modes. If the fiber bridging effect is increasing during crack initiation and propagation, multiple cracks can form. This behavior is also known as strain hardening behavior. On the other hand, if the fibers cannot carry more load after the formation of the first crack, then further deformation is characterized by opening of a single crack. This behavior is in terms called tension softening. Experimental tests to obtain constitutive parameters for both strain hardening and tension softening materials is an important issue with regards to fracture mechanical modeling. To model cracking in the overlay, constitutive para-meters are important, and should reflect the material behavior observed in experiments.
In this study, tension softening and strain hardening materials are analyzed as overlay material. In the case of tension softening materials, well established test methods are at hand, see e.g. (RILEM 2000) or (RILEM 2001). Furthermore, Østergaard (2003) made a full review and has compared standard test methods for tension softening materials.
In the case of strain hardening materials, little or no work has been performed so far to establish a standard test method. Paper VI contributes to the work in the field of a test method to achieve the constitutive strain hardening parameters, using a four-point bending set-up.
3.3 Verification of Numerical Modeling Tools
Experimental tests on composite beams using both tension softening and strain hardening materials have been performed. Numerical tools applied in this thesis are verified exper-imentally inPaper III, by comparing the modeling work to experimental data. Previous experimental studies have been carried out on beams reinforced with concrete overlays.
Early studies by Silfwerbrand (1984), show results from tests on concrete beams with concrete overlays. More recently, studies by Granju (1996), investigate the influence of fibers in cement-based overlays. Paper III contributes to these studies, and the major outcome of this paper is the treatment of the significant influence of overlay defects and their relationship to debonding.
Three different fiber reinforced composites have been tested as overlay material. Two tension softening materials: Fibre Reinforced Concrete (FRC), and Fibre Reinforced Densitr(FRD), as well as one strain hardening material, known as Engineered Cemen-titious Composites (ECC). The significant findings in this study are the experimental and numerical investigations of macro crack formation in the overlay and its influence on debonding. Furthermore, the verification of the numerical modeling work is carried out by comparing FE results with experimental data. Two experimental set-ups, one for FRC and FRD beams, cf. Figure 3.4, and one for ECC beams, cf. Figure 3.5, have been proposed. The experimental set-ups applied, have been utilized as the primary set-up to test tension softening and strain hardening materials in composite with steel.
The general experimental results of a test program is displayed in Figure 3.6. In the fig-ure, tests on FRC, FRD, and ECC composite beams are shown in a load vs. displacement diagram. As observed, the composite beam with the ECC material exhibits a larger load bearing capacity compared to FRC and FRD. Additionally, a second y-axis shows the measured debonding signal. This shows clearly the significance of macro cracks and their
3.3 Verification of Numerical Modeling Tools Composite Elements
Figure 3.4Experimental set-up for FRD and FRC composite beams. Since a single crack is formed at midspan a clip gauge is placed to measure the crack opening displacement (COD). The test set-up simulates a part of a stiffening overlay cast on a steel bridge deck loaded in negative bending.
Figure 3.5Experimental set-up for ECC composite beams, the crack width of the overlay cracks are monitored and debonding is measured. The test set-up simulates a part of a stiffening overlay cast on a steel bridge deck loaded in negative bending.
Figure 3.6Results from three representative tests of composite beams with FRD, FRC and ECC overlay materials. Result are plotted in a load versus displacement diagram with a second y-axis showing the corresponding debonding.
Department of Civil Engineering - Technical University of Denmark 29
Composite Elements 3.3 Verification of Numerical Modeling Tools
initiation of debonding. The two tension softening materials, FRC and FRD, form one single crack and for deflection values of 2-3 mm, debonding is observed. The FRD mate-rial, which has a much stronger matrix than FRC, initiates debonding for approximately for the same deflection value as for the FRC material. This concludes, that the governing mechanism for debonding is the magnitude of the crack width, also evident by numerical studies as showed in the previous section. Furthermore, observing the experimental data of the ECC composite beam, debonding initiates for a large beam deflection value com-pared to FRC and FRD. This is due to the fact that the ECC composite beam behavior is characterized by multiple cracking. The largest crack width, before localization in the ECC beam, was measured using a micro camera in the range of 100 micron. In compar-ison, crack openings of the discrete crack in the FRD and FRC tests, had a value in the range of 0.1 to 0.2 mm at debond initiation. It should be noted that when comparing these crack openings to the numerical crack opening in the previous section, debonding was measured 50 mm from the point where the vertical crack propagates. For a more complete and detailed review of the experimental set-up, and how debonding is measured, the reader is referred toPaper III.
The numerical tools applied using the finite element method has been verified comparing numerical results with experimental results. The comparisons are shown in Figures 3.7(a)-(b) and 3.8. As observed in the figures, the numerical results correlate well with the experimental data. It should be noted that for the FRC and FRD beams, the comparisons are shown in a load vs. Crack Opening Displacement (COD). When using numerical tools, it is possible to extract more information on the composite beam behavior than might be possible in the experiments. In the present case, it is possible via the numerical calculation to extract information on the deformation state in the steel plate. As very large deformations are achieved, yielding of the steel plate starts (marked in Figure 3.8), before a macro crack localizes in the ECC composite beam.
3.3 Verification of Numerical Modeling Tools Composite Elements
0 0.2 0.4 0.6 0.8 1
0 1 2 3
COD [mm]
(a)
Load [kN]
0 0.2 0.4 0.6 0.8 1
0 1 2 3
COD [mm]
(b)
Load [kN]
FRC composite beam FRD composite beam
FE model FE model
Figure 3.7Comparison between experimental and numerical results. (a), and (b) show comparison between numerical and experimental results for a FRC, and FRD composite beam test, respectively.
0 10 20 30
0 1 2 3 4 5 6 7
Deflection [mm]
P [kN]
Start yielding of steel plate Crack localization
FE Model ECC composite beam
Figure 3.8Comparison between experimental and numerical results for an ECC composite beam test.
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