• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.6
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• pp.1792-1798
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• 1991

In this paper the path independent $J_{k}$(k=1, 2) integrals are evaluated in a rectilinear anisotropic body for two dimensional case. The relationship among elastic constants are examined. Using those relationship the expression of $J_{2}$ Integral in terms of $K_{I}$ is found to be very simple.e.e.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.32 no.5
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• pp.411-418
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• 2008

In this work, the effect of strength mismatch on plastic limit loads is quantified for similar metal weld plates with cracks under tension load, via three-dimensional, small strain elastic-perfectly plastic finite element analyses. Relevant variables related to plate geometry and crack length are systematically varied, in addition to the weld width. An important finding is that mis-match limit loads can be uniquely quantified through strength mis-match ratio and one geometry-related parameter. Based on the proposed limit load solutions, reference stress based J-integral estimates is also investigated. When the reference stress is defined by the mis-match limit load, predicted J-integral values agree overall well with FE results.

• 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 Mechanical Science and Technology
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• v.17 no.2
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• pp.254-268
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• 2003

The explicit formulation of the J-integral and the M-integral is constructed in terms of the stress intensity factor and the higher order stress coefficients for Mode II cracks under small or large scale yielding. Furthermore, the stress intensity factor and the higher order stress coefficients as well are computed with the aid of the two-state J- and the M-integral, which is found to be accurate and efficient. It is found that the contribution from the higher order singularities to the J-integral is closely related to the configuration of the plastic zone.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.2158-2166
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• 1994

In order to understand the package crack emanating from the edge of leadframe after the delamination between leadframe and epoxy molding compound in an electronic packaging of surface mounting type, the M-integral and J-integral in fracture mechanics are obtained. The effects of geometry, material properties and molding process temperature on the package crack are investigated taking into account the temperature dependence of the material properties, which simulates a more realistic condition. If the temperature dependence of the material properties is considered the result of analysis conforms with observations that the crack is kinked at between 50 and 65 degree. However, in case of constant material properties at the room temperature it is found that the J-integral is underestimated and the kink crack angle is different form the observation. The effects of the material properties and molding process temperature on J-integral and crack angle are less significant that the chip size for the cases considered here. It is suggested that the geometric factors such as ship size, leadframe size are to be well designed in order to prevent(or control) the occurrence and propagation of the package crack.

• Transactions of the Korean Society of Pressure Vessels and Piping
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• v.16 no.2
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• pp.35-46
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• 2020

In this paper, a fracture mechanics evaluation system which can be used to assess the leak-before-break (LBB) of nuclear piping is developed. Existing solutions for calculating the fracture mechanics parameters (J-integral and crack opening displacement) required for LBB evaluation were firstly presented. Then a module for calculating J-integral and COD was developed, with an additional module for predicting the critical load based on the crack driving force diagram to finally develop a fracture mechanics evaluation system. To confirm the validity of the proposed evaluation system, finite element (FE) analysis was performed, and the FE J-integral and COD results were compared with prediction results using the J-integral and COD estimations program. Furthermore, the critical load assessment module was verified by comparing the actual pipe test results (Battelle test data) with prediction results using the proposed program.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.6
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• pp.937-946
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• 1986

In this paper, the plane stress fracture toughness of low carbon steel with 3mm thickness is investigated for various specimen widths and crack ratios using the J integral. The experiments is carried out for the compact tension(CT) specimen on an Instron machine. For materials that may be approximated by the Ramberg and Osgood stress strain law, the relevant crack parameter like the J integral and load line displacement are approximately normalized. Crack driving forces in terms of J integral is computed using the above estimation scheme. Abtained results are summarized as follows. (1) The plane stress fracture toughness, J$_{c}$, is almost constant in the range 50-70mm of width. Hence J$_{c}$ can be obtained by using smaller specimen than ASTM standard. (2) Yoon's and Simpson's formular which considers crack growth in obtaining J integral show more consevative J than Rice's and Merkle's (3) J$_{c}$ is almost constant in the range 0.499-0.701 crack ratios tested. J$_{c}$ obtained by using Kumar's formular is 28.14kgf/mm for base metal specimen and 32.51kgf/mm for annealed. (4) Comparison of the prediction with actual experimental measurements by Yoon's formular show good agreement for several different-size specimens.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.1
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• pp.105-112
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• 2002

In recent years, the integrity of reactor Pressure Vessel(RPV) under pressurized thermal shock (PTS) accident has been treated as one of the most critical issues. Under PTS condition, the combination of thermal and mechanical stress by steep temperature gradient and internal pressure causes considerably high tensile stress at the inside of RPV wall. As a result, cracks on inner surface of RPV may experience elastic-plastic behavior which can be characterized by J-integral. In such a case, however, J-integral may possibly lose its vapidity due to the constraint effect. The degree of constraint effect is influenced by the loading mode, crack geometry and material properties. In this paper, in order to investigate the effect of clad thickness and crack geometry on constraint effect, three dimensional finite element analyses were performed for various surface cracks. Total of 27 crack geometries were analyzed and results were presented by a two-parameter characterization based on the J-integral and the f-stress.

• Structural Engineering and Mechanics
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• v.3 no.6
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• pp.541-553
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• 1995

The determination of the stress intensity factors is investigated by using the surface integral defined around the crack tip of the structure. In this work, the integral method is derived naturally from the standard path integral J. But the use of the surface integral is also extended to the case where body forces act. Computer program for obtaining the stress intensity factors $K_I$ and $K_{II}$ is developed, which prepares input variables from the result of the conventional finite element analysis. This paper provides a parabolic smooth curve function. By the use of the function and conventional element meshes in which the aspect ratio (element length at the crack tip/crack length) is about 25 percent, relatively accurate $K_I$ and K_{II}$ values can be obtained for the outer integral radius ranging from 1/3 to 1 of the crack length and for inner one zero.

• 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.