• 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.

• Journal of Mechanical Science and Technology
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• v.17 no.6
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• pp.796-804
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• 2003

The use of fracture mechanics has traditionally concentrated on crack growth under an opening mechanism. However, many service failures occur from cracks subjected to mixed-mode loading. Hence, it is necessary to evaluate the fatigue behavior under mixed-mode loading. Under mixed-mode loading, not only the fatigue crack propagation rate is of importance, but also the crack propagation direction. In modified range 0.3$\leq$a/W$\leq$0.5, the stress intensity factors (SIFs) of mode I and mode II for the compact tension shear (CTS) specimen were calculated by using elastic finite element analysis. The propagation behavior of the fatigue cracks of cold rolled stainless steels (STS304) under mixed-mode conditions was evaluated by using K$\_$I/ and $_{4}$ (SIFs of mode I and mode II). The maximum tangential stress (MTS) criterion and stress intensity factor were applied to predict the crack propagation direction and the propagation behavior of fatigue cracks.

• 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.

• 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, K_I, K_II, and K_III, 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.

• Structural Engineering and Mechanics
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• v.56 no.4
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• pp.589-603
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• 2015

The mixed-mode stress intensity factors of 2-D angled cracks are evaluated by Petrov-Galerkin natural element (PG-NE) method in which Voronoi polygon-based Laplace interpolation functions and CS-FE basis functions are used for the trial and test functions respectively. The interaction integral is implemented in a frame of PG-NE method in which the weighting function defined over a crack-tip integral domain is interpolated by Laplace interpolation functions. Two Cartesian coordinate systems are employed and the displacement, strains and stresses which are solved in the grid-oriented coordinate system are transformed to the other coordinate system aligned to the angled crack. The present method is validated through the numerical experiments with the angled edge and center cracks, and the numerical accuracy is examined with respect to the grid density, crack length and angle. Also, the stress intensity factors obtained by the present method are compared with other numerical methods and the exact solution. It is observed from the numerical results that the present method successfully and accurately evaluates the mixed-mode stress intensity factors of 2-D angled cracks for various crack lengths and crack angles.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.6 s.165
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• pp.961-967
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• 1999

A model is constructed to evaluate the mode III stress intensity factor(SIF) for orthotropic three-layered material with a center crack subjected to uniform anti-plane shear 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 numerically analyzed to evaluate the effects of the ratio of shear modulus, strength of each layer and crack length to layer thickness on the stress intensity factor.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.6
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• pp.1448-1454
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• 1994

Data which gathered and used in the field of fatigue and fracture mechanics have a lot of uncertainties. In this case, those uncertainties will make scatter band in evaluation of fatigue life and fracture toughness. Thus, the probabilistic analysis of these data will be needed. For determining the fatigue life in mixed mode, using crack direction law and fatigue crack growth law, the problem is studied as a constrained life minimization. Stress intensity factor(SIF) is computed by approximate solution table(Ewalds/Wanhill 1984) and 0th order PFEM. The variance of fatigue life and SIF are computed by differentiation of tabulated approximate solution and 1st order PFEM. And these are used for criterion of design values, principal parameter determination and modelling. The problem of center cracked plate is solved for checking the PFEM model which is influenced by various parameters like as initial crack length, final crack length, two fatigue parameters in Paris Equation and applied stress.

• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.295-313
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• 2016

In this study, the three-dimensional finite element method is used to determine the stress intensity factor in Mode I and Mixed mode of a centered crack in an aluminum specimen repaired by a composite patch using contour integral. Various mesh densities were used to achieve convergence of the results. The effect of adhesive joint thickness, patch thickness, patch-specimen interface and layer sequence on the SIF was highlighted. The results obtained show that the patch-specimen contact surface is the best indicator of the deceleration of crack propagation, and hence of SIF reduction. Thus, the reduction in rigidity of the patch especially at adhesive layer-patch interface, allows the lowering of shear and normal stresses in the adhesive joint. The choice of the orientation of the adhesive layer-patch contact is important in the evolution of the shear and peel stresses. The patch will be more beneficial and effective while using the cross-layer on the contact surface.

• Journal of Mechanical Science and Technology
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• v.16 no.5
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• pp.599-608
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• 2002

Finite element analysis for the stress intensity factor (SIF) at the skin/stiffener structure with inclined central crack repaired by composite stiffened panels is developed. A numerical investigation was conducted to characterize the fracture behavior and crack growth behavior at the inclined crack. In order to investigate the crack growth direction, maximum tangential stress (MTS) criterion are used. Also, this paper is to study the performance of the effective bonded composite patch repair of a plate containing an inclined central through-crack. The main objective of this research is the validation of the inclined crack patching design. In this paper, the reduction of stress intensity factors at the crack-tip and prediction of crack growth direction are determined to evaluate the effects of various non-dimensional design parameter including; composite patch thickness and stiffener distance. We report the results of finite element analysis on the stiffener locations and crack slant angles and discuss them in this paper. The research on cracked structure subjected to mixed mode loading is accomplished and concludes that more work using a different approaches is necessary. The authors hope the present study will aid those who are responsible for the repair of damaged aircraft structures and also provide general repair guidelines.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1592-1602
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• 1990

Mixed mode surface crack in finite-width plate subjected to uniform tension and bending has been analyzed in 3-D problem by using boundary element method. The calculations were carried out for the surface crack angles(.a/pha.) of 0.deg., 15.deg., 30.deg., 45.deg., 60.deg., and 75.deg., and for the aspect ratio(a/c) of 0.2, 0.4, 0.6 and 1.0 to get stress intensity factors at the boundary points of the surface crack. For the aspect ratio of 1.0 and the surface crack angles, finite element method was used to check the results in this study. Comparison of the results from both methods showed good agreement.