf)
Ln(σ/σf Ln{Ln(1/
[1-Pf])}
Weibull
Modulus
1
2
3
230
270
270
38.4
38.4
38.4
12.7
12.68
12.76
10.978
12.949
12.707
0.1
0.3
0.5
-0.229
-0.064
-0.083
-2.250
-1.031
-0.367
4
390
38.4
12.68
18.703
0.7
0.304
0.186
5
280
38.4
AVERAGE MOR
370
38.4
390
38.4
480
38.4
460
38.4
480
38.4
420
38.4
AVERAGE MOR
460
38.4
430
38.4
420
38.4
390
38.4
420
38.4
12.6
13.686
13.804
17.744
19.430
23.914
22.377
23.461
20.725
21.275
21.956
19.136
16.325
18.354
20.142
0.9
-0.008
0.834
0.08
0.25
0.42
0.58
0.75
0.92
-0.181
-0.091
0.117
0.050
0.098
-0.026
-2.442
-1.246
-0.618
-0.133
0.327
0.910
6.93
0.08
0.25
0.42
0.58
0.75
0.155
0.018
-0.141
-0.024
0.069
-2.442
-1.246
-0.618
-0.133
0.327
6.59
0.92
-0.106
0.910
0.1
0.3
0.5
0.7
0.9
-0.102
0.025
0.071
0.010
-0.011
-2.250
-1.031
-0.367
0.186
0.834
20% SAND 80%
CLAY
MURANG'A
1
2
3
4
5
6
30% SAND 70%
CLAY
MURANG'A
1
2
3
4
5
6
40% SAND 60% CLAY
MURANG'A
SPAN
(L)
(mm)
1
2
3
4
5
380
38.4
AVERAGE MOR
370
38.4
420
38.4
430
38.4
410
38.4
400
38.4
AVERAGE MOR
12.68
12.52
12.52
12.62
12.6
12.56
12.7
13
13.6
12.76
12.68
13
13.2
13.2
13.1
13.16
13.14
16.911
18.804
15.729
17.854
18.701
17.589
17.238
17.422
30
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4
10.3
RESULTS FOR SPECIMENS SHOCKED TEN TIMES FROM 500⁰C TO ROOM TEMPERATURE FOR THE
MIXTURE OF MURANG’A CLAY SAND.
NO.
PLAIN
MURANG'A
CLAY
1
2
3
4
5
20%SAND
80% CLAY
MURANG'A
1
2
3
4
5
6
30%SAND70% CLAY
MURANG'A
1
2
3
4
5
6
7
40%SAND60% CLAY
MURANG'A
1
2
3
4
5
Probability
FRACTURE SPAN
DIAMETER MOR
Ln(σ/σf Ln{Ln(1/ Weibull
of
LOAD (N)
(L)
(mm)
(Mpa)
[1-Pf])}
Modulus
Failure(Pf)
(mm)
210
38.4
12.76
9.883
0.1
-0.254
-2.250
7.13
280
38.4
12.8
13.054
0.3
0.024
-1.031
290
38.4
12.7
13.842
0.5
0.083
-0.367
270
38.4
12.7
12.887
0.7
0.012
0.186
290
38.4
12.64
14.040
0.9
0.097
0.834
AVERAGE MOR
12.741
370
38.4
12.54
18.345
0.08
0.011
-2.442
0.96
400
38.4
12.64
19.366
0.25
0.065
-1.246
380
38.4
12.8
17.716
0.42
-0.024
-0.618
350
38.4
340
38.4
430
38.4
AVERAGE MOR
410
38.4
330
38.4
420
38.4
400
38.4
390
38.4
410
38.4
400
38.4
AVERAGE MOR
450
38.4
410
38.4
430
38.4
350
38.4
400
38.4
AVERAGE MOR
12.56
12.8
12.74
12.8
12.2
12.86
12.72
12.8
12.92
12.8
13.1
13.3
13.12
13.12
13.32
17.271
15.851
20.332
18.147
19.115
17.768
19.308
19.003
18.182
18.587
18.649
18.659
19.571
17.039
18.616
15.152
16.549
17.385
0.58
0.75
0.92
-0.050
-0.135
0.114
-0.133
0.327
0.910
0.07
0.21
0.36
0.50
0.64
0.79
0.93
0.024
-0.049
0.034
0.018
-0.026
-0.004
-0.001
-2.602
-1.422
-0.817
-0.367
0.029
0.432
0.970
6.25
0.1
0.3
0.5
0.7
0.9
0.118
-0.020
0.068
-0.137
-0.049
-2.250
-1.031
-0.367
0.186
0.834
8.62
31
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RESULTS FOR UNSHOCKED SPECIMENS FOR THE MIXTURE OF MURANG’A CLAY AND ALUMINA
20%
alumina80% clay
NO.
FRACTURE
LOAD (N)
1
2
3
4
5
700
740
780
760
700
1
2
3
4
5
6
30%alumina70%clay
40%alumina60%clay
1
2
3
4
5
SPAN(L)
(mm)
DIAMETER
(mm)
MOR
(Mpa)
Probabilityof
failure (Pf)
ln( σ/σf)
ln{ln(1
/1
[1-Pf])}
38.4
38.4
38.4
38.4
38.4
AVERAGE
12.3
12.2
12.1
12.2
12
36.779
39.844
43.048
40.921
39.607
40.040
0.10
0.30
0.50
0.70
0.90
-0.085
-0.005
0.072
0.022
-0.011
-2.250
-1.031
-0.367
0.186
0.834
12.33
680
530
660
490
360
370
38.4
38.4
38.4
38.4
38.4
38.4
0.267
0.051
0.261
-0.042
-0.393
-0.342
-2.442
-1.246
-0.618
-0.133
0.327
0.910
3.47
38.4
38.4
38.4
38.4
38.4
33.236
26.788
33.039
24.412
17.183
18.084
25.457
24.139
23.311
26.872
24.709
20.980
24.002
0.08
0.25
0.42
0.58
0.75
0.92
530
500
590
530
450
12.6
12.46
12.5
12.52
12.7
12.6
AVERAGE
12.9
12.8
12.9
12.8
12.8
AVERAGE
0.10
0.30
0.50
0.70
0.90
0.006
-0.029
0.113
0.029
-0.135
-2.250
-1.031
-0.367
0.186
0.834
4.28
32
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Weibull
modulus
RESULTS FOR SPECIMENS SHOCKED ONCE FROM 400⁰C TO ROOM TEMPERATURE FOR THE
MIXTURE OF MURANG’A CLAY AND ALUMINA
NO.
FRACTURE
LOAD (N)
SPAN(L)
(mm)
DIAMETER
(mm)
MOR
(Mpa)
Probabilityof
failure (Pf)
ln(
σ/σf)
ln{ln(1/1 Weibull
[1-Pf])}
modulus
20% alumina80% clay
1
2
3
4
5
410
390
430
400
450
38.4
38.4
38.4
38.4
38.4
13.32
13.2
13.28
13.2
13.2
AVERAGE
16.962
16.579
17.951
17.004
19.130
17.525
0.10
0.30
0.50
0.70
0.90
-0.033
-0.056
0.024
-0.030
0.088
-2.250
-1.031
-0.367
0.186
0.834
8.15
30%alumina70%clay
1
2
3
4
5
6
500
430
460
460
420
470
38.4
38.4
38.4
38.4
38.4
38.4
13.46
13.6
13.82
13.46
13.7
13.84
AVERAGE
20.047
16.713
17.039
18.443
15.970
17.334
17.591
0.08
0.25
0.42
0.58
0.75
0.92
0.131
-0.051
-0.032
0.047
-0.097
-0.015
-2.442
-1.246
-0.618
-0.133
0.327
0.910
9.11
40%alumina60%clay
1
2
3
4
5
420
310
320
410
450
38.4
38.4
38.4
38.4
38.4
13.7
13.6
14
13.7
13.6
AVERAGE
15.970
12.049
11.402
15.590
17.491
14.500
0.10
0.30
0.50
0.70
0.90
0.097
-0.185
-0.240
0.072
0.188
-2.250
-1.031
-0.367
0.186
0.834
1.39
33
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RESULTS FOR SPECIMENS SHOCKED ONCE FROM 600⁰C TO ROOM TEMPERATURE FOR THE
MIXTURE OF MURANG’A CLAY AND ALUMINA
NO.
FRACTURE
LOAD (N)
SPAN(L)
(mm)
DIAMETER
(mm)
MOR
(Mpa)
Probabilityof
failure (Pf)
ln(
σ/σf)
ln{ln(1/1 Weibull
[1-Pf])}
modulus
20%alumina80%clay
1
2
3
4
5
370
390
370
350
300
38.4
38.4
38.4
38.4
38.4
13.12
13.02
13.44
13.1
13.2
AVERAGE
16.018
17.276
14.901
15.222
12.753
15.234
0.10
0.30
0.50
0.70
0.90
0.050
0.126
-0.022
-0.001
-0.178
-2.250
-1.031
-0.367
0.186
0.834
7.87
30%alumina70%clay
1
2
3
4
5
6
370
280
330
270
260
310
38.4
38.4
38.4
38.4
38.4
38.4
13.34
13.74
13.7
13.64
13.74
13.9
AVERAGE
15.239
10.554
12.548
10.402
9.800
11.286
11.638
0.08
0.25
0.42
0.58
0.75
0.92
0.270
-0.098
0.075
-0.112
-0.172
-0.031
-2.442
-1.246
-0.618
-0.133
0.327
0.910
5.29
40%alumina60%clay
1
2
3
4
5
270
290
300
310
280
38.4
38.4
38.4
38.4
38.4
13.82
14
13.8
13.9
13.8
AVERAGE
10.001
10.333
11.161
11.286
10.417
10.640
0.10
0.30
0.50
0.70
0.90
-0.062
-0.029
0.048
0.059
-0.021
-2.250
-1.031
-0.367
0.186
0.834
13.06
34
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RESULTS FOR SPECIMENS SHOCKED ONCE FROM 800⁰C TO ROOM TEMPERATURE FOR THE
MIXTURE OF MURANG’A CLAY AND ALUMINA
NO.
FRACTURE
LOAD (N)
SPAN(L)
(mm)
DIAMETER
(mm)
MOR
(Mpa)
Probabilityof
failure (Pf)
ln(
σ/σf)
ln{ln(1/1 Weibull
[1-Pf])}
modulus
20%alumina80%clay
1
2
3
4
5
310
280
330
280
300
38.4
38.4
38.4
38.4
38.4
13.42
13.14
13.2
13.12
13.22
AVERAGE
12.541
12.067
14.028
12.122
12.695
12.691
0.10
0.30
0.50
0.70
0.90
-0.012
-0.050
0.100
-0.046
0.000
-2.250
-1.031
-0.367
0.186
0.834
2.01
30%alumina70%clay
1
2
3
4
5
6
250
290
280
230
240
220
38.4
38.4
38.4
38.4
38.4
38.4
13.54 9.847
13.52 11.473
13.84 10.327
14 8.195
14 8.551
14 7.839
AVERAGE
9.372
0.08
0.25
0.42
0.58
0.75
0.92
0.049
0.202
0.097
-0.134
-0.092
-0.179
-2.442
-1.246
-0.618
-0.133
0.327
0.910
5.76
40%alumina60%clay
1
2
3
4
5
280
210
210
240
230
38.4
38.4
38.4
38.4
38.4
13.6 10.883
13.74 7.915
14 7.483
13.8 8.929
13.84 8.483
AVERAGE
8.739
0.10
0.30
0.50
0.70
0.90
0.219
-0.099
-0.155
0.022
-0.030
-2.250
-1.031
-0.367
0.186
0.834
4.56
35
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RESULTS FOR SPECIMENS SHOCKED FIVE TIMES FROM 500⁰C TO ROOM TEMPERATURE FOR
THE MIXTURE OF MURANG’A CLAY AND ALUMINA.
NO.
FRACTURE
LOAD (N)
SPAN(L)
(mm)
DIAMETER
(mm)
MOR
(Mpa)
Probabilityof
failure (Pf)
ln(
σ/σf)
ln{ln(1/1 Weibull
[1-Pf])}
modulus
20%alumina80%clay
1
2
3
4
5
350
260
390
390
340
38.4
38.4
38.4
38.4
38.4
13
13.4
13.34
13.16
13.2
AVERAGE
15.576
10.565
16.062
16.731
14.453
14.678
0.10
0.30
0.50
0.70
0.90
0.059
-0.329
0.090
0.131
-0.015
-2.250
-1.031
-0.367
0.186
0.834
1.1
30%alumina70%clay
1
2
3
4
5
330
300
380
340
380
38.4
38.4
38.4
38.4
38.4
13.54
13.54
13.74
13.72
13.7
AVERAGE
12.998
11.816
14.323
12.872
14.449
13.292
0.10
0.30
0.50
0.70
0.90
-0.022
-0.118
0.075
-0.032
0.083
-2.250
-1.031
-0.367
0.186
0.834
7.19
40%alumina60%clay
1
2
3
4
5
240
340
310
300
290
38.4
38.4
38.4
38.4
38.4
13
13.6
13.76
13.66
13.6
AVERAGE
10.681
13.215
11.634
11.508
11.272
11.662
0.10
0.30
0.50
0.70
0.90
-0.088
0.125
-0.002
-0.013
-0.034
-2.250
-1.031
-0.367
0.186
0.834
1.31
36
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RESULTS FOR SPECIMENS SHOCKED TEN TIMES FROM 500⁰C TO ROOM TEMPERATURE FOR THE
MIXTURE OF MURANG’A CLAY AND ALUMINA.
20%alumina80%clay
1
2
3
4
5
300
320
290
280
310
38.4
38.4
38.4
38.4
38.4
13.2
13
13.2
13
13
AVERAGE
12.753
14.241
12.328
12.461
13.796
13.116
0.10
0.30
0.50
0.70
0.90
-0.028
0.082
-0.062
-0.051
0.051
-2.250
-1.031
-0.367
0.186
0.834
1.76
30%alumina70%clay
1
2
3
4
5
290
330
320
320
300
38.4
38.4
38.4
38.4
38.4
13.56
13.52
13.56
13.56
13.56
AVERAGE
11.372
13.056
12.548
12.548
11.764
12.258
0.10
0.30
0.50
0.70
0.90
-0.075
0.063
0.023
0.023
-0.041
-2.250
-1.031
-0.367
0.186
0.834
5
40%alumina60%clay
1
2
3
4
5
230
220
240
380
250
38.4
38.4
38.4
38.4
38.4
13.84 8.483
14 7.839
13.8 8.929
13.72 14.386
13.8 9.301
AVERAGE 9.787
0.10
0.30
0.50
0.70
0.90
-0.143
-0.222
-0.092
0.385
-0.051
-2.250
-1.031
-0.367
0.186
0.834
2.42
37
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RESULTS FOR UNSHOCKED SPECIMENS FOR THE MIXTURE OF NYERI CLAY AND SAND
NO.
Probability
FRACTURE SPAN
DIAMETER MOR
Ln(σ/σf Ln{Ln(1/ Weibull
LOAD (N)
(L)
(mm)
(Mpa) of
[1-Pf])}
Modulus
Failure(Pf)
(mm)
290
38.4
13.7 11.027
0.08
-0.083
-2.442
0.39
280
38.4
13.28 11.689
0.25
-0.025
-1.246
280
38.4
13.2 11.903
0.42
-0.006
-0.618
350
38.4
13.1 15.222
0.58
0.239
-0.133
310
38.4
13.3 12.883
0.75
0.073
0.327
220
38.4
13.3 9.143
0.92
-0.270
0.910
AVERAGE MOR
11.978
15% SAND 85% CLAY
NYERI
1
2
3
4
5
6
55% SAND 45% CLAY
NYERI
1
2
3
4
5
6
7
330
38.4
290
38.4
310
38.4
260
38.4
280
38.4
310
38.4
310
38.4
AVERAGE MOR
14.2
14.4
14.38
12.5
12.2
12.32
12.42
11.268
9.496
10.193
13.015
15.076
16.209
15.820
13.011
0.07
0.21
0.36
0.50
0.64
0.79
0.93
-0.144
-0.315
-0.244
0.000
0.147
0.220
0.195
-2.602
-1.422
-0.817
-0.367
0.029
0.432
0.970
4.33
65% SAND 35% CLAY
NYERI
1
2
3
4
5
6
7
8
280
38.4
230
38.4
200
38.4
230
38.4
260
38.4
200
38.4
250
38.4
200
38.4
AVERAGE MOR
12.6 13.686
14.4 7.531
14.6 6.283
14.6 7.226
12.4 13.333
14.6 6.283
14.52 7.985
12.76 9.412
8.967
0.06
0.19
0.31
0.44
0.56
0.69
0.81
0.94
0.423
-0.175
-0.356
-0.216
0.397
-0.356
-0.116
0.048
-2.740
-1.572
-0.982
-0.553
-0.190
0.151
0.515
1.020
1.12
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NO.
85% SAND 15% CLAY
NYERI
1
2
3
4
5
6
7
8
9
10
FRACTURE SPAN
DIAMETER MOR Probability
Ln(σ/σf Ln{Ln(1/ Weibull
of
LOAD (N)
(L)
(mm)
(Mpa)
[1-Pf])}
Modulus
Failure(Pf)
(mm)
140
38.4
13 6.230
0.05
0.276
-2.970
1.09
120
38.4
13 5.340
0.15
0.121
-1.817
130
38.4
13 5.785
0.25
0.201
-1.246
150
38.4
14.82 4.506
0.35
-0.049
-0.842
170
38.4
15 4.925
0.45
0.040
-0.514
150
38.4
14.7 4.617
0.55
-0.024
-0.225
160
38.4
14.76 4.865
0.65
0.028
0.049
150
38.4
15 4.345
0.75
-0.085
0.327
110
38.4
15 3.187
0.85
-0.395
0.640
120
38.4
15 3.476
0.95
-0.308
1.097
AVERAGE MOR
4.728
39
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RESULTS FOR SPECIMENS SHOCKED ONCE FROM 400⁰C TO ROOM TEMPERATURE FOR THE
MIXTURE OF NYERI CLAY AND SAND
NO.
Probability
FRACTURE SPAN
DIAMETER MOR
Ln(σ/σf Ln{Ln(1/ Weibull
LOAD (N)
(L)
(mm)
(Mpa) of
[1-Pf])}
Modulus
Failure(Pf)
(mm)
260
38.4
13.28 10.854
0.1
0.168
-2.250
1.73
180
38.4
13.26
7.548
0.3
-0.195
-1.031
200
38.4
13.22
8.464
0.5
-0.081
-0.367
240
38.4
13.52
9.495
0.7
0.034
0.186
230
38.4
13.32
9.515
0.9
0.036
0.834
AVERAGE MOR
9.175
15% SAND 85% CLAY
NYERI
1
2
3
4
5
55% SAND 45% CLAY
NYERI
1
2
3
4
5
6
230
38.4
280
38.4
300
38.4
240
38.4
280
38.4
250
38.4
AVERAGE MOR
14.46
14.5
14.5
14.64
14.32
14.26
7.438
8.980
9.621
7.478
9.323
8.429
8.545
0.08
0.25
0.42
0.58
0.75
0.92
-0.139
0.050
0.119
-0.133
0.087
-0.014
-2.442
-1.246
-0.618
-0.133
0.327
0.910
3.62
65% SAND 35% CLAY
NYERI
1
2
3
4
5
190
38.4
210
38.4
200
38.4
190
38.4
210
38.4
AVERAGE MOR
14.66
14.64
14.72
14.9
14.68
5.896
6.544
6.131
5.616
6.490
6.135
0.1
0.3
0.5
0.7
0.9
-0.040
0.064
-0.001
-0.088
0.056
-2.250
-1.031
-0.367
0.186
0.834
2.96
85% SAND 15% CLAY
NYERI
1
2
3
4
5
6
110
38.4
100
38.4
140
38.4
140
38.4
130
38.4
160
38.4
AVERAGE MOR
14.82
14.74
14.8
15
14.92
14.72
3.304
3.053
4.222
4.056
3.827
4.905
3.894
0.08
0.25
0.42
0.58
0.75
0.92
-0.163
-0.242
0.082
0.042
-0.016
0.232
-2.442
-1.246
-0.618
-0.133
0.327
0.910
5.54
40
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RESULTS FOR SPECIMENS SHOCKED ONCE FROM 600⁰C TO ROOM TEMPERATURE FOR THE
MIXTURE OF NYERI CLAY AND SAND
15% SAND 85% CLAY
NYERI
Probability
NO. FRACTURE SPAN
DIAMETER MOR
Ln(σ/σf Ln{Ln(1/ Weibull
LOAD (N)
(L)
(mm)
(Mpa) of
[1-Pf])}
Modulus
Failure(Pf)
(mm)
1
240
38.4
13.38 9.796
0.08
0.100
-2.442
0.3
2
230
38.4
13.26 9.645
0.25
0.085
-1.246
3
110
38.4
13.06 4.828
0.42
-0.607
-0.618
4
270
38.4
13.3 11.221
0.58
0.236
-0.133
5
230
38.4
13.24 9.689
0.75
0.089
0.327
6
190
38.4
13.24 8.004
0.92
-0.102
0.910
AVERAGE MOR
8.864
55% SAND 45% CLAY
NYERI
1
2
3
4
5
6
260
38.4
220
38.4
180
38.4
260
38.4
200
38.4
240
38.4
AVERAGE MOR
14.2
14.4
14.12
14.42
14.3
14.24
8.878
7.204
6.251
8.478
6.687
8.126
7.604
0.08
0.25
0.42
0.58
0.75
0.92
0.155
-0.054
-0.196
0.109
-0.128
0.066
-2.442
-1.246
-0.618
-0.133
0.327
0.910
2.17
65% SAND 35% CLAY
NYERI
1
2
3
4
5
200
38.4
200
38.4
180
38.4
170
38.4
170
38.4
AVERAGE MOR
14.52
14.52
14.62
14.52
14.48
6.388
6.388
5.632
5.430
5.475
5.862
0.1
0.3
0.5
0.7
0.9
0.086
0.086
-0.040
-0.077
-0.068
-2.250
-1.031
-0.367
0.186
0.834
12.85
85% SAND 15% CLAY
NYERI
1
2
3
4
5
6
80
38.4
130
38.4
90
38.4
120
38.4
110
38.4
120
38.4
AVERAGE MOR
14.72
14.72
14.9
14.76
15
14.9
2.452
3.985
2.660
3.649
3.187
3.547
3.247
0.08
0.25
0.42
0.58
0.75
0.92
-0.281
0.205
-0.199
0.117
-0.019
0.088
-2.442
-1.246
-0.618
-0.133
0.327
0.910
3.12
41
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RESULTS FOR SPECIMENS SHOCKED ONCE FROM 800⁰C TO ROOM TEMPERATURE FOR THE
MIXTURE OF NYERI CLAY AND SAND
15% SAND 85% CLAY
NYERI
Probability
NO. FRACTURE SPAN
DIAMETER MOR
Ln(σ/σf Ln{Ln(1/ Weibull
LOAD (N)
(L)
(mm)
(Mpa) of
[1-Pf])}
Modulus
Failure(Pf)
(mm)
1
170
38.4
13.2 7.227
0.08
-0.092
-2.442
4.07
2
200
38.4
13.44 8.055
0.25
0.017
-1.246
3
170
38.4
13.2 7.227
0.42
-0.092
-0.618
4
160
38.4
13.26 6.710
0.58
-0.166
-0.133
5
180
38.4
13.1 7.828
0.75
-0.012
0.327
6
250
38.4
13.26 10.484
0.92
0.280
0.910
AVERAGE MOR
7.922
55% SAND 45% CLAY
NYERI
1
2
3
4
5
6
260
38.4
180
38.4
210
38.4
200
38.4
190
38.4
220
38.4
AVERAGE MOR
14.4
14.24
14.36
14.32
14.22
14.32
8.513
6.095
6.934
6.659
6.461
7.325
6.998
0.08
0.25
0.42
0.58
0.75
0.92
0.196
-0.138
-0.009
-0.050
-0.080
0.046
-2.442
-1.246
-0.618
-0.133
0.327
0.910
4.35
65% SAND 35% CLAY
NYERI
1
2
3
4
5
6
190
38.4
190
38.4
150
38.4
170
38.4
140
38.4
190
38.4
AVERAGE MOR
14.7
14.5
14.74
14.44
14.68
14.54
5.848
6.093
4.579
5.520
4.327
6.043
5.402
0.08
0.25
0.42
0.58
0.75
0.92
0.079
0.120
-0.165
0.022
-0.222
0.112
-2.442
-1.246
-0.618
-0.133
0.327
0.910
2.2
85% SAND 15% CLAY
NYERI
1
2
3
4
5
110
38.4
70
38.4
90
38.4
100
38.4
100
38.4
AVERAGE MOR
15.1
14.82
14.8
14.9
15.1
3.124
2.103
2.714
2.956
2.840
2.747
0.1
0.3
0.5
0.7
0.9
0.129
-0.267
-0.012
0.073
0.033
-2.250
-1.031
-0.367
0.186
0.834
0.1
42
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RESULTS FOR SPECIMENS SHOCKED FIVE TIMES FROM 500⁰C TO ROOM TEMPERATURE FOR
THE MIXTURE OF NYERI CLAY AND SAND.
15% SAND
-85% CLAY
NYERI
Probability Ln(σ/σf Ln{Ln(1/ Weibull
NO. FRACTURE SPAN
DIAMETER
MOR
LOAD (N)
(L)
(mm)
(Mpa) of
[1-Pf])}
Modulus
Failure(Pf)
(mm)
1
330
38.4
13.44 13.290
0.08
0.343
-2.442
2.63
2
220
38.4
13.38
8.980
0.25
-0.049
-1.246
3
4
5
6
55% SAND
-45% CLAY
NYERI
1
2
3
4
5
6
65% SAND
-35% CLAY
NYERI
1
2
3
4
5
85% SAND
15% CLAY
NYERI
1
2
3
4
5
180
38.4
190
38.4
280
38.4
170
38.4
AVERAGE MOR
250
38.4
220
38.4
280
38.4
240
38.4
13.2
13.3
13.16
13.5
280
38.4
310
38.4
AVERAGE MOR
230
38.4
220
38.4
170
38.4
190
38.4
150
38.4
AVERAGE MOR
160
38.4
150
38.4
120
38.4
140
38.4
150
38.4
AVERAGE MOR
14.3
14.46
14.56
14.36
14.14
14.52
14.4
14.5
14.7
14.44
14.4
15
14.9
14.7
14.68
14.6
7.652
7.896
12.012
6.756
9.431
7.919
7.264
9.683
7.665
0.42
0.58
0.75
0.92
-0.209
-0.178
0.242
-0.334
-0.618
-0.133
0.327
0.910
0.08
0.25
0.42
0.58
-0.089
-0.175
0.113
-0.121
-2.442
-1.246
-0.618
-0.133
9.362
10.025
8.653
7.531
7.056
5.233
6.170
4.912
6.180
4.635
4.434
3.694
4.327
4.712
4.360
0.75
0.92
0.079
0.147
0.327
0.910
0.1
0.3
0.5
0.7
0.9
0.198
0.133
-0.166
-0.002
-0.230
-2.250
-1.031
-0.367
0.186
0.834
5.49
0.1
0.3
0.5
0.7
0.9
0.061
0.017
-0.166
-0.008
0.078
-2.250
-1.031
-0.367
0.186
0.834
1.07
43
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5.53
RESULTS FOR SPECIMENS SHOCKEDTEN TIMES FROM 500⁰C TO ROOM TEMPERATURE FOR THE
MIXTURE OF NYERI CLAY AND SAND
Probability
FRACTURE SPAN
DIAMETER MOR
Ln(σ/σf Ln{Ln(1/ Weibull
LOAD (N)
(L)
(mm)
(Mpa) of
[1-Pf])}
Modulus
Failure(Pf)
(mm)
1
230
38.4
13.24 9.689
0.08
0.197
-2.442
1.51
2
130
38.4
13.1 5.654
0.25
-0.342
-1.246
3
280
38.4
13.3 11.636
0.42
0.380
-0.618
NO.
15% SAND 85%
CLAY NYERI
55% SAND 45%
CLAY NYERI
4
5
6
210
38.4
130
38.4
180
38.4
AVERAGE MOR
13.5
13.14
13.7
8.345
5.602
6.844
7.962
0.58
0.75
0.92
0.047
-0.351
-0.151
-0.133
0.327
0.910
1
2
3
4
280
270
250
230
38.4
38.4
38.4
38.4
14.16
14.36
14.22
14.34
9.642
8.915
8.501
7.626
0.08
0.25
0.42
0.58
0.118
0.039
-0.008
-0.117
-2.442
-1.246
-0.618
-0.133
5
6
240
38.4
250
38.4
AVERAGE MOR
180
38.4
220
38.4
140
38.4
180
38.4
120
38.4
AVERAGE MOR
130
38.4
140
38.4
90
38.4
130
38.4
130
38.4
AVERAGE MOR
14.2
14.2
8.195
8.537
8.569
5.918
7.356
4.681
6.225
3.962
5.628
3.921
4.222
2.770
3.766
3.766
3.689
0.75
0.92
-0.045
-0.004
0.327
0.910
0.1
0.3
0.5
0.7
0.9
0.050
0.268
-0.184
0.101
-0.351
-2.250
-1.031
-0.367
0.186
0.834
2.75
0.1
0.3
0.5
0.7
0.9
0.061
0.135
-0.286
0.021
0.021
-2.250
-1.031
-0.367
0.186
0.834
1.69
65% SAND 35%
CLAY NYERI
1
2
3
4
5
85% SAND 15%
CLAY NYERI
1
2
3
4
5
14.38
14.3
14.3
14.14
14.36
14.8
14.8
14.7
15
15
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11.03
RESULTS FOR UNSHOCKED SPECIMENS FOR THE MIXTURE OF NYERI CLAY AND ALUMINA
NO.
FRACTURE
LOAD (N)
SPAN(L)
(mm)
DIAMETER
(mm)
MOR
(Mpa)
Probabilityof
failure (Pf)
ln(
σ/σf)
ln{ln(1/1 Weibull
[1-Pf])}
modulus
Plain Nyeri
1
2
3
4
5
6
180
150
240
140
180
160
38.4
38.4
38.4
38.4
38.4
38.4
12.9 8.198
12.24 7.998
13.06 10.534
13.1 6.089
12.9 8.198
13.16 6.864
AVERAGE
7.980
0.08
0.25
0.42
0.58
0.75
0.92
0.027
0.002
0.278
-0.271
0.027
-0.151
-2.442
-1.246
-0.618
-0.133
0.327
0.910
2.19
20%alumina80%clay
1
2
3
4
5
6
7
290
170
330
280
300
250
210
38.4
38.4
38.4
38.4
38.4
38.4
38.4
13.34
13.46
13.28
13.24
13.26
13.7
13.5
AVERAGE
11.944
6.816
13.776
11.795
12.581
9.506
8.345
10.680
0.07
0.21
0.36
0.50
0.64
0.79
0.93
0.112
-0.449
0.255
0.099
0.164
-0.117
-0.247
-2.602
-1.422
-0.817
-0.367
0.029
0.432
0.970
0.73
30%alumina70%clay
1
2
3
4
5
6
7
470
540
580
520
540
490
540
38.4
38.4
38.4
38.4
38.4
38.4
38.4
13.64
13.84
13.6
13.9
13.9
13.74
13.76
AVERAGE
18.108
19.916
22.544
18.931
19.659
18.469
20.265
19.699
0.07
0.21
0.36
0.50
0.64
0.79
0.93
-0.084
0.011
0.135
-0.040
-0.002
-0.064
0.028
-2.602
-1.422
-0.817
-0.367
0.029
0.432
0.970
3.1
40%alumina60%clay
1
2
3
4
5
590
590
520
580
620
38.4
38.4
38.4
38.4
38.4
14.1
14
13.8
14.16
14
AVERAGE
20.578
21.022
19.346
19.973
22.091
20.602
0.10
0.30
0.50
0.70
0.90
-0.001
0.020
-0.063
-0.031
0.070
-2.250
-1.031
-0.367
0.186
0.834
5.36
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RESULTS FOR SPECIMENS SHOCKED ONCE FROM 400⁰C TO ROOM TEMPERATURE FOR THE
MIXTURE OF NYERI CLAY AND ALUMINA
NO.
FRACTURE
LOAD (N)
SPAN(L)
(mm)
DIAMETER
(mm)
MOR
(Mpa)
Probabilityof
failure (Pf)
ln(
σ/σf)
ln{ln(1/1 Weibull
[1-Pf])}
modulus
Plain Nyeri
1
2
3
4
5
120
150
160
100
150
38.4
38.4
38.4
38.4
38.4
13.1
13
13
13
13.34
AVERAGE
5.219
6.675
7.120
4.450
6.178
5.929
0.10
0.30
0.50
0.70
0.90
-0.127
0.119
0.183
-0.287
0.041
-2.250
-1.031
-0.367
0.186
0.834
0.28
20%alumina80%clay
1
2
3
4
5
200
180
210
250
230
38.4
38.4
38.4
38.4
38.4
13.22
13.8
13.54
13.64
13.4
AVERAGE
8.464
6.697
8.271
9.632
9.346
8.482
0.10
0.30
0.50
0.70
0.90
-0.002
-0.236
-0.025
0.127
0.097
-2.250
-1.031
-0.367
0.186
0.834
4.18
30%alumina70%clay
1
2
3
4
5
340
380
460
540
440
38.4
38.4
38.4
38.4
38.4
13.64
13.78
13.9
14
13.74
AVERAGE
13.099
14.199
16.747
19.241
16.585
15.974
0.10
0.30
0.50
0.70
0.90
-0.198
-0.118
0.047
0.186
0.038
-2.250
-1.031
-0.367
0.186
0.834
6.5
40%alumina60%clay
1
2
3
4
5
470
500
380
420
470
38.4
38.4
38.4
38.4
38.4
14
14
13.9
14
13.84
AVERAGE
16.747
17.816
13.834
14.965
17.334
16.139
0.10
0.30
0.50
0.70
0.90
0.037
0.099
-0.154
-0.076
0.071
-2.250
-1.031
-0.367
0.186
0.834
2.08
46
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RESULTS FOR SPECIMENS SHOCKED ONCE FROM 600⁰C TO ROOM TEMPERATURE FOR THE
MIXTURE OF NYERI CLAY AND ALUMINA
NO.
FRACTURE
LOAD (N)
SPAN(L)
(mm)
DIAMETER
(mm)
MOR
(Mpa)
Probabilityof
failure (Pf)
ln(
σ/σf)
ln{ln(1/1 Weibull
[1-Pf])}
modulus
Plain Nyeri
1
2
3
4
5
6
110
150
110
130
160
130
38.4
38.4
38.4
38.4
38.4
38.4
13.4
13.2
13.14
13.1
13.08
12.84
AVERAGE
4.470
6.377
4.740
5.654
6.991
6.004
5.706
0.08
0.25
0.42
0.58
0.75
0.92
-0.244
0.111
-0.185
-0.009
0.203
0.051
-2.442
-1.246
-0.618
-0.133
0.327
0.910
4.3
20%alumina80%clay
1
2
3
4
5
6
260
160
230
160
180
190
38.4
38.4
38.4
38.4
38.4
38.4
13.4 10.565
13.5 6.358
13.34 9.473
13.52 6.330
13.2 7.652
13.6 7.385
AVERAGE
7.960
0.08
0.25
0.42
0.58
0.75
0.92
0.283
-0.225
0.174
-0.229
-0.040
-0.075
-2.442
-1.246
-0.618
-0.133
0.327
0.910
2.88
30%alumina70%clay
1
2
3
4
5
340
380
350
320
330
38.4
38.4
38.4
38.4
38.4
13.9
13.66
14
13.8
13.9
AVERAGE
12.378
14.576
12.471
11.905
12.014
12.669
0.10
0.30
0.50
0.70
0.90
-0.023
0.140
-0.016
-0.062
-0.053
-2.250
-1.031
-0.367
0.186
0.834
5.52
40%alumina60%clay
1
2
3
4
5
320
290
400
370
380
38.4
38.4
38.4
38.4
38.4
13.9
13.84
13.8
14.1
13.8
AVERAGE
11.650
10.696
14.881
12.905
14.137
12.854
0.10
0.30
0.50
0.70
0.90
-0.098
-0.184
0.146
0.004
0.095
-2.250
-1.031
-0.367
0.186
0.834
5.67
47
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RESULTS FOR SPECIMENS SHOCKED ONCE FROM 800⁰C TO ROOM TEMPERATURE FOR THE
MIXTURE OF NYERI CLAY AND ALUMINA
NO.
FRACTURE
LOAD (N)
SPAN(L)
(mm)
DIAMETER
(mm)
MOR
(Mpa)
Probabilityof
failure (Pf)
ln(
σ/σf)
ln{ln(1/1 Weibull
[1-Pf])}
modulus
Plain Nyeri
1
2
3
4
5
6
80
70
130
60
60
100
38.4
38.4
38.4
38.4
38.4
38.4
13.14
13
13.04
13.04
13.06
13.1
AVERAGE
3.448
3.115
5.732
2.646
2.634
4.349
3.654
0.08
0.25
0.42
0.58
0.75
0.92
-0.058
-0.160
0.450
-0.323
-0.327
0.174
-2.442
-1.246
-0.618
-0.133
0.327
0.910
0.1
20%alumina80%clay
1
2
3
4
5
6
210
230
120
200
210
200
38.4
38.4
38.4
38.4
38.4
38.4
13.44
13.4
13.4
13.36
13.8
13.44
AVERAGE
8.457
9.346
4.876
8.200
7.813
8.055
7.791
0.08
0.25
0.42
0.58
0.75
0.92
0.082
0.182
-0.469
0.051
0.003
0.033
-2.442
-1.246
-0.618
-0.133
0.327
0.910
0.67
30%alumina70%clay
1
2
3
4
5
6
310
340
310
310
240
280
38.4
38.4
38.4
38.4
38.4
38.4
14
13.76
14.12
14.5
14
13.7
AVERAGE
11.046
12.760
10.766
9.942
8.551
10.647
10.619
0.08
0.25
0.42
0.58
0.75
0.92
0.039
0.184
0.014
-0.066
-0.217
0.003
-2.442
-1.246
-0.618
-0.133
0.327
0.910
4.82
40%alumina60%clay
1
2
3
4
5
6
290
280
280
250
310
320
38.4
38.4
38.4
38.4
38.4
38.4
13.9
13.7
13.8
13.7
13.7
13.7
AVERAGE
10.558
10.647
10.417
9.506
11.787
12.168
10.847
0.08
0.25
0.42
0.58
0.75
0.92
-0.027
-0.019
-0.040
-0.132
0.083
0.115
-2.442
-1.246
-0.618
-0.133
0.327
0.910
6.29
48
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RESULTS FOR SPECIMENS SHOCKED FIVE TIMES FROM 500⁰C TO ROOM TEMPERATURE FOR
THE MIXTURE OF NYERI CLAY AND ALUMINA.
NO.
FRACTURE
LOAD (N)
SPAN(L)
(mm)
DIAMETER
(mm)
MOR
(Mpa)
Probabilityof
failure (Pf)
ln(
σ/σf)
ln{ln(1/1 Weibull
[1-Pf])}
modulus
Plain Nyeri
1
2
3
4
5
120
200
140
200
150
38.4
38.4
38.4
38.4
38.4
13.2
13.2
13
13.1
13.1
AVERAGE
5.101
8.502
6.230
8.698
6.524
7.011
0.10
0.30
0.50
0.70
0.90
-0.318
0.193
-0.118
0.216
-0.072
-2.250
-1.031
-0.367
0.186
0.834
2.41
20%alumina80%clay
1
2
3
4
5
6
280
220
230
290
270
250
38.4
38.4
38.4
38.4
38.4
38.4
13.3
13.44
13.22
13.2
13.52
13.48
AVERAGE
11.636
8.860
9.733
12.328
10.682
9.979
10.536
0.08
0.25
0.42
0.58
0.75
0.92
0.099
-0.173
-0.079
0.157
0.014
-0.054
-2.442
-1.246
-0.618
-0.133
0.327
0.910
0.86
30%alumina70%clay
1
2
3
4
5
6
310
280
290
310
300
280
38.4
38.4
38.4
38.4
38.4
38.4
13.74
13.5
14
13.74
13.9
13.44
AVERAGE
11.685
11.127
10.333
11.685
10.922
11.277
11.171
0.08
0.25
0.42
0.58
0.75
0.92
0.045
-0.004
-0.078
0.045
-0.023
0.009
-2.442
-1.246
-0.618
-0.133
0.327
0.910
4.96
40%alumina60% clay
1
2
3
4
5
340
320
320
300
300
38.4
38.4
38.4
38.4
38.4
13.6
14.1
13.94
13.8
14.1
AVERAGE
13.215
11.161
11.550
11.161
10.464
11.510
0.10
0.30
0.50
0.70
0.90
0.138
-0.031
0.003
-0.031
-0.095
-2.250
-1.031
-0.367
0.186
0.834
12.44
49
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RESULTS FOR SPECIMENS SHOCKED TEN FROM 500⁰C TO ROOM TEMPERATURE FOR THE
MIXTURE OF NYERI CLAY AND ALUMINA
NO.
Plain Nyeri
20%
ALUMINA80% CLAY
NYERI
30%
ALUMINA70% CLAY
NYERI
FRACTURE
LOAD (N)
1
2
3
4
5
6
DIAMETER
(mm)
38.4
38.4
38.4
38.4
38.4
38.4
13.86
13.38
13.1
13.1
13.32
13
AVERAGE
13.2
13.5
13.2
13.32
13.44
6.610
6.531
5.219
5.219
3.723
6.675
5.663
7.227
10.332
8.502
9.929
7.249
8.648
0.08
0.25
0.42
0.58
0.75
0.92
0.155
0.143
-0.082
-0.082
-0.419
0.164
-2.442
-1.246
-0.618
-0.133
0.327
0.910
2.11
0.1
0.3
0.5
0.7
0.9
-0.180
0.178
-0.017
0.138
-0.176
-2.250
-1.031
-0.367
0.186
0.834
0.66
38.4
38.4
38.4
38.4
13.4
13.8
13.76
13.82
12.597
11.905
10.508
11.853
0.1
0.3
0.5
0.7
0.138
0.082
-0.043
0.077
-2.250
-1.031
-0.367
0.186
4.96
210
38.4
AVERAGE MOR
13.7
7.985
10.970
0.9
-0.318
0.834
13.7
13.74
14.3
13.8
13.7
9.886
11.308
10.031
9.673
10.647
10.309
0.1
0.3
0.5
0.7
0.9
-0.042
0.092
-0.027
-0.064
0.032
-2.250
-1.031
-0.367
0.186
0.834
180
160
120
120
90
150
1
2
3
4
5
170
38.4
260
38.4
200
38.4
240
38.4
180
38.4
AVERAGE MOR
1
2
3
4
310
320
280
320
5
40%
ALUMINA60% CLAY
NYERI
SPAN(L)
(mm)
1
2
3
4
5
260
38.4
300
38.4
300
38.4
260
38.4
280
38.4
AVERAGE MOR
MOR
(Mpa)
Probabilityof
failure (Pf)
ln(
σ/σf)
ln{ln(1/1 Weibull
[1-Pf])}
modulus
50
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1.22
6.1 TABLES AND GRAPHS
6.2 NYERI CLAY
TABLE 6.1- PERCENTAGE SAND AND AVERAGE STRENGTH FOR NYERI CLAY
STRENGTH ( MPa)
UNSHOCKED
0
7.9801
SHOCKED ONCE
AT 400⁰C
5.9286
15
11.9778
9.1753
8.8639
7.9217
55
13.0111
8.5449
7.6041
6.9978
65
8.9673
6.1353
5.8623
5.4019
85
4.7278
3.8945
3.2466
2.7473
% SAND
SHOCKED ONCE
AT 600⁰C
5.7059
SHOCKED ONCE AT
800⁰C
3.6539
AVERAGE STRENGTH AGAINST % SAND FOR NYERI CLAY
AVERAGE STRENGTH (MPa)
14
12
10
8
UNSHOCKED
6
SHOCKED ONCE AT 400⁰C
4
SHOCKED ONCE AT 600⁰C
SHOCKED ONCE AT 800⁰C
2
0
0
20
40
60
80
100
% SAND
FIGURE 6.1- A GRAPH OF AVERAGE STRENGTH AGAINST % SAND FOR NYERI
CLAY
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TABLE 6.2- PERCENTAGE SAND AND AVERAGE STRENGTH FOR NYERI CLAY 5
& 10 SHOCKS
% SAND
AVERAGE STRENGTH (Mpa)
5 Shocks
10 Shocks
0
7.011107
5.66291
15
9.4308846
7.9618321
55
8.8530336
8.5693127
65
6.1800943
5.6284825
85
4.3602849
3.6890823
AVERAGE STRENGTH AGAINST % SAND FOR NYERI CLAY
AT 500⁰C
AVERAGE STRENGTH
12
10
8
6
5 Shocks
4
10 Shocks
2
0
0
20
40
60
80
100
% SAND
FIGURE 6.2- GRAPH OF AVERAGE STRENGTH AGAINST % SAND FOR 5 & 10
SHOCKS
52
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TABLE 6.3- PERCENTAGE ALUMINA AND AVERAGE STRENGTH FOR NYERI
CLAY
STRENGTH ( MPa)
UNSHOCKED
% ALUMINA
0
20
30
40
7.9801
10.6805
19.6989
20.6022
SHOCKED ONCE
AT 400⁰C
5.9286
8.4819
15.9741
16.1392
SHOCKED ONCE
AT 600⁰C
5.7059
7.9605
12.6688
12.8538
SHOCKED ONCE AT
800⁰C
3.6539
7.7912
10.6186
10.8469
AVERAGE STRENGTH (Mpa)
AVERAGE STRENGTH AGAINST % ALUMINA FOR NYERI CLAY
25
20
15
UNSHOCKED
10
SHOCKED ONCE AT 400⁰C
5
SHOCKED ONCE AT 600⁰C
SHOCKED ONCE AT 800⁰C
0
0
10
20
30
40
50
% ALUMINA
FIGURE 6.3- GRAPH OF AVERAGE STRENGTH AGAINST % ALUMINA
TABLE 6.4-PERCENTAGE ALUMINA AND AVERAGE STRENGTH FOR 5 & 10
SHOCKS FOR NYERI CLAY
% ALUMINA
AVERAGE STRENGTH(Mpa)
5 Shocks
10 Shocks
0
7.011107
5.66291
20
10.5364
8.647844
30
11.17125
10.969612
40
11.51014
10.30878
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AVERAGE STRENGTH(Mpa)
AVERAGE STRENGTH AGAINST PERCENTAGE ALUMINA FOR NYERI
CLAY
14
12
10
8
6
5 Shocks
4
10 Shocks
2
0
0
5
10
15
20
25
30
35
40
45
% ALUMINA
FIGURE 6.4- GRAPH OF AVERAGE STRENGTH AGAINST % ALUMINA FOR 5 & 10
SHOCKS
6.2.1 GRAPHS OF STRENGTH AGAINST SHOCKING TEMPERATURENYERI CLAY
Average Strength ( Mpa)
14
AVERAGE STRENGTH AGAINST SHOCKING TEMPERATURE- NYERI
CLAY
12
10
Plain Nyeri
8
15% Sand
6
55% Sand
4
65% Sand
2
85% Sand
0
0
200
400
600
Shocking Temperature (° C)
800
1000
FIGURE 6.5- GRAPH OF AVERAGE STRENGTH AGAINST SHOCKING TEMPERATURE FOR NYERI
CLAY-SAND
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AVERAGE STRENGTH (Mpa)
AVERAGE STRENGTH AGAINST SHOCKING TEMPERATURE FOR
NYERI CLAY-ALUMINA
25
20
15
plain nyeri
10
20% alumina
30% alumina
5
40% alumina
0
0
200
400
600
800
1000
SHOCKING TEMPERATURE (°C)
FIGURE 6.6- GRAPH OF AVERAGE STRENGTH AGAINST TEMPERATURE FOR
NYERI CLAY-ALUMINA
6.3 MURANG’A CLAY GRAPHS
TABLE 6.5-PERCENTAGE SAND AND AVERAGE STRENGTH FOR MURANG’A
CLAY
STRENGTH ( MPa)
UNSHOCKED
% SAND
0
20
30
40
29.6790
27.9903
24.1628
23.9364
SHOCKED ONCE AT
400⁰C
23.7154
21.3208
19.3602
17.9849
SHOCKED ONCE AT
600⁰C
14.7058
16.0579
14.441
12.3079
SHOCKED ONCE AT
800⁰C
11.8982
11.1754
9.0846
8.3110
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AVERAGE STRENGTH AGAINST % SAND FOR MURANG'A CLAY
35
30
STRENGTH (MPa)
25
20
UNSHOCKED
15
SHOCKED ONCE AT 400⁰C
SHOCKED ONCE AT 600⁰C
10
SHOCKED ONCE AT 800⁰C
5
0
0
10
20
30
40
50
% SAND
FIGURE 6.7- GRAPH OF AVERAGE STRENGTH AGAINST % SAND FOR
MURANG’A CLAY
TABLE 6.6-PERCENTAGE SAND AND AVERAGE STRENGTH FOR 5 & 10 SHOCKS
MURANG’A
% Sand
Average strength
0
5 shocks
13.8046
10 shocks
12.7413
20
21.2750
18.1468
30
18.8041
18.6589
40
17.4222
17.3854
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AVERAGE STRENGTH (Mpa)
AVERAGE STRENGTH AGAINST % SAND-MURANG'A CLAY
25
20
15
10
5 shocks
5
10 shocks
0
0
5
10
15
20
25
30
35
40
45
% SAND
FIGURE 6.8 -GRAPH OF AVERAGE STRENGTH AGAINST % SAND FOR 5 & 10
SHOCKS
TABLE 6.7-PERCENTAGE ALUMINA AND STRENGTH FOR MURANG’A CLAY
STRENGTH ( MPa)
0
29.6790
SHOCKED ONCE AT
400⁰C
23.7154
20
40.0399
17.6953
15.2341
12.6906
30
40
25.4571
24.0021
17.5911
14.5003
11.6381
10.6396
9.3721
8.7385
% ALUMINA
UNSHOCKED
SHOCKED ONCE AT
600⁰C
14.7058
SHOCKED ONCE AT
800⁰C
11.8982
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AVERAGE STRENGTH (Mpa)
AVERAGE STRENGTH AGAINST % ALUMINA FOR MURANG'A CLAY
45
40
35
30
25
UNSHOCKED
20
SHOCKED ONCE AT 400⁰C
15
SHOCKED ONCE AT 600⁰C
10
SHOCKED ONCE AT 800⁰C
5
0
0
10
20
30
40
50
% ALUMINA
FIGURE 6.9- GRAPH OF STRENGTH AGAINST % ALUMINA FOR MURANG’A
CLAY
TABLE 6.8-PERCENTAGE ALUMINA AND AVERAGE STRENGTH FOR 5 & 10
SHOCKS MURANG’A
% Alumina
Average strength
0
5 shocks
13.8046
10 shocks
12.7413
20
14.4535
13.1157
30
13.2916
12.2577
40
11.6618
9.7874
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AVERAGE STRENGTH (Mpa)
AVERAGE STRENGTH AGAINST % ALUMINA FOR MURANG'A CLAY
16
14
12
10
8
6
4
2
0
5 shocks
10 shocks
0
5
10
15
20
25
30
35
40
45
% ALUMINA
FIGURE 6.10 -GRAPH OF AVERAGE STRENGTH AGAINST % ALUMINA FOR 5 &
10 SHOCKS
6.3.1 GRAPHS OF AVERAGE STRENGTH AGAINST
SHOCKING TEMPERATURE-MURANG’A CLAY
Average Strength (Mpa)
Average Strength against Shocking Temperature- Murang'a clay
35
30
25
Plain Murang'a
20
20% Sand
15
30% Sand
10
40% Sand
5
0
0
200
400
600
Shocking Temperature
(° C)
800
1000
FIGURE 6.11- GRAPH OF AVERAGE STRENGTH AGAINST SHOCKING
TEMPERATURE-SAND
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AVERAGE STRENGTH (Mpa)
AVERAGE STRENGTH AGAINST SHOCKING TEMPERATURE FOR
MURANG'A CLAY-ALUMINA
50
40
30
PLAIN MURANG'A
20
20% ALUMINA
10
30% ALUMINA
0
40% ALUMINA
0
200
400
600
800
1000
SHOCKING TEMPERATURE (⁰C)
FIGURE 6.12- AVERAGE STRENGTH AGAINST SHOCKING TEMPERATURE ALUMINA
6.4 COMBINED RESULTS OF PREVIOUS RESEARCHERS AND OURS
TABLE 6.9-PERCENTAGE SAND AGAIST AVERAGE STRENGTH-NYERI CLAY
% SAND
AVERAGE STRENGTH (Mpa)
0
15
25
33
50
55
60
65
70
80
85
7.9801
11.9778
11.44
7.749
5.036
13.011
7.5798
8.9673
6.7721
6.0784
4.7278
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AVERAGE STRENGTH (Mpa)
COMBINED GRAPH OF AVERAGE STRENGTH AGAINST %
SAND FOR NYERI CLAY- UNSHOCKED
14
12
10
8
6
4
2
0
0
10
20
30
40
50
60
70
80
90
% SAND
FIGURE 6.13- COMBINED GRAPH OF AVERAGE STRENGTH AGAINST % SAND
TABLE 6.10-PERCENTAGE ALUMINA AND AVERAGE STRENGTH-NYERI CLAY
% ALUMINA
AVERAGE STRENGTH (MPa)
0
20
30
40
60
70
80
7.9801
10.6805
19.6989
20.6022
15.9567
18.4660
23.1787
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AVERAGE STRENGTH (Mpa)
COMBINED GRAPH OF AVERAGE STRENGTH AGAINST %
ALUMINA FOR NYERI CLAY-UNSHOCKED
25
20
15
10
5
0
0
10
20
30
40
50
60
70
80
% ALUMINA
FIGURE 6.14- COMBINED GRAPH OF AVERAGE STRENGTH AGAINST %
ALUMINA FOR NYERI CLAY
6.5 PERCENTAGE REDUCTION OF STRENGTH AFTER 10 SHOCKS
TABLE 6.11-PERCENTAGE REDUCTION OF STRENGTH AFTER 10 SHOCKS
Plain Murang’a
20% sand-Murang’a
30% sand-Murang’a
40% sand-Murang’a
20% alumina-Murang’a
30% alumina-Murang’a
40% alumina-Murang’a
Plain Nyeri
15% sand-Nyeri
55% sand-Nyeri
65% sand-Nyeri
85% sand-Nyeri
20% alumina-Nyeri
30% alumina-Nyeri
40% alumina-Nyeri
% strength reduction after 10 shocks
57.06
35.2
24.9
27.4
67.24
51.85
59.22
29.30
33.60
34.10
37.20
22.00
19.06
44.31
49.96
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90
TABLE 6.12-WEIBULL MODULUS VALUES
Unshocked
Plain
Murang’a
20% sand
30% sand
40% sand
20%-A
30%-A
40%-A
Plain Nyeri
15% sand
55% sand
65% sand
85% sand
20%-A
30%-A
40%-A
N/B
5.67
Shocked
once at
400°C
0.6
Shocked
once at
600°C
0.1
Shocked
once at
800°C
9.86
Shocked 5 Shocked 5 times at
times at
500°C
500°C
4.00
7.13
0.04
17.77
7.25
12.33
3.47
4.28
2.19
0.39
4.33
1.12
1.09
0.73
3.10
5.36
7.23
8.80
16.88
8.15
9.11
1.39
0.28
1.73
3.62
2.96
5.54
4.18
6.5
2.08
2.67
3.22
1.92
7.87
5.29
13.06
4.3
0.3
2.17
2.85
3.12
2.88
5.52
5.67
5.54
1.83
3.05
2.01
5.76
4.56
0.10
4.07
4.35
2.20
0.10
0.67
4.82
6.29
6.93
6.59
10.30
1.10
7.19
1.31
2.41
2.63
5.53
5.49
1.07
0.86
4.96
12.44
0.96
6.25
8.62
1.76
5.00
2.42
2.11
1.51
11.03
2.75
1.69
0.66
4.96
1.22
A-ALUMINA
6.6 COMPARISON OF RESULTS WITH THOSE OF PREVIOUS
RESEARCHERS
6.6.1 AVERAGE STRENGTH OF UNSHOCKED SPECIMEN- CHERONO
&MOSIRIA
TABLE 6.13-PERCENTAGE SAND/ALUMINA AND AVERAGE STRENGTH FOR
NYERI CLAY
% SAND
0
15
55
65
85
% ALUMINA
20
30
40
AVERAGE STRENGTH (Mpa)
7.9801
11.9778
13.0111
8.9673
4.7278
10.6805
19.6989
20.6022
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TABLE 6.14-PERCENTAGE SAND AND AVERAGE STRENGTH FOR MURANG’A
CLAY
% SAND
0
20
30
40
%ALUMINA
20
30
40
AVERAGE STRENGTH (Mpa)
29.6790
27.9903
24.1628
23.9364
40.040
25.457
24.002
6.6.2 RESULTS FOR AVERAGE STRENGTH AGAINST % SAND FOR
NZIOKI & MOGUSU
TABLE 6.15-PERCENTAGE SAND AND AVERAGE STRENGTH FOR NYERI CLAY
% SAND
0
25
33
50
AVERAGE STRENGTH (Mpa)
7.219
11.440
7.749
5.036
TABLE 6.16-PERCENTAGE SAND AND AVERAGE STRENGTH FOR MURANG’A
CLAY
% SAND
AVERAGE STRENGTH (Mpa)
0
28.900
25
17.290
33
13.130
50
9.785
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Average Strength against % sand for Nyeri clay
Average strength (Mpa)
14
12
10
8
CHERONO & MOSIRIA
6
NZIOKI & MOGUSU
4
2
0
0
20
40
60
80
100
% Sand
FIGURE 6.15- COMBINED GRAPHS FOR AVERAGE STRENGTH AGAINST % SAND
FOR UNSHOCKED SPECIMENS -NYERI CLAY
Average Strength (Mpa)
Average strength against % sand for murang'a clay
35
30
25
20
15
CHERONO & MOSIRIA
10
NZIOKI & MOGUSU
5
0
0
20
40
60
% Sand
FIGURE 6.16- COMBINED GRAPHS FOR AVERAGE STRENGTH AGAINST % SAND
FOR UNSHOCKED SPECIMENS-MURANG’A CLAY
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6.7 ACTUAL PERCENTAGES OF SILICA AND ALUMINA IN THE
MIXTURES
Full chemical analysis was carried out for Murang’a clay, Nyeri clay and sand where the actual
composition was found as shown in the appendix.
Then the actual percentages of silica and alumina were calculated for the various proportions of
mixtures as shown below.
Sample calculation
20% sand-80% Murang’a clay
0.2*59.6=11.832 %silica
0.8*52.18=41.744 %silica
Total silica percentage=53.576
The same calculation was done for the other mixtures and the results of the actual percentages of
silica and alumina are a shown in the tables below
TABLE 6.17-ACTUAL PERCENTAGE OF SILICA AND ALUMINA IN THE
MIXTURES FOR MURANG’A CLAY
20% sand-80% clay
30% sand-70% clay
40% sand-60% clay
20% alumina-80% clay
30% alumina-70% clay
40% alumina-60% clay
% silica
53.576
54.406
55.148
43.744
39.526
35.308
% alumina
19.494
19.846
20.198
32.312
38.373
45.834
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TABLE 6.18-ACTUAL PERCENTAGE OF SILICA AND ALUMINA IN THE
MIXTURES FOR NYERI CLAY
15% sand-85% clay
55% sand-45% clay
65% sand-35% clay
85% sand-15% clay
20% alumina-80% clay
30% alumina -70% clay
40% alumina -60% clay
% silica
53.210
56.216
56.968
58.472
43.664
39.456
35.248
% alumina
26.4665
24.5105
24.0215
23.0435
35.138
41.537
47.946
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CHAPTER 7: DISCUSSION OF THE RESULTS
The main objective was to determine the thermal shock and lifetime properties of refractory
ceramics and its improvements by addition of sand and alumina in different proportions. This
was done by measuring the weights of the different samples, making the mixtures, preparing the
specimens, testing the specimens and obtaining results then analyzing them. Graphs of average
strength versus percentage of sand and alumina added and average strength versus shocking
temperature were plotted.
Since this is a continuing project, we chose our ratio of mixing sand, alumina and clay based of
the previous mixtures. We did the percentage mixtures that had not been done by the previous
researchers to enable us to compare and establish the behavior of strengths at various percentage
mixtures. The main aim for doing this was to see what happens at those percentages as compared
to the percentages previously done. Songok and Suresh used sand to clay ratio and alumina to
clay ratio of 3:2(60%-40%), 7:3 (70%-30%) and 4:1(80%-20%)in both cases while Nzioki and
Mogusu used sand to clay ratio of 1:3 (25%-75%), 0.33:0.67 (33%-67%) and1:1 (50%-50%).We
used sand to clay ratio of 3:17 (15%-85%), 11:9 (55%-45%, 13:7 (65%-35%), 17:3 (85%-15%)
and alumina to clay ratio of 1:4 (20%-80%), 3:7 (30%-70%), and 2:3 (40%-60%).
The raw data obtained from the tests were used to calculate the modulus of rapture, Weibull
modulus and thermal shock resistance. The results were used to plot graphs from which different
comparisons were made. The various observations made from the results are as discussed in the
subsequent sections.
7.1 VARIATION OF AVERAGE FLEXURE STRENGTH WITH ADDITION OF
SAND AND ALUMINA
As seen from table 6.1 and 6.5 the general strength of plain Murang’a clay (29.679 Mpa) was
found to be higher than that of plain Nyeri clay (7.9801 Mpa). It was observed that after firing
the specimens made from plain Nyeri clay had developed small cracks whereas there were no
cracks in the specimens from plain Murang’a clay. This is a contributing factor to the low
strength of Nyeri clay as compared to Murang'a clay.
7.2 Effect of sand addition to clay
For Nyeri clay, it was found that as the amount of sand added increases, the strength increased
up to 55% sand then decreases beyond 55% sand. The maximum strength was at 55% sand
(13.011 Mpa) and the minimum strength was at 85% sand (4.7278 Mpa)
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For Murang’a clay, it was found that the strength decreases once the amount of sand was added
as from 20% sand onwards up to 40% sand .The maximum strength was that of plain Murang’a
clay (29.6790 Mpa) and the minimum was at 40% sand (23.9364 Mpa).
The variation of average strength with percentage of sand added is as shown in figure 6.1 for Nyeri clay
and figure 6.7 for Murang’a clay.
Full analysis of the composition of the Murang’a clay, Nyeri clay and sand was done. It was
found that the clays and sand had reasonable percentage of silica and alumina among other small
compositions of minerals. (i.e. Murang’a clay- 52.18% SiO2 and 18.79% Al2O3, Nyeri clay52.08% SiO2 and 27.2 % Al2O3, sand-59.6% SiO2 and 22.31% Al2O3).
The changes in strength of the specimens are believed to have occurred due to a number of
effects;
When clay and sand is mixed and fired a reaction occurs that forms a new compound known to
be mullite (3Al2O3.2SiO2). This is so because the silica and alumina present in the clay and sand
reacts to form mullite, a refractory compound which has good refractoriness and excellent creep
resistance. Mullite also has excellent high temperature properties with improved thermal shock
and thermal stresses resistance owing to the low thermal expansion, good strength and
interlocking grain structure. This formation of mullite is the reason why strength increased for
the Nyeri clay when sand was added. The presence of alumina in the mixture is also a
contributing factor in the increase in strength of Nyeri clay since alumina is known to be a strong
compound (flexural strength of 370Mpa). Beyond 55% addition of sand, the strength was
observed to decrease. This is attributed to the high amount of silica which has low strength.
Actual percentages of silica and alumina were calculated from the full analysis results as shown
in section 6.7 (page 67). Murang’a clay is seen to have a reasonable amount of silica i.e. above
50%. This amount of silica has effects of decreasing the mechanical strength. For the Nyeri clay
the effect of silica in decreasing the strength was seen when the sand percentage was beyond
55%. The silica content also has effects of increasing the thermal shock resistance as it seen that
Nyeri clay with sand is more thermal shock resistant. The weakening of strength as seen in the
Murang’a clay when sand was added and Nyeri clay when sand was added beyond 55% is due to
the introduction of discontinuities in the clay. It was seen that for Nyeri clay beyond 55% the
strength decreased and for Murang’a clay it decreased once sand was added. This is because
sand’s particles are much larger in size than clay’s therefore it creates a greater concentration of
discontinuities in the specimen when the percentage was increased. This discontinuities act as
points of crack initiation for new, and a series of weak points through which cracks propagate.
Therefore less energy is required to initiate and propagate cracks resulting to weaker specimens.
This is evident in the difference in the surface texture of the specimens. Specimens made from
plain clay had smooth surfaces while those made from clay mixed with sand had rough surfaces.
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As the sand content was increased the surfaces became rougher and could break easily even
though the same extrusion process and machine was used.
The weakening of the strength is also due to the fact that greater concentration of sand results in
a mixture with low volume fraction of clay. Since clay acts as a binder and it is what holds the
material together, replacing part of it with sand reduces the cohesive forces in the material. As a
result the greater the sand concentration, the less the clay content thus the weaker the resultant
specimen.
Therefore it can be concluded that addition of sand increases the strength of Nyeri clay upto 55%
sand and then it decreases up to 85%, whereas it decreases the strength of Murang’a clay upto
40%.
7.3 Effect of alumina addition to clay
For Nyeri clay, it was found that as the amount of alumina added increases, the strength
increases. The maximum strength was at 40% alumina (20.6022 Mpa) and the minimum strength
was that of plain clay (7.9801 Mpa).
For Murang’a clay, it was found that as the amount of alumina added increases, the strength
increases up to 20% alumina then decreases beyond 20% alumina. The maximum strength was at
20% alumina (40.0399 Mpa) and the minimum was at 40% alumina (24.0021 Mpa).
The variation of average strength with percentage of alumina added is as shown in figure 6.3 for
Nyeri clay and figure 6.9 for Murang’a clay.
Considering the alumina specimens, the increase in strength is due to the fact that alumina itself
is known to be a strong compound (with flexural strength of 370 Mpa) and high thermal shock
resistance. However the presence of clay in the specimens increased bonding of the alumina
particles which is due to the fact that clay begins to sinter at a temperature well below that of
alumina cementing alumina particles together thus explaining the high strengths.
It was noted that for Murang’a clay addition of alumina beyond 20% led to decrease in strength.
Therefore we can say that addition of alumina increases the strength of Nyeri clay and Murang’a
clay, but for the Murang’a clay the increase in strength is only up to 20% alumina of which it
then decreases.
7.4 VARIATION OF AVERAGE STRENGTH WITH QUENCHING/
THERMAL SHOCKING
As seen from table 6.1 and 6.5, when shocked once plain clays decreased in strength and also as
the shocking temperature increased the strength decreased. The various percentages of the
mixtures of sand and alumina with clay also showed the same trend.
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Figures 6.1 and 6.8, shows the variation of the strength with percentage sand and alumina
respectively for specimens shocked once at different temperatures i.e. 400°C, 600°C and 800° C.
Figure 6.5, 6.6, 6.11 and 6.12 shows the variation of strength with shocking temperature for
different percentages of sand and alumina.
Also it was observed that strength decreased with the increased number of shocks as seen in
tables 6.2, 6.4, 6.6 and 6.8 and for five and ten shocks. However the percentage decrease in
strength between 5 and 10 shocks was quite small as seen in figures 6.2, 6.4, 6.8 and 6.10.
From table 6.11 above it can be seen that mixture of 20% alumina-80% Murang’a clay had the
highest percentage reduction of strength thus least resistant to thermal shocks, while 20%
alumina-80% Nyeri clay had the least percentage reduction of strength hence most resistant to
thermal shocks.
Generally it was observed that the various percentage mixtures of Murang’a clay and alumina
had the highest percentage reduction of strength on average thus the least resistant to thermal
shock. On the other hand, the various percentage mixtures of Nyeri clay and sand had the least
percentage reduction of strength and thus most resistant to thermal shocks.
Though Nyeri clay mixed with sand was the weakest in terms of the flexural strength when
unshocked, it was found to be the most thermal shock resistant compared to other specimens.
This is because the specimens of Nyeri clay mixed with sand has high silica content, which has
low strength and high thermal shock resistance.
Thermal shocking was performed by heating the specimens to the required temperature and then
quenching them in water at room temperature. Shocking in water weakens inter- atomic bonds of
the specimen thus weakening the specimens as it is depicted by low strength after shocking. The
pores in the specimens absorb water during the shocking process which when heated back to the
shocking temperature is transformed into superheated steam exerting pressure in the walls of the
pore. The superheated steam in the verge of escaping out of the pores leads to formation and
propagation of cracks, and to weakening of inter- molecular bonds.
Thermal stresses generated during shocking process lead to significant reduction of strengths of
the specimen. The thermal stresses generated lead to formation and propagation of cracks on the
surface of the specimen. This is due to the fact that the resultant forces on the surface on
shocking are tensile thus there is high tendency of formation or propagation of cracks already
present on the surface. The decrease in strength with increase in shocking temperature is
attributed to increase in thermal stresses induced and the increased superheated steam effect with
increasing temperature.
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7.5 WEIBULL MODULUS
The plot of ln {ln (1/ [1-Pf])} against ln (σ/σf) gave a straight line of slope m.
From the summary of the Weibull modulus in the table 6.12, Nyeri clay generally had low values
of Weibull modulus, for example unshocked plain Nyeri clay value was 2.19. Most values of
Weibull modulus for Nyeri clay whether plain clay, mixed with sand or mixed with alumina lie
below 5. This means there is high variation of strength in the Nyeri clay specimens.
The Murang’a clay generally had high values of Weibull modulus, just to name a few for
example, plain Murang’a clay was 5.67, mixture with 30% sand was 17.77, mixture with 40%
alumina was 13.06 etc. This indicates that the strengths were reasonably uniform i.e. low
variation of strength.
The Weibull modulus varied with different degrees of thermal shocks for the different clays and
mixtures therefore the variation of strength was unpredictable. The Weibull distribution and
hence the scatter can be attributed to presence of impurities, non-uniform flaw distribution, size
and geometry in addition to brittle nature of ceramics materials.
If the measurements show little variation from sample to sample, the calculated Weibull modulus
will be high and a single strength value would serve as a good description of the sample-tosample performance. It may be concluded that its physical flaws, whether inherent to the material
itself or resulting from the manufacturing process, are distributed uniformly throughout the
material. If the measurements show high variation, the calculated Weibull modulus will be low;
this reveals that flaws are clustered inconsistently and the measured strength will be generally
weak and variable. Specimens made from components of low Weibull modulus will exhibit low
reliability and their strengths will be broadly distributed. This explains why Nyeri clay has a
lower strength than Murang’a clay.
7.6 COMPARISON OF THE RESULTS WITH PREVIOUS RESEARCHERS
Generally, the flexure strengths of our specimens are higher as compared to Nzioki and
Mogusu’s. This is attributed to the fact that we mixed our components in powder form before
adding water to make it moldable. This method of mixing the components in powder form led to
even mixing of the components. The variation of average strength against percentage sand follow
the same trend as shown in figures 6.15 and 6.16 for Nyeri and Murang’a clay mixtures
respectively.
A similar trend was observed between Nzioki and Mogusu results and ours. In both cases, for the
mixture of Murang’a clay and sand the strength was found to decrease as the percentage of sand
added increases (Unshocked specimens).It was found by both Suresh and Songok and us that the
silica specimens are more thermal shock resistant than alumina specimens.
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A similar trend was observed between Suresh and Songok results and our results. It was found
that for the mixture of Nyeri clay and sand, the strength was increasing as the sand content
increased beyond 60%.
It was found in the results of Suresh and Songok, Nzioki and Mogusu and ours that the strength
was decreasing with increase in the number of shocks and the shocking temperature.
Considering the mixture of Nyeri clay and alumina, it was noted that as the amount of alumina
increases the average strength increases in both cases i.e our results and Songok & Suresh’s as
shown in tables 6.13 and 6.16 respectively.
7.7 ASSUMPTIONS

The production method for all the clay samples were the same (i.e. soaking, kneading,
and extrusion, drying) and they were all fired under the similar conditions.
 The loading rate during testing was uniform and pure bending load applied
 The time transfer of the specimen from furnace into the quenching water-bath was
negligible, and that all the specimens shocked between a particular pre-determined
temperature experienced the same degree of thermal shock
 The specimen constituents were homogeneously mixed and sufficiently de-aired to the
same degree before extrusion
 The furnace used provided uniform heating of all the specimens at any particular time.
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CHAPTER 8: CONCLUSIONS
Arising from the results and discussions the following conclusions were made;
8.1 Average strength
1. Plain clay from Murang’a was found to be stronger than that from Nyeri before any
quenching/ shocking was done (unshocked specimens)
2. Addition of sand to Nyeri clay led to increase in average strength up to 55% sand then
decreases beyond 55% sand. Addition of alumina to Nyeri clay led to increase in average
strength.
3. Addition of sand to Murang’a led to decrease in average strength as from 20% sand
onwards up to 40% sand. Addition of alumina to Murang’a clay led to increase in
strength up to 20% alumina then decreases beyond 20%.
8.2 Thermal shock resistance
1. Generally various percentage mixtures of Murang’a clay and alumina had the highest
percentage reduction of strength on average thus the least resistant to thermal shock. On
the other hand, the various percentage mixtures of Nyeri clay and sand had the least
percentage reduction of strength and thus most resistant to thermal shock. From our
results it was therefore found that, a mixture of 20% alumina-80% Murang’a was the
least resistant to thermal shock, while 20% alumina-80% Nyeri clay was most resistant to
thermal shock.
2. Though Nyeri clay mixed with sand was the weakest in terms of the flexural strength
when unshocked, it was found to be the most thermal shock resistant compared to other
specimens. Therefore the higher the sand content, the lower the mechanical strength but
higher the thermal shock resistance.
3. For a mixture of Nyeri clay and alumina, the lower the alumina content the lower the
mechanical strength but the higher the thermal shock resistance and vice versa.
4. In general a mixtures of sand and clay were found to be more thermal shock resistant than
mixtures of alumina and clay, but a compromise has to be reached between mechanical
strength and thermal shock resistance for best results.
8.3 Weibull modulus
Nyeri clay generally had low values of Weibull modulus and thus high variation of strength. The
Murang’a clay generally had high values of Weibull modulus thus it indicates that the strengths
were reasonably uniform i.e. low variation of strength. This explains why Nyeri clay has a lower
strength than Murang’a clay.
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8.4 APPLICATION TO INDUSTRIES
Due to its high thermal shock resistance, i.e. low percentage reduction of strength after thermal
shock, Nyeri clay mixed with sand can be utilized in the lining of cooking stoves, furnaces,
ovens and kilns which undergo reasonable amount of thermal shocking. Also the raw materials,
clay and sand are cheaply and locally available.
Due to its high strength, alumina and clay mixture can be used on a large scale lining of furnaces
and kilns.
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CHAPTER 9: CHALLENGES AND RECOMMENDATIONS
9.1 CHALLENGES
The project came along with some challenges. They include:
1. Late and insufficient funding by the university which caused delays in material
collection, subsequent preparations and limited the extent of the project.
2. Breakdown of the extrusion machine during extrusion which led to delays.
3. Lack of a weighing machine and sieves in the department’s workshop which led to
difficulties since we had to borrow from the Civil Engineering department .
9.2 RECOMMENDATIONS
1. Development of a better quenching apparatus that reduces the time spent moving the
specimens from hot to cold environment
2. Sieving process should be automated to reduce the time taken during sieving and to
improve the fineness of the product.
3. Drying process should be done in a conditioned room with controlled temperature and
humidity
4. The effect of shocking by air should be investigated
5. Based on thermal shock resistance and strength, for the mixture of Nyeri specimens with
sand, we recommend 55% sand-45% clay to be utilized for the lining of domestic stoves.
6. Based on strength, for the mixture of Murang’a specimens with alumina, we recommend
20% alumina-80% clay to be utilized for the lining of the electric resistance furnaces
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LIST OF REFERENCES
1. GEORGE O.RADING, “Concise Notes on MATERIAL SCIENCE AND
ENGINEERING” (University of Nairobi 2007) Trafford PUBLISHING.
2. Michael F Ashby & David R Jones, “ENGINEERING MATERIALS 2-An
Introduction to Microstructures, Processing and Design.”(Cambridge
University 1986)
3. James A. Jacobs &Thomas F. Kilduff, “Engineering Materials TechnologyStructures, Processing & Selection” (THIRD EDITION 1997)
4. Nature and Properties of ENGINEERING MATERIALS-ZBIGNIEW D.
JASTRZEBSKI 195
5. R.S Khurmi and R.S Sedha “MATERIAL SCIENCE” (First Edition 1987)
6. JOHN B.WATCHMAN, “MECHANICAL PROPERTIES of
CERAMICS”(Rutgers University 1996)
7. Internet
8. Richard A. Flinn & Paul K. Trojan "ENGINEERING MATERIALS and
Their Applications”(Fourth Edition 1990)
9. Serope Kalpakjian. Steven R. Schmid “MANUFACTURING
ENGINEERING AND TECHNOLOGY”(Fifth edition 2006)
10. Jude Kipkoech Songok & Patel Jaymit Suresh, “THERMAL SHOCK AND
LIFETIME PROPERTIES OF CERAMIC MATERIALS” Dept. of
Mechanical Engineering, University of Nairobi, 2010.
11. Nzioki Joseph Ndata & Mogusu Clive Ontomwa, “THERMAL SHOCK
AND LIFETIME PROPERTIES OF CERAMIC MATERIALS” Dept. of
Mechanical Engineering, University of Nairobi, 2011.
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APPENDIX
GRAPHS USED TO DETERMINE THE WEIBULL MODULUS
Unshocked Plain Murang'a
Unshocked 20% sand-80% clay Murang'a
2.000
0.000
-0.100
-0.050
-1.0000.000
0.050
-2.000
-3.000
Ln{ln(1/[1-Pf])}
Ln{ln(1/[1-Pf])}
1.000
0.100
0.200
y = -0.041x - 0.539
1.000
0.000
-0.200
-0.100
-1.0000.000
0.100
0.200
0.300
-2.000
-3.000
Ln(σ/σf)
y = 17.75x - 0.521
y = 7.246x - 0.513
20% sand-80% clay Murang'a shocked
once at 400⁰C
1.000
0.200
0.400
0.600
y = 0.600x - 0.517
Ln{ln(1/[1-Pf])}
Ln{ln(1/[1-Pf])}
-3.000
2.000
Plain Murang'a shocked once at 400⁰C
Ln(σ/σf)
-2.000
Unshocked 40% sand-20% clay Murang'a
Ln{ln(1/[1-Pf])}
Ln{ln(1/[1-Pf])}
3.000
2.000
1.000
0.000
-1.000
-0.100
0.000
-2.000
-3.000
-4.000
Ln(σ/σf)
-0.400
-0.300 -0.200 -0.100
-1.0000.000 0.100 0.200 0.300
Ln(σ/σf)
Unshocked 30% sand-70% clay Murang'a
1.000
0.500
0.000
-0.5000.000
-0.200
-1.000
-1.500
-2.000
-2.500
0.000
y = -5.694x - 0.531
Ln(σ/σf)
-0.200
1.000
0.000
-0.300
-0.200
-0.100
0.000
-1.000
0.100
0.200
-2.000
-3.000
Ln(σ/σf)
y = 7.729x - 0.511
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-0.400
3.000
2.000
1.000
0.000
-0.200-1.0000.000
-2.000
-3.000
ln(σ/σf)
40% sand-60% clay Murang'a shocked
once at 400⁰C
4.000
0.200
0.400
ln{ln(1/[1-Pf])}
ln{ln(1/[1-Pf])}
30% sand-70% Murang'a shocked once
at 400⁰C
0.000
-2.000
-4.000
ln(σ/σf)
0.200
0.400
-3.000
ln{ln(1/[1-Pf])}
0.000
0.000
-0.400
-0.200-1.0000.000
ln(σ/σf)
1.000
1.000
0.200
0.400
-3.000
y = -0.389x - 0.538
ln{ln(1/[1-Pf])}
ln{ln(1/[1-Pf])}
2.000
-2.000
ln(σ/σf)
0.400
y = -0.961x - 0.536
Unshocked 55% sand-45% clay Nyeri
2.000
-0.200
-1.0000.000
0.200
-2.000
y = 7.128x - 0.471
0.000
-0.400
y = 16.88x - 17.41
-3.000
Unshocked 15% sand-85%clay Nyeri
-0.600
1.500
1.000
-4.000
Ln(σ/σf)
1.000
2.000
1.000
-0.200-1.0000.000
-2.000
0.500
20% sand-80%clay Murang'a shocked 10
times at 500⁰C
2.000
ln{ln(1/[1-Pf])}
0.000
y = -8.800x - 0.568
Plain Murang'a shocked 10 times at
500⁰C
-0.400
2.000
0.000
-0.600
-0.400
-0.200
-1.0000.000
0.200
0.400
-2.000
-3.000
ln(σ/σf)
y = 4.334x - 0.452
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Unshocked 85% silica-15% clay Nyeri
2.000
0.000
-1.000
-0.500
0.000
-2.000
0.500
1.000
ln{ln(1/[1-Pf])}
ln{ln(1/[1-Pf])}
Unshocked 65% silica-35% clay
Murang'a
4.000
2.000
0.000
-1.000
-0.500
ln(σ/σf)
y = -1.118x - 0.592
1.000
0.000
-0.400
-0.200-1.0000.000
0.200
0.400
-2.000
-3.000
ln(σ/σf)
0.200
-4.000
ln{ln(1/[1-Pf])}
ln{ln(1/[1-Pf])}
0.000
ln(σ/σf)
y = 3.616x - 0.515
0.000
-0.400
-0.200-2.0000.000
0.200
0.400
-4.000
ln(σ/σf)
y = 5.537x - 0.472
55% sand-45% Nyeri clay shocked 5
times at 500⁰C
0.500
y = -2.633x - 0.614
ln{ln(1/[1-Pf])}
ln{ln(1/[1-Pf])}
-0.500
0.400
2.000
y = 2.959x - 0.520
15% sand-85% Nyeri clay shocked 5
times at 500⁰C
2.000
1.000
0.000
-1.0000.000
-2.000
-3.000
0.200
85% sand-15%Nyeri clay shocked once
at 400⁰C
2.000
0.100
2.000
1.000
0.000
-0.200-1.0000.000
-2.000
-3.000
ln(σ/σf)
65% sand-35% Nyeri clay shocked once
at 400⁰C
ln(σ/σf)
-0.400
y = -1.734x - 0.538
-0.300 -0.200 -0.100 0.000
-2.000
y = -5.086x - 0.648
55% sand-45% Nyeri clay shocked once
at 400⁰C
ln{ln(1/[1-Pf])}
ln{ln(1/[1-Pf])}
15% sand-85% Nyeri clay shocked
once at 400⁰ C
0.500
-4.000
-4.000
ln(σ/σf)
-2.0000.000
-0.400
2.000
1.000
0.000
-1.000
-0.200
0.000
-2.000
-3.000
ln(σ/σf)
0.200
0.400
y = 5.528x - 0.490
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85% sand-15% Nyeri clay shocked 5
times at 500⁰C
ln{ln(1/[1-Pf])}
2.000
1.000
0.000
-0.400
-0.200-1.0000.000
0.200
0.400
-2.000
ln(σ/σf)
ln{ln(1/[1-Pf])}
65% sand-35% Nyeri clay shocked 5
times at 500⁰C
1.000
2.000
0.000
1.000
ln(σ/σf)
0.200
0.400
ln(σ/σf)
0.200
y = -1.067x - 0.529
0.000
-0.600
-0.400
-0.200
-1.0000.000
0.200
0.400
-2.000
-3.000
ln(σ/σf)
y = 0.663x - 0.518
20% Alumina-80% Murang'a clay
shocked once at 400ºC
y = -4.960x - 0.588
30%Alumina-70% Murang'a Clay
shocked once at 400ºC
2
0.1
0.2
0.3
ln{ln(1/[1-pf])}
2
1
0
-0.1 -1 0
-2
-3
0.100
-2.000
ln(σ/σf)
ln{ln(1/[1-Pf])}
ln{ln(1/[1-Pf])}
-0.100 0.000
-1.000
30% alumina-70% Nyeri clay shocked 10
times at 500⁰C
-3.000
ln{ln(1/[1-pf])}
-0.200
y = -5.491x - 0.599
-0.200
0.000
-1.000
-0.2
-0.300
-3.000
-2.000
-0.3
0.000
-3.000
20%alumina-80% Nyeri clay shocked 10
times at 500⁰C
-0.400
1.000
1
0
-0.3
-0.2
-0.1 -1 0
0.1
0.2
0.3
-2
-3
y = -8.512x - 0.825
ln(σ/σf)
y = -9.105x - 0.558
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-0.4
1
0.5
0
-0.5 0
-1
-1.5
-2
-2.5
-0.2
20% Alumina-80% Murang'a Clay shocked
once at 600ºC
2
0.2
ln{ln(1/[1-pf])}
ln{ln(1/[1-pf])}
40% Alumina-60% Murang'aClay once at
400ºC
0.4
1
0
-0.4
ln(σ/σf)
y = 1.386x - 0.506
2
1
1
ln{ln(1/[1-pf])}
ln{ln(1/[1-pf])}
40%Alumina-60% Murang'a Clay shocked
once at 600ºC
0
0.2
0.4
0.6
-2
0
-0.2
-0.1
-1 0
30 % Alumina-70 %Murang'a Clay shocked
once at 800ºC
1
0
0.1
0.2
y = 13.06x - 0.511
ln(σ/σf)
y = -5.285x - 0.593
ln{ln(1/[1-pf])}
ln{ln(1/[1-pf])}
0.2
-3
20% Alumina-80% Murang'a Clay
shocked once at 800ºC
-0.1 -1 0
0.1
-2
-3
ln(σ/σf)
-0.2
0.4
y = -7.869x - 0.564
2
-1 0
0.2
-2
30%Alumina-70% Murang'a Clay
shocked once at 600ºC
-0.2
-1 0
-3
ln(σ/σf)
-0.4
-0.2
0.3
-2
-3
2
1
0
-0.4
-0.2
-1 0
0.2
0.4
-2
-3
ln(σ/σf)
y = 2.012x - 0.522
ln(σ/σf)
y = -5.762x - 0.587
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20% Alumina-80% Murang'a Clay
shocked 5 times at 500ºC
2
ln{ln(1/[1-pf])}
ln{ln(1/[1-pf])}
40% Alumina-60% Murang'a Clay
shocked once at 800ºC
0
-0.4
-0.2
-2
0
0.2
0.4
-4
ln(σ/σf)
2
0
-0.6
0.2
0.4
-4
ln(σ/σf)
ln{ln(1/[1-pf])}
ln{ln(1/[1-pf])}
-2
0.1
0.2
-4
ln(σ/σf)
y = 1.763x - 0.522
ln{ln1/[1-Pf])}
ln{ln(1/[1-pf])}
0
0.5
1
-2
-3
ln(σ/σf)
-1 0
0.2
0.4
-2
-3
y = 1.309x - 0.522
2
0
-0.2
-0.1
-2
0
0.1
0.2
-4
y = 5.007x - 0.519
40% alumina-60% Nyeri clay shocked
10 times at 500⁰C
1
-1 0
-0.2
ln(σ/σf)
40% Alumina-60% Murang'a Clay
shocked 10 times at 500ºC
-0.5
-0.4
30% Alumina-70%Murang'a Clay
shocked 10 times at 500ºC
0
0
y = 1.102x - 0.511
0
ln(σ/σf)
2
-0.1
0.4
1
y = 7.190x - 0.505
20% Alumina-80 % Murang'a Clay
shocked 10 times at 500ºC
-0.2
0.2
-4
ln{ln(1/[1-pf])}
ln{ln(1/[1-pf])}
0
0
40% Alumina-60% Murang'a Clay
shocked 5 times at 500ºC
0
-2
-2
ln(σ/σf)
2
-0.2
-0.2
y = -4.557x - 0.564
30%Alumina-70% Murang'a Clay
shocked 5 times at 500ºC
-0.4
-0.4
1.000
0.000
-0.200 -0.100
-1.0000.000
0.100
0.200
0.300
-2.000
-3.000
y = 2.427x - 0.466
ln(σ/σf)
y = 1.218x - 0.523
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Unshocked 20%Alumina-80% Nyeri
Clay
0
-0.5
-2 0
-4
ln(σ/σf)
0.5
-1
0
-2 0
0.2
0.4
-4
ln(σ/σf)
y = 3.095x - 0.532
0
0.2
0.4
-2
ln{ln(1/[1-pf])}
ln{ln(1/[1-pf])}
-1
-3
Ln(σ/σf)
Unshocked 40% Alumina-60% Nyeri
Clay
2
0
-0.2
-0.1
-2 0
0.1
0.2
-4
y = 5.358x - 0.520
20% Alumina-80% Nyeri Clay shocked
once at 400ºC
0
-0.2
0.5
y = -0.727x - 0.558
ln(σ/σf)
1
-0.4
-2 0
-4
Plain Nyeri shocked once at 400ºc
-0.6
-0.5
ln(σ/σf)
2
-0.2
0
y = -2.189x - 0.565
Unshocked 30% Alumina-70% Nyeri
Clay
-0.4
2
ln{ln(1/[1-pf])}
ln{ln(1/[1-pf])}
ln{ln(1/[1-pf])}
2
ln{ln(1/[1-pf])}
Unshocked Plain Nyeri
2
0
-0.4
-0.2
0
0.2
0.4
-4
ln(σ/σf)
y = 0.279x - 0.521
-2
y = 4.177x - 0.492
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0
-0.2
-2
0
0.2
0.4
-4
ln(σ/σf)
ln{ln(1/[1-pf])}
-0.2
2
1
0
-1 0
-2
-3
ln(σ/σf)
0.2
-0.2
1
0
-1 0
-2
0.2
0.4
-3
ln(σ/σf)
y = 6.505x - 0.466
Plain Nyeri shocked once at 600°C
-0.4
-0.4
y = -2.079x - 0.535
20%Alumina-80% Nyeri Clay shocked
once at 600ºC
0.4
y = 4.332x - 0.480
ln{ln(1/[1-pf])}
-0.4
40% Alumina-60% Nyeri Clay
shocked once at 400ºC
ln{ln(1/[1-pf])}
ln{ln(1/[1-pf])}
30% Alumina-70% Nyeri Clay
shocked once
at 400ºC
2
-0.4
-0.2
2
1
0
-1 0
-2
-3
ln(σ/σf)
0.2
0.4
0.6
y = -2.877x - 0.587
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40%Alumina-60%Nyeri Clay shocked
once at 600ºC
ln{ln(1/[1-pf])}
ln{ln(1/[1-pf])}
30%Alumina-70% Nyeri Clay shocked
once at 600ºC
1
0
-0.2
-1 0
0.2
0.4
-2
2
1
0
-0.4
-0.2
ln(σ/σf)
y = -5.523x - 0.541
y = 5.671x - 0.484
20% Alumina-80 %Nyeri Clay shocked
once at 800ºC
2
ln{ln(1/[1-pf])}
ln{ln(1/[1-pf])}
Plain Nyeri shocked once at 800ºC
1
0
-1 0
0.2
0.4
0.6
-2
-0.8
-3
-0.2
ln(σ/σf)
0.2
-0.4
2
1
0
-0.2 -1 0
-2
-3
0.2
0.4
y = -0.673x - 0.546
40% Alumina-60% Nyeri Clay shocked
once at 800ºC
ln{ln(1/[1-pf])}
ln{ln(1/[1-pf])}
30% Alumina-70%Nyeri Clay
shocked once at 800ºC
2
1
0
-1 0
-2
-3
-0.6
ln(σ/σf)
ln(σ/σf) y = 0.058x - 0.531
-0.4
0.4
-3
ln(σ/σf)
-0.2
0.2
-2
-3
-0.4
-1 0
0.4
y = -4.815x - 0.568
-0.3
-0.2
-0.1
ln(σ/σf)
2
1
0
-1 0
-2
-3
0.1
0.2
0.3
y = 6.292x - 0.512
86
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20% Alumina-80% Nyeri Clay shocked
5 times at 500ºC
1
ln{ln(1/[1-pf])}
ln{ln(1/[1-pf])}
Plain Nyeri shocked 5 times at 500ºc
0
-0.6
-0.4
-0.2
-1 0
0.2
0.4
-3
ln(σ/σf)
0.1
-2
0
0.2
-4
ln(σ/σf)
y = -0.856x - 0.538
4
0.2
-0.3
2
0
-0.2
-0.1 -2 0
0.2
ln{ln(1/[1-pf])}
-0.5
ln(σ/σf)
0.3
-4
ln(σ/σf)
y = 4.958x - 0.102
0.1
y = -12.44x - 0.563
Plain Nyeri shocked 10 times at
500ºc
-1
0.4
40% Alumina-60% Nyeri Clay shocked 5
timea at 500ºC
ln{ln(1/[1-pf])}
ln{ln(1/[1-pf])}
2
1
0
-1 0
-2
-3
-0.1
-0.2
y = 2.414x - 0.477
30% Alumina-70% Nyeri Clay
shocked 5 times at 500ºC
-0.2
0
-0.4
-2
ln(σ/σf)
2
2
1
0
-1 0
0.5
-2
-3
y = -2.114x - 0.576
87
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-0.2
1
0.5
0
-0.5
-0.1
0
-1
-1.5
-2
-2.5
0.2
-0.4
0
-1 0
0.2
0.4
-2
-3
ln σ/σf
-0.4
y = -3.224x - 0.554
ln{ln(1/[1-Pf])}
ln{ln(1/[1-PF])}
0.2
-0.2
-0.4
0.4
-2
0.2
0.4
-2
-3
y = 1.915x - 0.514
1
0
-0.2
-1
-3
ln σ/σf
y = 9.863x - 0.485
0
0.2
0.4
-2
-4
ln σ/σf
-1 0
20% sand-80% Murang'a clay
shocked once at 800°C
0
0
y = -2.666x - 0.547
0
ln σ/σf
2
-0.2
0.4
1
Plain muranga'a clay shocked
once at 800°C
-0.4
0.2
40% sand-60% Murang'a clay
shocked once at 600°C
1
-0.2
1
0.5
0
-0.5 0
-1
-1.5
-2
-2.5
ln σ/σf
30% sand-70% murang'a clay
shocked once
at 600°C
2
-0.4
-0.2
y = -0.015x - 0.525
ln{ln(1/[1-Pf])}
ln{ln(1/[1-Pf])}
ln σ/σf
0.1
20% sand-80% murang'a clay
shocked once at 600°C
ln{ln(1/[1-Pf])}
ln{ln(1/[1-Pf])}
Plain Murang'a shocked once at
600°C
y = -5.541x - 0.553
88
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30% sand-70% Murang'a clay
shocked once at 800°C
40% sand-60% Murang'a clay
shocked once 800°C
ln{ln(1/[1-Pf])}
ln{ln(1/[1-Pf])}
2
1
0
-0.2
-1 0
0.2
0.4
0.6
-2
1
0
-0.4
ln σ/σf
0.2
0.4
-2
20% sand-80% Murang'a clay
shocked 5 times at 500°C
ln{ln(1/[1-Pf])}
ln{ln(1/[1-Pf])}
2
1
0
-0.5
-1 0
0.5
-2
ln σ/σf
2
1
0
-0.4
ln {ln(1/[1-Pf])}
1
0
0.2
0.4
-2
-3
0.2
0.4
-2
y = 6.932x - 0.495
40% sand-60% Murang'a clay
shocked 5 times at 500°C
2
ln σ/σf
-1 0
ln σ/σf
y = 4.004x - 0.462
-1 0
-0.2
-3
-3
30% sand-70% Murang'a clay
shocked 5 times at 500°C
-0.2
y = -3.052x - 0.536
ln σ/σf
y = -1.829x - 0.209
Plain Murang'a clay shocked 5
times at 500°C
ln{ln(1/[1-Pf])}
-1 0
-3
-3
-0.4
-0.2
y = -6.586x - 0.567
2
0
-0.4
-0.2
0
0.2
-2
ln σ/σf
-4
y = 10.30x - 0.509
89
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40% sand-60% Murang'a clay
shocked 10 times at 500°C
30% sand-70% Murang'a clay
shocked 10 times at 500°C
ln{ln(1/[1-Pf])}
ln {ln(1/[1-Pf])}
2
1
0
-0.2
-0.1
-1 0
0.1
0.2
-2
-3
ln σ/σf
-1 0
0.5
-0.2
-1 0
0.2
0.4
-2
y = -2.166x - 0.551
0.3
2
1
0
-0.6
-0.4
-0.2
y = -12.85x - 0.560
-1 0
0.2
0.4
-2
-4
ln σ/σf
0.2
85% sand-15% Nyeri clay shocked
once at 600°C
ln {ln(1/[1-Pf])}
ln {ln(1/[1-Pf])}
-2
0
-3
0
0.1
y = -8.624x - 0.560
ln σ/σf
2
0
0.4
-4
y = -0.388x - 0.546
65% sand-35% Nyeri clay shocked
once at 600°C
-0.1
0.2
1
-0.4
-2
-3
0
-2
2
ln{ln(1/[1-Pf])}
ln {ln(1/[1-Pf])}
0
-0.2
-0.2
55% sand-45% Nyeri clay shocked
once 600°C
1
ln σ/σf
-0.4
ln σ/σf
2
-0.5
0
y = -6.249x - 0.542
15% sand-85% Nyeri clay shocked
once at 600°C
-1
2
ln σ/σf
-3
y = 3.120x - 0.487
90
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15% sand-85% Nyeri clay shocked once
at 800°C
55% sand-45% Nyeri clay shocked
once at 800°C
2
ln{ln(1/[1-Pf])}
ln{ln(1/[1-Pf])}
2
1
0
-0.4
-0.2
-1 0
0.2
0.4
0.6
-2
-3
ln σ/σf
0
-0.4
-0.2
-1 0
0.2
ln{ln(1/[1-Pf])}
ln{ln(1/[1-Pf])}
-2
-4
ln σ/σf
0.2
-2
-3
y = 0.092x - 0.524
55% sand-45% Nyeri clay shocked 10
times at 500°C
0
0.5
-1 0
ln σ/σf
2
0
-0.2
y = -2.215x - 0.553
15% sand-85% Nyeri clay shocked
10 times at 500°C
-0.5
0
-0.4
0.4
-3
ln σ/σf
1
ln{ln(1/[1-Pf])}
0
-1 0
-2
y = -4.353x - 0.559
85%sand-15% Nyeri clay shocked
once at 800°C
1
-0.2
0.4
-3
ln σ/σf
2
-0.4
0.2
-2
y = 4.067x - 0.489
65% sand-35% Nyeri clay shocked
once at 800°
ln{ln(1/[1-Pf])}
1
1
-0.4
4
2
0
-0.2
-2 0
0.4
-4
ln σ/σf
y = -1.510x - 0.589
0.2
y = -11.03x - 0.563
91
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65% sand-35% Nyeri clay shocked
10 times at 500°
85%sand-15% Nyeri clay shocked 10
times at 500°C
0
-0.5
-1 0
0.5
-2
-3
ln σ/σf
1
ln{ln(1/[1-Pf])}
ln{ln(1/[1-Pf])}
1
0
-0.6
-0.4
-0.2 -1 0
-3
ln σ/σf
y = -2.750x - 0.589
y = -1.687x - 0.542
20% alumina-80% Murang'a
clay-unshocked
2
ln{ln(1/[1-Pf])}
ln{ln(1/[1-Pf])}
1
0
-0.2
-1 0
0.2
0.4
-0.3
-2
-3
ln σ/σf
0.4
-2
40% alumina-60% Murang'a clayunshocked
-0.4
0.2
0
-0.2
-0.1
0
0.1
0.2
-2
-4
y = -4.283x - 0.539
ln σ/σf
y = 12.33x - 0.509
ln{ln(1/[1-Pf])}
30% alumina-70%Murang'a clayunshocked
2
0
-1
-0.5
ln σ/σf
-2
-4
0
0.5
y = -3.467x - 0.648
92
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PHOTOGRAPHS
Mined Clay (Murang’a)
Sand Mines (Murang’a)
Specimens in a Rack
Specimen holder (Rack)
Specimens in Furnace
Extruded Nyeri clay specimens
Extruded Murang’a clay Specimens
Quenching basin
93
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Extrusion machine
MICROSTRUCTURES
Plain Nyeri clay
15%Sand-85% Nyeri Clay
55% Sand-45% Nyeri Clay
65% Sand-35% Nyeri Clay
94
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85%Sand-15% Nyeri Clay
30% Alumina-70% Nyeri Clay
Plain Murang’a Clay
30% sand-70% Murang’a Clay
20% Alumina-80% Nyeri Clay
40% Alumina-60% Nyeri Clay
20% sand-80% Murang’a Clay
40% sand-60% Murang’a Clay
95
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20% Alumina-80 % Murang’a Clay
30% Alumina-70% Murang’a Clay
40% Alumina-60% Murang’a Clay
96
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