• International Journal of Concrete Structures and Materials
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• 제19권1E호
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• pp.25-32
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• 2007

The fracture energy evaluated from the previous experimental results can be simulated by using the modified singular fracture process zone (S-FPZ) model. The fracture model has two fracture properties of strain energy release rate for crack extension and crack close stress versus crack width relationship $f_{ccs}(w)$ for fracture process zone (FPZ) development. The $f_{ccs}(w)$ relationship is not sensitive to specimen geometry and crack velocity. The fracture energy rate in the FPZ increases linearly with crack extension until the FPZ is fully developed. The fracture criterion of the strain energy release rate depends on specimen geometry and crack velocity as a function of crack extension. The behaviors of micro-cracking, micro-crack localization and full development of the FPZ in concrete can be explained theoretically with the variation of strain energy release rate with crack extension.

• Computers and Concrete
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• 제1권1호
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• pp.47-60
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• 2004

The influence of the fracture process zone (FPZ) on the fracture properties is one of the hottest topics in the field of fracture mechanics for cementitious materials. Within the FPZ in front of a traction free crack, cohesive forces are distributed in accordance with the softening stress-separation constitutive relation of the material. Therefore, further crack propagation necessitates energy dissipation, which is the work done by the cohesive forces. In this paper $g_f$, the local fracture energy characterizing the energy consumption due to the cohesive forces, is discussed. The computational expression of $g_f$ in the FPZ can be obtained for any stage during the material fracture process regarding the variation of FPZ, whether in terms of its length or width. $G_{fa}$, the average energy consumption along the crack extension region, has also been computed and discussed in this paper. The experimental results obtained from the wedge splitting tests on specimens with different initial notch ratios are employed to investigate the property of the local fracture energy $g_f$ and the average value $G_{fa}$ over the crack extension length. These results can be used to indicate the influence of the FPZ. Additionally, changes in the length of the FPZ during the fracture process are also studied.

• Steel and Composite Structures
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• 제44권6호
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• pp.817-828
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• 2022

In this study, considering dissipated energy in fracture process zone (FPZ), a novel criterion based on maximum strain energy release rate (SER) for orthotropic materials is presented. General case of in-plane loading for cracks along the fibers is assumed. According to the experimental observations, crack propagation is supposed along the fibers and the reinforcement isotropic solid (RIS) concept is employed as a superior model for orthotropic materials. SER in crack initiation and propagation phases is investigated. Elastic properties of FPZ are extracted as a function of undamaged matrix media and micro-crack density. This criterion meaningfully links between dissipated energy due to toughening mechanisms of FPZ and the macroscopic fracture by defining stress intensity factors of the damaged zone. These coefficients are used in equations of maximum SER criterion. The effect of crack initiation angle and the damaged zone is considered simultaneously in this criterion and mode II stress intensity factor is extracted in terms of stress intensity factors of damage zone and crack initiation angle. This criterion can evaluate the effects of FPZ on the fracture behavior of orthotropic material. Good agreement between extracted fracture limit curves (FLC's) and available experimental data proves the ability of the new proposed criterion.

• 콘크리트학회논문집
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• 제16권4호
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• pp.511-520
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• 2004

이 연구에서는 기존의 콘크리트 실험에서 평가된 파괴에너지를 수정 특이-파괴진행대 이론에 대해 해석하였다. 수정 특이-파괴진행대 이론은 균열성장에 대한 에너지해방률과 균열면의 파괴진행에 대한 균열면응력-균열폭 관계의 두 파괴특성을 필요로 한다. 해석결과 균열면응력-균열폭 관계는 시험편의 형상과 균열속도에 민감하지 않았다. 파괴진행대에서 파괴에너지율은 파괴진행대가 완전히 형성될 때까지 균열성장길이에 선형으로 증가하였으며, 이후에는 파괴에너지밀도로 일정한 값을 유지하였다. 변형에너지방출률은 시험편의 형상과 균열속도에 큰 변화를 보였으며, 균열속도에 대해서는 선형의 대수함수로 표현될 수 있다. 균열성장에 대한 변형에너지방출률의 변화는 다른 실험의 미세균열의 성장과 국부화 그리고 완전 파괴진행대의 형성에 대한 이론적인 근거를 보여준다.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 1995년도 봄 학술발표회 논문집
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• pp.237-244
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• 1995

Fracture properties for LEFM, S-FPZ and NS-FPZ models were determined using by finite element method and energy balance from the experimental results of three-point bend tests. For the LEFM model the stress intensity factor needed to increase continuously with crack extension, and for the S-FPZ model the fracture process zone characteristics need to change continuously if the critical stress intensity factor was to remain constant. The LEFM model showed the largest resistance and the slowest crack extension, while the NS-FPZ model showed the smallest resistance and the fastest crack extension. The responses for the S-FPZ model were intermediate between those for the LEFM and NS-FPZ models and the total fracture energy densities for the S-FPZ and NS-FPZ models and the total fracture energy densities for the S-FPZ and NS-FPZ models were equal.

• Coupled systems mechanics
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• 제4권2호
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• pp.115-136
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• 2015

We present for one-dimensional model for elastoplastic bar with combined hardening in FPZ - fracture process zone and softening with embedded strong discontinuities. The simplified version of the model without FPZ is directly compared and validated against analytical solution of Bazant and Belytschko (1985). It is shown that deformation localizes in an area which is governed by the chosen element size and therefore causes mesh sensitivity and that the length of the strain-softening region tends to localize into a point, which also agrees with results obtained by stability analysis for static case. Strain increases in the softening domain with a simultaneous decrease of stress. The problem unloads elastically outside the strain-softening region. The more general case with FPZ leads to more interesting results that also account for induced strain heterogeneities.

• International Journal of Concrete Structures and Materials
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• 제18권3E호
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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.

• Coupled systems mechanics
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• 제4권3호
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• pp.211-235
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• 2015

In this work we present a one-dimensional damage model capable of representing the dynamic fracture for elastodamage bar with combined hardening in fracture process zone - FPZ and softening with embedded strong discontinuities. This model is compared with another one we recently introduced (Do et al. 2015) and it shows a good agreement between two models. Namely, it is indicated that strain-softening leads to a sensitivity of results on the mesh discretization. Strain tends to localization in a single element which is the smallest possible area in the finite element simulations. The strain-softening element in the middle of the bar undergoes intense deformation. Strain increases with increasing mesh refinement. Strain in elements outside the strain-softening element gradually decreases to zero.

• 한국세라믹학회지
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• 제44권7호
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• pp.343-348
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• 2007

Alumina/silver nanocomposites were fabricated using a soaking method through a sol-gel route to construct an intra-type nanostructure. The pulse electric-current sintering (PECS) technique was used to sinter the nanocomposites. Several specimens were annealed after sintering. The microstructure, mechanical properties, critical frontal process zone (FPZ) size, and thermo-mechanical properties of the nanocomposites were estimated. The relative densities of the specimens sintered at 1350 and $1450^{\circ}C$ were 95% and 99%, respectively. The maximum value of the three-point bending strength was found to be 780 MPa for the $2{\times}2{\times}10 mm$ specimen sintered at $1350^{\circ}C$. The fracture toughness of the specimen sintered at $1350^{\circ}C$ was measured to be $3.60 MPa{\cdot}m^{1/2}$ using the single-edge V-notched beam (SEVNB) technique. The fracture mode of the nanocomposites was transgranular, in contrast to the intergranular mode of monolithic alumina. The fracture morphology suggested that dislocations were generated around the silver nanoparticles dispersed within the alumina matrix. The specimens sintered at $1350^{\circ}C$ were annealed at $800^{\circ}C$ for 5 min, following which the maximum fracture strength became 810 MPa and the fracture toughness improved to $4.21 MPam^{1/2}$. The critical FPZ size was the largest for the specimen annealed at $800^{\circ}C$ for 5 min. Thermal conductivity of the alumina/silver nanocomposites sintered at $1350^{\circ}C$ was 38 W/mK at room temperature, which was higher than the value obtained with the law of mixture.

• 산업기술연구
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• 제19권
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• pp.197-208
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• 1999

The process of localization of cracks and movement of the fracture process zone(FPZ) was studied using the acoustic-emission(AE) techniques. The rate of AE events and sources of AE activity were studied for mortar and rock specimens loaded in uniaxial compression. A series of transducers could be used to detect and AE activity. Based on the time differences between detection of the event at different transducers, source of AE activity could be detected. The rate of AE events increased sharply before peak load. The highest rate occurred just after peak load was attained. The effective crack length estimated from the modified linear-elastic fracture mechanics seemed consistent with the optical and AE measurements.