• 한국해양공학회지
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• 제9권2호
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• pp.112-122
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• 1995

In this work, prediction of fatigue life and fatigue crack growth are studied. 4th order polynominal function is presented to describe the crack growth behaviors from artifical pit of SM45C steel. Crack growth curves obtained from 4th order polyminal growth equations are in good agreement with experimental data The crack growth behaviors at arbitrary stress levels and investigated by the concept of elastic-plastic fracture mechanics using ${\Delta}J$. Fatigue life prediction are carried out by numerical integral method. Prediction lives obtained by proposed method in this study, is in good agreement with the experimental ones. Life prediction results calculated by using of ${\Delta}J$ better than those of ${\Delta}K$.

• 대한기계학회논문집
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• 제13권2호
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• pp.252-256
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• 1989

본 연구에서는 탄성-소성 피로파괴 시험을 하여 dN/dn과 .DELTA.J의 관계와 dN/과 da/dn의 관계에 대한 실험식을 얻고 이론적인 해석결과와 비교 검토하고자 한다.

• 한국해양공학회지
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• 제9권2호
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• pp.98-111
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• 1995

High temperature low cycle fatigue shows that cycle-dependent crack growth owing to cyclic plastic deformation occurred simultaneosly with time-dependent crack growth owing to intergranular deformation. Consequently, to estimate crack growth rate uniquely, many to investigators have proposed various kinds of parameters and theories but these could not produce satisfactory results. Therefore the goal of this study is focused on prediction of crack growth rate using predominant damage rule, linear cumulative damage rule and transitional parameter ${\Delta}J_c/{\Delta}J_f$. On the basis of these sinusoidal loading waveform at 600$^{\circ}C$ and 700$^{\circ}C$.

• 대한수학회논문집
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• 제27권4호
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• pp.721-732
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• 2012

The principal aim of the paper is to investigate new integral expression $${\int}_0^{\infty}x^{s+1}e^{-{\sigma}x^2}L_m^{(\gamma,\delta)}\;({\zeta};{\sigma}x^2)\;L_n^{(\alpha,\beta)}\;({\xi};{\sigma}x^2)\;J_s\;(xy)\;dx$$, where $y$ is a positive real number; $\sigma$, $\zeta$ and $\xi$ are complex numbers with positive real parts; $s$, $\alpha$, $\beta$, $\gamma$ and $\delta$ are complex numbers whose real parts are greater than -1; $J_n(x)$ is Bessel function and $L_n^{(\alpha,\beta)}$ (${\gamma};x$) is generalized Laguerre polynomials. Some integral formulas have been obtained. The Maple implementation has also been examined.

• 대한수학회논문집
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• 제20권2호
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• pp.339-350
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• 2005

We obtain the following two inequalities on a strongly pseudoconvex domain $\Omega\;in\;\mathbb{C}^n\;:\;for\;f\;{\in}\;O(\Omega)$ $$\int_{0}^{{\delta}0}t^{a{\mid}a{\mid}+b}M_p^a(t, D^{a}f)dt\lesssim\int_{0}^{{\delta}0}t^{b}M_p^a(t,\;f)dt\;\int_{O}^{{\delta}O}t_{b}M_p^a(t,\;f)dt\lesssim\sum_{j=0}^{m}\int_{O}^{{\delta}O}t^{am+b}M_{p}^{a}\(t,\;\aleph^{i}f\)dt$$. In [9], Shi proved these results for the unit ball in $\mathbb{C}^n$. These are generalizations of some classical results of Hardy and Littlewood.

• 한국안전학회지
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• 제15권2호
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• pp.8-12
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• 2000

The fatigue crack propagation tests were performed in triangular and holding-time stress waveforms at $650^{\circ}C$. The behavior of fatigue crack propagation was investigated according to waveform. The analysis of high temperature fatigue crack propagation by the stress intensity factor range ${\Delta}K$, elastic fracture mechanics parameter, was not available. The behaviors of high temperature fatigue crack propagation by the J-integral(${\Delta}J_f$, J' and ${\Delta}J_c$), elasto-plastic fracture mechanics parameter, were investigated in a number of stress waveforms. The fast-fast waveform exhibited cycle-dependent(fatigue type), the slow-fast and the hold time with 500sec waveforms appear to be time-dependent(creep type) and the fast-slow and the hold time with 5, 25sec waveforms exhibited conbined behavior of both types(fatigue-creep conbined type).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권3호
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• pp.147-163
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• 2014

In this paper, we study the existence of positive solutions for singular impulsive differential equations with integral boundary conditions $$\{u^{{\prime}{\prime}}(t)+q(t)f(t,u(t),u^{\prime}(t))=0,\;t{\in}\mathbb{J}^{\prime},\\{\Delta}u(t_k)=I_k(u(t_k),u^{\prime}(t_k)),\;k=1,2,{\cdots},p,\\{\Delta}u^{\prime}(t_k)=-L_k(u(t_k),u^{\prime}(t_k)),\;k=1,2,{\cdots},p,\\u=(0)={\int}_{0}^{1}g(t)u(t)dt,\;u^{\prime}=0,$$) where the nonlinearity f(t, u, v) may be singular at v = 0. The proof is based on the theory of Leray-Schauder degree, together with a truncation technique. Some recent results in the literature are generalized and improved.

• 대한기계학회논문집
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• 제9권5호
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• pp.539-547
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• 1985

본 논문에서는 이상과 같은 연구현상을 배경으로 응력비 R.geq.0인 사인응력파 에서도 사이클의존형 크랙전파가 공존하는가, 공존한다면 그 전이를 결정짓는 조건을 구하기 위해, 대표적인 고온용 재료인 SUS 304강을 이용하여 온도 650.deg. C, 대기중에서 반복속도 .nu., 응력비 R, 응력레벨 .sigma.$_{maxo}$등의 실험조건을 바꾸어 고온저사이클 피로실험을 하였다. 또 이 현상의 기초과정을 이해하는데 도움을 주기 위하여 파면 관찰을 행하였다.

• 대한기계학회논문집
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• 제11권3호
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• pp.376-385
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• 1987

본 연구에서는 평면응력 파괴인성치의 거동에 관한 일련의 연구로서 위와 같 은 점을 고려하여 얇은 두께의 시험편을 이용하여 z의 변화에 대한 평면응력 파괴인성 치와 J저항곡선을 실험적으로 고찰하였으며 크랙성장을 고려한 J적분식도 검토하였다. 크랙길이는 하중제거 컴플라이언스법에 의하여 구하였고, ASTM E813의 방법으로J= .sigma.$_{f}$ .DELTA.(2ａ)인 크랙둔화선과 J저항곡선의 교점에서 구한 J적분값을 J$_{c}$로 정 의하였다. 또한, 재료를 변형경화재료로 가정하여 HRR응력변형율장의 특성을 이용 하여 J적분값을 구한 후 실험치와 상호 비교 검토하였다.이때 입력자료는 실험치의 그것과 동일하게 하였다. 동시에 z의 변화에 대한 T의 변화도 함께 고찰하였다.다.

• 대한수학회지
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• 제53권4호
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• pp.929-967
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• 2016

Let p(t, x) be the fundamental solution to the problem $${\partial}^{\alpha}_tu=-(-{\Delta})^{\beta}u,\;{\alpha}{\in}(0,2),\;{\beta}{\in}(0,{\infty})$$. If ${\alpha},{\beta}{\in}(0,1)$, then the kernel p(t, x) becomes the transition density of a Levy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t, x) and its space and time fractional derivatives $$D^n_x(-{\Delta}_x)^{\gamma}D^{\sigma}_tI^{\delta}_tp(t,x),\;{\forall}n{\in}{\mathbb{Z}}_+,\;{\gamma}{\in}[0,{\beta}],\;{\sigma},{\delta}{\in}[0,{\infty})$$, where $D^n_x$ x is a partial derivative of order n with respect to x, $(-{\Delta}_x)^{\gamma}$ is a fractional Laplace operator and $D^{\sigma}_t$ and $I^{\delta}_t$ are Riemann-Liouville fractional derivative and integral respectively.