• KCI Concrete Journal
• /
• v.14 no.1
• /
• pp.30-35
• /
• 2002

The fractal geometry is a non-Euclidean geometry which describes the naturally irregular or fragmented shapes, so that it can be applied to fracture behavior of materials to investigate the fracture process. Fractal curves have a characteristic that represents a self-similarity as an invariant based on the fractal dimension. This fractal geometry was applied to the crack growth of cementitious composites in order to correlate the fracture behavior to microstructures of cementitious composites. The purpose of this study was to find relationships between fractal dimensions and fracture energy. Fracture test was carried out in order to investigate the fracture behavior of plain and fiber reinforced cement composites. The load-CMOD curve and fracture energy of the beams were observed under the three point loading system. The crack profiles were obtained by the image processing system. Box counting method was used to determine the fractal dimension, D$_{f}$. It was known that the linear correlation exists between fractal dimension and fracture energy of the cement composites. The implications of the fractal nature for the crack growth behavior on the fracture energy, G$_{f}$ is apparent.ent.

• Computational Structural Engineering
• /
• v.9 no.4
• /
• pp.173-179
• /
• 1996

Study of weldment fracture behavior includes thermal analysis, residual stress analysis, and fracture analysis. The J-integral loses its path-independency in a residual stress field. Therefore, it is necessary to develop a program to calculate the J-integral in a welded plate. In this study, theoretical formulation and program were developed for the evaluation of the J-integral at the crack tip of weldments. To verify equations and program, welded thin plate and thick plate were used to calculate residual stress and the J-integral.

• Fibers and Polymers
• /
• v.5 no.4
• /
• pp.259-263
• /
• 2004

Rubber-modified epoxy resins have been employed as adhesive and matrix materials for glass and corbon-fiber composites. The behavior of fracture around a crack tip for rubber-modified epoxy resin is investigated through the acoustic emission (AE) analysis of compact tension specimens. Damage zone and rubber particles distributed around a crack tip were observed by a polarized optical microscope and an atomic force microscope (AFM). The damage zone in front of pre-crack tip in rubber-modified specimen $(15wt\%\; rubber)$ began to form at about $13\%$ level of the fracture load and grew in size until $57\%$ load level. After that, the crack propagated in a stick-slip manner. Based on time-frequency analysis of AE signals and microscopic observation of damage zone, it was thought that AE signals with frequency bands of 0.15-0.20 MHz and 0.20­0.30 MHz were generated from cavitation in the damage zone and crack propagation, respectively.

• Computers and Concrete
• /
• v.17 no.4
• /
• pp.553-566
• /
• 2016

Fracture energy is one of the key parameters reveal cracking resistance and fracture toughness of concrete. The main purpose of this study is to determine fracture behavior, mechanical properties and microstructural analysis of high strength basalt fiber reinforced concrete (HSFRC). For this purpose, three-point bending tests were performed on notched beams produced using HSFRCs with 12 mm and 24mm fiber length and 1, 2 and $3kg/m^3$ fiber content in order to determine the value of fracture energy. Fracture energies of the notched beam specimens were calculated by analyzing load versus crack mouth opining displacement curves by the help of RILEM proposal. The results show that the effects of basalt fiber content and fiber length on fracture energy are very significant. The splitting tensile and flexural strength of HSFRC increased with increasing fiber content whereas a slight drop in flexural strength was observed for the mixture with 24mm fiber length and $3kg/m^3$ fiber content. On the other hand, there was no significant effect of fiber addition on the compressive strength and modulus of elasticity of the mixtures. In addition, microstructural analysis of the three components; cement paste, aggregate and basalt fiber were performed based on the Scanning Electron Microscopy and Energy-Dispersive X-ray Spectroscopy examinations.

• Structural Engineering and Mechanics
• /
• v.64 no.1
• /
• pp.59-69
• /
• 2017

The field of fracture mechanics has gained significance because of its ability to address the behaviour of cracks. Predicting the fracture properties of concrete based on experimental investigations is a challenge considering the quasi-brittle nature of concrete. So, there is a need for developing a standard numerical tool which predicts the fracture energy of concrete which is at par with experimental results. The present study is an attempt to evaluate the fracture energy and characteristic length for different grades of concrete using Concrete Damage Plasticity (CDP) model. Indian Standard and EUROCODE are used for the basic input parameters of concrete. Numerical evaluation is done using Finite Element Analysis Software ABAQUS/CAE. Hsu & Hsu and Saenz stress-strain models are adopted for the current study. Mesh sensitivity analysis is also carried to study the influence of type and size of elements on the overall accuracy of the solution. Different input parameters like dilatation angle, eccentricity are varied and their effect on fracture properties is addressed. The results indicated that the fracture properties of concrete for various grades can be accurately predicted without laboratory tests using CDP model.

• Journal of the Korea Concrete Institute
• /
• v.12 no.1
• /
• pp.3-12
• /
• 2000

A fracture energy concept proposed by Ouyang and Shah's fracture mechanics approach was used to predict cracking of reinforced concrete members subjected to tension. In this approach, fracture properties in plain concrete which incorporate the presence of the fracture process zone are first determined from the generalized size effect method, then fracture energy required for crack propagation with the same dimension and material properties are evaluated using an R-curve. Subsequently taking into account the material properties in Ouyang and Shah's approach, a theoretical analysis to predict the mechanical behavior of reinforced concrete members subjected to tension was performed and compared to observed experimental results. It is seen that the predicted average crack spacing curves agree well with the experimental results, whereas the analytical method seems to predict lower values for this study. The analytical approach predicts well responses of stress-strain curves before and after the first crack is formed. It is concluded from this study that a fracture energy concept based on the R-curve and the generalized size effect method is a rational approach to predict cracking of reinforced concrete members subjected to tension.

• International journal of steel structures
• /
• v.18 no.5
• /
• pp.1784-1800
• /
• 2018

Tension-shear loading is a common loading condition in steel structures during the earthquake shaking. To study ductile fracture in structural steel under multiple stress states, experimental investigations on the different fracture mechanisms in Chinese Q235 steel were conducted. Different tension-shear loading conditions achieved by using six groups of inclined notch butterfly configurations covering pure shear, tension-shear and pure tension cases. Numerical simulations were carried out for all the specimens to determine the stress and strain fields within the critical sections. Two tension-shear fracture models were calibrated based on the hybrid experimental-numerical procedure. The equivalent fracture strain obtained from the round bar under tensile loading was used for evaluating these two models. The results indicated that the tension-shear criterion as a function of the shear fracture parameter had better performance in predicting the fracture initiation of structural steel under different loading conditions.

• International Journal of Concrete Structures and Materials
• /
• v.18 no.3E
• /
• pp.213-219
• /
• 2006

Modified singular fracture process zone(S-FPZ) model is proposed in this paper to determine a fracture criterion for continuous crack propagation in concrete. The investigated fracture properties of the proposed fracture model are strain energy release rate at a micro-crack tip and the relationship between crack closure stress(CCS) and crack opening displacement(COD) in the FPZ. The proposed model can simulate the actual fracture energy of experimental results fairly well. The results of the experimental data analysis show that specimen geometry and loading condition did not affect the CCS-COD relation. However, the strain energy release rate is a function of not only specimen geometry but also crack extension. The strain energy release rate remained constantly at the minimum value up to the crack extension of 25 mm, and then it increased linearly to the maximum value. The maximum fracture criterion occurred at the peak load for specimens of large size. The fracture criterion remained at the maximum value after the peak load. The variation of the fracture criterion is caused by micro-cracking and micro-crack localization. The fracture criterion of strain energy release rate can simply be the size effect of concrete fracture, and it can be used to quantify the micro-cracking and micro-crack localizing behavior of concrete.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.4 no.4
• /
• pp.1-11
• /
• 1984

Developed is a nonlinear fracture theory which can model the complex fracture behavior of concrete. This theory is based on the nonlinear behavior due to progressive microcracking and strain-softening in the fracture process zone of concrete cracks. The simplified realistic fracture model which preserves the same fracture energy for the different fracture process zone widths is also derived. By modeling fracture through stress-strain behavior, the effect of compressive stresses parallel to the crack plane can be easily taken into account. The comparisons of the present theory with valuable fracture test data available in the literature show good agreements, and the existing linear theory exhibits in many cases large deviations from the actual test results. A simple approximate formula for the fracture energy of concrete which should, be necessary for the fracture analysis of concrete structures is derived. Finally, the application of fracture theory to reinforced concrete and the necessity of further research are discussed.

• Journal of Soil and Groundwater Environment
• /
• v.9 no.1
• /
• pp.79-86
• /
• 2004

Hydraulic conductivity along rock fracture is mainly dependent on fracture geometries such as orientation, aperture, roughness and connectivity. Therefore, it needs to consider fracture geometries sufficiently on a fracture model for a numerical analysis to calculate permeability coefficient in a fracture. This study performed new type of numerical analysis using a homogenization analysis method to calculate permeability coefficient accurately along single fractures with several fracture models that were considered fracture geometries as much as possible. First of all, fracture roughness and aperture variation due to normal stress applied on a fracture were directly measured under a confocal laser scaning microscope (CLSM). The acquired geometric data were used as input data to construct fracture models for the homogenization analysis (HA). Using the constructed fracture models, the homogenization analysis method can compute permeability coefficient with consideration of material properties both in microscale and in macroscale. The HA is a new type of perturbation theory developed to characterize the behavior of a micro inhomogeneous material with a periodic microstructure. It calculates micro scale permeability coefficient at homogeneous microscale, and then, computes a homogenized permeability coefficient (C-permeability coefficient) at macro scale. Therefore, it is possible to analyze accurate characteristics of permeability reflected with local effect of facture geometry. Several computations of the HA were conducted to prove validity of the HA results compared with the empirical equations of permeability in the previous studies using the constructed 2-D fracture models. The model can be classified into a parallel plate model that has fracture roughness and identical aperture along a fracture. According to the computation results, the conventional C-permeability coefficients have values in the range of the same order or difference of one order from the permeability coefficients calculated by an empirical equation. It means that the HA result is valid to calculate permeability coefficient along a fracture. However, it should be noted that C-permeability coefficient is more accurate result than the preexisting equations of permeability calculation, because the HA considers permeability characteristics of locally inhomogeneous fracture geometries and material properties both in microscale and macroscale.