Calculation of K-factor and T-stress for cracks in anisotropic bimaterials (original) (raw)
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Two-Dimensional Stress Intensity Factor Analysis of Cracks in Anisotropic Bimaterial
Mathematical Problems in Engineering, 2013
This paper presents a 2D numerical technique based on the boundary element method (BEM) for the analysis of linear elastic fracture mechanics (LEFM) problems on stress intensity factors (SIFs) involving anisotropic bimaterials. The most outstanding feature of this analysis is that it is a singledomain method, yet it is very accurate, efficient, and versatile (i.e., the material properties of the medium can be anisotropic as well as isotropic). A computer program using the BEM formula translation (FORTRAN 90) code was developed to effectively calculate the stress intensity factors (SIFs) in an anisotropic bi-material. This BEM program has been verified and showed good accuracy compared with the previous studies. Numerical examples of stress intensity factor calculation for a straight crack with various locations in both finite and infinite bimaterials are presented. It was found that very accurate results can be obtained using the proposed method, even with relatively simple discretization. The results of the numerical analysis also show that material anisotropy can greatly affect the stress intensity factor.
International Journal of Fracture, 2007
The problem of an edge-bridged crack terminating perpendicular to a bimaterial interface in a half-space is analyzed for a general case of elastic anisotropic bimaterials and specialized for the case of orthotropic bimaterials. The edge crack lies in the surface layer of thickness h bonded to semi-infinite substrate. It is assumed that long fibres bridge the crack. Bridging model follows from the assumption of "large" slip lengths adjacent to the crack faces and neglect of initial stresses. The crack is modelled by means of continuous distribution of dislocations, which is assumed to be singular at the crack tip. With respect to the bridged crack problems in finite dissimilar bodies, the reciprocal theorem ( -integral) is demonstrated as to compute, in the present context, the generalized stress intensity factor through the remote stress and displacement field for a particular specimen geometry and boundary conditions using FEM. Also the application of the configurational force mechanics is discussed within the context of the investigated problem.
1979
Methods for obtaining stress intensity factors for bimaterial bodies using numerical crack flank displacement data are presented and compared. The stress analysis of a cracked bimaterial is reviewed. The analysis results in a data reduction scheme for the stress intensity factors via the crack flank displacement data. The data reduction scheme produces adequate resolution of the magnitude of the complex stress intensity factor but is incapable of resolving the angle when the moduli of the adjoining materials are close. An extended form of the J-integral is shown to provide increased accuracy for the magnitude of the complex stress intensity factor without yielding the angle.
Engineering Fracture Mechanics, 2005
The problem of a crack in general anisotropic material under LEFM conditions is presented. In Part I, three methods are presented for calculating stress intensity factors for various anisotropic materials in which z = 0 is a plane of symmetry. All of the methods employ the displacement field obtained by means of the finite element method. The first one is known as displacement extrapolation and requires the values of the crack face displacements. The other two are conservative integrals based upon the J-integral. One employs symmetric and asymmetric fields to separate the mode I and II stress intensity factors. The second is the M-integral which also allows for calculation of K I and K II separately.
The Abstracts of ATEM : International Conference on Advanced Technology in Experimental Mechanics : Asian Conference on Experimental Mechanics
Numerical solutions of singular integral equations are discussed in the analysis of a planar rectangular interfacial crack in three dimensional bimaterials. The problem is formulated as a system of singular integral equations on the basis of the body force method. In the numerical analysis, unknown body force densities are approximated by the products of the fundamental density functions and power series, where the fundamental density functions are chosen to express a two-dimensional interface crack exactly. The calculation shows that the present method gives smooth variations of stress intensity factor along the crack front for various aspect ratios. The present method gives rapidly converging numerical results and highly satisfied boundary conditions throughout the crack boundary. The stress intensity factors are given with varying the material combination and aspect ratio of the crack. It is found that the stress intensity factors I K and II K are determined by bimaterials constant alone, independent of elastic modulus ratio and Poisson's ratio.
Stress Intensity Factor for a Planar Interfacial Crack in Three Dimensional Bimaterials
Journal of Computational Science and Technology, 2009
In this paper, stress intensity factors for a three dimensional planar interfacial crack are considered on the idea of the body force method. The formulation leads to a system of singular integral equation, whose unknowns are three types of crack opening displacements. The unknown body force densities are approximated by the products of the fundamental density functions and power series; here, the fundamental density functions are chosen to express singular stress fields due to a two-dimensional interface crack exactly. The calculation shows that the present method gives rapidly converging numerical solutions. It is found that the stress intensity factors K I and K II are determined by bimaterials constant ε alone, independent of elastic modulus ratio and Poisson's ratio.
International Journal of Solids and Structures, 2008
Numerical solutions of singular integral equations are discussed in the analysis of a planar rectangular interfacial crack in three-dimensional bimaterials subjected to tension. The problem is formulated as a system of singular integral equations on the basis of the body force method. In the numerical analysis, unknown body force densities are approximated by the products of the fundamental density functions and power series, where the fundamental density functions are chosen to express singular behavior along the crack front of the interface crack exactly. The calculation shows that the present method gives smooth variations of stress intensity factors along the crack front for various aspect ratios. The present method gives rapidly converging numerical results and highly satisfied boundary conditions throughout the crack boundary. The stress intensity factors are given with varying the material combination and aspect ratio of the crack. It is found that the stress intensity factors K I and K II are determined by the bimaterial constant e alone, independent of elastic modulus ratio and Poisson's ratio.
Mixed-mode stress intensity factors for a crack in an anisotropic bi-material strip
International Journal of Solids and Structures, 2004
This paper provides a method for obtaining the mixed-mode stress intensity factors for a bi-material interface crack in the infinite strip configuration and in the case where both phases are fully anisotropic. First, the dislocation solution in a bi-material anisotropic infinite strip is investigated (the boundary of the strip is parallel to the bi-material interface). A surface distributed dislocation approach is employed to ensure the traction-free conditions at the strip bounding surfaces. Subsequently, the derived dislocation solution is applied to calculate the mixed-mode stress intensity factors of a crack located at, or parallel to, the interface in the bi-material anisotropic infinite strip. The crack itself is modelled as a distribution of the derived dislocation solutions for the strip. Results are presented and the effects of material mismatch, the length of the crack and the material interface on the stress intensity factors are investigated.