CHAPTER 6 :
RESULTS
6.1 Results after shocking once
Results for unshocked specimens for Nyeri clay
UNSHOCKED FRACTURE
SPECIMEN
LOAD
Plain Nyeri
137
140
162
164
168
172
186
190
192
196
205
208
NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
SPAN
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
DIAMETER
13.4
13.4
13.4
13.4
13.3
13.4
13.4
13.4
13.4
13.4
13.4
13.3
AVERAGE
MOR
5.533E+6
5.667E+6
6.587E+6
6.714E+6
6.971E+6
7.057E+6
7.546E+6
7.743E+6
7.860E+6
7.952E+6
8.411E+6
8.592E+6
7.219E+6
Probability
of Failure
0.04
0.13
0.21
0.29
0.38
0.46
0.54
0.63
0.71
0.79
0.88
0.96
ln(σ/σf)
-0.2659
-0.2420
-0.0916
-0.0726
-0.0350
-0.0227
0.0443
0.0701
0.0850
0.0967
0.1528
0.1741
Weibull
ln {ln (1/[1-Pf])} Modulus
-3.157
8.5
-2.013
-1.454
-1.065
-0.755
-0.489
-0.248
-0.019
0.209
0.450
0.732
1.156
Nyeri 3:1
300
285
300
295
310
310
320
325
320
330
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.8
13.8
13.8
13.9
13.8
13.8
13.8
13.8
13.9
13.8
AVERAGE
1.112E+7
1.049E+7
1.114E+7
1.082E+7
1.151E+7
1.151E+7
1.189E+7
1.197E+7
1.173E+7
1.226E+7
1.144E+7
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.0284
-0.0863
-0.0263
-0.0561
0.0065
0.0065
0.0383
0.0451
0.0252
0.0690
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
20
Nyeri 2:1
206
216
204
222
219
232
224
240
246
242
264
224
1
2
3
4
5
6
7
8
9
10
11
12
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
4.835
14.3
14.4
14.3
14.4
14.3
14.4
14.3
14.3
14.3
14.3
14.3
14.3
AVERAGE
6.877E+6
7.136E+6
6.810E+6
7.318E+6
7.311E+6
7.600E+6
7.478E+6
8.012E+6
8.212E+6
8.045E+6
8.758E+6
9.428E+6
7.749E+6
0.04
0.13
0.21
0.29
0.38
0.46
0.54
0.63
0.71
0.79
0.88
0.96
-0.1194
-0.0825
-0.1292
-0.0572
-0.0582
-0.0194
-0.0356
0.0334
0.0581
0.0375
0.1224
0.1961
-3.157
-2.013
-1.454
-1.065
-0.755
-0.489
-0.248
-0.019
0.209
0.450
0.732
1.156
10.43
Nyeri 1:1
126
144
146
152
147
159
157
155
159
158
204
218
1
2
3
4
5
6
7
8
9
10
11
12
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
14.6
14.6
14.6
14.6
14.6
14.7
14.7
14.6
14.6
14.6
14.6
14.6
AVERAGE
3.960E+6
4.564E+6
4.627E+6
4.729E+6
4.649E+6
4.916E+6
4.874E+6
4.842E+6
5.039E+6
4.926E+6
6.399E+6
6.909E+6
5.036E+6
0.04
0.13
0.21
0.29
0.38
0.46
0.54
0.63
0.71
0.79
0.88
0.96
-0.2403
-0.0985
-0.0847
-0.0629
-0.0799
-0.0241
-0.0326
-0.0393
0.0006
-0.0222
0.2395
0.3162
-3.157
-2.013
-1.454
-1.065
-0.755
-0.489
-0.248
-0.019
0.209
0.450
0.732
1.156
7.13
Table 6.1.1
Page 28
Results for unshocked specimens for Murang'a clay
UNSHOCKED FRACTURE
SPECIMEN
LOAD
NUMBER
Plain
Murang'a
460
1
460
2
500
3
510
4
540
5
560
6
600
7
600
8
620
9
850
10
Probability
of Failure
ln(σ/σf)
2.299E+7
2.299E+7
2.499E+7
2.643E+7
2.699E+7
2.902E+7
3.028E+7
3.065E+7
3.213E+7
4.248E+7
2.890E+7
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.2315
-0.2315
-0.1481
-0.0921
-0.0712
0.0014
0.0438
0.0559
0.1032
0.3825
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
6.01
SPAN
DIAMETER
MOR
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
12.5
12.5
12.5
12.4
12.5
12.4
12.5
12.4
12.4
12.5
AVERAGE
Weibull
ln {ln (1/[1-Pf])} Modulus
Murang'a 3:1
365
400
395
410
405
420
415
440
435
440
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.3
13.3
13.2
13.3
13.2
13.3
13.2
13.3
13.2
13.2
AVERAGE
1.514E+7
1.660E+7
1.669E+7
1.701E+7
1.719E+7
1.743E+7
1.761E+7
1.830E+7
1.834E+7
1.859E+7
1.729E+7
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.1325
-0.0409
-0.0354
-0.0162
-0.0058
0.0079
0.0186
0.0567
0.0588
0.0725
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
19.78
Murang'a 2:1
280
285
310
320
330
340
350
360
355
365
1
2
3
4
5
6
7
9
8
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.4
13.5
13.5
13.5
13.5
13.4
13.5
13.6
13.5
13.5
AVERAGE
1.136E+7
1.141E+7
1.225E+7
1.272E+7
1.298E+7
1.367E+7
1.398E+7
1.403E+7
1.424E+7
1.461E+7
1.313E+7
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.85
0.75
0.95
-0.1448
-0.1405
-0.0698
-0.0314
-0.0117
0.0404
0.0627
0.0665
0.0813
0.1069
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.640
0.327
1.097
12.91
Murang'a 1:1
230
247
248
252
256
260
264
266
270
280
285
270
1
2
3
4
5
6
7
8
9
11
12
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.8
13.8
13.8
13.7
13.7
13.8
13.8
13.7
13.7
13.8
13.9
13.6
AVERAGE
8.543E+6
9.155E+6
9.292E+6
9.484E+6
9.634E+6
9.700E+6
9.892E+6
1.005E+7
1.034E+7
1.038E+7
1.047E+7
1.048E+7
9.785E+6
0.04
0.13
0.21
0.29
0.38
0.46
0.54
0.63
0.71
0.88
0.96
0.79
-0.1357
-0.0666
-0.0517
-0.0313
-0.0155
-0.0088
0.0109
0.0271
0.0552
0.0588
0.0678
0.0684
-3.157
-2.013
-1.454
-1.065
-0.755
-0.489
-0.248
-0.019
0.209
0.732
1.156
0.450
19.25
Table 6.1.2
Page 29
Graphs of the modulus of fracture for unshocked specimens against the
concentration of sand
Graph of MOR against concentration
of sand in Nyeri clay
14.0
12.0
MOR
(MN/m2)
10.0
8.0
6.0
4.0
2.0
0.0
0
5
10
15
20
25
30
35
40
45
50
40
45
50
Percentage sand concentration
Figure 6.1.3
Graph of MOR against percentage
sand concentration in Murang'a clay
35.0
30.0
MOR
(MN/m2)
25.0
20.0
15.0
10.0
5.0
0.0
0
5
10
15
20
25
30
35
Percentage sand concentration
Figure 6.1.4
Page 30
Results for specimens shocked once from 400°C to room temperature for Nyeri
clay
SHOCKED
ONCE FROM
400°C-25°C
Plain Nyeri
FRACTURE
LOAD
90
90
110
130
145
150
165
165
210
210
NUMBER
1
2
3
4
5
6
7
8
9
10
SPAN
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
DIAMETER
13.4
13.3
13.4
13.4
13.4
13.3
13.4
13.3
13.4
13.4
AVERAGE
MOR
3.651E+6
3.718E+6
4.513E+6
5.322E+6
5.857E+6
6.182E+6
6.770E+6
6.816E+6
8.539E+6
8.597E+6
5.996E+6
Probability
of Failure
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
ln(σ/σf)
Nyeri 3:1
225
245
255
250
265
265
255
270
285
290
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.8
13.8
13.8
13.8
13.8
13.9
13.9
13.8
13.9
13.8
AVERAGE
8.321E+6
9.100E+6
9.472E+6
9.246E+6
9.779E+6
9.653E+6
9.269E+6
1.003E+7
1.036E+7
1.077E+7
9.600E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.1429
-0.0534
-0.0134
-0.0376
0.0185
0.0055
-0.0351
0.0437
0.0761
0.1152
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
15.49
Nyeri 2:1
210
220
220
230
245
240
240
240
270
275
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
14.3
14.3
14.3
14.3
14.4
14.3
14.3
14.3
14.4
14.3
AVERAGE
6.981E+6
7.313E+6
7.344E+6
7.662E+6
8.043E+6
8.012E+6
8.012E+6
7.945E+6
8.901E+6
9.180E+6
7.939E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.1286
-0.0821
-0.0779
-0.0355
0.0130
0.0091
0.0091
0.0008
0.1144
0.1453
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
13.3
Nyeri 1:1
115
140
140
150
160
165
185
200
215
230
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
14.6
14.6
14.6
14.7
14.6
14.6
14.6
14.6
14.7
14.6
AVERAGE
3.645E+6
4.364E+6
4.437E+6
4.610E+6
5.071E+6
5.229E+6
5.803E+6
6.338E+6
6.607E+6
7.289E+6
5.339E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.3818
-0.2016
-0.1851
-0.1469
-0.0516
-0.0208
0.0833
0.1716
0.2131
0.3113
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
5.5
-0.4960
-0.4780
-0.2841
-0.1193
-0.0235
0.0306
0.1214
0.1281
0.3536
0.3603
Weibull
ln {ln (1/[1-Pf])} Modulus
-2.970
3.86
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
Table 6.1.5
Page 31
Results for specimens shocked once from 400°C to room temperature for
Murang'a clay
SHOCKED
ONCE FROM FRACTURE
400°C-25°C
LOAD
Plain Murang'a
50
90
120
120
135
140
150
145
150
160
NUMBER
1
2
3
4
5
6
7
8
9
10
SPAN
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
DIAMETER
12.4
12.4
12.5
12.4
12.4
12.4
12.5
12.4
12.4
12.4
AVERAGE
MOR
2.591E+6
4.664E+6
5.998E+6
6.219E+6
6.895E+6
7.255E+6
7.533E+6
7.514E+6
7.774E+6
8.192E+6
6.464E+6
Probability
of Failure
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
ln(σ/σf)
-0.9141
-0.3263
-0.0749
-0.0387
0.0646
0.1155
0.1531
0.1506
0.1845
0.2369
Weibull
ln {ln (1/[1-Pf])} modulus
-2.970
3.29
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
Murang'a 3:1
355
370
385
380
385
395
405
405
410
405
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.2
13.3
13.3
13.2
13.3
13.2
13.3
13.3
13.3
13.2
AVERAGE
1.521E+7
1.549E+7
1.601E+7
1.606E+7
1.616E+7
1.661E+7
1.692E+7
1.696E+7
1.717E+7
1.719E+7
1.638E+7
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.0744
-0.0558
-0.0228
-0.0200
-0.0137
0.0142
0.0324
0.0346
0.0469
0.0482
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
27.61
Murang'a 2:1
140
145
145
165
170
170
195
205
215
220
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.6
13.5
13.5
13.5
13.4
13.5
13.5
13.5
13.5
13.4
AVERAGE
5.445E+6
5.817E+6
5.817E+6
6.605E+6
6.836E+6
6.745E+6
7.823E+6
8.206E+6
8.626E+6
8.886E+6
7.081E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.2627
-0.1966
-0.1966
-0.0696
-0.0353
-0.0486
0.0997
0.1475
0.1973
0.2270
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
6.63
Murang'a 1:1
215
235
235
235
240
240
260
260
285
290
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.8
13.9
13.8
13.8
13.7
13.7
13.8
13.8
13.7
13.8
AVERAGE
7.986E+6
8.616E+6
8.653E+6
8.653E+6
9.032E+6
9.052E+6
9.679E+6
9.700E+6
1.073E+7
1.087E+7
9.296E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.1489
-0.0729
-0.0686
-0.0686
-0.0258
-0.0236
0.0433
0.0455
0.1461
0.1591
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
11.74
Table 6.1.6
Page 32
Graphs of the modulus of fracture for specimens shocked from 400°C to room
temperature against the concentration of sand
Graph of MOR against concentration
of sand in Nyeri clay
12.0
10.0
MOR
(MN/m2)
8.0
6.0
4.0
2.0
0.0
0
5
10
15
20
25
30
35
40
45
50
45
50
Percentage sand concentration
Figure 6.1.7
Graph of MOR against percentage
sand concentration in Murang'a clay
18.0
16.0
MOR
(MN/m2)
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0.0
0
5
10
15
20
25
30
35
40
Percentage sand concentration
Figure 6.1.8
Page 33
Results for specimens shocked once from 600°C to room temperature for Nyeri
clay
SHOCKED
ONCE FROM FRACTURE
600°C-25°C
LOAD
NUMBER
Plain Nyeri
SPAN
DIAMETER
MOR
Probability
of Failure
Weibull
ln(σ/σf) ln {ln (1/[1-Pf])} Modulus
56
64
72
90
110
114
120
124
130
138
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.4
13.4
13.4
13.3
13.4
13.3
13.3
13.4
13.3
13.4
AVERAGE
2.298E+6
2.626E+6
2.950E+6
3.718E+6
4.483E+6
4.709E+6
4.935E+6
5.031E+6
5.370E+6
5.574E+6
4.169E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.5958
-0.4623
-0.3458
-0.1146
0.0726
0.1218
0.1686
0.1879
0.2531
0.2904
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
3.7
Nyeri 3:1
172
178
186
192
210
210
214
218
220
222
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.8
13.8
13.8
13.7
13.8
13.8
13.8
13.7
13.8
13.8
AVERAGE
6.389E+6
6.612E+6
6.849E+6
7.226E+6
7.733E+6
7.800E+6
7.949E+6
8.276E+6
8.172E+6
8.246E+6
7.525E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.1618
-0.1275
-0.0922
-0.0387
0.0291
0.0378
0.0567
0.0970
0.0843
0.0934
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
12.5
Nyeri 2:1
180
198
198
200
204
222
238
254
264
280
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
14.3
14.3
14.3
14.3
14.3
14.3
14.3
14.3
14.3
14.3
AVERAGE
6.009E+6
6.610E+6
6.610E+6
6.677E+6
6.810E+6
7.411E+6
7.945E+6
8.479E+6
8.813E+6
9.347E+6
7.471E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.2178
-0.1225
-0.1225
-0.1124
-0.0926
-0.0081
0.0615
0.1266
0.1652
0.2240
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
7.73
Nyeri 1:1
96
104
106
108
118
128
130
140
146
164
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
14.6
14.6
14.6
14.6
14.6
14.6
14.6
14.6
14.6
14.6
AVERAGE
3.042E+6
3.296E+6
3.359E+6
3.423E+6
3.740E+6
4.057E+6
4.120E+6
4.437E+6
4.627E+6
5.197E+6
3.930E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.2560
-0.1760
-0.1569
-0.1382
-0.0497
0.0317
0.0472
0.1213
0.1633
0.2795
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
6.79
Table 6.1.9
Page 34
Results for specimens shocked once from 600°C to room temperature for
Murang'a clay
SHOCKED
ONCE FROM FRACTURE
600°C-25°C
LOAD
Plain
0
Murang'a
0
0
92
96
100
116
122
128
146
Murang'a 3:1
Murang'a 2:1
Murang'a 1:1
Probability
of Failure
ln(σ/σf)
0.000E+0
0.000E+0
0.000E+0
4.631E+6
4.975E+6
5.182E+6
5.882E+6
6.098E+6
6.633E+6
7.566E+6
4.097E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
Err:502
Err:502
Err:502
0.1168
0.1883
0.2292
0.3558
0.3918
0.4760
0.6076
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
Plain Nyeri
13.3
13.2
13.3
13.3
13.2
13.3
13.2
13.2
13.2
13.3
AVERAGE
1.219E+7
1.343E+7
1.340E+7
1.406E+7
1.409E+7
1.424E+7
1.482E+7
1.493E+7
1.500E+7
1.501E+7
1.412E+7
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.1474
-0.0501
-0.0525
-0.0044
-0.0021
0.0082
0.0485
0.0559
0.0604
0.0608
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
18.32
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.6
13.5
13.5
13.5
13.4
13.5
13.5
13.4
13.6
13.5
AVERAGE
6.906E+6
7.061E+6
7.382E+6
8.425E+6
8.846E+6
8.907E+6
8.987E+6
9.209E+6
9.162E+6
9.549E+6
8.443E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.2009
-0.1787
-0.1343
-0.0021
0.0466
0.0535
0.0624
0.0868
0.0817
0.1231
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
9.66
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.8
13.9
13.8
13.8
13.8
13.8
13.7
13.8
13.7
13.8
AVERAGE
6.760E+6
7.553E+6
7.652E+6
7.875E+6
7.909E+6
8.023E+6
8.129E+6
8.469E+6
8.731E+6
8.764E+6
7.986E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.1657
-0.0549
-0.0419
-0.0132
-0.0088
0.0055
0.0186
0.0596
0.0901
0.0938
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
15.58
NUMBER
SPAN
DIAMETER
MOR
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
12.5
12.4
12.4
12.5
12.4
12.4
12.4
12.5
12.4
12.4
AVERAGE
295
315
320
335
335
340
350
355
355
360
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
176
176
184
210
220
222
224
228
234
238
1
2
3
4
5
6
7
8
9
10
182
206
206
212
212
216
216
228
232
238
1
2
3
4
5
6
7
8
9
10
Weibull
ln {ln (1/[1-Pf])} modulus
Table 6.1.10
Page 35
Graphs of the modulus of fracture for specimens shocked from 600°C to room
temperature against the concentration of sand
Graph of MOR against concentration
of sand in Nyeri clay
10.0
9.0
8.0
MOR
(MN/m2)
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
0
5
10
15
20
25
30
35
40
45
50
Percentage sand concentration
Figure 6.1.11
Graph of MOR against percentage
sand concentration in Murang'a clay
16.0
14.0
12.0
MOR
(MN/m2)
10.0
8.0
6.0
4.0
2.0
0.0
0
5
10
15
20
25
30
35
40
45
50
Percentage sand concentration
Figure 6.1.12
Page 36
Results for specimens shocked once from 800°C to room temperature for Nyeri
clay
SHOCKED
ONCE FROM FRACTURE
800°C-25°C
LOAD
NUMBER
Plain Nyeri
40
1
80
2
132
3
102
4
148
5
104
6
108
7
120
8
110
9
154
10
SPAN
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
DIAMETER
13.3
13.3
13.3
13.3
13.4
13.4
13.4
13.4
13.5
13.5
AVERAGE
MOR
1.679E+6
3.350E+6
5.477E+6
4.232E+6
6.005E+6
4.219E+6
4.382E+6
4.847E+6
4.413E+6
6.110E+6
4.471E+6
Probability
of Failure
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
Weibull
ln(σ/σf) ln {ln (1/[1-Pf])} Modulus
-0.9797
-0.2888
0.2030
-0.0549
0.2949
-0.0579
-0.0202
0.0807
-0.0130
0.3123
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
2.52
Nyeri 3:1
196
204
206
214
218
230
238
240
252
280
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.8
13.7
13.8
13.7
13.7
13.8
13.8
13.8
13.8
13.8
AVERAGE
7.344E+6
7.694E+6
7.619E+6
8.053E+6
8.204E+6
8.469E+6
8.860E+6
8.876E+6
9.381E+6
1.038E+7
8.488E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.1336
-0.0871
-0.0969
-0.0414
-0.0229
0.0089
0.0540
0.0558
0.1111
0.2122
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
10.76
Nyeri 2:1
130
158
166
170
178
184
200
204
210
226
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
14.3
14.3
14.3
14.4
14.3
14.3
14.4
14.3
14.4
14.3
AVERAGE
4.304E+6
5.274E+6
5.542E+6
5.593E+6
5.917E+6
6.142E+6
6.593E+6
6.810E+6
6.865E+6
7.545E+6
6.058E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.3419
-0.1385
-0.0891
-0.0799
-0.0235
0.0138
0.0847
0.1170
0.1251
0.2194
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
7.48
Nyeri 1:1
72
100
100
100
106
108
114
114
118
150
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
14.6
14.7
14.6
14.7
14.7
14.6
14.6
14.6
14.6
14.7
AVERAGE
2.240E+6
3.098E+6
3.117E+6
3.079E+6
3.238E+6
3.367E+6
3.547E+6
3.613E+6
3.740E+6
4.629E+6
3.367E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.4076
-0.0832
-0.0770
-0.0893
-0.0392
0.0000
0.0520
0.0705
0.1050
0.3182
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
6.25
Table 6.1.13
Page 37
Graph of the modulus of fracture for specimens shocked from 800°C to room
temperature against the concentration of sand for Murang'a clay
SHOCKED
ONCE FROM FRACTURE
800°C-25°C
LOAD
NUMBER
Plain
0
1
Murang'a
0
2
0
3
0
4
0
5
0
6
0
7
54
8
76
9
78
10
Probability
of Failure
Weibull
ln(σ/σf) ln {ln (1/[1-Pf])} modulus
SPAN
DIAMETER
MOR
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
12.4
12.4
12.4
12.5
12.4
12.4
12.5
12.4
12.4
12.4
AVERAGE
0.000E+0
0.000E+0
0.000E+0
0.000E+0
0.000E+0
0.000E+0
0.000E+0
2.745E+6
3.939E+6
4.042E+6
1.073E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
0.9393
1.3004
1.3263
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
1.51
Murang'a 3:1
210
220
246
250
270
290
295
300
310
365
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.2
13.3
13.3
13.3
13.2
13.3
13.3
13.2
13.2
13.2
AVERAGE
8.873E+6
9.211E+6
1.021E+7
1.037E+7
1.136E+7
1.203E+7
1.224E+7
1.262E+7
1.310E+7
1.539E+7
1.154E+7
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.2628
-0.2254
-0.1227
-0.1066
-0.0161
0.0418
0.0589
0.0893
0.1266
0.2877
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
6.97
Murang'a 2:1
156
190
194
202
200
202
216
230
260
266
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.5
13.5
13.5
13.6
13.5
13.5
13.5
13.5
13.4
13.5
AVERAGE
6.259E+6
7.606E+6
7.783E+6
7.891E+6
8.024E+6
8.104E+6
8.666E+6
9.228E+6
1.045E+7
1.067E+7
8.469E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.3048
-0.1099
-0.0868
-0.0730
-0.0563
-0.0464
0.0206
0.0834
0.2083
0.2289
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
7.36
Murang'a 1:1
140
154
162
172
176
186
192
214
224
236
1
2
3
4
5
6
7
8
9
10
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.8
13.9
13.8
13.8
13.8
13.9
13.8
13.8
13.9
13.8
AVERAGE
5.178E+6
5.646E+6
5.978E+6
6.389E+6
6.552E+6
6.820E+6
7.085E+6
7.880E+6
8.231E+6
8.728E+6
6.849E+6
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
-0.2797
-0.1931
-0.1360
-0.0696
-0.0444
-0.0043
0.0339
0.1402
0.1838
0.2424
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0.327
0.640
1.097
7.11
Table 6.1.14
Page 38
Graphs of the modulus of fracture for specimens shocked from 600°C to room
temperature against the concentration of sand
Graph of MOR against concentration
of sand in Nyeri clay
9.0
8.0
7.0
MOR
(MN/m2)
6.0
5.0
4.0
3.0
2.0
1.0
0.0
0
5
10
15
20
25
30
35
40
45
50
Percentage sand concentration
Figure 6.1.15
Graph of MOR against percentage
sand concentration in Murang'a clay
14.0
12.0
MOR
(MN/m2)
10.0
8.0
6.0
4.0
2.0
0.0
0
5
10
15
20
25
30
35
40
45
50
Percentage sand concentration
Figure 6.1.16
Page 39
Graph of the MOR against the shocking temperature difference after one quench
Graph of MOR against shocking temperature for Nyeri clay
30.0
25.0
MOR
20.0
15.0
10.0
5.0
0.0
0
100
200
300
400
500
600
700
800
shocking temperature
Figure 6.1.17
Graph of MOR against shocking temperature for Murang'a clay
35.0
30.0
25.0
MOR
20.0
15.0
10.0
5.0
0.0
0
100
200
300
400
500
600
700
800
Shocking temperature
Figure 6.1.18
Page 40
6.2
Weibull modulus
Table of Weibull modulus for the various clay specimens. Graphs used to obtain
these values are shown in the appendix on page 69.
Table showing the values of Weibull modulus for various clay specimens
table 6.2.1
Weibull modulus (m)
Nyeri clay
Murang'a clay
Unshocked specimens
Plain clay
8.5
6.01
Clay with 25% sand
20
19.78
Clay with 33% sand
11.12
12.91
Clay with 50% sand
6.9
19.25
Plain clay
3.86
3.29
Clay with 25% sand
15.49
27.61
Clay with 33% sand
13.3
6.63
Clay with 50% sand
5.5
11.43
3.7
3.88
Clay with 25% sand
12.21
17.84
Clay with 33% sand
7.73
9.66
Clay with 50% sand
6.79
15.58
Plain clay
2.52
1.51
Clay with 25% sand
10.76
6.97
Clay with 33% sand
7.48
7.36
Clay with 50% sand
6.25
7.11
0
1.39
Clay with 25% sand
2.89
8.75
Clay with 33% sand
9.26
8.75
Clay with 50% sand
17.09
5.28
Shocked once from 400°C-25°C
Shocked once from 600°C-25°C
Plain clay
Shocked once from 800°C-25°C
Shocked 10 times from 500°C-25°C
Plain clay
Graphs of Weibull modulus against percentage sand for Nyeri and Murang'a clay
Graph of Weibull modulus against
percentage sand added for Nyeri clay
25
15
10
5
0
0
5
10
15
20
25
30
35
40
45
50
Percentage sand added
Figure 6.2.2
Graph of weibull moduluss m against
percentage sand content
25
20
Weibull modulus
Weibull modulus
20
15
10
5
0
0
5
10
15
20
25
30
35
Percentage sand added
40
45
50
Figure 6.2.3
Page 42
6.3
Results for shocking specimens ten times across a temperature
difference of approximately 500°C For Nyeri clay
SHOCKED TEN
TIMES FROM FRACTURE
500°C-25°C
LOAD
Plain Nyeri
0
0
0
0
0
0
0
NUMBER
1
2
3
4
5
6
7
SPAN
3.835
3.835
3.835
3.835
3.835
3.835
3.835
DIAMETER
13.4
13.3
13.4
13.4
13.4
13.3
13.4
AVERAGE
MOR
0.000E+0
0.000E+0
0.000E+0
0.000E+0
0.000E+0
0.000E+0
0.000E+0
0.000E+0
Probability
of Failure
0.05
0.15
0.25
0.35
0.45
0.55
0.65
(1/[1- Weibull
ln(σ/σf) ln {ln
Pf])}
modulus
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
-2.970
-1.817
-1.246
-0.842
-0.514
-0.225
0.049
0
Nyeri 3:1
0
135
145
165
215
230
270
285
1
2
3
4
5
6
7
8
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.8
13.8
13.8
13.9
13.9
13.8
13.8
13.8
AVERAGE
0.000E+0
5.014E+6
5.351E+6
6.010E+6
7.815E+6
8.506E+6
1.003E+7
1.054E+7
6.658E+6
0.06
0.19
0.31
0.44
0.56
0.69
0.81
0.94
Err:502
-0.2835
-0.2185
-0.1023
0.1602
0.2450
0.4097
0.4594
-2.740
-1.572
-0.982
-0.553
-0.190
0.151
0.515
1.020
2.89
Nyeri 2:1
120
135
140
155
155
160
170
180
1
2
3
4
5
6
7
8
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
14.3
14.3
14.3
14.3
14.3
14.4
14.3
14.3
AVERAGE
4.006E+6
4.488E+6
4.674E+6
5.131E+6
5.174E+6
5.253E+6
5.663E+6
5.984E+6
5.047E+6
0.06
0.19
0.31
0.44
0.56
0.69
0.81
0.94
-0.2310
-0.1174
-0.0769
0.0165
0.0249
0.0399
0.1152
0.1703
-2.740
-1.572
-0.982
-0.553
-0.190
0.151
0.515
1.020
9.26
Nyeri 1:1
210
235
250
245
250
255
255
265
1
2
3
4
5
6
7
8
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
14.6
14.6
14.7
14.6
14.6
14.6
14.6
14.6
AVERAGE
6.655E+6
7.447E+6
7.683E+6
7.685E+6
7.923E+6
8.081E+6
8.081E+6
8.261E+6
7.727E+6
0.06
0.19
0.31
0.44
0.56
0.69
0.81
0.94
-0.1493
-0.0368
-0.0057
-0.0055
0.0250
0.0448
0.0448
0.0669
-2.740
-1.572
-0.982
-0.553
-0.190
0.151
0.515
1.020
17.09
Table 6.3.1
Page 43
Results for shocking specimens ten times across a temperature difference
of approximately 500°C for Murang'a clay
SHOCKED TEN
TIMES FROM FRACTURE
500°C-25°C
LOAD
Plain Murang'a
0
0
0
0
0
0
90
125
NUMBER
1
2
3
4
5
6
7
8
SPAN
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
DIAMETER
12.4
12.4
12.5
12.4
12.5
12.4
12.4
12.4
AVERAGE
MOR
0.000E+0
0.000E+0
0.000E+0
0.000E+0
0.000E+0
0.000E+0
4.664E+6
6.478E+6
1.393E+6
Probability
of Failure
0.06
0.19
0.31
0.44
0.56
0.69
0.81
0.94
(1/[1- Weibull
ln(σ/σf) ln {ln
Pf])}
modulus
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
1.2084
1.5369
-2.740
-1.572
-0.982
-0.553
-0.190
0.151
0.515
1.020
1.54
Murang'a 3:1
165
205
215
245
1
2
3
4
3.835
3.835
3.835
3.835
13.3
13.2
13.2
13.3
AVERAGE
6.862E+6
8.780E+6
9.084E+6
1.026E+7
8.746E+6
0.13
0.38
0.63
0.88
-0.2426
0.0039
0.0379
0.1595
-2.013
-0.755
-0.019
0.732
6.8
Murang'a 2:1
205
200
205
215
215
220
245
250
1
2
3
4
5
6
7
8
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.6
13.5
13.5
13.5
13.5
13.4
13.5
13.5
AVERAGE
7.973E+6
8.024E+6
8.206E+6
8.607E+6
8.626E+6
8.846E+6
9.829E+6
9.919E+6
8.754E+6
0.06
0.19
0.31
0.44
0.56
0.69
0.81
0.94
-0.0934
-0.0871
-0.0646
-0.0170
-0.0147
0.0105
0.1159
0.1249
-2.740
-1.572
-0.982
-0.553
-0.190
0.151
0.515
1.020
12.85
Murang'a 1:1
0
120
125
160
165
170
185
210
1
2
3
4
5
6
7
8
3.835
3.835
3.835
3.835
3.835
3.835
3.835
3.835
13.8
13.9
13.8
13.8
13.8
13.8
13.7
13.7
AVERAGE
0.000E+0
4.400E+6
4.653E+6
5.892E+6
6.076E+6
6.315E+6
6.977E+6
7.903E+6
5.277E+6
0.06
0.19
0.31
0.44
0.56
0.69
0.81
0.94
Err:502
-0.1818
-0.1258
0.1102
0.1410
0.1795
0.2793
0.4039
-2.740
-1.572
-0.982
-0.553
-0.190
0.151
0.515
1.020
4.17
Table 6.3.2
Table of specimens that failed during the quenching
QUENCHING CYCLE
1st quench
2nd quench
4th quench
6th quench
SPECIMENS THAT FAILED
Plain Nyeri
Plain Murang'a
Plain Nyeri
Plain Murang'a
25% Murang'a
50% Nyeri
NUMBER OF
SPECIMENS THAT
FAILED
2
2
4
6
1
1
Table 6.3.3
Page 44
Graphs of average MOR against sand concentration after shocking 10 times
Graph of Average MOR agianst percentage concentration
of sand for Nyeri clay
14.0
Average MOR (MN/m2)
12.0
10.0
8.0
6.0
4.0
2.0
0.0
0
5
10
15
20
25
30
35
40
45
50
Percentage concentration of sand
Figure 6.3.4
Graph of Average MOR agianst percentage concentration
of sand for Murang'ai clay
Average MOR (MN/m2)
35.0
30.0
25.0
20.0
15.0
10.0
5.0
0.0
0
5
10
15
20
25
30
35
40
45
50
Percentage concentration of sand
Figure 6.3.5
Page 45
6.4 Values of ceramic constant n
Sample readings were taken from each of the clays. Specimens of Nyeri clay
with 50% sand content and Murang'a clay with 33% sand content were tested
and the results are displayed on table 6.4.1 and 6.4.2 below.
Table showing results for loading Nyeri specimens at a different strain rate
FRACTURE
LOAD
120
120
170
130
125
UNSHOCKED
Nyeri 1:1
NUMBER
1
2
3
4
5
SPAN
3.835
3.835
3.835
3.835
3.835
DIAMETER
13.8
13.9
13.8
13.8
13.7
AVERAGE
MOR
4.457E+6
4.400E+6
6.260E+6
4.787E+6
4.704E+6
4.922E+6
Table 6.4.1
Use of the equation 3.6.13 i.e.
 

1
1

=
ln
=1.5335 ln o

n−1 0.6521
'
 
Eq 3.6.13
Where σ0 : Average MOR at the initial strain rate (5.036MPa)
σ : Average MOR at a different strain rate (4.922MPa)
Substituting the values of σ0 and σ,


1
1
5.036
=
ln
=0.0351
n−1 0.6521
4.922
Eq 6.4.1
Simplifying gives the value of n as:
n=
10.0351
=29.48
0.0351
Eq 6.4.2
Table showing results for loading Murang'a specimens at a different strain rate
UNSHOCKED
FRACTURE
SPECIMEN
LOAD
NUMBER
SPAN
DIAMETER
MOR
Murang'a 3:1
430
1
3.835
13.8
1.590E+7
425
2
3.835
13.8
1.579E+7
460
3
3.835
13.8
1.709E+7
490
4
3.835
13.8
1.812E+7
AVERAGE
1.672E+7
Table 6.4.2
Page 46
Similarly, when the values of σ0 and σ are substituted into equation 3.6.13,
equation 6.4.3 below is obtained.


1
1
17.290
=
ln
=0.05141
n−1 0.6521
16.720
Eq 6.4.3
Simplifying gives:
n=
10.05141
=20.45
0.05141
Eq 6.4.4
Substituting the value of n in equation 3.5.1 gives the equations 6.4.5 &
6.4.6 for Nyeri clay and Murang'a clay respectively.
Nyeri clay:
Murang'a clay:
29.48
 
T N '
N
'=
N
TN
Eq 6.4.5
20.45
 
TN '
N
'=
N
TN
Eq 6.4.6
Page 47
CHAPTER 7 :
7.1
DISCUSSION
Modified extruder
Attaching the extruder to a lathe machine improved the extrusion work.
Below are some of the advantages observed,
1. The high torque of the lathe allowed continuous and steady rotation
of the plug mill (refer to figure 4.4.1) through all kinds of loading.
As a result, the clay required little water content to make it plastic
enough to be extruded. This reduced the porosity of the final
specimens and the degree of shrinkage when drying.
2. The lathe rotated at a constant speed thus it extruded the clay at
an approximately constant rate. This resulted in uniformly compacted
specimens.
3. The clay was sufficiently de-aired (kneaded) as it was given enough
time to get compacted through the de-airing chamber (refer to figure
4.4.1). Therefore, the quality of samples produced was increased.
4. Extrusion was continuous since there was little need to pause and
rest as it was for past researchers. The process was less tedious
and less time-consuming, thus the effectiveness and efficiency of
processing was greatly improved.
The above points (1-3) were proved true by the reduced number of
specimens that broke during firing. Porosity and uneven compaction are
responsible for cracking and breaking of specimens during firing. These
lead to uneven expansion that result in internal stresses that ultimately
cause the breaking of a specimen without application of external forces.
Specimens in the previous years broke in large numbers before the actual
testing. The modified extruder made good specimens of which only five in
four hundred samples broke.
7.2
Effect of sand addition to mechanical strength
When sand was added to clay, it caused an increase in the strength
of
all the specimens. The strength of the clay then dropped when the
sand content went beyond 25%. Plain Murang'a clay specimens experienced
a drop in strength with increase in the percentage sand concentration. The
graphs in figure 7.2.1 & 7.2.2 below show this behavior.
Page 48
Graph of average MOR against the percentage sand content for Nyeri and Murang'a
clay specimens when shocked through different temperature differences
Graph of average MOR against
percentage sand added for Nyeri clay
Average MOR (MN/m2)
14.000
12.000
10.000
8.000
6.000
4.000
2.000
0.000
0
10
20
30
40
50
60
Percentage sand added
Figure 7.2.1
Graph of average MOR against
percentage sand added for Murang'a clay
Average MOR (MN/m2)
35.000
30.000
25.000
20.000
15.000
10.000
5.000
0.000
0
10
20
30
40
50
60
Percentage sand added
Figure 7.2.2
Page 49
The changes in strength are believed to have occured due to a
number of effects. The first is the change in strength of the specimens
due to the formation of a different compound when the clay reacts with
the sand. This compound is believed to be mullite / porcelainite which is
is known to have high strength and high thermo-shock resistance.
In section 1.8, reaction 1.8.2 showed that at 975°C clay turns into
sillimanite. Further rise in temperature initiates the formation of mullite which
is a reaction between the sillimanite and silica already present in the clay.
i.e.
Al2 O 3⋅SiO 2 s SiO 2 s ⇒ Al 2 O3⋅2SiO2  s
The absence of
Reaction 1.8.1
enough silica prevents complete conversion of
sillimanite to mullite in the plain clays. Addition of sand provides the
required silica thus enabling complete conversion of sillimanite to mullite to
take place. Mullite is a commercially used refractory material with high
strength and high thermo-shock resistance. It is stronger than plain Nyeri
clay but weaker than plain Murang'a clay. Its formation causes an increase
in strength in Nyeri clay, but a decrease in the strength of Murang'a clay.
This is attributed to the differences in element compositions in the two
clays. Figure 7.2.1 & 7.2.2 show this variation.
The compound (mullite) formed has a high thermo-shock resistance.
When quenched, plain Murang'a clay drops in strength drastically. However,
increase in percentage of sand content results in a greater amount of the
compound which in turn makes the specimens stronger even after
quenching.
The formation of a new compound is proved by the behaviour of the
specimens. All the specimens except plain Murang'a clay show an increase
in strength up to 25% sand content, and then a drop in strength
afterwards. Chemical reactions are known to use up reactants in fixed
proportions. The reaction stops when one reactant is exhausted; regardless
of the quantity of the other reactants. In this situation, the sand reacted
with the clay and when all the sillimanite had been used up, further
addition of sand beyond the fixed percentage (25%) could not result in the
formation of the compound. The strength of the specimens increases with
Page 50
increase in sand until it reaches a fixed point where it stops increasing.
From the graphs, the maximum percentage of sand required to form the
new compound is 25% (or less).
The second is weakening of the specimens through introduction of
discontinuities in the clay. It was seen that the specimens' strength dropped
when sand was added beyond 25%. Sand's particles are much larger in
size than clay's therefore it creates a greater concentration of discontinuities
in the specimens when increased in the specimens. This is evident in the
difference in surface texture of the specimens.
Figure 7.2.3 Pictures showing the difference in surface texture with
increase in sand content
Specimens made from plain clay had very smooth surfaces while
those made from clay mixed with sand, especially that of clay with 50%
sand content, had very rough surfaces, even though the same extrusion
process and machine was used. Figure 7.2.3 above show these differences.
The more the sand in the specimens, the more the discontinuities. These
discontinuities act as points of crack initiation for new cracks, and a series
of weak points through which cracks propagate. Therefore, less energy is
required to initiate and propagate potentially fatal cracks resulting in weaker
specimens.
The third is that a greater concentration of sand results in a mixture
with less clay. Since clay is what holds the specimens 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 specimens.
Page 51
Research by Mbithi and Florida[8] differs with this data. Addition of
sand to a concentration of 25% led to an increase in the strength of
Murang'a clay and a decrease in that from Nyeri. This is believed to have
been due to the extra sand that went into their specimens because of the
large pore sized sieves they used (1mm pore size). Results from
Kipng'etich and Thure[10] show that addition of 50% sand decreased the
strength in Murang'a clay and increased that of Nyeri clay. The data
obtained from tallies with our data.
Table showing variation of average MOR with addition of sand for past
researchers
Mbithi and Florida
CLAY
PLAIN CLAY
MURANG'A CLAY
16.05
23.34
45.41
Mbithi and Florida
NYERI CLAY
9.64
4.95
-48.6
DATA FROM:
Kipng'etich and Thure MURANG'A CLAY
Kipng'etich and Thure
NYERI CLAY
50% SAND
ADDED
PERCENTAGE
INCREASE IN
STRENGTH
25% SAND
ADDED
18.26
17.26
-5.48
9.43
19.7
108.9
Table 7.2.3
Graphs of MOR against percentage sand added for Murang'a clay
Graph of average MOR against
sand concentration for Murang'a clay
25.0
Average MOR
20.0
15.0
10.0
5.0
0.0
0
5
10
15
20
25
30
35
40
45
50
Percentage sand concentration
Figure
7.2.4
Page 52
Graphs of MOR against percentage sand added for Nyeri clay
Graph of average MOR against
sand concentration for Nyeri clay
25.0
Average MOR
20.0
15.0
10.0
5.0
0.0
0
5
10
15
20
25
30
35
40
45
50
Percentage sand concentration
Figure 7.2.5
7.3
Quenching / thermal-shock
When quenched, the plain clays dropped drastically in strength
especially plain Murang'a clay (from 28.9MPa to 1.1MPa). The trend of the
average MOR against the shocking temperature of all the specimens with
sand more or less alike. Specimens with progressively higher sand content
however retained their strength to a large extent, giving gradually gentler
slopes across the temperatures differences they were shocked through as
their sand content was increased. Murang'a clay specimens with 25%, 33%
and 50% sand in them had progressively lower drops in strength, with
those with 33% sand in clay giving an almost straight line.
The graphs (figure 6.1.18 and 6.1.19) below shows the behaviour.
Page 53
Graph of the MOR against the shocking temperature difference after one quench
Graph of MOR against shocking temperature for Nyeri clay
30.0
25.0
MOR
20.0
15.0
10.0
5.0
0.0
0
100
200
300
400
500
600
700
800
shocking temperature
Figure 6.1.17
Graph of the MOR against the shocking temperature difference after one quench
Graph of MOR against shocking temperature for Murang'a clay
30.0
25.0
MOR
20.0
15.0
10.0
5.0
0.0
0
100
200
300
400
500
600
700
800
Shocking temperature
Figure 6.1.18
Page 54
Plain clay specimen had the highest drop in strength due to their
high coefficient of thermal expansion. Specimens with sand experienced a
lower drop in strength across the temperature they were shocked through
due to the formation of the compound mullite. All the specimens had a
comparatively similar trend due to the presence of mullite in all of them.
Specimens with more than 25% sand content had lower values of MOR
but the trend was still similar to that with 25% sand content. They
however had gentler slopes thus suggesting that a higher percentage of
sand aided their thermo-shock resistance. This is because the sand
contains silica which has a very low coefficient of thermal expansion.
Addition of sand to the clay made the resultant mixture have a lower
coefficient of thermal expansion.
Values obtained by Mbithi and Florida[8], and Kipng'etich and Thure[10]
agree with this data. Mbithi and Florida[8] added 25% sand to their clay
specimens. These experienced a steeper drop in strength than those made
by Kipng'etich and Thure[10 having 50% sand content. Figure 7.33 & 7.34
show this.
Graph of average MOR against shocking temperature for specimens with
25% and 50% sand for Nyeri clay specimens
Graph of average MOR against shocking
Temperature difference for Nyeri clay specimen
25.0
Average MOR (MN/m2)
20.0
15.0
10.0
5.0
0.0
0
100
200
300
400
500
600
700
800
Shocking temperature difference (C)
Figure 7.3.3
Page 55
Graph of average MOR against shocking temperature for specimens with 25% and
50% sand for Murang'a clay specimens
Graph of average MOR against shocking
temperature difference for Murang'a clay specimens
Average MOR (MN/m2)
25.0
20.0
15.0
10.0
5.0
0.0
0
100
200
300
400
500
600
700
800
Shocking temperature difference
Figure 7.3.4
When the mechanical strength is considered, Murang'a (50% sand
added) and Nyeri (50% sand added) gave the lowest strengths at all
shocking temperatures. Clay with 25% sand had the highest strength in
both clays. The table below shows the specimens with the highest and
lowest mechanical strength.
Table showing highest and lowest average MOR for Nyeri clay specimens
NYERI CLAY
SHOCKING BETWEEN
UNSHOCKED
400°C-25°C
600-C-25°C
800°C-25°C
AVERAGE MOR
HIGHEST
(MN/m2)
25% sand
11.5
25% sand
9.7
25% sand
7.5
25% sand
8.5
AVERAGE MOR
LOWEST
(MN/m2)
50% sand
5.5
50% sand
5.5
50% sand
4
50% sand
3.4
Table 7.3.1
Page 56
Table showing highest and lowest average MOR for Nyeri clay specimens
MURANG'A CLAY
SHOCKING BETWEEN
UNSHOCKED
400°C-25°C
600-C-25°C
800°C-25°C
AVERAGE MOR
Plain clay
25.5
25% sand
16.2
25% sand
14
25% sand
11.8
AVERAGE MOR
50% sand
10
33% sand
7
Plain clay
4
Plain clay
1
Table 7.3.2
7.4
Weibull modulus
As stated earlier (in section 3.3), the Weibull modulus is a measure of the
scatter and brittleness in a set of strength measurements. Materials such as
metals have high values of Weibull modulus due to little scatter in their values of
strength. The Weibull modulus for the specimens lay within the expected range
for ceramics i.e. (3-24). The trend of variation of the modulus calculated and the
percentage sand is surprisingly similar to that of average MOR with sand obtained
earlier on (Figure 7.2.1 and 7.2.2). The values show a rise in the Weibull
modulus for all the specimen with sand addition to 25%, then subsequent drop
for values beyond that. It implies that the specimens with high modulus values
have high strength and low scatter and vice versa. The high modulus observed
at 25% sand content suggests a lower scatter and high strength.
Graphs of Weibull modulus against percentage sand content for Nyeri clay
Graph of Weibull modulus against
percentage sand added for Nyeri clay
25.00
Weibull modulus
20.00
15.00
10.00
5.00
0.00
0
5
10
15
20
25
30
35
40
45
50
Percentage sand added
Figure 6.2.1
Page 57
Graphs of Weibull modulus against percentage sand content for Murang'a clay
Graph of weibull modulus m against
percentage sand content for murang'a clay
30.00
Weibull modulus
25.00
20.00
15.00
10.00
5.00
0.00
0
5
10
15
20
25
30
35
40
45
50
Percentage sand added
Figure 6.2.2
This is believed to have occurred due to the formation of the
compound stated earlier on (section 7.2) when clay reacts with sand. The
compound formed is a uniform material with a uniform internal structure.
This makes it to fracture at a relatively constant stress with little scatter
resulting in a high modulus value. Further addition of sand beyond 25%
introduces discontinuities in the compound making it to fracture at stresses
that are not dependent on the strength of the material but on the scatter
of discontinuities at the site of stress application. This increases the
variation in strength which in turn decreases the value of the Weibull
modulus.
7.5
Thermal fatigue
Table 7.5.1 is a list of the specimen that failed before the end of
the ten cycles of quenching. (Failing was considered as the breaking of
the specimen.)
Table of specimen that failed when quenching repeatedly
QUENCHING CYCLE
1st quench
2nd quench
4th quench
6th quench
SPECIMEN THAT FAILED
Plain Nyeri
Plain Murang'a
Plain Nyeri
Plain Murang'a
25% Murang'a
50% Nyeri
NUMBER OF
SPECIMEN THAT
FAILED
2
2
4
6
1
1
Table 7.5.1
page 58
The plain clay specimens did not withstand more than three
quenches. Specimens with sand added to 25% dropped by 42% and 75%
in strength. (as shown in the table 7.5.2) Nyeri clay with the highest
concentration of sand survived shocking for the greatest number of cycles.
Generally, Murang'a clay dropped the most in strength. This means that
Murang'a clay has little thermo-fatigue resistance while Nyeri had the most.
Some plain Nyeri specimens survived the ten shocks while all Murang'a
specimen broke on after only two cycles of quenching.
Addition of sand increased the thermo-fatigue resistance and enabled
both clays to survive the majority of the shocks. Nyeri clay with 50% sand
actually showed an increase in strength when compared to its unquenched
state. The quenching did not weaken it at all but had the opposite effect.
Table of the average MOR and the difference in strength after shocking
ten times
NYERI
MURANG'A
PLAIN CLAY
25% SAND ADDED
33% SAND ADDED
50% SAND ADDED
AVERAGE MOR
SHOCKED TEN TIMES PERCENTAGE DROP
UNSHOCKED BETWEEN 500°C-25°C
IN STRENGTH
7.219
0.00
100%
11.440
6.658
42%
7.749
5.047
35%
5.036
7.727
-53%
PLAIN CLAY
25% SAND ADDED
33% SAND ADDED
50% SAND ADDED
SHOCKED TEN TIMES PERCENTAGE DROP
IN STRENGTH
UNSHOCKED BETWEEN 500°C-25°C
28.900
1.393
95%
17.290
4.373
75%
13.130
8.754
33%
9.785
5.277
46%
Table 7.5.2
7.6
Lifetime of ceramics
n
 
N 1 T 2
=
Manipulation of the equation 3.5.1
N 2 T 1
n
n
N 1  T 1=N 2  T 2 =K
gives:
Eq 7.6.1
Page 59
where N: number of thermal cycles to failure
ΔT: temperature difference
n: ceramic constant
One may use equation 7.6.1 to calculate the lifetime of a particular
ceramic once the constant n is known. For this project, the value of n for
Nyeri clay will be assumed to be that calculated from Nyeri clay with 50%
sand i.e. n=29.48. Similarly, that for Murang'a clay be that obtained from
Murang'a clay with 33% sand i.e.
n=20.45. These high values of n that
imply a low rate of crack propagation and a low rate of strength
reduction.
The specimen that failed after repeated quenching are shown below.
(Table 7.5.1) The lifetime of those specimens that failed completely can be
obtained.
Table of specimen that failed when quenching repeatedly
QUENCHING CYCLE
1st quench
2nd quench
4th quench
6th quench
SPECIMEN THAT FAILED
Plain Nyeri
Plain Murang'a
Plain Nyeri
Plain Murang'a
25% Murang'a
50% Nyeri
NUMBER OF
SPECIMEN THAT
FAILED
2
2
4
6
1
1
Table 7.5.1
Two of the eight plain Murang'a clay specimens failed after the first
quenching cycle and the remaining six failed on the second cycle.
2
6
Therefore, they can be said to have failed after N=1⋅ 2⋅ =1.75 cycles
8
8
of shocking across a temperature difference of ΔT= 500°C – 25°C= 475°C.
 
Plain Murang'a clay will have: N 1  T n1=1.75×475 20.45 =9.5813×10 54
This value i.e. 9.5813 x 1054
Eq 7.6.2
can be used to calculate the lifetime in
cycles of shocking at other temperatures.
For example, the number of quenching cycles plain Murang'a clay can
Page 60
withstand when the temperature difference is 200°C will be obtained as:
20.45
N×200
54
=9.5813×10
Eq 7.6.3
54
therefore
N=
9.5813×10
=84.2091×106
20.45
200
Eq 7.6.4
This states that repeated shocking through a temperature difference of
200°C will lead to failure of the ceramic after no more than 84.21x106
cycles.
It was not possible to obtain the lifetimes of the other specimen since
they did not fail completely after shocking ten times.
7.7
Possible sources of error
The data obtained was valuably reliable, though there are possible
errors that might have occurred during the course of the project. Any
errors are expected to affect the results by no more than 10%. Some of
these could have been due to:
Differences in the surface texture of the specimens was observed.
Specimens with no sand had very smooth surfaces while those with the
highest percentage of sand were the roughest. This variation is undesirable
since it led to fracture occuring at stresses different from those they
should have. A rough surface provided a larger initial crack size than a
smooth surface. Cracks were therefore initiated differently. All specimens
should have the same surface for similar crack initiation conditions.
Specimens made from pure clay formed long distinct cracks that ran
axially along their length. These cracks weakened them greatly and made
then fracture axially during quenching and three point testing. The cracks
are believed to come from the non-uniform contraction that is observed in
these pure clay specimens specifically. The contractions that are greater on
the surface than in the body of the specimen create forces that caused
them to split at their centre. Specimens made from clay with sand added
showed reduced shrinkage. Their diameters did not change as much as
Page 61
pure clay did therefore contraction forces were weak leading to no
cracking.
The water left in the specimens after quenching creates a chemical
environment around the crack front resulting in different readings from those
that would be taken from dry samples. This affected the specimens that
had been shocked.
Page 62
CHAPTER 8 :
CONCLUSIONS
The conclusions below were made:
•
Modification of the equipment used was greatly beneficial. It resulted
in well made specimen that gave relatively consistent results.
•
Plain clay from Murang'a was found to be stronger than that from
Nyeri before any quenching was done (for unshocked specimens).
This is shown by the graphs represented by figures 6.1.3 and 6.1.4
This agrees with past researchers' findings.
•
Addition of sand to clay results in the formation of a new compound,
believed to be mullite / porcelainite. This causes Nyeri clay to
increase in strength and Murang'a clay to decrease in strength.
Addition of sand beyond 25%causes a decline in strength for both
clays. This is explained in article 7.2.
•
The higher the sand content, the higher the thermo-shock resistance
of both clays. However, the higher the sand concentration, the lower
the mechanical strength of the clay (beyond a concentration of 33%
for both clays.) A compromise has to be reached between mechanical
strength and thermo-shock resistance for best results. This is
explained in article 7.3.
•
The higher the concentration of sand, the higher the thermal fatigue
resistance of the clay as explained in article 7.5.
•
High values of ceramic constant, n for both clays imply a low rate
of crack propagation and a low rate of strength reduction therefore
longer life, as discussed in article 7.6.
Page 63
CHAPTER 9 : CHALLENGES AND RECOMMENDATIONS
Challenges
9.1
The project came along with many challenges. They include:
•
Non-functioning equipment especially the furnaces in the departmental
workshop causing inconveniences in firing and thermal shocking.
•
Out dated equipment that gave unreliable readings such as weighing
machines.
•
Lack of equipment required for testing of specimen. i.e. universal
testing machine which rendered the testing process difficult.
•
Travelling to and from KIRDI posed a great challenge since much
time was lost on the roads.
•
Late funding of the project by the university which caused delays in
material collection and subsequent preparations.
•
Bad weather (rainy season) caused delays in the drying of clay.
•
The lathe machines were not well maintained resulting in failure of
two machines after limited and valuable time had been spent setting
them up for operation.
9.2
Recommendations
Below are some recommendations that would enable achievement of
desired objectives:
•
Improvement of specimen production methods such that a uniform
surface finish is obtained would remove variation due to differing
surface texture.
•
Development of better quenching apparatus that reduced the time
spent moving the specimens from the hot to cold environment.
•
Repair of facilities in the workshop, especially the furnaces and the
universal testing machine, which were very vital in this project,
otherwise this project would become a complete impossibility in future.
•
The department should establish better working relationships with other
institutions with similar research objectives especially KIRDI.
•
Research into heat treatment methods of increasing thermo-shock
Page 64
resistance.
•
Studying the behavior of thermo-shock over a narrower range of sand
content addition especially between 0% to 25% sand content.
•
Compare the strength and thermo-shock properties of clay with 25%
sand in them with mullite to verify the data obtained.
Page 65
References
1. Norman E. Dowling, “MECHANICAL BEHAVIOUR OF MATERIALS” (2nd
Edition
-Prentice Hall 1963*)
2. Serope Kalpakjian “MANUFACTURING PROCESSES FOR ENGINEERING
MATERIALS” (Addison Wesley publishing company. 1954*)
3. John B. Watchman,“MECHANICAL PROPERTIES OF CERAMICS” (John
Wiley and Sons Inc. 1982*)
4. P.K. Panda, T.S. Kannan, J. Duboisb, C. Olagnonb, G. Fantozzib“THERMAL
SHOCK AND THERMAL FATIGUE STUDY OF CERAMIC MATERIALS ON A
NEWLY DEVELOPED ASCENDING THERMAL SHOCK TEST EQUIPMENT”
(Materials Science Division, National Aerospace Laboratories, Bangalore,India
2002)
5. Jin Kim, “THERMAL SHOCK RESISTANCE AND THERMAL EXPANSION
BEHAVIOR OF AL2TIO5 CERAMICS PREPARED FROM ELECTROFUSED
POWDERS” (Institute for processing and application of inorganic materials
2000)
6. Chris DiRuggiero,“ADVANCED CERAMICS EXCEL IN HIGH-SPEED METAL
FORMING TOOLS” (2000)
7. N. Kamiya & Kamigaito,“PREDICTION OF THERMAL FATIGUE LIFE OF
CERAMICS” (Toyota Central Research and Development Laboratories Inc
1979)
8. F. M. Mbithi & S. N. Florida “THERMAL SHOCK AND LIFETIME
PROPERTIES OF CERAMIC MATERIALS” (UON, B.Sc. Mechanical
engineering, 2009)
9. Ernst Rosenthal, “POTTERY AND CERAMICS” (Penguin books ,1954)
10. B. W. Kipng'etich & P. O. Thure “THERMAL SHOCK AND LIFETIME
PROPERTIES OF CERAMIC MATERIALS” (UON B.Sc. Mechanical
engineering, 2006)
Page 66
Photographs
Clay collection site in Nyeri district
Site of clay collection in Maragua
Shocking process (removing specimens from furnace)
Page 67
Shocking process (dipping specimens into water)
Page 68
APPENDIX
GRAPHS USED TO DETERMINE THE WEIBULL MODULUS
Unshocked Nyeri clay
Graph of ln (ln (1/1-Pf)) against ln()σ/σ
for 25% specimen
2.000
1.000
f(x) = 8.5x - 0.48
0.000
-1.000
-2.000
-3.000
-4.000
-0.3000 -0.2000 -0.1000 0.0000 0.1000 0.2000
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for unshocked plain clay
σ/σ
2.000
1.000
f(x) = 20x 0.000
-1.000
-2.000
-3.000
-4.000
-0.1000 -0.0500
0.0000
0.0500
0.1000
ln (/f)
σ/σ
ln (/f)
Graph of ln (ln (1/1-Pf)) against ln
for 33% clay
σ/σ
Graph of ln (ln (1/1-Pf)) against ln
for 50% clay
2.000
f(x) = 11.12x - 0.5
1.000
0.000
-1.000
-2.000
-3.000
-4.000
-0.2000 -0.1000 0.0000 0.1000 0.2000 0.3000
2.000
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
0.54
σ/σ
f(x) = 6.9x - 0.48
0.000
-2.000
-4.000
-0.4000
-0.2000
0.0000
ln (/f)
ln (/f)
0.2000
0.4000
σ/σ
Unshocked Murang'a clay
Graph of ln (ln (1/1-Pf)) against ln
for plain clay
2.000
2.000
f(x) = 6.01x - 0.44
1.000
0.000
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
1.000
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 25% clay
σ/σ
-1.000
-2.000
-3.000
-3.000
σ/σ
0.0500
0.1000
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 50% clay
2.000
f(x) = 12.91x - 0.5
1.000
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
1.000
-2.000
σ/σ
ln (/f)
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 33% clay
2.000
-1.000
-4.000
-0.1500 -0.1000 -0.0500 0.0000
-4.000
-0.4000 -0.2000 0.0000 0.2000 0.4000 0.6000
ln (/f)
f(x) = 19.78x - 0.52
0.000
0.000
-1.000
-2.000
-3.000
-4.000
-0.2000
-0.1000
0.0000
σ/σ
ln (/f)
0.1000
0.2000
0.000
f(x) = 19.25x - 0.52
-1.000
-2.000
-3.000
-4.000
-0.1500 -0.1000 -0.0500 0.0000
ln (/f)
σ/σ
0.0500
0.1000
GRAPHS USED TO DETERMINE THE WEIBULL MODULUS
Nyeri Specimen shocked from 400°C-25°C
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 25% clay
2.000
f(x) = 3.86x - 0.39
1.000
0.000
-1.000
-2.000
-3.000
-4.000
-0.6000-0.4000-0.2000 0.0000 0.2000 0.4000 0.6000
2.000
1.000
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for plain specimen
f(x) = 15.49x - 0.51
0.000
-1.000
-2.000
-3.000
-4.000
-0.2000
-0.1000
ln (/f)
σ/σ
1.000
0.000
-1.000
-2.000
-3.000
-4.000
-0.2000
-0.1000
0.2000
2.000
f(x) = 13.3x - 0.51
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
1.000
0.1000
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 50% specimen
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 33% clay
2.000
0.0000
ln (/f)σ/σ
0.0000
0.1000
f(x) = 5.5x - 0.44
0.000
-1.000
-2.000
-3.000
-4.000
-0.6000 -0.4000 -0.2000 0.0000
0.2000
ln (/f)σ/σ
0.2000
0.4000
ln (/f)
σ/σ
Murang'a Specimen shocked from 400°C-25°C
Graph of ln (ln (1/1-Pf)) against ln
for plain specimen
σ/σ
Graph of ln (ln (1/1-Pf)) against ln
for 25% specimen
2.000
0.000
2.000
f(x) = 3.29x - 0.4
1.000
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
1.000
-1.000
-2.000
-3.000
-4.000
-1.0000
-0.5000
0.0000
f(x) = 27.61x - 0.52
0.000
-1.000
-2.000
-3.000
-4.000
-0.1000
0.5000
-0.0500
0.0500
0.1000
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 50% specimen
σ/σ
2.000
1.000
- 0.46
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
Graph of ln (ln (1/1-Pf)) against ln
for 33% specimen
0.0000
ln (/f)
0.0000
ln (/f) σ/σ
ln (/f)
2.000
f(x) = 6.63x
1.000
0.000
-1.000
-2.000
-3.000
-4.000
-0.4000
-0.2000
σ/σ
σ/σ
0.2000
0.4000
f(x) = 11.43x - 0.53
0.000
-1.000
-2.000
-3.000
-4.000
-0.2000
-0.1000
0.0000
ln (/f)
σ/σ
0.1000
0.2000
GRAPHS USED TO DETERMINE THE WEIBULL MODULUS
Nyeri Specimen shocked from 600°C-25°C
Graph of ln (ln (1/1-Pf)) against ln
for 25% specimen
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for plain specimen
f(x) = 3.7x - 0.39
0.000
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
2.000
-2.000
-4.000
-1.0000
-0.5000
0.0000
0.5000
ln (/f)
σ/σ
2.000
f(x) = 12.21x
1.000
0.000
-1.000
-2.000
-3.000
-4.000
-0.2000
-0.1000
2.000
1.000
0.000
-1.000
-2.000
-3.000
-0.2000
0.0000
0.1000
0.2000
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 50% specimen
f(x) = 7.73x - 0.47
-4.000
-0.4000
0.0000
σ/σ
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
1.000
- 0.52
ln (/f)
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for plain specimen
2.000
σ/σ
0.2000
f(x) = 6.79x - 0.46
0.000
-1.000
-2.000
-3.000
-4.000
-0.4000
0.4000
σ/σ
ln (/f)
-0.2000
0.0000
0.2000
0.4000
ln (/f)
σ/σ
Murang'a Specimen shocked from 600°C-25°C
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for plain specimen
1.500
2.000
f(x) = 3.88x - 1.23
1.000
ln (ln (1/1-Pf))
1.000
ln (ln (1/1-Pf))
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 25% specimen
0.500
0.000
-0.500
-1.000
0.0000
0.2000
0.4000
0.6000
0.8000
f(x) = 17.84x - 0.51
0.000
-1.000
-2.000
-3.000
-4.000
-0.2000
-0.1000
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 33% specimen
Graph of ln (ln (1/1-Pf)) against lnσ/σ
for 50% specimen
2.000
1.000
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
0.000
2.000
f(x) = 9.66x - 0.49
-1.000
-2.000
-3.000
-4.000
-0.3000 -0.2000 -0.1000 0.0000
σ/σ
ln (/f)
0.1000
0.2000
0.1000
ln (/f)
σ/σ
ln (/f)
σ/σ
1.000
0.0000
f(x) = 15.58x - 0.52
0.000
-1.000
-2.000
-3.000
-4.000
-0.2000
-0.1000
0.0000
σ/σ
ln (/f)
0.1000
0.2000
GRAPHS USED TO DETERMINE THE WEIBULL MODULUS
Nyeri Specimen shocked from 800°C-25°C
2.000
1.000
0.000
f(x) = 2.52x - 0.42
-1.000
-2.000
-3.000
-4.000
-1.5000
-1.0000
-0.5000
Graph of ln (ln (1/1-Pf)) against ln
for 25% specimen
2.000
1.000
0.0000
-2.000
-3.000
-4.000
-0.2000 -0.1000 0.0000
0.5000
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
1.000
0.000
-2.000
-3.000
0.0000
0.3000
Graph of ln (ln (1/1-Pf)) against lnσ/σ
for 50% specimen
2.000
-1.000
-0.2000
0.2000
σ/σ
f(x) = 7.48x - 0.47
-4.000
-0.4000
0.1000
ln (/f)
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 33% specimen
1.000
f(x) = 10.76x - 0.61
-1.000
ln (/f)
σ/σ
2.000
σ/σ
0.000
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for plain specimen
0.2000
0.4000
f(x) = 6.25x - 0.46
0.000
-1.000
-2.000
-3.000
-4.000
-0.6000 -0.4000 -0.2000 0.0000
σ/σ
ln (/f)
ln (/f) σ/σ
0.2000
0.4000
Murang'a Specimen shocked from 400°C-25°C
Graph of ln (ln (1/1-Pf)) against ln
for plain specimen
σ/σ
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 25% specimen
1.200
0.800
2.000
1.000
f(x) = 1.51x - 1.1
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
1.000
0.600
0.400
0.200
0.000
0.9000
1.0000
1.1000
1.2000
1.3000
f(x) = 6.97x - 0.46
0.000
-1.000
-2.000
-3.000
-4.000
-0.4000
1.4000
-0.2000
σ/σ
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 33% specimen
2.000
2.000
f(x) = 7.36x - 0.45
1.000
0.000
-1.000
-2.000
-3.000
-4.000
-0.4000
-0.2000
0.0000
ln (/f)σ/σ
0.2000
0.4000
Graph of ln (ln (1/1-Pf)) against lnσ/σ
50% specimen
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
1.000
0.0000
σ/σ
ln (/f)
ln (/f)
0.2000
0.4000
f(x) = 7.11x - 0.46
0.000
-1.000
-2.000
-3.000
-4.000
-0.4000
-0.2000
0.0000
ln (/f)σ/σ
0.2000
0.4000
GRAPHS USED TO DETERMINE THE WEIBULL MODULUS
Nyeri Specimen shocked from 500°C-25°C ten times
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 25% specimen
ln (ln (1/1-Pf))
2.000
1.000
f(x) = 2.89x - 0.51
0.000
-1.000
σ/σ
-2.000
-0.4000 -0.2000 0.0000
0.2000
0.4000
0.6000
ln (/f)
Graph of ln (ln (1/1-Pf)) against ln
for 50% specimen
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 33% specimen
2.000
2.000
1.000
1.000
f(x) = 9.26x - 0.48
0.000
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
σ/σ σ/σ
-1.000
-2.000
σ/σ
-3.000
-0.3000 -0.2000 -0.1000 0.0000
σ/σ
0.1000
0.000
f(x) = 17.09x - 0.51
-1.000
-2.000
-3.000
-0.2000
0.2000
ln (/f)
σ/σ
-0.1000
0.0000
0.1000
ln (/f)
Murang'a Specimen shocked from 500°C-25°C ten times
1.200
1.000
f(x) = 1.54x - 1.34
0.800
0.600
0.400
σ/σ
0.200
0.000
1.1000 1.2000 1.3000 1.4000
Graph of ln (ln (1/1-Pf)) against ln
for 25% specimen
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for plain specimen
1.5000
1.6000
1.000
f(x) = 6.8x - 0.44
0.500
0.000
-0.500
-1.000
-1.500
σ/σ
-2.000
-2.500
-0.3000 -0.2000 -0.1000
ln (/f)
2.000
f(x) = 12.85x - 0.5
1.000
0.000
-1.000
-2.000
-3.000
-0.2000
σ/σ
-0.1000
0.0000
ln (/f)
0.2000
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 50% specimen
ln (ln (1/1-Pf))
ln (ln (1/1-Pf))
1.000
0.1000
ln (/f)
Graph of ln (ln (1/1-Pf)) against ln σ/σ
for 33% specimen
2.000
0.0000
σ/σ
0.1000
0.2000
f(x) = 4.17x - 0.71
0.000
-1.000
σ/σ
-2.000
-0.4000 -0.2000 0.0000
ln (/f)
0.2000
0.4000
0.6000