• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.36 no.2
• /
• pp.149-156
• /
• 2012

In fracture mechanics, the weight function can be used for calculating stress intensity factors. In this paper, a two-dimensional electroelastic analysis is performed on a transversely isotropic piezoelectric material with an open crack. A plane strain formulation of the piezoelectric problem is solved within the Leknitskii formalism. Weight function theory is extended to piezoelectric materials. The stress intensity factors and electric displacement intensity factor are calculated by the weight function theory.

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

• Structural Engineering and Mechanics
• /
• v.66 no.5
• /
• pp.649-663
• /
• 2018

The scaled boundary finite element method is extended to evaluate the dynamic stress intensity factors and T-stress with a numerical procedure based on the improved continued-fraction. The improved continued-fraction approach for the dynamic stiffness matrix is introduced to represent the inertial effect at high frequencies, which leads to numerically better conditioned matrices. After separating the singular stress term from other high order terms, the internal displacements can be obtained by numerical integration and no mesh refinement is needed around the crack tip. The condition numbers of coefficient matrix of the improved method are much smaller than that of the original method, which shows that the improved algorithm can obtain well-conditioned coefficient matrices, and the efficiency of the solution process and its stability can be significantly improved. Several numerical examples are presented to demonstrate the increased robustness and efficiency of the proposed method in both homogeneous and bimaterial crack problems.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.4 no.2
• /
• pp.69-79
• /
• 1996

Dynamic stress intensity factors are derives when the crack is propagating with constant velocity under longitudinal shear stress in orthotropic disk plate. General stress fields of crack tip propagating with constant velocity and least square method are used to obtain the dynamic stress intensity factor. The dynamic stress intensity factors of GLV/GTV=1(=isotropic material or transversely isotropic material) which is obtained in out study nearly coincides with Chiang's results when mode Ⅲ stress is applied to boundary of isotropic disk. The D.S.I.F. of mode Ⅲ stress is greater when α(=angle of crack propagation direction with fiber direction) is 90° than that when α is 0°. In case of a/D(a:crack length, D:disk diameter)<0. 58, the faster crack propagation velocity, the less D.S.I.F. but when crack propagation velocity arrive on ghear stress wave velocity, the D.S.I.F. but when crack propagation velocity arrive on shear stress wave velocity, the D.S.I.F. unexpectedly increases and decreases to zero.

• East Asian mathematical journal
• /
• v.34 no.5
• /
• pp.623-632
• /
• 2018

In [7, 8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous boundary conditions, compute the finite element solutions using standard FEM and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. Their algorithm involves an iteration and the iteration number depends on the acuracy of stress intensity factors, which is usually obtained by extraction formula which use the finite element solutions computed by standard Finite Element Method. In this paper we investigate the dependence of the iteration number on the convergence of stress intensity factors and give a way to reduce the iteration number, together with some numerical experiments.

• Journal of the Korean Society for Precision Engineering
• /
• v.15 no.11
• /
• pp.244-250
• /
• 1998

In this study, the stress intensity factors of center crack are analyzed when it is surrounded by symmetrically distributed small cracks. The values of stress intensity factors of the center crack are greatly influenced by the locations of distributed small cracks. When small cracks overlap or approach near the tip of a center crack, the effect of interaction arisen by these cracks becomes noticeable. In case of multiple distributed small cracks, the stress intensity factor of a center crack is found to be efficiently determined by the superposition method.

• Structural Engineering and Mechanics
• /
• v.3 no.6
• /
• pp.541-553
• /
• 1995

The determination of the stress intensity factors is investigated by using the surface integral defined around the crack tip of the structure. In this work, the integral method is derived naturally from the standard path integral J. But the use of the surface integral is also extended to the case where body forces act. Computer program for obtaining the stress intensity factors $K_I$ and $K_{II}$ is developed, which prepares input variables from the result of the conventional finite element analysis. This paper provides a parabolic smooth curve function. By the use of the function and conventional element meshes in which the aspect ratio (element length at the crack tip/crack length) is about 25 percent, relatively accurate $K_I$ and K_{II}$ values can be obtained for the outer integral radius ranging from 1/3 to 1 of the crack length and for inner one zero.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
• /
• 2002.10a
• /
• pp.267-272
• /
• 2002

Pitting corrosion is a very common occurrence in marine structures. Therefore, the 3-D finite element analysis is carried out to determine the stress intensity factors at the pit depth and also at the surface of the pit. The pits are modeled as a part of sphere, based on the pit depth and the pit diameter as specified by the Ship Structural Committee. The pit depth and pit diameter are function of the percentage of pitting that the plate is subjected to. A dog-bone shaped specimen is subjected to different intensities of pitting and the stress intensity factors are determined under axial tensile loads.

• Journal of the Korean Society of Safety
• /
• v.6 no.2
• /
• pp.5-13
• /
• 1991

In this paper, the interfacial stress intensity factors( $K_{i}$＝ $K_1$＋i $K_2$) for the edge interface crack in the dissimilar materials(isotropic-isotropic materials, isotropic-composite materials) were analysed by BEM(Boundary Element Method). The fatigue crack growth behaviour was investigated by load constant fatigue test. From the experimental results, the relationship between da/dN and interfacial stress intensity facto, ( $K_{i}$ or $K_1$) can be expressed by Paris'law for homogeneous materials.s.s.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2000.11a
• /
• pp.469-472
• /
• 2000

a crack with electrically impermeable surfaces in an electrostrictive material subjected to uniform electric loading is analysed. A strip yield zone model is employed to investigate the effect of electric yielding on stress intensity factor. complete forms of electric fields and elastic fields for the crack are derived by using complex function theory. /the stress intensity factors are obtained based on the strip yield zone model.