• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.4
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• pp.290-295
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• 2012

Due to importance of the concepts of ${\theta}$-closure and ${\delta}$-closure, it is natural to try for their extensions to fuzzy topological spaces. So, Ganguly and Saha introduced and investigated the concept of fuzzy ${\delta}$-closure by using the concept of quasi-coincidence in fuzzy topological spaces. In this paper, we will introduce the concept of ${\delta}$-closure in intuitionistic fuzzy topological spaces, which is a generalization of the ${\delta}$-closure by Ganguly and Saha.

• Journal of the Korean Institute of Intelligent Systems
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• v.10 no.6
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• pp.557-563
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• 2000

We introduce r-fuzzy $\delta$-cluster ($\theta$-cluster) points and r-fuzzy $\delta$-closure ($\theta$-closure) sets in smooth fuzzy topological spaces in a view of the definition of A.P. Sostak [13]. We study some properties of them.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.6
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• pp.898-905
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• 1986

In order to obtain the microstructure improving fatigue crack propagation resistance of steels, fatigue crack propagation behavior of martensite-ferrite dual phase steels is investigated in terms of crack deflection and crack closure. The results obtained are as follows; (1) .DELTA.K$_{th}$ and fatigue crack propagation resistance in low .DELTA.K region increases with increasing hardness of second phase. But the difference of this crack propagation resistance decreases with increasing .DELTA.D. (2) In low .DELTA.K region, crack closure increases with increasing hardness of second phase, when the materials have all the sam volume fractionof second phase, or when yield strengths are similar in all materials. (3) These crack closure can be explained by fracture surface roughness due to crack deflection.n.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.6
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• pp.1343-1349
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• 1988

In this study, it is investigated for the effects of stress ratio and grain size on fatigue crack growth behavior and crack closure, in ferrite-martensite dual phase steels. The results obtained are as follows ; .DELTA. $K_{th}$ is independent of the ferrite grain size, but decreases with increasing stress ratio. The relation between .DELTA. $K_{th}$ and stress ratio R is as follows : .DELTA. $K_{th}$ =15.1(1-0.95R). But (.DELTA. $K_{eff}$)$_{th}$ in terms of crack closure is approximately 2.5 MPa.root.m. Also, variation of the degree of crack deflection to crack tip opening displacement at the minimum load is considered as a parameter of crack closure.e.e.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.4
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• pp.336-344
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• 2013

In this paper, we characterize the intuitionistic fuzzy ${\delta}$-continuous, intuitionistic fuzzy weakly ${\delta}$-continuous, intuitionistic fuzzy almost continuous, and intuitionistic fuzzy almost strongly ${\theta}$-continuous functions in terms of intuitionistic fuzzy ${\delta}$-closure and interior or ${\theta}$-closure and interior.

• Journal of the Korean Institute of Intelligent Systems
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• v.9 no.4
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• pp.404-410
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• 1999

We will prove the existence of initial fuzzy closure structures. From this fact we can define subspaces and products of fuzzy closure spaces. Furthermore the family $\Delta$(X) of all fuzzy closure operators on X is a complete lattice. In particular an initial structure of fuzzy topological spaces can be obtained by the initial structure of fuzzy closure spaces induced by those. We suggest some examples of it.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.2
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• pp.208-214
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• 1986

To establish the evaluation of the fatigue crack growth behavior in 5083-O aluminum alloy, constant load-amplitude fatigue crack growth tests were carried out under the small scale yielding conditions. Crack length and closure of this material were measured by the compliance method using a clip-on gage. The main results obtained as follows: The fatigue crack growth rate against stress intensity factor range .DELTA.K exhibits the trilinear form with two transitions at the growth rate 5.5*10$^{-6}$ and 5.5*10$^{-5}$ mm/cycle, in the so-caled Region II. The trilinear form appears still in the plot of growth rate versus effective stress intensity factor range .DELTA. $K_{eff}$. Stress ratio R affects the relationship of crack growth rates versus .DELTA.K but does not affect the reation of crack growth rate versus .DELTA. $K_{eff}$. The experimental results indicate that the effective stress intensity range ratio U depends on the maximum stress intensity factor $K_{max}$, but not on the stress ratio R.o R.R.

• Journal of the Korean Society of Safety
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• v.6 no.4
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• pp.81-87
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• 1991

We propose the crack growth rate equation which will model fatigue crack growth rate behavior such that constant stress amplitude fatigue crack growth behavior can be predicted. Constant stress amplitude fatigue tests are conducted for four materials under three stress ratios of R＝0.2, R＝0.4 and R＝0.6. Materials which have different mechanical properties i.e. stainless steel, low carbon steel, medium carbon steel and aluminum alloy are used. Through constant stress amplitude fatigue test by using unloading elastic compliance method, it is confirmed that crack closure is a close relationship with fatigue crack propagation. We describe simply fatigue crack propagation behavior as a function of the effective stress intensity factor range ($\Delta$ $K_{eff}$＝U .$\Delta$K) for all three regions (threshold region, stable region). The fatigue crack growth rate equation is given by da / dN＝A($\Delta$ $K_{eff}$­$\Delta$ $K_{o}$ )$^{m}$ / ($\Delta$ $K_{eff}$­$\Delta$K) Where, A and m are material constants, and $\Delta$ $K_{o}$ is stress intensity factor range at low $\Delta$K region. $K_{cf}$ is critical fatigue stress intensity factor.actor.

• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.735-742
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• 2010

In this paper, we define and study the concept of $\wedge^s_{\delta}$-closure operator and the associated topology $\tau^{\wedge}^s_{\delta}$ on a topological space (X, $\tau$) in terms of g.$\wedge^s_{\delta}$-sets.

• Transactions of the Korean Society of Mechanical Engineers
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• v.4 no.2
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• pp.47-53
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• 1980

Kikukawa-Compliance method using a conventional clip-on gauge was employed to investigate fatigue crack growth and crack closure in 2017-T3 aluminum alloy. The crack growth rate plot against stress intensity range .DELTA.K on a log-log diagram exhibits a bilinear form with a transition at the growth rate of 10$\^$-4/ mm/cycle. The bilinear form appears still in the plot of growth rate versus effective stress intensity range .DELTA.K$\_$eff/. Fatigue crack growth rate could be well represented by .DELTA.K$\_$eff. The experimental results indicate that the effective stress intensity range ratio U depends on the maximum stress intensity factor K$\_$max/, but the stress ratio R does not affect U. The crack opening stress intensity factor K$\_$op/ tends to increase with increasing K$\_$max/ and decrease with increasing .DELTA.K.