• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.8 no.2
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• pp.126-136
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• 1999

We studied on crack growth retardation in single overloading condition. Crack tip branching which as the second mechanism on crack growth retardation was examined. Crack tip branching was observed to kinked type and forked type. It was found that the branching angle range was from 25 to 53 degree. The variations of crack driving force with branching angle were calculated with finite element method The variation of {{{{ KAPPA _I}}}}, {{{{ KAPPA _II}}}} and total crack driving force(K) were examined respectively So {{{{ KAPPA _I}}}}, {{{{ KAPPA _II}}}} and K mean to mode I, II and total crack driving force. Present model(Willenborg's model) for crack growth retardation prediction was modified to take into consideration the effects of crack tip branching When we predicted retardation with modified model. it was confirmed that predicted and experimental results coincided with well each other.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.9
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• pp.1605-1614
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• 1992

The effects of % overload (% O.L), baseline stress intensity factor range (.DELTA. $K_{b}$) and dimension-less crack depth (a/W) are examined for the retardation behaviors after a single overload and high-low block loads in 7075-T73 aluminum alloy. And wheeler model, which is one of the fatigue life prediction models, is modified to predict retardation life using these test results. The retardation cycles( $N_{d}$) increased with a decrease in a/W and an increase in % O.L. and (.DELTA. $K_{b}$) These effects are more severe after high-low block loads than single overload. In the case of single overload, the main mechanisms of the retardation are the crack closure and the relaxation of K due to crack branching. But in the case of high-low block loads, that of the main mechanism is the crack closure caused by the accumulated compressive residual stree at the crack tip, which is related with the contact of fracture surfaces. Test results were multiple regression analyzed and got regressed shaping correction factors, (n)$_{REG}$, as function of %O.L., a/W and (.DELTA. $K_{b}$) Wheeler model is modified by using these (n)$_{REG}$. The number of delay cycles calculated by modified Wheeler model were in good agreement with the test results of this study.y.udy.y.y.y.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.7 s.166
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• pp.1164-1172
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• 1999

In this study, to investigate the fatigue crack retardation behavior and the variability of retardation cycles, fatigue crack growth tests were conducted on 7075-T6 aluminum alloy under single tensile overload. A retardation coefficient, D was introduced to describe fatigue crack retardation behavior and a random variable, Z to describe the variability of fatigue crack growth. The retardation coefficient was separately formulated according to retardation behavior which is composed of delayed retardation part and retardation part. The random variable, Z was evaluated from experimental data which was obtained from fatigue crack growth tests under constant amplitude load. Using these variables, a probabilistic model was developed on the basis of the modified Forman's equation, and retardation behavior and cycles were predicted under certain overload condition. The predicted retardation curve well agrees with the trend of experimental crack retardation behavior. And this model well predicts the scatter of experimental retardation cycles.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.928-932
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• 1996

Single overload fatigue tests with overload sizes ranging from 50% and 100% have been performed to investing ate the fatigue crack growth retardation behavior. A modified and experimental method of Willenborg's model for prediction of crack growth retardation behavior has been developed, based on evaluations of equivalent plastic zone size (EPZS) changing its size along the overload plastic zone boundary. The minimum crack growth rates of each overload size are linearly decreased with overload size increasing, but fatigue lives extended by single overload are increasing much more unlike the crack growth rates. Comparisons of crack growth behavior predicted by EPZS model and Willenborg model have shown that the EPZS model accounts for overload effects better than Willenborg model. These effects include delayed retardation, large retardation region, minimum crack growth rate, and the increase rate of crack growth rate in the region crack growth rate recovered.

• Journal of The Korean Society of Agricultural Engineers
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• v.48 no.7
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• pp.55-63
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• 2006

Bacterial transport models were evaluated in this study to determine the suitable model at describing bacterial transport in saturated column experiments. Four models used in the evaluation were: advective-dispersive equation (ADE) + equilibrium sorption/retardation (ER) + kinetic reversible sorption (KR) (Model I), ADE + two-site sorption (Model 2), ADE + ER + kinetic irreversible sorption (KI) (Model 3), ADE + KR + KI (Model 4). Firstly, analyses were performed with the first experimental data, showing that Model 4 is appropriate for describing bacterial transport. Even if Model 1 and 2 fit well to the observed data, they have a defect of not including the irreversible sorption, which is directly related to mass loss of bacteria. Model 3 can not properly describe the tailing observed in the data. However, further analysis with the second data indicates that Model 4 can not describe retardation of bacteria, even if the sorption-related parameters are varied. Therefore, Model 4 is modified by incorporating retardation factor into the model, resulting in the improved fitting to the data. It indicates that the transport model, into which retardation, kinetic reversible sorption, and kinetic irreversible sorption are incorporated, is suitable at describing bacterial transport in saturated column experiments. It is expected that the selected transport model could be applied to properly analyze the bacterial transport in saturated porous media.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.8 s.179
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• pp.2074-2082
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• 2000

In this study, to investigate and to predict the crack growth behavior under variable amplitude loading, crack growth tests are conducted on 7075-T6 aluminum alloy. The loading wave forms are generated by normal random number generator. All wave forms have same average and RMS(root mean square) value, but different standard deviation, which is to vary the maximum load in each wave. The modified Forman's equation is used as crack growth equation. Using the retardation coefficient D defined in previous study, the load interaction effect is considered. The variability in crack growth process is described by the random variable Z which was obtained from crack growth tests under constant amplitude loading in previous work. From these, a statistical model is developed. The curves predicted by the proposed model well describe the crack growth behavior under variable amplitude loading and agree with experimental data. In addition, this model well predicts the variability in crack growth process under variable amplitude loading.

• Advances in nano research
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• v.16 no.4
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• pp.413-426
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• 2024

This paper investigates the dynamic behavior of a simply supported viscoelastic plate made of functionally graded carbon nanotube reinforced composite under dynamic loading. Carbon nanotubes are distributed in 5 different shapes: U, V, A, O and X, depending on the shape they form through the thickness of the plate. The displacement fields are derived in the Laplace domain using a higher-order shear deformation theory. Equations of motion are obtained through the application of the energy method and Hamilton's principle. The resulting equations of motion are solved using Navier's method. Transforming the Laplace domain displacements into the time domain involves Durbin's modified inverse Laplace transform. To validate the accuracy of the developed algorithm, a free vibration analysis is conducted for simply supported plate made of functionally graded carbon nanotube reinforced composite and compared against existing literature. Subsequently, a parametric forced vibration analysis considers the influence of various parameters: volume fractions of carbon nanotubes, their distributions, and ratios of instantaneous value to retardation time in the relaxation function, using a linear standard viscoelastic model. In the forced vibration analysis, the dynamic distributed load applied to functionally graded carbon nanotube reinforced composite viscoelastic plate is obtained in terms of double trigonometric series. The study culminates in an examination of maximum displacement, exploring the effects of different carbon nanotube distributions, volume fractions, and ratios of instantaneous value to retardation times in the relaxation function on the amplitudes of maximum displacements.