Self-Similar Crack Expansion Method for Three-Dimensional Crack Analysis

1997 ◽  
Vol 64 (4) ◽  
pp. 729-737 ◽  
Author(s):  
Yonglin Xu ◽  
B. Moran ◽  
T. Belytschko
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Numerical Solutions ◽  
Crack Surface ◽  
Three Dimensional ◽  
Expansion Method ◽  
Infinite Medium ◽  
Boundary Integral ◽  
Intensity Factors ◽  
Self Similar

The self-similar crack expansion method is developed to calculate stress intensity factors for three-dimensional cracks in an infinite medium or semi-infinite medium by the boundary integral element technique. With this method, the stress intensity factors at crack tips are determined by calculating the crack-opening displacements over the crack surface, and the crack expansion rate, which is related to the crack energy release rate, is estimated by using a technique based on self-similar (virtual) crack extension. For elements on the crack surface, regular integrals and singular integrals are evaluated based on closed-form expressions, which improves the accuracy. Examples show that this method yields very accurate results for stress intensity factors of penny-shaped cracks and elliptical cracks in the full space, with errors of less than one percent as compared with exact solutions. The stress intensity factors of subsurface cracks are in good agreement with other numerical solutions.

Effects of thermal and electric boundary conditions on fracture of three-dimensional thermopiezoelectric media

2017 ◽  
Vol 29 (6) ◽  
pp. 1255-1271 ◽  
Author(s):  
MingHao Zhao ◽  
Yuan Li ◽  
CuiYing Fan
Keyword(s):  
Stress Intensity ◽  
Boundary Conditions ◽  
Stress Intensity Factors ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Boundary Integral ◽  
Displacement Discontinuity ◽  
Green Functions ◽  
Intensity Factors

An arbitrarily shaped planar crack under different thermal and electric boundary conditions on the crack surfaces is studied in three-dimensional transversely isotropic thermopiezoelectric media subjected to thermal–mechanical–electric coupling fields. Using Hankel transformations, Green functions are derived for unit point extended displacement discontinuities in three-dimensional transversely isotropic thermopiezoelectric media, where the extended displacement discontinuities include the conventional displacement discontinuities, electric potential discontinuity, as well as the temperature discontinuity. On the basis of these Green functions, the extended displacement discontinuity boundary integral equations for arbitrarily shaped planar cracks in the isotropic plane of three-dimensional transversely isotropic thermopiezoelectric media are established under different thermal and electric boundary conditions on the crack surfaces, namely, the thermally and electrically impermeable, permeable, and semi-permeable boundary conditions. The singularities of near-crack border fields are analyzed and the extended stress intensity factors are expressed in terms of the extended displacement discontinuities. The effect of different thermal and electric boundary conditions on the extended stress intensity factors is studied via the extended displacement discontinuity boundary element method. Subsequent numerical results of elliptical cracks subjected to combined thermal–mechanical–electric loadings are obtained.

A Variational Technique for Element Free Analysis of Static and Dynamic Fracture Mechanics

2010 ◽  
Vol 454 ◽  
pp. 31-46
Author(s):  
P.H. Wen ◽  
M.H. Aliabadi
Keyword(s):  
Stress Intensity ◽  
Fracture Mechanics ◽  
Stress Intensity Factors ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Inversion Method ◽  
Variational Technique ◽  
Intensity Factors ◽  
Element Free ◽  
Benchmark Solutions

. In this paper a variational technique is developed to calculate stress intensity factors with high accuracy using the element free Glerkin method. The stiffness and mass matrices are evaluated by regular domain integrals and the shape functions to determine displacements in the domain are calculated with radial basis function interpolation. Stress intensity factors were obtained by a boundary integral with a variation of crack length along the crack front. Based on a static reference solution, the transformed stress intensity factors in the Laplace space are obtained and Durbin inversion method is utilised in order to determine the physical values in time domain. The applications of proposed technique to two and three dimensional fracture mechanics are presented. Comparisons are made with benchmark solutions and indirect boundary element method.

scholarly journals Dynamic stress intensity factors of interacting branched cracks

2019 ◽  
Vol 285 ◽  
pp. 00004
Author(s):  
Piotr Fedeliński
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Dynamic Stress ◽  
Numerical Solutions ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Inversion Method ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Element Method

In the present work the boundary element method (BEM) is applied to analysis of statically and dynamically loaded infinite plates with multiple stationary branched cracks. The material of the plates is linear-elastic, homogenous and isotropic. In the applied BEM approach the displacement and traction boundary integral equations are used simultaneously for nodes on crack surfaces. Contrary to the finite element method (FEM) in the BEM numerical solutions are obtained by discretization of external boundaries and crack surfaces. The dynamic problem is solved by using the Laplace transform method and the solution in the time domain is computed by the Durbin numerical inversion method. Numerical examples of multiple branched cracks in infinite plates subjected to static and dynamic loadings are presented. An influence of orientation, distances between cracks and the number of cracks on static and dynamic stress intensity factors (SIF) is studied.

Dynamic Behavior of an Orthotropic Material Containing a Central Crack

1989 ◽  
Vol 111 (2) ◽  
pp. 172-176 ◽  
Author(s):  
Y. M. Tsai
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Orthotropic Material ◽  
Crack Surface ◽  
Frequency Factor ◽  
Wave Frequency ◽  
Intensity Factors ◽  
Central Crack ◽  
Material Constants ◽  
Principal Axes

The dynamic response of a central crack in an orthotropic material is investigated. The crack is situated along one of the principal axes of the material. The load is harmonic in time and normally applied to the crack surface. The Fourier transform is used to solve the dynamic fracture problem, and the results are simplified through a complete contour integration. The dynamic stress intensity factor is obtained in an exact expression in terms of the frequency factor and the material constants. The frequency factor is defined as the product of the wave frequency and the half-crack length, divided by the shear wave speed. Glass/epoxy and graphite/epoxy composite materials are used as example materials in calculating the numerical values of the stress intensity factors. The maximum values of the stress intensity factors are shown to be dependent on the value of the nondimensional frequency factor and the material anisotropy. The motion of the crack surface is also investigated. The crack surface distortion from the associated static crack shape also depends on the wave frequency and the orthotropic material constants.

Analysis of Crack Propagation in Roller Bearings Using the Boundary Integral Equation Method—A Mixed-Mode Loading Problem

1988 ◽  
Vol 110 (3) ◽  
pp. 408-413 ◽  
Author(s):  
L. J. Ghosn
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Crack Propagation ◽  
Boundary Integral Equation ◽  
Stress Intensity Factors ◽  
High Speed ◽  
Roller Bearing ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Intensity Factors

Crack propagation in a rotating inner raceway of a high-speed roller bearing is analyzed using the boundary integral method. The model consists of an edge plate under plane strain condition upon which varying Hertzian stress fields are superimposed. A multidomain boundary integral equation using quadratic elements was written to determine the stress intensity factors KI and KII at the crack tip for various roller positions. The multidomain formulation allows the two faces of the crack to be modeled in two different subregions making it possible to analyze crack closure when the roller is positioned on or close to the crack line. KI and KII stress intensity factors along any direction were computed. These calculations permit determination of crack growth direction along which the average KI times the alternating KI is maximum.

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