• Journal of the Korean Society for Precision Engineering
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• v.27 no.3
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• pp.80-88
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• 2010

A simple computational model for modeling of subsurface crack growth under cyclic contact loading is presented. In this model, it is assumed that the initial fatigue crack will initiate in the region of the maximum equivalent stress at certain depth under the contacting surface. The position and magnitude of the maximum equivalent stress are determined by using the equivalent contact model, which is based on the Hertzian contact conditions with frictional forces. The virtual crack extension method is used for simulation of the fatigue crack growth from the initial crack up to the formation of the surface pit due to contact fatigue. The relationships between the stress intensity factor and crack length are then determined for various combinations of equivalent contact radii and loadings.

• Structural Engineering and Mechanics
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• v.2 no.3
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• pp.245-256
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• 1994

A new axisymmetric crack model is proposed on the basis of p-version of the finite element method limited to theory of small scale yielding. To this end, axisymmetric stress element is formulated by integrals of Legendre polynomial which has hierarchical nature and orthogonality relationship. The virtual crack extension method has been adopted to calculate the stress intensity factors for 3-D axisymmetric cracked bodies where the potential energy change as a function of position along the crack front is calculated. The sensitivity with respect to the aspect ratio and Poisson locking has been tested to ascertain the robustness of p-version axisymmetric element. Also, the limit value that is an exact solution obtained by FEM when degree of freedom is infinite can be estimated using the extrapolation equation based on error prediction in energy norm. Numerical examples of thick-walled cylinder, axisymmetric crack in a round bar and internal part-thorough cracked pipes are tested with high precision.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.2
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• pp.221-228
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• 1989

The objective of this paper is to develop a numerical technique for analyzing crack driving forces in multi-phase materials. The analysis was based on finite element method coupled with a virtual crack extension technique which is known as the most efficient tool in computational fracture mechanics analysis. The modified J-integral method, proposed by Miyamoto and Kikuchi for the analysis of dual-phase material was carried out by subtracting the J-values for contours surrounding each phase boundary from the J-values for overall contour. It was shown that the proposed numerical procedure, based on the modified J-integral coupled with a virtual crack extension technique, can be used as an effective numerical tool for determining crack driving forces in multi-phase materials.

• Structural Engineering and Mechanics
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• v.50 no.5
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• pp.665-677
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• 2014

A numerical method, using a special mixed finite element associated with the virtual crack extension technique, has been developed to evaluate the energy release rate for kinking cracks. The element is two dimensional 7-node mixed finite element with 5 displacement nodes and 2 stress nodes. The mixed finite element ensures the continuity of stress and displacement vectors on the coherent part and the free edge effect. This element has been formulated starting from a parent element in a natural plane with the aim to model different types of cracks with various orientations. Example problems with kinking cracks in a homogeneous material and bimaterial are presented to assess the computational accuracies.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.9
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• pp.2172-2180
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• 1993

Under general loadings, including body forces, crack-face tractions and thermal loading, the energy release rate equation for a two-dimensional cracked body is presented. Defining the virtual crack extension as the variation of the geometry, the equation is directly derived by a shape design sensitivity of the potential energy. Although the form of the derived energy release rate equation is different from other researchers's results, the three example show that the former is exactly the same as the latter. However, the final integral equation do not involve the derivative of the displacement on the crack surface and crack tip region, thereby improving the numerical accuracy in the computation of the energy relase rate. Moreover, as it was derived from the governing equation including non-linear elasticity without special assumptions, the energy release rate of a elasto-plastic fracture can be obtained and any numerical stress analysis method can be applied.

• Structural Engineering and Mechanics
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• v.25 no.6
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• pp.733-751
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• 2007

The metis element method (Hung 1978) has been applied to analyse free edge interlaminar stresses and delamination in composite laminates, which are subjected to extension and bending. The paper recalls Lekhnitskii's solution for generalized plane strain state of composite laminate and Wang's singular solution for determination of stress singularity order and of eigen coefficients $C_m$ for delamination problem. Then the formulae of metis displacement finite element in two-dimensional problem are established. Computation of the stress intensity factors and the energy release rates are presented in details. The energy release rate, G, is computed by Irwin's virtual crack technique using metis elements. Finally, results of interlaminar stresses, the three stress intensity factors and the energy release rates for delamination crack in composite laminates under extension and bending are illustrated and compared with the literature to demonstrate the efficiency of the present method.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.6A
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• pp.411-418
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• 2012

In this study, behavior of unpatched and patched cylindrical shells with through-wall cracks has been estimated using numerical experiments, and patching effect of them has been investigated according to various patching parameters. To show credibility of numerical models considered, two ways such as h- and p-methods have been adopted. Also, domain integral method and virtual crack extension method have been considered to calculate energy release rates based on linear elastic fracture mechanics. For examples, the unpatched cylindrical shells with circumferential cracks under remote tension have firstly been analyzed to show the validity of finite element modeling with h-method or p-method, and then the results have been compared with literature values published. Next, the sensitive analysis of patch repaired problems in terms of thickness of patch and adhesive, shear modulus of adhesive, composite material type of patch, crack length, etc. has been carried out.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.172-177
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• 2004

Fatigue life prediction is based on fracture mechanics and database which is established from experimental method. Rubber material also uses the same way for fatigue life prediction. But the absence of standardization of rubber material, various way of composition by each rubber company and uncertainty of fracture criterion makes the design of fatigue life by experimental method almost impossible. Tearing energy which has its origin in energy release rate is evaluated as fracture criterion of rubber material and the applicability of fatigue life prediction method are considered. The system of measuring tearing energy using the principal of virtual crack extension method and fatigue life prediction by the minimum number of experiments are proposed.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.04a
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• pp.19-26
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• 1993

The p-version crack model based on integrals of Legendre polynomial and virtual crack extension method is proposed with its potential for application to stress intensity factor computations in linear elastic fracture mechanics. The main advantage of this model is that the data preparation effort is minimal because only a small number of elements are used and the high accuracy and the rapid rate of convergence can be achieved in the vicinity of crack tip. There are two important findings from this study. Firstly, the limit value, the strain energy of the exact solution can be estimated with successive three p-version approximations by ascertaining the approximations is entered the asymptotic range. Secondly, the rate of convergence of p-version model is almost twice that of h-version model on the basis of uniform or quasiuniform mesh refinement for the cracked panel problem subjected tension.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.507-512
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• 2007

A new type of extended element-free Galerkin method (XFEM) is proposed on this paper. The blending region which was inevitable in the extended finite element method and the extended meshfree method is removed in this method. For this end, two different techniques are developed. The first one is the modification of the domain of influence so that the crack tip is always placed on the edge of a domain of influence. The second method is the use of the Lagrange multiplier. The crack is virtually extended beyond the actual crack tip. The virtual extension was forced close by the Lagrange multiplier. The first method can be applied to two dimensional problems only Lagrange multiplier method can be used in both two and three dimensions.