• International Journal of Concrete Structures and Materials
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• v.18 no.3E
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• pp.191-198
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• 2006

The objective of this study is to examine fracture characteristics of concrete at early ages, i.g. critical stress intensity factor, critical crack-tip opening displacement, fracture energy, and bilinear softening curve based on the concepts of effective-elastic crack model and cohesive crack model. A wedge splitting test for Mode I was performed on cubic wedge specimens with a notch at the edge. By experimenting with various strengths and ages, load-crack mouth opening curves were obtained, and the results were analyzed by linear elastic fracture mechanics and FEM(finite element method). The results from the test and analysis showed that critical stress intensity factor and facture energy increased while critical crack-tip opening displacement decreased with concrete aging from 1 day to 28 days. Four parameters of bilinear softening curve from 1 day to 28 days were obtained from a numerical analysis. The obtained fracture parameters and bilinear softening curves at early ages from this study are to be used as a fracture criterion and an input data for the finite element analysis of concrete at early ages.

• Computers and Concrete
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• v.5 no.3
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• pp.261-277
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• 2008

This paper presents methodologies for remaining life prediction of plain concrete structural components considering tension softening effect. Non-linear fracture mechanics principles (NLFM) have been used for crack growth analysis and remaining life prediction. Various tension softening models such as linear, bi-linear, tri-linear, exponential and power curve have been presented with appropriate expressions. A methodology to account for tension softening effects in the computation of SIF and remaining life prediction of concrete structural components has been presented. The tension softening effects has been represented by using any one of the models mentioned above. Numerical studies have been conducted on three point bending concrete structural component under constant amplitude loading. Remaining life has been predicted for different loading cases and for various tension softening models. The predicted values have been compared with the corresponding experimental observations. It is observed that the predicted life using bi-linear model and power curve model is in close agreement with the experimental values. Parametric studies on remaining life prediction have also been conducted by using modified bilinear model. A suitable value for constant of modified bilinear model is suggested based on parametric studies.

• Journal of the Korea Concrete Institute
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• v.14 no.1
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• pp.58-66
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• 2002

The objective of this study is to examine the fracture characteristics of concrete at early ages such as critical stress intensity factor, critical crack-tip opening displacement, fracture energy, and bilinear softening curve based on the concepts of the effective-elastic crack model and the cohesive crack model. A wedge splitting test for Mode I was performed on cubic wedge specimens with a notch at the edge. By taking various strengths and ages, load-crack mouth opening displacement curves were obtained, and the results were analyzed by linear elastic fracture mechanics and the finite element method. The results from the test and analysis showed that critical stress intensity factor and fracture energy increased, and critical crack-tip opening displacement decreased with concrete ages from 1 day to 28 days. By numerical analysis four parameters of bilinear softening curve from 1 day to 28 days were obtained. The obtained fracture parameters and bilinear softening curves at early ages may be used as a fracture criterion and an input data for finite element analysis of concrete at early ages.

• International Journal of Concrete Structures and Materials
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• v.8 no.2
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• pp.129-139
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• 2014

In this study, the concrete fracture energy was obtained using the three point notched beam test method developed by Hillerborg et al. (Cem Concr Res 6(6):773-782, 1976). A total of 12 notched concrete beams were tested under two different loading conditions: constant stroke control and constant crack mouth opening displacement (CMOD) control. Despite individual fracture energies obtained from the two different loading conditions showing some variation, the average fracture energy from both loading conditions was very similar. Furthermore, the results obtained support the idea that a far tail constant "A" could change the true fracture energy by up to 11 %, if it is calculated using CMOD instead of LVDT. The far tail constant "A" is determined using a least squares fit onto a straight line according to Elices et al. (Mater Struct 25(148):212-218, 1992) and RILEM report (2007). It was also observed that the selection of the end point can produce variations of the true fracture energy. The end point indicates the point in the experiment at which to stop. An end point of 2 mm has been recommended, however, in this study other end points were also considered. The final form of the bilinear softening curve was determined based on Elices and Guinea's methods (1992, 1994) and RILEM report (2007). This paper proposes a bilinear stress-crack opening displacement curve according to test results as well as the CEB-FIP model code.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.05a
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• pp.902-907
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• 2003

Substantial experimental and theoretical work exists on the bond characteristics of FRP-concrete adhesive joints. Analytic solutions based on fracture mechanics are most commonly accepted for theoretical work on joint. The solutions may be derived for the simple form of the shear strees-slip curve. And it is difficult to determine the model parameters consisting the curve. In this study, the bilinear curve with softening branch is introduced. The model parameters are determined by the method described by the companion paper with comparison of test results. There are many uncertainties in the test results of CFRP sheet adhesive joints, so that test results used for the construction of the regression problem should be reasonably selected.

• Journal of the Korea Concrete Institute
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• v.22 no.3
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• pp.427-435
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• 2010

One of the most vulnerable properties in concrete is tensile cracking, which usually happens at early ages due to hydration heat and shrinkage. In order to accurately predict the early age cracking, it needs to find out how stress-crack opening relation is varying over time. In this study, inverse analyses were performed with the existing experimental data for wedge-splitting tests, and the parameters of the softening curve for the stress-crack opening relation were determined from the best fits of the measured load-CMOD curves. Based on the optimized softening curve, variation of fracture energy over time was first examined, and a model for the stress-crack opening relation at early ages was suggested considering the found feature of the fracture energy. The model was verified by comparisons of the peak loads, CMODs at peak loads, and fracture energies obtained from the experiments and the inverse analysis.

• Computers and Concrete
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• v.4 no.3
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• pp.221-241
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• 2007

Based on the experiment results, the damage and fracture behavior of concrete at the ages of 1d, 2d, 7d and 28d, in three-point bending and uniaxial tensile tests, were simulated with a finite element program, ABAQUS. The critical stress intensity factor $K_{IC}^s$ and the critical crack tip opening displacement ($CTOD_C$) of concrete were calculated with effective-elastic crack approach for the three-point bending test of grade C30 concrete. Based on the crack band model, a bilinear strain-softening curve was derived to simulate the LOAD-CMOD curves and LOAD-Displacement curves. In numerical analysis of the uniaxial tension test of concrete of grade C40, the damage and fracture mechanics were combined. The smeared cracking model coupling with damaged variable was adopted to evaluate the onset and development of microcracking of uniaxial tensile specimen. The uniaxial tension test was simulated by invoking the damage plastic model which took both damage and plasticity as inner variables with user subroutines. All the numerical simulated results show good agreement with the experimental results.