• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.10 s.253
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• pp.1255-1260
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• 2006

To maintain the structural integrity of steam generator tubes, 40% of wall thickness plugging criterion has been developed. The approach is for the steam generator tube with single crack, so that the interaction effect of multiple cracks can not be considered. Although, recently, several approaches have been proposed to assess the integrity of steam generator tube with two identical cracks whilst actual multiple cracks reveal more complex shape. In this paper, the coalescence pressure of steam generator tube containing multiple cracks of different length is evaluated based on the detailed 3-dimensional (3-D) elastic-plastic finite element (FE) analyses. In terms of the crack shape, two collinear axial through-wall cracks with different length were considered. Furthermore, the resulting FE coalescence pressures are compared with FE coalescence pressures and experimental results for two identical collinear axial through-wall cracks to quantify the effect of crack length ratio on failure behavior of steam generator tube with multiple cracks. Finally, based on 3-D FE results, the coalescence evaluation diagrams were proposed.

• Tunnel and Underground Space
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• v.11 no.4
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• pp.301-310
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• 2001

Gypsum blocks with sixteen flaws have been prepared and tested in uniaxial compression. Results from these experiments are compared with observations from the same material with two and three flaws. The results indicate that the cracking pattern observed in specimens wish multiple flaws is analogous to the pattern obtained in specimens with two and three flaws such as initiation and propagation of wing, and secondary cracks and coalescence. Wing cracks initiate at an angle with the flaw and propagate in a stable manner towards the direction of maximum compression. Secondary cracks initiate and propagate in a stable manner. As the load is increased, secondary cracks may propagate in an unstable manner and produce coalescence. Two types of secondary cracks are observed: quasi-coplanar, and oblique secondary cracks. Coalescence is produced by the linkage of two flaws: wing and/or secondary cracks. From the sixteen flaws test, four types of coalescence are observed. Observed types of coalescence and initiation stress of wing and secondary crackle depend on flaw geometries, such as spacing, continuity, flaw inclination angle, ligament angle, and steppings.

• Geomechanics and Engineering
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• v.15 no.5
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• pp.1047-1059
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• 2018

This paper focuses on the cracking and fragmentation process in rock materials containing a pair of non-parallel flaws, which are through the specimen thickness, under vertical compression. Several numerical experiments are conducted with varying flaw arrangements that affect the initiation and tensile wing cracks, shear crack growth, and crack coalescing behaviors. To obtain realistic numerical results, a parallelized peridynamics formulation coupled with a finite element method, which is able to capture arbitrarily occurring cracks, is employed. From previous studies, crack initiation and propagation of tensile wing cracks, horsetail cracks, and anti-wing cracks are well understood along with the coalescence between two parallel flaws. In this study, the coalescence behaviors, their fragmentation sequences, and the role of an x-shaped shear band in rock material containing two non-parallel flaws are discussed in detail on the basis of simulation results strongly correlated with previous experimental results. Firstly, crack initiation and propagation of tensile wing cracks and shear cracks between non-parallel flaws are investigated in time-history and then sequential coalescing behavior is analyzed. Secondly, under the effect of varying inclination angles of two non-parallel flaws and overlapping ratios between a pair of non-parallel flaws, the cracking patterns including crack coalescence, fragmentation, and x-shaped shear band are investigated. These numerical results, which are in good agreement with reported physical test results, are expected to provide insightful information of the fracture mechanism of rock with non-parallel flaws.

• Journal of Ocean Engineering and Technology
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• v.9 no.1
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• pp.63-72
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• 1995

The crack which is discovered in various structures and machine elements is multi-cracks. Multi-cracks may cause serious problems because they grow individually, and coalesce into one and it leads to fracture. Fatigue tests have been carried out to study the growth and coalescence behavior of multi-surface-cracks initiated at the semicircular surface notch in type 304 stainless steel at elevated temperature. The results are as follows; When multi-surface-cracks are lying on the surface of material, the major surface crack has greater influence on the fatigue life than the subcracks. The aspect ratio of multi-surface-cracks is lower than that of single crack because of the interaction and coalescence of surface cracks. Crack growth shape turns to semiellipse from the semicircle notch. After coalescence, the surface crack length increases rapidly, and it leads to fracture. Further, the slope transition of Paris law was found in the da/dN-$\Delta$K$_1$ plots.

• Nuclear Engineering and Technology
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• v.32 no.5
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• pp.465-476
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• 2000

In a nuclear power plant, steam generator tubes cover a major portion of the primary pressure-retaining boundary. Thus very conservative approaches have been taken in the light of steam generator tube integrity According to the present criteria, tubes wall-thinned in excess of 40% should be plugged whatever causes are. However, many analytical and experimental results have shown that no safety problems exist even with thickness reductions greater than 40%. The present criterion was developed about twenty years ago when wear and pitting were dominant causes for steam generator tube degradation. And it is based on tubes with single cracks regardless of the fact that the appearance of multiple cracks is more common in general. The objective of this study is to review the conservatism of the present plugging criteria of steam generator tubes and to propose a new coalescence model for two adjacent through-wall cracks existing in steam generator tubes. Using the existing failure models and experimental results, we reviewed the conservatism of the present plugging criteria. In order to verify the usefulness of the proposed new coalescence model, we performed finite element analysis and some parametric studies. Then, we developed a coalescence evaluation diagram.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.11
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• pp.1813-1821
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• 2004

Until now, the 40% of wall thickness criterion, which is generally used for the plugging of steam generator tubes, has been applied only to a single cracked geometry. In the previous study by the authors, a total number of 9 local failure prediction models were introduced to estimate the coalescence load of two collinear through-wall cracks and, then, the reaction force model and plastic zone contact model were selected as the optimum ones. The objective of this study is to estimate the coalescence load of two collinear through-wall cracks in steam generator tube by using the optimum local failure prediction models. In order to investigate the applicability of the optimum local failure prediction models, a series of plastic collapse tests and corresponding finite element analyses for two collinear through-wall cracks in steam generator tube were carried out. Thereby, the applicability of the optimum local failure prediction models was verified and, finally, a coalescence evaluation diagram which can be used to determine whether the adjacent cracks detected by NDE coalesce or not has been developed.

• Journal of Ocean Engineering and Technology
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• v.9 no.1
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• pp.142-151
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• 1995

A simulation program concerned with multi-surface fatigue cracks which initiated at the semi-circular surface notches has been developed to predict their growth and coalescence behaviors at the elevated temperature. Three kinds of coalescence models such as SPC(surface point connection), ASME and BSI(British Standards Institution) conditions were applied, and the results of the simulation were compared with those of the experiment. This simulation is able to enhance the reliance and integrity of structures especially under the elevated temperature which have lots of difficulties in experiments and applications. This shows that the simulation result has utility for fatigue life prediction. Even though all the specimens were the same shape, the error rate was increased in accordance with the applied stress to the specimen. Among the material constants C and m in the narrow band, the results applied upper values of the band to the simulation has shown quite small error compared with the experiment results.

• Geomechanics and Engineering
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• v.8 no.4
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• pp.541-557
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• 2015

This research aims to analyze the fracture coalescence characteristics of brittle sandstone specimen ($80{\times}160{\times}30mm$ in size) containing various flaws (a single fissure, double squares and combined flaws). Using a rock mechanics servo-controlled testing system, the strength and deformation behaviours of sandstone specimen containing various flaws are experimentally investigated. The results show that the crack initiation stress, uniaxial compressive strength and peak axial strain of specimen containing a single fissure are all higher than those containing double squares, while which are higher than those containing combined flaws. For sandstone specimen containing combined flaws, the uniaxial compressive strength of sandstone increase as fissure angle (${\alpha}$) increases from $30^{\circ}$ to $90^{\circ}$, which indicates that the specimens with steeper fissure angles can support higher axial capacity for ${\alpha}$ greater than $30^{\circ}$. In the entire deformation process of flawed sandstone specimen, crack evolution process is discussed detailed using photographic monitoring technique. For the specimen containing a single fissure, tensile wing cracks are first initiated at the upper and under tips of fissure, and anti-tensile cracks and far-field cracks are also observed in the deformation process; moreover anti-tensile cracks usually accompanies with tensile wing cracks. For the specimen containing double squares, tensile cracks are usually initiated from the top and bottom edge of two squares along the direction of axial stress, and in the process of final unstable failure, more vertical splitting failures are observed in the ligament region. When a single fissure and double squares are formed together into combined flaws, the crack coalescence between the fissure tips and double squares plays a significant role for ultimate failure of the specimen containing combined flaws.

• Smart Structures and Systems
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• v.22 no.6
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• pp.675-687
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• 2018

In the previous studies on the porous rock strength the effect of pore number and its diameter is not explicitly defined. In this paper crack initiation, propagation and coalescence in Brazilian model disc containing a single cylindrical hole and or multiple holes have been studied numerically using PFC3D. In model with internal hole, the ratio of hole diameter to model diameter was varied between 0.03, 0.17, 0.25, 0.33, and 0.42. In model with multiple hole number of holes was different in various model, i.e., one hole, two holes, three holes, four holes, five holes, six holes, seven holes, eight holes and nine holes. Diameter of these holes was 5 mm, 10 mm and 12 mm. The pre-holed Brazilian discs are numerically tested under Brazilian test. The breakage load in the ring type disc specimens containing an internal hole with varying diameters is measured. The mechanism of cracks propagation in the wall of the ring type specimens is also studied. In the case of multi-hole Brazilian disc, the cracks propagation and b cracks coalescence are also investigated. The results shows that breaking of the pre-holed disc specimens is due to the propagation of radially induced tensile cracks initiated from the surface of the central hole and propagating toward the direction of diametrical loading. In the case of disc specimens with multiple holes, the cracks propagation and cracks coalescence may occur simultaneously in the breaking process of model under diametrical compressive loading. Finally the results shows that the failure stress and crack initiation stress decreases by increasing the hole diameter. Also, the failure stress decreases by increasing the number of hole which mobilized in failure. The results of these simulations were comprised with other experimental and numerical test results. It has been shown that the numerical and experimental results are in good agreement with each other.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.3
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• pp.716-728
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• 1994

In this paper, fatigue tests were carried out to study the behavior of growth and coalescence of multi-surface cracks which were initiated at the semi-circular surface notches, and a simulation program was developed to predict their growth and coalescence behavior. By comparing the experimental result with those of the simulation based on SPC(surface point connection), ASME and BSI(British Standards Institution) conditions, we tried to enhance the reliance and integrity of structures. This shows that the simulation result has utility for fatigue life prediction.