• Structural Engineering and Mechanics
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• 제37권2호
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• pp.149-162
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• 2011

The aim of this research is a comprehensive review and evaluation of beam theories resting on elastic foundations that used to model mode-I delamination in multidirectional laminated composite by DCB specimen. A compliance based approach is used to calculate critical strain energy release rate (SERR). Two well-known beam theories, i.e. Euler-Bernoulli (EB) and Timoshenko beams (TB), on Winkler and Pasternak elastic foundations (WEF and PEF) are considered. In each case, a closed-form solution is presented for compliance versus crack length, effective material properties and geometrical dimensions. Effective flexural modulus ($E_{fx}$) and out-of-plane extensional stiffness ($E_z$) are used in all models instead of transversely isotropic assumption in composite laminates. Eventually, the analytical solutions are compared with experimental results available in the literature for unidirectional ($[0^{\circ}]_6$) and antisymmetric angle-ply ($[{\pm}30^{\circ}]_5$, and $[{\pm}45^{\circ}]_5$) lay-ups. TB on WEF is a simple model that predicts more accurate results for compliance and SERR in unidirectional laminates in comparison to other models. TB on PEF, in accordance with Williams (1989) assumptions, is too stiff for unidirectional DCB specimens, whereas in angle-ply DCB specimens it gives more reliable results. That it shows the effects of transverse shear deformation and root rotation on SERR value in composite DCB specimens.

• 한국안전학회지
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• 제34권6호
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• pp.1-6
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• 2019

Carbon fiber has excellent specific strength, corrosion resistance and heat resistance. And p-Aramid fiber has high toughness and heat resistance and high elasticity, and is used in various fields such as industrial protective materials, bulletproof helmets and vests, as well as industrial fields. However, carbon fiber is relatively expensive, and is susceptible to brittle fracture behavior due to its low fracture strain. On the other hand, the aramid fiber tends to decrease in elastic modulus and strength when applied to the epoxy matrix, but it is inexpensive and has higher elongation and fracture toughness than carbon fiber. Thus the twill hybrid carbonaramid fiber reinforced composite laminate composite was investigated for a delamination fracture toughness under Mode I loading by 2 kinds of MBT and MCC deduction. The specimen was fabricated with 20 hybrid fabric plies. The initial crack was made by inserting the teflon tape in the center plane with a₀/W=0.5 length. The results show that SERR(Strain Energy Release Rate) as the critical and stable delamination fracture toughness were 0.09 kJ/㎡, 0.386 kJ/㎡ by MBT deduction, and 0.192 kJ/㎡, 0.67 kJ/㎡ by MCC deduction, respectively.

• 풍력에너지저널
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• 제14권3호
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• pp.83-90
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• 2023

The purpose of this study is to evaluate the inter-laminar fracture toughness characteristics of CFRP pultrusion spar cap materials reinforced with non-woven glass fabric. Test specimens were fabricated by the infusion technique. A non-woven glass fabric and artificial defects were embedded on the middle surface between two pultruded CFRP panels. Double cantilever beam (DCB) and End Notched Flexure (ENF) tests were performed according to ASTM standards. Fracture toughness and crack propagation characteristics were evaluated with load-displacement curves and delamination resistance curves (R-Curve). The fracture toughness results were calculated by compliance calibration (CC) method. The initiation and propagation values of Mode-I critical strain energy release rate value G_Ic were 1.357 kJ/m2 and 1.397 kJ/m2, respectively, and Mode-II critical strain energy release rate values G_IIc were 4.053 kJ/m2 for non-precracked test and 4.547 kJ/m2 for precracked test. It was found that the fracture toughness properties of the CFRP pultrusion spar-cap are influenced by the interface between the layers of CFRP and glass fiber non-woven.

• Steel and Composite Structures
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• 제23권3호
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• pp.263-271
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• 2017

A theoretical study was carried-out of mode II delamination fracture behavior of the End Loaded Split (ELS) functionally graded beam configuration with considering the material non-linearity. The mechanical response of ELS was modeled analytically by using a power-law stress-strain relation. It was assumed that the material is functionally graded transversally to the beam. The non-linear fracture was investigated by using the J-integral approach. Equations were derived for the crack arm curvature and zero axes coordinate that are needed for the J-integral solution. The analysis developed is valid for a delamination crack located arbitrary along the beam height. The J-integral solution was verified by analyzing the strain energy release rate with considering material non-linearity. The effects of material gradient, non-linear material behavior and crack location on the fracture were evaluated. The solution derived is suitable for parametric analyses of non-linear fracture. The results obtained can be used for optimization of functionally graded beams with respect to their mode II fracture performance. Also, such simplified analytical models contribute for the understanding of delamination fracture in functionally graded beams exhibiting material non-linearity.

• Composites Research
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• 제14권1호
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• pp.8-14
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• 2001

복합재 적층판의 자유단 층간분리의 모드별 변형률 에너지 해방률을 구하는 간이 계산법을 제안하였다. 층간응력은 층간에서의 평형식으로부터 층간의멘트와 층간전단력으로 평가하였다. 적층판 자유단 층간분리의 변형은 일반화된 준3차원 고전적층이론에 의하여 계산하였다. 이 간이 계산법은 변형균 에너지 해방률의 세성분을 구하는 간편한 식으로 나타내었다 복합재 적층판이 일축인장을 받는 경우에 대하여 적층판 중앙면에 대칭과 비대칭인 층간분리가 발생한 경우에 대하여 해석을 행하였다. 해석결과는 가상분리진전법에 의한 유한요소해석결과와 잘 일치하였다.

• Structural Engineering and Mechanics
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• 제18권6호
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• pp.731-744
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• 2004

Modified virtual crack closure integral (MVCCI) technique has become very popular for computation of strain energy release rate (SERR) and stress intensity factor (SIF) for 2-D crack problems. The objective of this paper is to propose a numerical integration procedure for MVCCI so as to generalize the technique and make its application much wider. This new procedure called as numerically integrated MVCCI (NI-MVCCI) will remove the dependence of MVCCI equations on the type of finite element employed in the basic stress analysis. Numerical studies on fracture analysis of 2-D crack (mode I and II) problems have been conducted by employing 4-noded, 8-noded (regular & quarter-point), 9-noded and 12-noded finite elements. For non-singular (regular) elements at crack tip, NI-MVCCI technique generates the same results as MVCCI, but the advantage for higher order regular and singular elements is that complex equations for MVCCI need not be derived. Gauss numerical integration rule to be employed for 8-noded singular (quarter-point) element for accurate computation of SERR and SIF has been recommended based on the numerical studies.

• 한국해양공학회지
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• 제9권2호
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• pp.89-97
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• 1995

The investigate the effect of fiber orientation on the interlaminar fracture toughness of carbon fiber reinforced plastics three prepregs which are domestic products are used in this paper. Those are used for the unidirectional composites, but only one is used for the cross-ply laminate composites which is molded $[0/90]_{6s},\;[0/45]_{6s},\;and\;[0/45/90]_{4s}$. The specimens used for the mode I and mode II Tests are DCB and ENF samples are examined by scanning electron microscope(SEM). The value of $G_{IC}$ is almost same when modified three calculating methods are applied. The highest value of $G_{IC}$at crack initiation is obtained at the $[0/90]_{6s}$ interlaminar and the lowest one is at the $[0/45/90]_{4s}$ interlaminar. The highest value of $G_{IIC}$ at crack initiation, however, is obtained at the $[0/90]_{6s}$ interlaminar and the lowest one is at the $[0/45]_{6s}$. The photographs of SEM show a difference behaviour between mode I and mode II fracture surface.

• 수산해양기술연구
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• 제39권4호
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• pp.262-268
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• 2003

하이브리드 복합재료(Hybrid composite)의 모드 I 층간파괴인성치에 영영향 주는 인자 중 적층순서, 하중점변위율, 초기크랙길이를 변화 시켰을 때의 실험 결과는 다음과 같다. (1) CF/CF, CF/GF, GF/GF로 적층하였을 경우 층간파괴인성치값은 서로 같은 계면을 성형한 것보다 서로 다른 계면을 적층한 CF/GF 의 경우가 강도면에서 가장 높게 나타나는 것을 알 수 있다. (2) 하중점변위율을 0.2, 2, 20mm/min로 변화하였을 때, 미세한 변동은 있었으나, 허중점변위율의 영향은 거의 받지 않는 것을 알 수 있었다. (3) 초기크랙을 25, 30, 35, 40, 50mm로 변화시켰을 때 초기크랙길이의 영향은 일정하지 않았다. CF/CF인 경우는 초기크랙이 짧은 경우, CF/GF, GF/GF인 경우는 초기크랙이 긴 경우에 높은 값을 나타냈다. 이것은 GF 섬유가 직조형태의 프리프레그로 되어 있어 크랙의 진전에 따라 섬유부스러기 등의 생성에 따른 영향이라고 생각된다. (4) 적층순서에 따라 파면의 섬유 분포 형태가 달랐으며, CF/GF인 경우가 섬유의 파손형태가 가장 복잡하게 나타났으며, 이것이 높은 층간파괴인성치를 나타내는 원인이라고 판단된다.

• 대한기계학회논문집A
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• 제38권5호
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• pp.521-526
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• 2014

본 논문에서는 초기균열을 갖고 있는 폐포형 구조, 발포알루미늄의 축방향 기계적 거동을 실험 및 유한요소해석으로 연구하였다. 재료시험에서 MTS 사의 10kN Landmarks 를 사용하여, 모드 I 형상의 15mm/min 의 하중속도로 변위를 제어하였다. 또한 유한요소해석 범용프로그램인 ABAQUS 6.10 으로 3 차원 형상의 실험과 동일한 조건으로 모델을 구성하여 해석을 수행하였다. 실험의 축방향 변위-하중 그래프와 시간에 대한 균열 길이를 기반으로 에너지 해방률을 계산하였으며, 이 값을 해석에서 파손 에너지 조건으로 사용하였다. 결과적으로 변위 값에 따른 하중 거동을 확인할 수 있었으며, 발포알루미늄이 접착제에 비해 상대적으로 큰 밀도와 탄성계수를 가지므로 발포알루미늄의 변형이 상대적으로 작다는 것을 확인할 수 있었다.

• 한국전산구조공학회논문집
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• 제15권3호
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• pp.389-398
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• 2002

동전모양의 균열이 이상복합 실린더 계면에 존재하는 혼합모드 조건(I, II)에 대해 유한요소법을 사용하여 에너지해방율을 구하였다. 두재료의 탄성비와 노치율을 변화시켜 상업용 FEM 프로그램인 ABAQUS로부터 얻은 결과를 가상 균열법과 J 적분법에 적용하였으며 에너지해방율을 구하여 무차원함수로 표현하였다. 모드 II의 무차원 에너지해방율($\sqrt{G_{II}E^*}/\sqrt[p]{\pi a}$)은 균열길이와 탄성비가 증가되면서 그 값이 증가됨을 알수 있었다. 반면, 모드 I의 무차원 에너지해방율($\sqrt{G_{I}E^*}/\sqrt[p]{\pi a}$)은 탄성비가 증가하면서 그 값이 감소하며, 두재료의 탄성비가 3 이상인 경우에 균열길이가 증가되면서 무차원 에너지해방율이 감소하다가 다시 증가하게 나타났다. 또한 수치해석된 결과치를 무한판 실린더의 응력확대계수에 대한 정해와 비교하여 본 해석의 신뢰성을 확보하였다.