• Journal of the korean Society of Automotive Engineers
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• v.12 no.1
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• pp.26-32
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• 1990

This study investigated a method for the determination of the J-integral for a tough glassy polymer such as polycarbonate plates by using the method of caustics. Comparing the values of J-integral determined by a numerical analysis and by the method of caustics, the method of caustics was found to be an effective experimental technique for the determination of the J-integral. The ratio between two J-integrals determined by the method of caustics and by finite element method converged into 1 within the limit of low load. However, it was noticed that the greater the plastic zone at the crack tip was, the lower the J-integral obtained by the reflect method of caustics. This difference may be deduced from the damage at the crack tip such as craze appeared in the polycarbonate plate. It was confirmed that the ratio of longitudinal diameter( $D_{l}$ ) to transverse diameter ( $D_{t}$) of caustics generally converged into 1 at the low load. The transition of the state of stress at the vicinity of a crack tip from plane strain to plane stress was deduced by noticing that the longitudinal diameter( $D_{l}$ ) grew faster than the transverse diameter( $D_{t}$) of caustics within the higher load range.

• Journal of the Korean Society for Nondestructive Testing
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• v.8 no.1
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• pp.22-29
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• 1988

The optical method of reflected and transmitted caustics has been utilized in mechanics investigations. This relatively new experimental technique has been successfully applied on various fracture analysis such as static and dynamic c rack propagation studies, some elasticity problems and contact stress, etc, In this study, the stress intensity factors in thin polycarbonate specimens, a kind of optically anisotropic material, under Mode I loading condition are estimated by the method of caustics. The values of stress intensity factors obtained from theoretical caustics shape are compared by the experiment. It is confirmed that the two stress intensity factors agree well with Srawley's solution.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.10
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• pp.2543-2553
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• 1994

Caustics method has been applied successfully to determine the fracture parameters such as stress intensity factor and the J-integral for elastic and/or elastic-plastic stress field around the crack tip. For stress fields at the vicinity of crack tip in the creep domain, no experimental report concerning fracture mechanics parameters by using the caustics method has been published up to date. This study investigated creep behavior at the vicinity of crack tips at high temperature($175^{\circ}C$) and attempted to determine of proper fracture parameters for A1 5086 H24 specimens by using the caustics method. The results obtained from the limited experimental investigation are as follows; $J_{th}/J_{caus}$ is found to approach to 1 more rapidly than $K_{th}/K_{caus}$ does during incipient period(within 80 minutes). It is confirmed that experimental $K_{caus}$ approached to theoretical $K_{th}$ after 80 minutes by analyzing the ratio of $K_{th}$ to $K_{caus}$. Unlike the case of room temperature, it is confirmed experimentally that caustics diameter enlarged gradually even the distance between specimen and screen keeps constant. It showed that initial curve of the caustics was initially located in the plastic zone, but it grew out rapidly into the elastic zone for Al 5086 H24 at $175^{\circ}C$. It is confirmed that caustics is a function of time, temperature and distance between specimen and screen at high temperature.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2331-2338
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• 1994

Experimental conditions of the optical shadow methods of caustics for measurement of the stress intensity factor and the J-integral in various materials(polycarbonate, PMMA, Al 5586D) are investigated. The necessary experimental requirements toe determine accurate values of the stress intensity factors and the J-integrals are described. The ratio of $r_o$ (radius of initial curve) to $r_p$ (plastic zone size) is selected as a parameter to verify the experimental limitation of the method of caustics in determination of fracture parameters. In this study, transmission caustics method was used for compact tension specimens made of polycarbonate and PMMA. while reflection caustics method was applied to c-shaped tension specimen made of Al 5586D. The appropriate ranges of $r_o/r_p$ tp determine accurate values of stress intensity factors were found to be 1.5~1.8. Existing experimental results have been obtained mainly by changing $r_p$ with different loads in $r_o/r_p$. However, in this study we could obtain varying $K_{caus}/K_{th}$ over the wide range of $r_o/r_p$ at fixed load conditions with newly designed optical arrangement. Thus, we could find the range in which theoretical and experimental results agree well each other by changing $r_o$ values only. In Al 5586D specimen, experimental caustics were located inside of the plastic zone, and $K_{caus}/K_{th}$ were found to be not unity in this range. It is found that $J_{caus}/J_{th}=1{\;}with{\;}r_o/t{\geq}0.8$ and the experimental plastic zone includes the contours of caustics.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.12
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• pp.2226-2240
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• 1992

This paper studies the applicability of the method of caustics into anisotropic materials under mode I and mixed static loading conditions and introduces the procedure to obtain stress intensity factors(S.I.F.) in anisotropic materials by the method of caustics. The mapping equations for initial and caustic curves in anisotropic materials were introduced and their computer graphical images were compared to the experimental ones to check the validity of the mapping equations proposed in this paper. The agreement between them was found to satisfactory. Two kinds of method to determine S.I.F. in anisotropic materials by the method of caustics were proposed in this paper and applied into the orthotropic materials under various loading conditions. In the case of mode I loading condition, the S.I.F.'s obtained by this paper's methods were found to be quite similar to the results by other method, boundary element method(B.E.M) and in the case of mixed loading condtion, the S.I.F's by this paper and B.E.M. showed a little differences(2.2-24.4%) with respect to the slanted angle of crack.

• Journal of The Korean Astronomical Society
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• v.31 no.1
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• pp.27-37
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• 1998

We have made semi-analytical studies to investigate the configurations of caustics and the probability distribution of the flux factor K for the binary microlensing including external shears. A parametric equation of critical curve is derived in a 4th order complex polynomial. We present the topological dependencies of the caustics for selected gamma parameters (0, 0.3, 0.6, 1.3, 2.0, and 2.5) and convergence terms (0., 0.4, 0.8, 1.2, 1.6, and 2.0). For the purpose of analyzing the efficiency of High Amplification Event (HAE) on each caustics, we examine the probability distribution of the flux factor by a Monte Carlo method. Changing the separation of the binary system from 0.8 to 1.3 (in normalied unit), we examine the probability distribution of the K-values in various gamma parameters. The relationship between gamma parameters, seperations and their probabilties of the flux factor K have been studied. Our results show that the relatively higher K values (K>1.5) are increased as increasing the separation of the binary system. We therfore conclude that, in the N-body microlensing, the probabilities of higher HAEs are inversely proportional to the star density as well. We also point out that the present research might be used as a preliminary step toward investigating heavy N-body microlensing simulations.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.3
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• pp.944-953
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• 1991

본 연구에서는 일반적인 이방성재료에 대한 코스틱방법의 적용을 검토하는 일 환으로서, 직교이방성재료중 특성방정식의 근이 동일함으로 인하여 균열의 응력장이 특이성을 갖게 되고, 따라서 지금까지는 코스틱법의 적용이 어려웠던 재료(의사등방성 재료)에 대하여, 코스틱상 및 초기곡선의 식을 이론적으로 구하였고, 이 식을 예상되 는 여러가지 경계조건 하에서 컴퓨터 그래픽(computer graphic)으로 가시화하여, 시편 제작의 어려움으로 인하여 실험이 곤란한 의사등방성재료의 코스틱상을 예시하였으며, 또 이들 재료에 대한 응력확대계수 산출법을 제시함과 동시에 이 산출법이 등방성 재 료 및 일반적 직교이방성재료에도 사용가능함을 밝혀 다음 제2부에서 실험을 통하여 검증되도록 하였다.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1998.03a
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• pp.123-128
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• 1998

In fracture problems, stress intensity factors obtained theoretically and experimentally have been effectively utilized in the analytical evaluation of the cracks effect. The effect of surface crack of a cylindrical and a hollow cylindrical bar is investigated, as well as the effect of the thickness of a hollow cylindrical bar and inclined crack of a hollow cylinder subjected to torsion moment. In this study, stress intensity factor Km of mode III which expresses the stress state in the neighborhood of a crack tip is used. Stress analysis was conducted of the inside of a hollow cylinder in the axial direction of three dimensional crack tip subjected to torsion moment by combining the caustics method and the stress freezing method.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.7 no.5
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• pp.46-52
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• 1998

In fracture problems, stress intensity factors obtained theoretically and experimentally have been effectively utilized in the analytical evolution of the cracks effect. The effect of surface crack of a cylindrical and a hollow cylindrical bar is investigated, as well as the effect of the thickness of a hollow cylindrical bar and inclined crack of a hollow cylinder subjected to torsion moment. In this study, stress intensity factor Km of mode III which expresses the stress state in the neighborhood of a crack tip is used. stress analysis was conducted on the inside of hollow cylinder inthe axial direction of three dimensional crack tip subjected to torsion moment by combining the caustics method and the stress freezing method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.7
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• pp.1630-1641
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• 1995

The dynamic stress intensity factors (DSIF ; $K_{I}$$^{dyn}$) were studied in some polymeric materials using caustics method with a high speed camera system. Also crack tip propagation speed was measured by dynamic crack propagation velocity measuring device. To calculate DSIF a finite element analysis program-INha Stress Analysis Moving CRack(INSAMCR) was utilized. Dynamic fracture characteristics were investigated to verify a relationship between DSIF and crack tip propagation speed and acceleration in PMMA, Homalite-100 and Polycarbonate. The relationship between dynamic stress intensity factor and crack tip velocity revealed typical shapes. Measured crack tip acceleration data envelope converges to the zero level with increasing DSIF. Equivalently crack tip velocities show a wide spread range at low values of DSIF, but become a constant with a higher DSIF. $1.2MPa{\sqrt{m}}$, $1.4MPa{\sqrt{m}}$ and $1.3 MPa{\sqrt{m}}$ were obtained as $K_{I}$$^{dyn}$ values to arrest the dynamic crack for PMMA, Homalite-100 and Polycarbonate, respectively. INSAMCR was run to verify experimental results in PMMA and shows good agreementment.