• Structural Engineering and Mechanics
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• v.36 no.5
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• pp.575-598
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• 2010

The shape and size of the plastic zone around the crack tip are analyzed under pure mode I, pure mode II and mixed mode (I+II) loading for small scale yielding and for both plane stress and plane strain conditions. A new analytical formulation is presented to determine the radius of the plastic zone in a non-dimensional form. In particular, the effect of T-stress on the plastic zone around the crack tip is studied. The results of this investigation indicate that the stress field with a T-stress always yields a larger plastic zone than the field without a T-stress. It is found that under predominantly mode I loading, the effect of a negative T-stress on the size of the plastic zone is more dramatic than a positive T-stress. However, when mode II portion of loading is dominating the effect of both positive and negative T-stresses on the size of the plastic zone is almost equal. For validating the analytical results, several finite element analyses were performed. It is shown that the results obtained by the proposed analytical formulation are in very good agreements with those obtained from the finite element analyses.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.14 no.1
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• pp.78-84
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• 2015

The stress state acting on mechanical parts and structures is generally mixed stress. This complex stress state, which is subject to changes in the environment, will produce many. Cars running on roads with different road conditions will subject the automotive parts to combined stress state. In the x direction and the y direction, a different amplitude and frequency of the fatigue load can be present. However, the load amplitude for Mode I and Mode II in a 2-axis fatigue test is limited to a constant ratio; the load frequency is always the same for any mode. In this paper, it is verified how the variation of the load frequency for mode II affects the behavior of fatigue crack propagation under mixed mode.

• Transactions of the Korean Society of Automotive Engineers
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• v.4 no.4
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• pp.171-178
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• 1996

DCB(pure mode I) and CLS(mixed mode) tests were performed to investigate the effect of fracture mode on the interlaminar fracture of composite laminate. Mode I critical strain energy release rate was found to be $133J/m^2$ from the DCB test and total strain energy release rate decreased from $1, 270J/m^2$ as thickness ratio(tl/t) varied from 0.333 to 0.667 from the crease from the CLS test. Crack length had no effect on the total strain energy release rate and load was almost constant during the crack growth of the specimen which had the specific thickness ratio. Crack initiated when the stress of the strap ply reached constant stress $42kgf/mm^2$ which was found to be independent of the thickness ratio.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.6
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• pp.907-915
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• 2001

Application of bonded dissimilar materials in many industries are increasing. When these materials are to be used in structures, it needs to evaluate the failure strength applying fracture mechanics. Al/Epoxy bonded dissimilar materials with an interface crack and an interface crack emanating from an edge semicircular hole were prepared, experiment of fracture toughness were carried out. Stress intensity factors of interface cracks in bonded dissimilar materials were computed with boundary element method(BEM) and the fracture criteria of mixed mode crack were analyzed. From the results, the fracture criteria and the method of strength evaluation by the fracture toughness in Al/Epoxy bonded dissimilar materials were proposed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.6
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• pp.993-1000
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• 2002

The objective of this work is to develop the capability to analyze accurately the mixed-mode propagation of a crack in composite structures with elastic orthotropic material stiffness properties and anisotropic material strength characteristics. In order to develop the capability to fully analyze fracture growth and failure in anisotropic structures, we examined the fundamental problem of mixed mode fracture by carrying out the analysis on orthotropic materials with an inclined crack subject to biaxial loading. Our goal here is to include an additional term in the asymptotic expansion of the crack tip stress field and to show that the direction of crack initiation can be significantly affected by that term. We employ the normal stress ratio theory to predict the direction of crack extension. It is shown that the angle of crack extension can be altered by horizontal loads and the use of second order term in the series expansion is important f3r the accurate determination of crack growth direction.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.3
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• pp.569-578
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• 1998

The mode I and II stress intensity factors have been calculated theoretically for the cracked plate reinforced with a plate by symmetric spot welding under remote mixed mode loading. This is the extension of authors' previous work for the reinforced cracked plate under remote normal stress. Regardless of loading types, the reinforcement effect gets better as one joining spot is closer to the crack tip and the others are closer to the crack surface, and optimum number of the joining spots can be existed. For the present model, the remote loading parallel to crack surface produces the mode I stress intensity factor.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.8
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• pp.1458-1467
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• 1992

Recently, the composite materials have been researched actively by many researchers because of its useful properties. Especially, an interface crack on the dissimilar material exposes the behavior of the mixed mode crack even though under only the tension stress. In the previous papers, crack energy density(CED) was shown as the crack behavior evaluation parameter which can be expressed consistently from the onset until a final fracture. In a present paper, the basic properties of CED on the interface crack are examined because the results by CED at the homogeneous material above are also expected to be held at the dissimilar material. And we proposed that the contribution of each mode of CED can be separated and be evaluated. Furthermore, the total CED and contribution of each mode are evaluated by domain integral through a finite element analysis at the elastic crack model and the basic examination are carried out.

• Steel and Composite Structures
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• v.31 no.1
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• pp.43-51
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• 2019

This paper is concerned with the numerical calculation of mixed-mode stress intensity factors (SIFs) of 2-D isotropic functionally graded materials (FGMs) by the natural element method (more exactly, Petrov-Galerkin NEM). The spatial variation of elastic modulus in non-homogeneous FGMs is reflected into the modified interaction integral ${\tilde{M}}^{(1,2)}$. The local NEM grid near the crack tip is refined, and the directly approximated strain and stress fields by PG-NEM are enhanced and smoothened by the patch recovery technique. Two numerical examples with the exponentially varying elastic modulus are taken to illustrate the proposed method. The mixed-mode SIFs are parametrically computed with respect to the exponent index in the elastic modulus and external loading and the crack angle and compared with the other reported results. It has been justified from the numerical results that the present method successfully and accurately calculates the mixed-mode stress intensity factors of 2-D non-homogeneous functionally graded materials.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.1
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• pp.58-65
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• 2007

Mixed mode interlaminar fracture behaviors of carbon fabric/epoxy composites were investigated through MMF (Mixed Mode Flexural) test by varying mixed mode ratio ranging from 20% to 90%. Mixed mode interlaminar fracture criteria based on NL point and 5% offset point were also suggested in order to predict mixed mode interlaminar fracture behaviors. Fracture surfaces and crack propagating behaviors were examined through a travelling scope and a scanning electron microscope. According to the results, mixed mode interlaminar fracture behaviors can be predicted by mixed mode interlaminar fracture criterion with m=1.5 and n=0.5 on the basis of NL point or mixed mode interlaminar fracture criterion with m=2 and n=3 on the basis of 5% offset point. Fracture surfaces and crack propagating behaviors are sensitive to mixed mode ratios. MMF test can be successfully applicable in evaluating mixed mode interlaminar fracture toughness of carbon fabric/epoxy composites.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1998.10a
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• pp.254-260
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• 1998

Application of bonded dissimilar materials in various industries are increasing. When these materials are used in structures, it needs to investigate strength evolution applying fracture mechanics. Al/Epoxy bonded dissimilar materials with an interface crack and an interface crack emanating from an edge semicircular hole were prepared for the static tests so that experiment of fracture toughness were carried out. Stress intensity factors of interface cracks in bonded dissimilar materials were computed with boundary element method(BEM) and the fracture criterion of mixed mode crack were analyzed. From the results, the fracture criterion and the method of strength evolution by the fracture toughness in Al/Epoxy bonded dissimilar materials were proposed.