• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.1
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• pp.164-172
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• 1997

Two parameter technique that uses far-field stress and displacement distributions was applied to composite laminates in order to calculate mode II energy release rate, $G_{II}$ . The $G_{II}$ calculated by two parameter technique was compared with that calculated from the crack closure method to inspect the effectiveness of two parameter technique. Sensitivity study of two parameter technique to the crack extension size was also performed. The results showed that both methods produced comparable $G_{II}$ results. In particular, it was found that although the crack closure method was affected by the crack extension size, the two parameter technique was less affected by the crack extension size.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.9
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• pp.2223-2233
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• 1993

An engineering method is suggested to calculate the applied load versus crack extension in the elastic-plastic fracture. The condition for an increment of crack extension is set by a critical increment of crack-up opening displacement(CTOD). The ratio of the CTOD increment to the incremental crack extention is a critical crack-tip opening angle(CTOA), assumed to be constant for a material of a given thickness. The Dugdale model of crack-tip deformation in an infinite plate is applied to the method, and a complete solution for crack extension and crack instability is obtained. For finite-size specimens of arbitrary geometry in general yielding, an approximate generalization of the Dugdale model is suggested so that the approximation approaches the small-scale yielding solution in a low applied load and the finite-element solution in a large applied load. Maximum load is calculated so that an applied load attains either a limit load on an unbroken ligament or a peak load during crack extension. The proposed method was applied to three-point bend specimens of a carbon steel SM45C in various sizes. Reasonable agreements are found between calculated maximum loads and experimental failure loads. Therefore, the method can be a viable alternative to the J-R curve approach in the elastic-plastic fracture analysis.

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

• Journal of the Korea Concrete Institute
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• v.14 no.3
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• pp.357-364
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• 2002

The resistance curves (R-curves) for 381 m crack extension of CLWL-DCB specimens had been determined. The average velocities of the crack extension measured with strain gages were 0.70 and 55 ㎜/sec. The measured rotation angle of the notch faces showed the existence of the singularity at least before 171 and 93 mm crack extensions for the 0.70 and 55 ㎜/sec crack velocities, respectively. The maximum slopes of the R-curves occurred between 25 and 89 ㎜ crack extensions for 0.70 ㎜/sec crack velocity and between 51 and 127 ㎜ crack extensions for 55 ㎜/sec crack velocity During the maximum slopes of the R-curves, the micro-crack localization can be expected, and faster crack velocity may form longer micro-cracking and micro-crack localizing zones. The fracture resistance of 0.70 ㎜/sec crack velocity reached a roughly constant maximum value of 143 N/m at 152 ㎜ crack extension, while that of 55 ㎜/sec crack velocity increased continuously to 245 N/m at 254 ㎜ crack extension and then decreased to the value of 0.70 ㎜/sec crack velocity. The R-curve of 55 ㎜/sec crack velocity was similar to that of the small size three-point bend test, and it showed that small size specimen or fast crack velocity could cause more brittle behavior.

• Journal of the Korean Ceramic Society
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• v.37 no.4
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• pp.368-375
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• 2000

Fracture toughness of particulate composites of Al2O3/SiC, Al2O3/ZrO2 and Al2O3/ZrO2/SiC was analysed theoretically. According to the suggested particle bridging model for obtaining the R-curve height, the crack extension resistance for the long crack was linearly proportional to the residual calmping stress at the interface between the second phase and the matrix. It was also a function of the particle size and the content. It was confirmed that the rising R-curve behavior of Al2O3 containing 30 vol% SiC particles of 3${\mu}{\textrm}{m}$ was owing to the strong crack bridging by SiC particles. For Al2O3/ZrO2/SiC composites, the tensional stress from the 3${\mu}{\textrm}{m}$ SiC particles was large enough to activate the spontaneous transformation of the ZrO2. The crack extension resistance due to the particle bridging mechanism did not seem to be affected much by the coupled toughening, but its resultant toughness increase could be significantly smaller due to the dependency on the matrix toughness.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.3
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• pp.29-36
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• 1991

This experimental research evaluated the length of crack extension with the measured compliances as the mutual comparison factors instead of the method proposed in ASTM E561-80. And this research measured the R-curves with the application to the concept of the strain energy release rate that was formulated from the inelastic energy absorbed during the crack growth. With the interpretation of R-curves, this research obtained the starting point of the unstable crack growth, and compared the values of critical fracture toughness with each other, and then examined the effects of variations of the maximum size of coarse aggregate and the thickness of specimen on the values of the critical fracture toughness.

• Journal of the Korean Ceramic Society
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• v.22 no.5
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• pp.76-84
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• 1985

Mechanical property enhancing mechanisms of $Al_2O_3-ZrO_2$ two phase ceramic composites were studied for several compositions of different $ZrO_2$/$Al_2O_3$ ratio. Microstructural analysis of $Al_2O_3-ZrO_3$(pure) composites indicated that pre-existing microcrack due to larger $ZrO_2$ particle at grain boundary extended along alumina grain boundaries within process zone. Microcracks also nucleated when very small $ZrO_2$ particles at the grain boundaries transformed to monoclinic phase at near of main crack tip. These types of microcracks could contribute to the toughening achieved by creating additional crack surface area during crack propagation. Microstructural analyses also showed that the average grain size and abnormal grain size of $Al_2O_3$ were decreased with increasing $ZrO_2$ vol% in $Al_2O_3$ matrix. As a result it could be concluded as follows In TEX>$Al_2O_3-ZrO_3$(pure) system 1. Microcrack nucleation (stress-induced microcracking) and extension was effective mechanism for absorpiton of fracture energy 2, More narrow distribution and smaller grain size of $Al_2O_3$ due to $ZrO_2$particles mainly contributed to main-tatin the strength and hardness.

• Journal of the Korea Concrete Institute
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• v.15 no.6
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• pp.802-810
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• 2003

In this paper, the modified singular fracture process zone (S-FPZ) model is proposed to consider variation of a fracture criterion for continuous crack propagation in concrete. The fracture properties of the proposed fracture model are strain energy release rate at a micro-crack tip and crack closure stress (CCS) versus crack opening displacement (COD) relationship in the FPZ. The proposed model can simulate the estimated fracture energy of experimental results. The analysis results of the experimental data shows that specimen geometry and loading condition did not affect the CCS-COD relation. But the strain energy release rate is a function of not only specimen geometry but also crack extension. Until 25 mm crack extension, the strain energy release rate is a constant minimum value, and then it increased linearly to the maximum value. The maximum fracture criterion occurred at the peak load for an large size specimen. The fracture criterion remains the maximum value after the peak load. The variation of the fracture criterion is caused by micro-cracking and micro-crack localizing. 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-tracking and micro-crack localizing behaviors of concrete.

• Computers and Concrete
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• v.18 no.3
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• pp.337-354
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• 2016

To study the influence on fracture properties of reinforced concrete wedge splitting test specimens by the addition of reinforcement, and the restriction of steel bars on crack propagation, 7 groups reinforced concrete specimens of different reinforcement position and 1 group plain concrete specimens with the same size factors were designed and constructed for the tests. Based on the double-K fracture criterion and tests, fracture toughness calculation model which was suitable for reinforced concrete wedge splitting tensile specimens has been obtained. The results show that: the value of initial craking load Pini and unstable fracture load Pun decreases gradually with the distance of reinforcement away from specimens's top. Compared with plain concrete specimens, addition of steel bar can reduce the value of initial fracture toughness KIini, but significantly increase the value of the critical effective crack length ac and unstable fracture toughness KIun. For tensional concrete member, the effect of anti-cracking by reinforcement was mainly acted after cracking, the best function of preventing fracture initiation was when the steel bar was placed in the middle of the crack, and when the reinforcement was across the crack and located away from crack tip, it plays the best role in inhibiting the extension of crack.

• Computers and Concrete
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• v.11 no.5
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• pp.365-382
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• 2013

Although shear reinforcement in beams typically consists of steel bars bent in the form of stirrups or hoops, the addition of deformed steel fibres to the concrete has been shown to enhance shear resistance and ductility in reinforced concrete beams. This paper presents a model that can be used to predict the shear strength of fibrous concrete rectangular members without stirrups. The model is an extension of the plasticity-based crack sliding model originally developed for plain concrete beams. The crack sliding model has been improved in order to take into account several aspects: the arch effect for deep beams, the post-cracking tensile strength of steel fibre reinforced concrete and its ability to control sliding along shear cracks, and the mitigation of the shear size effect due to presence of fibres. The results obtained by the model have been validated by a large set of experimental tests taken from literature, compared with several models proposed in literature, and numerical analyses are carried out showing the influence of fibres on the beam failure mode.