• Structural Engineering and Mechanics
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• 제15권2호
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• pp.159-180
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• 2003

In this paper spacing and width of flexural cracks in reinforced concrete beams are determined using two-dimensional finite element analysis. At early loading stages on the beam the primary crack spacing is based on the slip length, which is the development length required to resist the steel stress increment that occurs at a cracked section on the formation of the first flexural crack. A semi-empirical formula is presented in this paper for the determination of the slip length for a given beam. At higher load levels, the crack spacing is based on critical crack spacing, which is defined as the particular crack spacing that would produce a concrete tensile stress equal to the flexural strength of concrete. The resulting crack width is calculated as the relative difference in extensions of steel reinforcement and adjacent concrete evaluated at the cracked section. Finally a comparative study is undertaken, which indicates that the spacing and width of cracks calculated by this method agree well with values measured by other investigators.

• 대한기계학회논문집
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• 제5권3호
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• pp.223-229
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• 1981

A study has been made of the fracture strength and ductility of the dual phase microstructure, in which the martensitic phase encapsulated islands of ferritic phase in association with the cleavage cracking of ferrite grains. It was found the final fracture occured in a brittle manner, starting from the Griffith crack which consisted of the cleavage crack in the ferrite grains and the cracks in second phase. Furthermore, the effects of the ferrite grain sizes on the Griffith crack were also discussed.

• 대한기계학회논문집
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• 제17권7호
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• pp.1794-1804
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• 1993

The thermal stress intensity factors for interface cracks of Griffith and symmetric lip cusp types under vertical uniform heat flow in a finite body are calculated by boundary element method. The boundary conditions on the crack surfaces are insulated or fixed to constant temperature. The relationship between the stress intensity factors and the displacements on the nodal point of a crack tip element is derived. The numerical values of the thermal stress intensity factors for interface Griffith crack in an infinite body and for symmetric lip cusp crack in a finite and homogeneous body are compared with the previous solutions. The thermal stress intensity factors for symmetric lip cusp interface crack in a finite body are calculated with respect to various effective crack lengths, configuration parameters, material property ratios and the thermal boundary conditions on the crack surfaces. Under the same outer boundary conditions, there are no appreciable differences in the distribution of thermal stress intensity factors with respect to each material properties. But the effect of crack surface thermal boundary conditions on the thermal stress intensity factors is considerable.

• Journal of applied mathematics & informatics
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• 제8권1호
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• pp.59-69
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• 2001

The paper deals with the interaction between three Griffith cracks propagating under antiplane shear stress at the interface of two dissimilar infinite elastic half-spaces. The Fourier transform technique is used to reduce the elastodynamic problem to the solution of a set of integral equations which has been solved by using the finite Hilbert transform technique and Cooke’s result. The analytical expressions for the stress intensity factors at the crack tips are obtained. Numerical values of the interaction efect have been computed for and results show that interaction effects are either shielding or amplification depending on the location of each crack with respect to other and crack tip spacing. AMS Mathematics Subject Classification : 73M25.

• Interaction and multiscale mechanics
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• 제2권1호
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• pp.31-44
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• 2009

While the classical theory of Griffith is the foundation of modern understanding of brittle fracture, it has a number of significant shortcomings: Griffith theory does not predict crack initiation and path and it suffers from the presence of unphysical stress singularities. In 1998, Francfort and Marigo presented an energy functional minimization method, where the crack (or its absence) as well as its path are part of the problem's solution. The energy functionals act on spaces of functions of bounded variations, where the cracks are related to the discontinuity sets of such functions. The new model presented here uses modified energy functionals to account for molecular interactions in the vicinity of crack tips, resulting in Barenblatt cohesive forces, such that the model becomes free of stress singularities. This is done in a physically consistent way using recently published concepts of Sinclair. Here, for the consistency of the model, it becomes necessary to allow for crack reversibility and to consider local minimizers of the energy functionals. The latter is achieved by introducing different time scales. The model is solved in its global as well as in its local version for a simple one-dimensional example, showing that local minimization is necessary to yield a physically reasonable result.

• Composites Research
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• 제15권4호
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• pp.37-42
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• 2002

면외전단하중(anti-plane shear loading)을 받는 기능경사 압전 세라믹 무한 스트립(functionally graded piezoelectric ceramic strip)의 상하 양쪽 끝단의 중앙에 평행하게 존재하는 유한한 크기의 균열(Griffith crack)에 대한 특이응력(singular stress)과 전기장(electric field)을 선형 압전 이론(theory of linear piezoelectricity)을 이용하여 결정한다. 푸리에 변환(Fourier transform)을 이용하여 복합적분 방정식을 구성하며, 이를 제2종 Fredholm 적분 방정식(Fredholm integral equation of the second kind) 으로 표현한다. 또한 응력세기계수(stress intensity factor)와 에너지 해방률(energy release rate)에 대한 수치 결과를 제시하였다.

• 대한기계학회논문집
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• 제16권9호
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• pp.1700-1710
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• 1992

본 연구에서는 경계요소법에 의해 천이상태 열전도문제를 해석하는 프로그램 과 Sladek등이 제안한 열탄성 경계적분방정식을 기초로 하여 열탄성문제를 해석하는 프로그램을 개발하여, 유한체 내에 존재하는 Griffith 균열에 대해 정상 및 천이상태 에서 계산한 열응력세기계수와 유한체 내에 존재하는 대칭 입술형 커스프균열(symme- tric lip cusp crack)에 대해 정상상태에서 열응력세기계수를 계산한다. 그 결과를 기존의 해와 비교하여 프로그램의 타당성을 입증한다. 그후 대칭 입술형 커스프균열 에 대한 천이상태에서의 열응력세기계수를 계산하고자 한다.

• 대한기계학회논문집
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• 제15권2호
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• pp.604-610
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• 1991

In this paper, the weight functions for the Mode I and Mode II in SEN(single edge notched) specimen are obtained by superposition of the displacement in the singular field of the Buckner type and the displacements by opposite tractions induced by the singular field. The stress intensity factors, $K_{I}$ and $K_{II}$ are calculated by the weight function theory in SEN specimen under the loading equivalent to uniform tension and shear at infinity in Griffith crack. And the results are compared with the exact solutions.s.

• Journal of Mechanical Science and Technology
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• 제18권9호
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• pp.1549-1558
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• 2004

This study is concerned with the general solution of the field intensity factors and energy release rate for a Griffith crack in a piezoelectric ceramic of finite radius under combined anti-plane mechanical and in-plane electrical loading. Both electrically continuous and impermeable crack surface conditions are considered. Employing Mellin transforms and Fourier series, the problem is reduced to dual integral forms. The solution to the resulting expressions is expressed in terms of Fredholm integral equation of the second kind. The solutions are provided to study the influence of the crack length, the crack surface boundary conditions on the intensity factors and the energy release rate.

• Medical Lasers
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• 제10권4호
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• pp.214-219
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• 2021

Background and Objectives To evaluate the difference in near-infrared (810 nm) laser energy transmission through teeth with and without cracks. Materials and Methods Extracted teeth were sectioned and examined visually for the presence of cracks with the aid of photographs and a trans-illuminator. Fourteen sections, each with cracks (Group A) and no cracks (Group B) were identified and placed 15 mm from the tip of a 300 micron fiber, prior to activation with an 810 nm diode laser (0.1W, 50 ms interval,100 ms duration). A power meter positioned behind the tooth recorded the average energy that was transmitted through the samples. Unpaired t-test analysis was used to determine if the tooth sections with cracks allowed higher power passage compared to sound teeth. Results The mean power recording for the cracked teeth (Group A) was significantly greater (p = 0.0005) than that for the non-cracked teeth (Group B). Conclusion Within the limitations of this study, it is evident that significantly higher laser energy passes through teeth with cracks in comparison to teeth without cracks. A recent clinical study has also shown that lasers could be used to assess symptomatic cracked teeth. Hence, further research is required to determine the relative increase in energy required to identify symptomatic cracked teeth.