• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.5
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• pp.631-640
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• 2013

This paper provides a comparison of the J-integral estimation method under combined primary and secondary stress in the R6, RCC-MR A16 code. The comparisons of each code are based on finite element analysis using ABAQUS with regard to the crack shape, crack depth, and magnitude of secondary load. The estimate of the R6 code is conservative near $L_r=1$, and that of the RCC-MR A16 code is conservative near $L_r=0$. As a result, this paper proposes a modified method of J-integral estimation in the R6, RCC_MR A16 code. The J-integral using the modified method corresponds to the finite element analysis result.

• Advances in aircraft and spacecraft science
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• v.4 no.6
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• pp.679-699
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• 2017

The aim of this study is to perform a finite element analysis of the Von Mises stresses distribution in the adhesive layer and of the J-Integral for a damaged plate repaired by a composite patch. Firstly, we study the effect of the fiber orientation, especially the position of the layers that have orientation angle different of $0^{\circ}$ from the first layer which is in all cases of our study oriented at ($0^{\circ}$) on the J-Integral. Secondly, we evaluate the effects of the mechanical properties of the patch and the use of a hybrid patch on the reduction of stresses distribution and J-Integral. The results show clearly that the stacking sequence for the composite patch must be selected to absorb optimally the stresses from the damaged area and to position the various layers of the composite under the first layer whose fibers orientation will remain in all cases equal to $0^{\circ}$. The use of a hybrid composite reduces significantly the J-Integral and the stresses in both damaged plate and the adhesive layer.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1568-1575
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• 1990

Fatigue crack growth behavior was investigated in the center cracked plate of KS SB41 steel and the relation between the crack growth rate and various mechanical parameters was studied at small scale yielding, large scale yielding and full scale yielding. The crack opening ratio U was about 0.6-0.8 and had the larger value in the case of load control than that of strain control. Effective stress intensity factor range, .DELTA.K$_{eff}$ and J integral range, .DELTA.J were obtained from the notion of crack opening, and the crack growth rate was expressed with these values. The value of J integral range increased rapidly at stress ratio, R=0 in full scale yielding of load control test. COD value also increased rapidly with the increase of ligament net stress at large scale yielding of load control test.t.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.11
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• pp.3498-3506
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• 1996

A loading device to be used in fracture experiment is presented. It's loading angle can be adjusted from $-45^{\circ}$ to $105^{\circ}$ at intervals of $15^{\circ}$ for a CTS ( compact tension-shear) specimen, so that it is to be useful to measure mixed mode toughness. The equations to give the $K_ I$, $K_ I1$ and J-integral for the experiment are evluated though finite elemetn analysis in which the loading procedure is simulated and the behaviors of the specimen such as load-displacement curve are estimated. In the course of the evaluation the values $K_ I$, $K_ I1$ and J-integral calculated through recentrly released numerical methods are employed as the reference ones.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.9
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• pp.2133-2141
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• 1995

The thermo-mechanical fatigue tests were performed on the specimens extracted from 1.5Cr-0. 67Mo-0.33V alloy. The characteristics of thermo-mechanical fatigue crack propagation were examined and reviewed in view of fracture mechanics. The results obtained from the present study are summarized as follows : (1) The propagation characteristics of isothermal low-cycle fatigue crack are dominated by .DELTA.J$_{f}$ in case of PP waveform, and .DELTA.J$_{c}$ in case of CP waveform. (II)The propagation characteristics of thermo-mechanical fatigue crack are dominated by .DELTA.J$_{c}$ for in-phase case, and by .DELTA.J$_{c}$ for out-of-phase. The present results were in good agreement with the equation of propagation law for isothermal low-cycle fatigue crack in case of thermo-mechanical fatigue.tigue.e.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.2139-2157
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• 1994

In order to understand the delamination between leadframe and epoxy molding compound in an electronic packaging of surface mounting type, the stress intensity factor, T-stress and J-integral in fracture mechanics are obtained. The effects of geometry, material properties and molding process temperature on the delamination are investigated taking into account the temperature dependence of the material properties, which simulates as more realistic condition. As the crack length increases the J-integral increases, which suggest that the crack propagates if it starts growing from the small size. The effects of the material properties and molding process temperature on stress intensity factor, T-stress is and J-integral are less significant than the chip size for the practical cases considered here. The T-stress is negative in all eases, which is in agreement with observation that interfacial crack is not kinked until the crack approaches the edge of the leadframe.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.207-212
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• 2022

In this paper, an interesting integral involving the Ī-function of one variable introduced by Rathie has been derived. Since Ī-function is a very generalized function of one variable and includes as special cases many of the known functions appearing in the literature, a number of integrals can be obtained by reducing the Ī function of one variable to simpler special functions by suitably specializing the parameters. A few special cases of our main results are also discussed.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.109-118
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• 2015

In the present paper, a new analytic function valued integral operator is introduced which is defined on n-copies of a subset of the class of normalized analytic functions on the unit disc of the complex plane. This operator, which is denoted here by $\mathfrak{J}^{{\alpha}_i,{\beta}_i}(f_1,{\ldots},f_n)$, unifies and generalizes several integral operators studied earlier. Interesting sufficient conditions are derived for the univalent starlikeness of $\mathfrak{J}^{{\alpha}_i,{\beta}_i}(f_1,{\ldots},f_n)$.

• Coupled systems mechanics
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• v.11 no.6
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• pp.543-556
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• 2022

Delamination of multilayered inhomogeneous beam that exhibits non-linear relaxation behavior is analyzed in the present paper. The layers are inhomogeneous in the thickness direction. The dealamination crack is located symmetrically with respect to the mid-span. The relaxation is treated by applying a non-linear stress-straintime constitutive relation. The material properties which are involved in the constitutive relation are distributed continuously along the thickness direction of the layer. The delamination is analyzed by applying the J-integral approach. A time-dependent solution to the J-integral that accounts for the non-linear relaxation behavior is derived. The delamination is studied also in terms of the time-dependent strain energy release rate. The balance of the energy is analyzed in order to obtain a non-linear time-dependent solution to the strain energy release rate. The fact that the strain energy release rate is identical with the J-integral value proves the correctness of the non-linear solutions derived in the present paper. The variation of the J-integral value with time due to the non-linear relaxation behavior is evaluated by applying the solution derived.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.3
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• pp.479-489
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• 1989

The $J_{k}$ integral method for determining mixed mode stress intensity factors separately in the cracked anisotropic plate is developed. Stress intensity factors are indirectly determined from the values of $J_{1}$ and $J_{2}$. The $J_{2}$ integral can be evaluated efficiently from a finite element solution, neglecting the contribution from the portion of the integration contour along the crack faces, by selecting the integration contour in the vicinity of the crack tip. Using functions of a complex variable, the complete relations between $J_{1}$, $J_{2}$ and $K_{I}$ , $K_{II}$ for anisotropic materials are derived conveniently by selecting narrow rectangular contours shrinking to the crack tip. Compared to the existing path independent integral methods, the present method does not involve calculating the auxiliary solution and hence numerical procedures become quite simple. Numerical results to various problems are given and demonstrate the accuracy, stability and versatility of the method.