• Title/Summary/Keyword: mixed mode (I+II)

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Stress Intensity Factors for an Interlaminar Crack in Composites under Arbitrary Crack Surface Loadings (임의의 균열표면 하중을 받는 복합채 중앙균열의 응력세기계수)

  • Lee, Gang-Yong;Park, Mun-Bok;Kim, Seong-Ho
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.20 no.3
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    • pp.901-909
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    • 1996
  • A model is constructed to evaluate the stress intensity factors(SIFs) for composites with an interlaminar crack subjected to as arbitrary crack surface loading. A mixed boundary value problem is formulated by Fourier integral transform method and a Fredholm integral equation of the second kind is derived. The integral equation is solved numerically and the mode I and II SIFs are evaluated for various shear modulus ratios between each layer, crack length to layer thickness, each term of crack surface polynomial loading and the number of layers. The mode I and II SIFs for the E- glass/epoxy composites as well as the hybrid composites are also evaluated.

Analysis of mixed mode crack problems for anisotropic composite laminates using the $J_k$ integral ($J_k$ 적분을 이용한 이방성 복합적층판에 대한 혼합 모우드 파괴문제의 해석)

  • 주석재;홍창선
    • 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.

The Effect of the CFRP/GFRP Composite Thickness on AE Characteristics and Mixed Mode Crack Behavior (CFRP/GFRP 적층복합재의 두께가 혼합모드 균열거동과 AE에 미치는 영향)

  • Yun, Yu-Seong;Kim, Da-Jin-Sol;Kwon, Oh-Heon
    • Journal of the Korean Society of Safety
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    • v.29 no.6
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    • pp.9-14
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    • 2014
  • Recently many efforts and researches have been done to cope with industrial facilities that require a low energy machines due to the gradual depletion of the natural resources. The fiber-reinforced composite materials in general have good properties and have the proper mechanical properties according to the change of the ply sequences and fiber distribution types. However, in the fiber-reinforced composite material, there are several problems, including fiber breaking, peeling, layer lamination, fiber cracking that can not be seen from the metallic material. Particularly, the fracture and delamination are likely to be affected by the thickness of the stacking laminates when the bi-material laminated structure is subjected to a load of the mixed mode. In this study, we investigated the effect of the thickness ratio of the difference in the CFRP/GFRP bi-material laminate composites by measuring the cracking behavior and the AE characteristics in a mixed mode loading, which may be generated in the actual structure. The results show that the thickness of the CFRP becomes more thick, the mode I energy release rate becomes a larger, and also the influence of mode I is greater than that of mode II. In addition, AE amplitude which shows the level of the damage in the structure was obtained the more damage in the CFRP with the thin thickness.

Determination and Applications of U and K$_{op}$ for Crack Closure Evaluation under Mixed-mode loading (혼합모드 하중 하에서 균열닫힘 평가에 대한 K$_{op}$와 U의 결정과 적용)

  • Song Samhong;Seo Kijeong;Lee Jeongmoo
    • Transactions of the Korean Society of Automotive Engineers
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    • v.13 no.3
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    • pp.178-185
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    • 2005
  • Crack tip displacement is originated by tensile stress component, s and shear stress component, t on pure Mode I and pure Mode II. The crack tip displacement(CTD) depends on combined types of different two stress components under mixed-mode loading conditions (MMLC). Thus, the analysis of crack tip displacement must be CTD vector, dv which is composition of ds and dt under MMLC. In this paper, various effects of MMLC on the crack closure are studied experimentally. The crack closure magnitude is calculated from the information of crack tip displacement under MMLC. This information has been obtained from the high resolution optical microscope in direct observations of crack displacement behavior at the crack tip. Observed crack tip displacement is analyzed by using CTD vector to determine crack opening load. The various effects of MMLC on the crack closure are explained using crack opening ratio with crack length and mode mixture. The effective stress intensity factor considering crack closure is also discussed.

Photoelastic Analysis of Stress Field in the Neighborhood of a Mixed Mode Crack Tip (혼합모드 크랙 선단응력의 광탄성해석)

  • 백태현
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.11
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    • pp.2072-2081
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    • 1992
  • Theoretical fringe patterns were calculated and regenerated by using power series type Williams equations and coefficients estimated from the photoelastic data. Results of calculated values were evaluated by comparing experimental data points with the regenerated theoretical fringe loops. Statistical accuracy evaluation between regenerated fringe values and experimental ones showed that standard deviation was minimum and correlation coefficient was maximum when the first four terms of Wiliams equations were used.

Fracture analysis for nozzle cracks in nuclear reactor pressure vessel using FCPAS

  • Abdurrezzak Boz;Oguzhan Demir
    • Nuclear Engineering and Technology
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    • v.56 no.6
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    • pp.2292-2306
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    • 2024
  • This study addresses cracks and fracture problems in engineering structures that may cause significant challenges and safety concerns, with a focus on pressure vessels in nuclear power plants. Comprehensive parametric three-dimensional mixed mode fracture analyses for inclined and deflected nozzle corner cracks with various crack shape aspect ratios and depth ratios in nuclear reactor pressure vessels are carried out. Stress intensity factor (SIF) solutions are obtained using FRAC3D, which is part of Fracture and Crack Propagation Analysis System (FCPAS), employing enriched finite elements along the crack front. Also, improved empirical equations are developed to allow the determination of mixed mode SIFs, KI, KII, and KIII, for any values of the parameters considered in the study. This study provides practical solutions to assess the remaining life and fail-safe conditions of nuclear reactors by providing accurate SIF determination.

Failure Paths of Polymer/Roughened Metal Interfaces under Mixed-Mode Loading (혼합 하중하에서의 고분자/거친금속 계면의 파손경로)

  • Lee Ho-Young;Kim Sung-Ryong
    • Korean Journal of Materials Research
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    • v.14 no.5
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    • pp.322-327
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    • 2004
  • Copper-based leadframe sheets were oxidized in two kinds of hot alkaline solutions to form brown-oxide or black-oxide layer on the surface. The oxide coated leadframe sheets were molded with epoxy molding compound (EMC). After post mold curing, the oxide-coated EMC-leadframe joints were machined to form sandwiched Brazil-nut (SBN) specimens. The SBN specimens were used to measure the fracture toughness of the EMC/leadframe interfaces under mixed-mode (mode I + mode II) loading conditions. Fracture surfaces were analyzed by various equipment to investigate failure path. The results revealed that the failure paths were strongly dependent on the oxide type. In case of brown oxide, hackle-type failure was observed and failure path lay near the EMC/CuO interface with a little inclining to CuO at all case. On the other hand, in case of black oxide, quite different failure path was observed with respect to the distance from the tip of pre-crack and phase angle. Different failures occurred with oxide type is presumed to be due to the difference in microstructure of the oxides.

Numerical study of bonded composite patch repair in damaged laminate composites

  • Azzeddine, Nacira;Benkheira, Ameur;Fekih, Sidi Mohamed;Belhouari, Mohamed
    • Advances in aircraft and spacecraft science
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    • v.7 no.2
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    • pp.151-168
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    • 2020
  • The present study deals with the repair of composite structures by bonding composite patches. The composite structure is a carbon/epoxy laminate with stacking sequence [45/-45/0/90]S. The damaged zone is simulated by a central crack and repaired by bonding symmetrical composite patches. The repair is carried out using composite patches laminated from the same elemental folds as those of the cracked specimen. Three-dimensional finite element method is used to determine the energy release rate along the front of repaired crack. The effects of the repair technique used single or double patch, the stacking sequence of the cracked composite patch and the adhesive properties were highlighted on the variations of the fracture energy in mode I and mixed mode I + II loading.

A Public-Transportation Guidance System using the GIS and the GA

  • Jun, Chul-Min
    • Proceedings of the KSRS Conference
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    • 2003.11a
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    • pp.21-23
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    • 2003
  • Developing a public transportation guidance system requires the following aspects: (i) people may change transportation means not only within the same type but also among different modes such as between buses and subways, and (ii) the system should take into account the time taken in transfer from one mode to the other. This study suggest the framework for developing a public transportation guidance system that generates optimized paths in the transportation network of mixed means including buses, subways and other modes. For this study, the Genetic Algorithms are used to find the best routes that take into account transfer time and other servicetime constraints.

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Mixed Mode Fracture of the Crack Inclined to the Grain Direction in Wood (목재(木材)의 섬유방향(纖維方向)에 경사(傾斜)진 균열의 혼합모-드파괴(破壞)에 관한 연구)

  • Lee, Jun-Jae
    • Journal of the Korean Wood Science and Technology
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    • v.17 no.4
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    • pp.83-88
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    • 1989
  • 목재의 섬유방향에 경사진 균열의 모-드I과 모-드II의 혼합모-드파괴시의 파괴거동을 조사하기 위하여 라왕(Shorea Spp.)의 LA시스템에 있어서 서로 다른 경사각도를 가진 SEN시험편(Single edge notch specimen)에 대하여 휨 시험을 행하였다. 얻이진 결과는 혼합모-드파괴시, 모-드I응력확대계수$K_I$과 모-드II응력확대계수$K_II$간에 일정한 상호작용이 존재한다는 것을 나타내었다. 또한, 모-드I과 모-드II의 임계응력확대계수(Critical stress intensity factor) $K_{IC}$$K_{IIC}$ 이용하여 혼합모-드파괴시의 $K_I$$K_II$간의 상호관계를 규정할 수 있었으며, 이미 보고된 여러 실험식과 본 실험결과를 비교하여 가장 적합한 관계로서 아래와 같은 관계를 얻을 수 있었다.

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