• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.04a
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• pp.76-79
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• 2000

Polymeric composites exhibit highly nonlinear and rate dependent behavior during loading and unloading in off-axis directions. The equilibrium state of stress during loading is lower than the state of stress produced at finite strain rates. The amount of stress relaxation during loading decreases. Interestingly, however, the stress goes up to reach to the equilibrium state of stress for a fixed displacement during unloading. The unloading behavior is quite similar to the loading behavior. The stress relaxation patterns during loading and unloading is also similar, and those depend on the fiber orientation angles and the loading and unloading rates. The AS4/PEEK thermoplastic composite is used to characterize the relaxation behavior for different off-axis angles and loading rates. There exists a transient loading region at the beginning of unloading. The effective stress and effective plastic strain concept is used to establish a master curve of stress recovery pattern for different off-axis angles and unloading rates.

• Structural Engineering and Mechanics
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• v.30 no.2
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• pp.177-190
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• 2008

Material failure behavior is generally dependent on loading rate. Especially in brittle and quasi-brittle materials, rate dependent material behavior can be significant. Empirical formulations are often used to predict the rate dependency, but such methods depend on extensive experimental works and are limited by practical constraints of physical testing. Numerical simulation can be an effective means for extracting knowledge about rate dependent behavior and for complementing the results obtained by testing. In this paper, the failure behavior of a brittle material under different loading rates is simulated by molecular dynamics analysis. A notched specimen is modeled by sub-million particles with a normalization scheme. Lennard-Jones potential is used to describe the interparticle force. Numerical simulations are performed with six different loading rates in a direct tensile test, where the loading velocity is normalized to the ratio of the pseudo-sonic speed. As a consequence, dynamic features are achieved from the numerical experiments. Remarkable failure characteristics, such as crack surface interaction/crack arrest, branching, and void nucleation, vary in case of the six loading cases. These characteristics are interpreted by the energy concept approach. This study provides insight into the change in dynamic failure mechanism under different loading rates.

• Computers and Concrete
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• v.24 no.6
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• pp.527-539
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• 2019

In this paper, the fracture characteristics of concrete specimens with different notch depths under three-point flexural loads are studied by finite element and fracture mechanics methods. Firstly, the concrete beams (the size is 700×100×150 mm) with different notch depths (a=30 mm, 45 mm, 60 mm and 75 mm respectively) are tested to study the influence of notch depths on the mechanical properties of concrete. Subsequently, the concrete beams with notch depth of 60 mm are loaded at different loading rates to study the influence of loading rates on the fracture characteristics, and digital image correlation (DIC) is used to monitor the strain nephogram at different loading rates. The test results show that the flexural characteristics of the beams are influenced by notch depths, and the bearing capacity and ductility of the concrete decrease with the increase of notch depths. Moreover, the peak load of concrete beam gradually increases with the increase of loading rate. Then, the fracture energy of the beams is accurately calculated by tail-modeling method and the bilinear softening constitutive model of fracture behavior is determined by using the modified fracture energy. Finally, the bilinear softening constitutive function is embedded into the finite element (FE) model for numerical simulation. Through the comparison of the test results and finite element analysis, the bilinear softening model determined by the tail-modeling method can be used to predict the fracture behavior of concrete beams under different notch depths and loading rates.

• KCI Concrete Journal
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• v.13 no.1
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• pp.53-60
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• 2001

Tests of cylindrical concrete specimens under lateral confining pressure of up to 5,000 psi were conducted for two different axial loading cases: monotonic compression and monotonic tension. The purpose of this experimental investigation is to provide stress-strain characteristics of plain concrete in triaxial stress conditions. Lateral confining pressure levels, loading rates, and strength of concrete specimens are varied as parameters. The loading rates are $34.75$\times$10^{-5}$ in/in/sec for fast, $\times$$6.95x10^{-5}$ in/in/sec for normal. and $0.579$\times$10^{-5}$ in/in/sec for slow loading cases. The concrete specimens used in the experiment have compressive strength of 3,500 psi and 6,500 psi, respectively. Findings of this experiment include dependency of the stress-strain behavior of concrete on the above parameters under two different types of loading conditions. The parametric study includes a series of 106 triaxial tests.

• Computers and Concrete
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• v.20 no.3
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• pp.339-350
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• 2017

Dynamic behaviours of reinforced concrete (RC) bending beams subjected to monotonic loading with different loading rates were studied. A dynamic experiment was carried out with the electro-hydraulic servo system manufactured by MTS (Mechanical Testing and Simulation) Systems Corporation to study the effect of loading rates on the mechanical behaviours of RC beams. The monotonic displacement control loading, with loading rates of 0.1 mm/s, 0.5 mm/s, 1 mm/s, 5 mm/s and 10 mm/s, was imposed. According to the test results, the effects of loading rates on the failure model and load-displacement curve of RC beams were investigated. The influences of loading rates on the cracking, ultimate, yield and failure strengths and displacements, ductility and dissipated energy capability of RC beams were studied. Then, the three-dimensional finite element models of RC beams, with the rate-dependent DP (Drucker-Prager) model of concrete and three rate-dependent model of steel reinforcement, were described and verified using the experimental results. Finally, the dynamic mechanical behaviours and deformation behaviours of the numerical results were compared with those of the experimental results.

• Fisheries and Aquatic Sciences
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• v.2 no.1
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• pp.52-57
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• 1999

Air-drived rotating biological contactor (RBC) system, which is effective method in filtering performance, was tested for the nitrification capacity in a recirculating system. At ammonia concentrations between 0.029 and 0.528 mg/l, the effect of ammonia loading rate on ammonia removal rate at three different hydraulic loading rates could be defined by the following first­order regression models: Hydraulic loading rate of $14.8 m^3/m^3/day:\;y=39.2\times+3.4 (r^2=0.9137)$, Hydraulic loading rate of $26.5 m^3/m^3/day: y=53.3\times+4.0 (r^2=0.8686)$, Hydraulic loading rate of $37.3 m^3/m^3/day: y=58.4\times+4.2 (r^2=0.7755)$, where, $\times$ is ammonia loading rate (mg/l), y is ammonia removal rate $(g/m^3/day)$, The equations showed the optimal ammonia removal rate at the hydraulic loading rate of $26.5m^3/m^3/day$. Below the ammonia concentration of 2.72 mg/l, first-order regression models between ammonia loading rate and ammonia removal rate at three different rates of speed are defined as follows: Rotational speed of $0.75 rpm: y=28.5\times+4.7 (r^2=0.9143)$, Rotational speed of $1.0 rpm: y=33.6\times+8.4 (r^2=0.9534)$, Rotational speed of $2.0 rpm: y=28.9\times+3.6 (r^2=0.9488)$, where, x is ammonia loading rate (mg/l), y is ammonia removal rate $(g/m^3day)$. The equations show the ammonia removal rate at the rotational speed of 1.0 rpm is significantly higher than that at the rotational speed of either 0.75 rpm or 2.0 rpm (P<0.05).

• Ocean and Polar Research
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• v.25 no.3
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• pp.277-286
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• 2003

Nitrification performance of fixed film biofilters using coarse sand, loess bead, or styrofoam beads in biofilter columns 1 meter high and 30cm in diameter were studied at different hydraulic and organic matter loading rates. Synthetic wastewater was supplied to the culture tank in order to maintain desired TAN concentrations in inlet water to biofilters. All the biofilters were conditioned 5 months before start of sampling. TAN and $NO_2-N$ conversion rates increased with an increase in the hydraulic loading rate (HLR). However, the improvement in biofilter performance was not linearly correlated to HLR in styrofoam bead filters. This is mainly due to the characteristics of the styrofoam beads used. TAN conversion rates of sand filters increased with the increase of HLR up to $200m^3/m^2$. per day. No increase in the TAN conversion rate was observed at the highest HLR since flooding on the media surface took place. HLR had a significant impact on the TAN conversion rates in loess bead filter up to the highest HLR tested (P<0.05). TAN conversion rates were much less at organic matter loading rates of 9 and 18kg $O_2/m^3$ per day than those without the addition of organic matter in styrofoam bead filters. The addition of glucose resulted in a reduction of the TAN conversion rate from 540 to 284g $TAN/m^3$ per day. No significant difference of TAN conversion rates between the two organic matter loading rates was found (p<0.05). This indicates that the impact of organic matter on nitrification becomes less and less sensitive with an increase in the COD/TAN ratio. At an organic matter loading rate of 9kg $O_2/m^3$. per day, a great reduction of TAN conversion rates was observed in sand filters and loess bead filters. Clearly, organic matter can be one of the most Important Impacting factors on nitrification. $NO_2-N$ conversion rates showed a similar trend for TAN. Based on the TAN and nitrite conversion rates, styrofoam beads showed the best performance among the three filter media tested. Also, the low gravity and price of styrofoam beads make the handling easier and more cost-effective for commercial application. The results obtained at the highest organic matter loading rates can be used in the biofilter design in recirculating aquaculture system.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.56 no.6
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• pp.870-877
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• 2023

The purpose of this study was to assess the efficiency of nitrification based on ammonia loading rates and hydraulic air-loading rates in a moving bed bioreactor (MBBR) under seawater conditions. The goal was to provide foundational data for the design of these bio reactors. At an ammonia loading rate of 0.2 g TAN·m^-2 surface area·day^-1, the influent TAN concentration was determined to be 1.76±0.33 mg·L^-1, which is below the safe concentration for fish survival (2 mg·L^-1). Considering operational aspects, the optimal ammonia-loading rate was derived. Subsequently, experimental results for nitrification efficiency at the optimal ammonia-loading rate revealed that the optimum hydraulic air-loading rate was 1.8 L·air·m^-2 surface area·min^-1. This condition resulted in the lowest concentrations of TAN and NO₂-N in the influent water, thus establishing the optimal hydraulic air-loading rate. A regression equation was derived for the ammonia-removal rate (Y) based on the ammonia-loading rate (x) and expressed as a 0.5-order equation (Y=ax^0.5+b). Specifically, for TAN concentrations of 0-6 mg·L-1, the regression equation Y=0.1683x^0.5-0.13628, was established.

• Computers and Concrete
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• v.7 no.4
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• pp.317-329
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• 2010

The paper describes localization of deformation in a bar under tensile loading. The material of the bar is considered as non-linear viscous elastic and the bar consists of two symmetric halves. It is assumed that the model represents behavior of the quasi-brittle viscous material under uniaxial tension with different loading rates. Besides that, the bar could represent uniaxial stress-strain law on a single plane of a microplane material model. Non-linear material property is taken from the microplane material model and it is coupled with the viscous damper producing non-linear Maxwell material model. Mathematically, the problem is described with a system of two partial differential equations with a non-linear algebraic constraint. In order to obtain solution, the system of differential algebraic equations is transformed into a system of three partial differential equations. System is subjected to loadings of different rate and it is shown that localization occurs only for high loading rates. Mathematically, in such a case two solutions are possible: one without the localization (unstable) and one with the localization (stable one). Furthermore, mass is added to the bar and in that case the problem is described with a system of four differential equations. It is demonstrated that for high enough loading rates, it is the added mass that dominates the response, in contrast to the viscous and elastic material parameters that dominated in the case without mass. This is demonstrated by several numerical examples.

• Structural Engineering and Mechanics
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• v.23 no.2
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• pp.147-161
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• 2006

Recent developments in fractal theory suggest that fractal may provide a more realistic representation of characteristics of cementitious materials. In this paper, the roughness of fracture surfaces in cementitious material has been characterized by fractal theory. A systematic experimental investigation was carried out to examine the dependency of fracture parameters on the aggregate sizes as well as the loading rates. Three maximum aggregate sizes (4.76 mm, 12.7 mm, and 19.1 mm) and two loading rates (slow and fast loading rate) were used. A total of 25 compression tests and 25 tension tests were performed. All fracture parameters exhibited an increase, to varying degrees, when aggregates were added to the mortar matrix. The fracture surfaces of the specimens were digitized and analyzed. Results of the fractal analysis suggested that concrete fracture surfaces exhibit fractal characteristics, and the fractal geometry provide a useful tool for characterizing nonlinear fracture behavior of concrete. Fractal dimension D was monotonically increased as maximum aggregate sizes increase. A new fractal fracture model was developed which considers the size and shape of aggregate, and the crack paths in the constituent phases. Detailed analyses were given for four different types of fracture paths. The fractal fracture model can estimate fractal dimension for multiphase composites.