• Multiscale and Multiphysics Mechanics
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• v.1 no.1
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• pp.35-51
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• 2016

In this paper, a mixed-mode cohesive law for an interface crack between epoxy and TR (transparent thermoplastic) resin is inversely estimated by the field projection method using numerical solutions and experimentally measured displacements. Displacements in a region far away from the crack tip are measured by digital image correlation technique. An inverse analysis, the field projection method formulated from the interaction J- and M-integrals with numerical auxiliary fields, is carried out to estimate a mixed-mode cohesive law for an interface crack between dissimilar materials. In the present approach, nonlinear deformations and damage near the crack tip are converted into the relationships of tractions and separations on crack surfaces behind the crack tip. The phase angle of mixed-mode singularities of the interface crack is also obtained from measured displacements in this study.

• 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.

• Structural Engineering and Mechanics
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• v.65 no.6
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• pp.699-706
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• 2018

In the present contribution, fracture resistance of U-notched GPPS members under mixed mode I/III loading conditions is assessed by using the Averaged Strain Energy Density (ASED) criterion. This criterion has been founded based on the ASED parameter averaged over a well-defined control volume embracing the notch edge. The validation of the theoretical criterion predictions is evaluated through comparing with the results of a series of mixed mode I/III fracture tests conducted on rectangular-shaped GPPS specimens weakened by a single edge U-notch. A recently developed apparatus for mixed mode I/III fracture experiments is employed for measuring the fracture loads of the specimens. The test samples are fabricated with different notch tip radii with the aim of evaluating the influence of this major feature of the U-notched components on the mixed mode I/III fracture behavior. It is shown that the onset of brittle fracture in U-notched GPPS specimens under various combinations of tension and out-of-plane shear can well be predicted by means of the ASED criterion.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.137-142
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• 2003

In this study, the propagation behavior of fatigue crack effected hole defects was investigated under mixed-mode I+II loading. To create mixed-mode stress field at crack tip, the compact tension shear (CTS) specimen and loading device were used in this tests. The propagation experiments of fatigue crack were performed by changing of the loading application angle(${\phi}$) and the distance(L) estimated from pre-crack tip to hole center located side by side by side with a pre-crack. As L changes, the variation for propagation aspect of fatigue crack, fatigue life and crack propagation rate were examined under mixed-mode loading. Under mixed-mode loading, the propagation rate of fatigue crack increased while the propagation direction changed dramatically because of the interference of hole defects.

• Journal of the Korean Society of Safety
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• v.28 no.4
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• pp.14-18
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• 2013

Blades of horizontal axis are nowadays made of composite materials. Generally, composite materials satisfy design provides lower weight and good stiffness, while laminate composites have often damages as like the delamination and cracks at the interface of laminates. The box spar and tail parts of a blade are composed of the CFRP/GFRP hybrid laminate composites. However, delamination and the interfacial crack often occur in the interface of CFRP/GFRP hybrid laminate composites under the mixed mode fracture condition, especially mode I and mode II. Therefore, there is a need for the evaluation of the mixed mode fracture behavior during the delamination of CFRP/GFRP hybrid laminates. This study shows the experimental results for the delamination fracture toughness in CFRP/GFRP hybrid laminate composites. Fracture toughness experiments and estimation are performed by using DMMB(Dissimilar mixed mode bending) specimen. The materials used in the test are a commercial woven type CFRP(Carbon fiber reinforced plastic) prepreg(CF3327) and UD type GFRP(Glass fiber reinforced plastic) prepreg(HD224A). A CFRP/GFRP hybrid laminate composite is composed by the 10 plies CFRP and GFRP prepreg for DMMB. A thickness of CFRP and GFRP layer is 2.5mm and 3.0mm, respectively. Also the fulcrum location which is a loading parameter is changed from 80 to 100mm on the specimen of length 120mm because it defines the ratio of mode I to mode II. In this study, the effects of the fulcrum location are evaluated in the viewpoint of energy release rate in mode I and mode II contribution. The results show that the delamination crack initiates at higher displacement and lower load according to the increase of the fulcrum location ratio. And the variation of the energy release rate for mode I and II contributions for the mode mixity are shown.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.4
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• pp.1263-1274
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• 1996

In this paper, as elastic-plastic fracture toughness test under mixed mode loading was proposed using a single edge-cracked specimen subjected to bending moment(M), shearing force(F), and twisting moment(T). The J-integral of a crack in the specimen is expressed in the form J=$J_I$+ $J_II$$J_III$, where $J_I$, $J_II$ and $J_III$ are the components of mode I, mode II and mode III deformation, respectively. $J_I$, $J_II$ and $J_III$ can be estimated from M-$\theta$ ($\theta$;crack opening angle), F-U(U; crack shear displacement) and T-$\alpha$ ($\alpha$;crack twisting angle). In order to obtain the the M<-TEX>$\theta$, F-U and T-$\alpha$ diagram inreal time, a new deformaiton gage for mixed mode loading was proposed using the optical position sensing device(PSD). The elastic-plastic fracture toughness test was carried out with an aluminum alloy. The loading apparatus was designed and manufactured for this experiment. For the loading condition of the crack initatio in the mixed mode, the MMT -3(mode I+ mode II+ mode III) has the lowest values out of the all specimens. This implies that MMT-3 is possible of the crackinitation at lower load, if the specimen acts on together with the torque under the same loading condition. An elastic-plastic fracture toughness test using the PSD brings a successful experimentation in measuring the crack deformation(mode I+ mode II+ mode III).

• Transactions of the Korean Society of Mechanical Engineers A
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• v.41 no.9
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• pp.853-860
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• 2017

To evaluate the effects of mode II on the crack initiation and propagation stages, the effects in the fatigue threshold region under a mixed-mode I+II loading state was experimentally investigated. In the case of mixed-mode I + II, during the crack initiation stage, as the loading application angle (${\theta}$) increased, cracks occurred in the lower load owing to the effects of mode II, while the crack propagation rate decreased. The effects of mode II were experimentally investigated in the crack propagation stage by means of multilevel loading direction variation. Following mixed-mode I+II ($0^{\circ}{\rightarrow}{\theta}{\rightarrow}60^{\circ}$), as the load application angle increased, the fatigue crack propagation rate decreased, as did the fatigue crack propagation rate, which occurred later. Following mixed-mode I + II in case of(${\theta}{\geq}75^{\circ}$), the fatigue crack propagation rate was found to increase, while the fatigue life decreased.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.6 s.165
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• pp.1039-1047
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• 1999

It is necessary to evaluate the fatigue behavior of rail steel under the multi-axial stress state to assure the railway vehicle's safety. For this purpose, the stress analysis to investigate the crack initiation criteria, static failure and fatigue behavior under mixed-mode are performed. The stress analysis results show that the initiation of the transverse fissure depends on the maximum shear stress below the surface. For the mixed mode, the fatigue crack growth behavior which is represented by the projection crack length and comparative S.I.F, ${\Delta}K_v$, shows the more conservative results. Also, its rate is lower than that of the case of the mode I, and this difference decreases with increasing the stress ratio, R.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1998.03a
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• pp.220-226
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• 1998

In this pater, a method of strength evaluation applying fracture mechanics in adhesively bonded joints of A1/A1 materials was investigated. Various adhesively bonded joints of double-cantilever beam with a interfacial crack in its adhesive layer were prepared for the fracture toughness test of comprehensive mixed mode conditions from nearly pure mode I to mode II. The experiment of fracture toughness was carried out under various mixed mode conditions with an interfacial crack and critical energy release rate, Gc by the experimental measurements of compliances was determined. From the results, fracture toughness on mixed mode with an interfacial crack is well characterized by strain energy release rate and a method of strength evaluation by the fracture toughness in adhesively bonded joints of A1/A1 materials was discussed.

• Journal of the Korea Concrete Institute
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• v.12 no.2
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• pp.63-69
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• 2000

This study investigates a new method of using a concrete disk to calculate stress intensity factor (SIF) for mixed mode cases. The results indicate that the disk method is more accurate than three point bending test (TPB) in obtaining correct SIF values for mixed mode fracture propagation. Stress intensity factors $K_{I}$ and $K_{II}$ are calculated using a center notched disk subjected to splitting load. The notch angle is calculated by finite element (FEM). Fracture toughness $K_\textsc{k}$ of the concrete is obtained from the load intensities at the initiation of crack propagation. According to the finite element analysis(FEA) and disk test, the results show that mode I and mixed mode cracks propagate toward the directions of crack face and loading point, respectively. The results from FEA with maximum stress theory compare well with the experimental date. Unlike TPB method where an accurate fracture toughness value is difficult to obtain due to the irregular shape of load deflection curve and delayed final crack propagation (following slow stable cracking). fracture toughness value is easily measured in the disk test from the crack initial load. Therefore, it is safe to conclude that disk method is more advantageous than TPB method in analyzing combined mode fracture problems.