1 Introduction
2 Objectives
3 Experiment Programs
4 Apparatus for the Bending Test
5 Splitting Tensile Test Setup
6 Three Point Bending Test Setup
7 Results of the Three Point Bending Tests
LVDT and CMOD data | LVDT data | CMOD data | ||||||
---|---|---|---|---|---|---|---|---|
Specimen | E (GPa) | G
FM
(N/m) | A (N mm2) | G
F
(N/m) | G
f
(N/m) | A (N mm2) | G
F
(N/m) | G
f
(N/m) |
Stroke | ||||||||
T5-1 | 38.87 | 122.29 | 353 | 154.84 | 25.83 | 730 | 173 | 26.05 |
T5-2 | 35.34 | 133.35 | 419 | 171.25 | 32.3 | 787 | 184.14 | 32.15 |
T20-1 | 37.41 | 127.92 | 315 | 157 | 71.23 | 626 | 168.35 | 71.08 |
T20-2 | 42.67 | 175.46 | 530 | 223.07 | 153.64 | 999 | 240.09 | 153.17 |
T30-1 | 34.55 | 185.99 | 839 | 261.82 | 73.7 | 1448 | 279.58 | 72.05 |
T30-2 | 35.7 | 132.29 | 384 | 169.03 | 75.58 | 811 | 184.68 | 75.36 |
Avg. | 37.42 | 146.22 | 473 | 189.50 | 72.05 | 900 | 204.97 | 71.64 |
CMOD | ||||||||
T5-3 | 30.6 | 128.17 | 289 | 156.33 | 57.22 | 648 | 169.99 | 57.14 |
T20-3 | 36.42 | 155.78 | 509 | 202.83 | 71.94 | 1074 | 221.61 | 71.71 |
T20-4 | 29.14 | 143.19 | 648 | 202.23 | 52.34 | 1200 | 220.65 | 51.65 |
T28-1 | 31.32 | 194.87 | 497 | 239.44 | 123.89 | 864 | 250.64 | 122.34 |
T30-3 | 38.11 | 103.8 | 198 | 123.17 | 61 | 446 | 132.56 | 60.92 |
Avg. | 33.12 | 145.16 | 428 | 184.80 | 73.28 | 836 | 199.09 | 72.75 |
8 Obtained Fracture Energy of Concrete
9 Sensitivity Study on the Far Tail Constant (A)
10 Sensitivity Study on Different Loading Conditions
11 Sensitivity Study on the End Points for the Three Point Bending Tests
Specimen | End point (mm) | G
FM
(N/m) | A (N mm2) | G
F
(N/m) | G
f
(N/m) |
---|---|---|---|---|---|
T20-4 | 2 | 143.19 | 648 | 202.23 | 52.34 |
T20-4 | 3 | 173.52 | 903 | 227.74 | 56.84 |
T20-4 | 4 | 187.38 | 951 | 230.05 | 57.18 |
T20-4 | 5 | 200.49 | 1092 | 239.7 | 58.28 |
12 Proposed Bilinear Stress–Crack Opening Displacement Curves
13 Conclusions
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The average true fracture energies are 189 and 185 N/m from the stroke control and the CMOD control, respectively, after considering the possible sources of energy dissipation. The final forms of the bilinear stress–crack opening curves of concrete from both loading rates were also very similar.
-
It was found that the fracture energy could be sensitive to the far tail constant (A) value and to the selection of the end points used to calculate the true fracture energy. When CMOD data was used to calculate A, a maximum increase of 11 % of the true fracture energy (G F ) was found. However, the size effect fracture energy (G f ) did not change with the value of A.
-
It was also observed that an end point of 5 mm yields an 18 % larger true fracture energy (G F ) than that of the 2 mm end point. Therefore, appropriate selection of the end point of the test should be considered along with the maximum aggregate size in order to obtain the true fracture energies. However, the size effect fracture energy (G f ) was not influenced by the selection of the end point.
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It is concluded that the loading rate is not a significant factor to control the fracture energy of the concrete as well as the final forms of the bilinear softening curves.
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The overall shape of the bilinear stress crack opening curve estimated by the CEB-FIP model is similar to the experimentally obtained bilinear curves. However, it tends to exhibit smaller tail fracture energy (G tail ) and a larger size effect fracture energy (G f ) when compared to the experimental ones.
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In this study, a new bilinear curve is proposed based upon both the CEB-FIP recommended bilinear curves and experimentally obtained bilinear curves. The proposed bilinear curve in this study fits the experimental bilinear curves well.
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The accuracy of the size effect fracture energy (G f ) determined using one size of notched beam and one size of cylinder has recently been brought into question. As a further study, a comparison of the size effect fracture energy (G f ) as determined using multiple sizes of notched beams along with the results obtained from this study is recommended.
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The biases of the various concrete toughness tests developed is still unknown. Sufficient data should be gathered and sufficient research conclusions should be collected in order to define a reliable test standard. It is hoped that results obtained from this study might be helpful for building a consensus on the concrete fracture toughness test method.