Boundary integral equation fracture mechanics analysis of plane orthotropic bodies (original) (raw)
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Study of crack propagation in orthotropic materials by using the boundary element method
Engineering Fracture Mechanics, 1990
The application of the Boundary Element Method (BEM) to the computation of stress intensity factors (SIF) and the crack propagation angle in orthotropic materials is the aim of this paper. The computer program includes isoparamet~c linear, quadratic and quarter-point-tmctionsingular elements in order to obtain the stress distribution around the crack tips. A multidomain approach is followed in order to avoid the geometric singularity that appears in the double-node method. Different methods to compute the SIF are compared for several cases. Finally, the maximum circumferential stress approach is used to obtain the crack propagation angle in a mixed-mode propagation problem in an orthotropic material.
Symmetric Galerkin boundary integral fracture analysis for plane orthotropic elasticity
Computational mechanics, 1997
This paper discusses the formulation and implementation of the symmetric Galerkin boundary integral method for two dimensional linear elastic orthotropic fracture analysis. For the usual case of a traction-free crack, the symmetry of the coecient matrix can be eectively exploited to signicantly reduce the computational work required to construct the linear system. In addition, computation time is reduced by employing ecient analytic integration formulas for the analysis of the orthotropic singular and hypersingular integrals. Test calculations demonstrate that the method is both accurate and ecient.
A general boundary element analysis of 2-D linear elastic fracture mechanics
1997
This paper presents a boundary element method (BEM) analysis of linear elastic fracture mechanics in two-dimensional solids. The most outstanding feature of this new analysis is that it is a single-domain method, and yet it is very accurate, efficient and versatile: Material properties in the medium can be anisotropic as well as isotropic. Problem domain can be finite, infinite or semi-infinite. Cracks can be of multiple, branched, internal or edged type with a straight or curved shape. Loading can be of in-plane or anti-plane, and can be applied along the no-crack boundary or crack surface. Furthermore, the body-force case can also be analyzed. The present BEM analysis is an extension of the work by Pan and Amadei (1996a) and is such that the displacement and traction integral equations are collocated, respectively, on the no-crack boundary and on one side of the crack surface. Since in this formulation the displacement and/or traction are used as unknowns on the no-crack boundary and the relative crack displacement (i.e. displacement discontinuity) as unknown on the crack surface, it possesses the advantages of both the traditional displacement BEM and the displacement discontinuity method (DDM) and yet gets rid of the disadvantages associated with these methods when modeling fracture mechanics problems. Numerical examples of calculation of stress intensity factors (SIFs) for various benchmark problems were conducted and excellent agreement with previously published results was obtained.
Computational Materials Science, 2009
An elastic orthotropic material containing a crack in Mode I is considered to formulate a new analytical model. The boundary conditions for the crack existence in the material lead to the solution of the homogeneous Riemann-Hilbert problems. The mathematical model was elaborated for a single and two collinear cracks of different lengths and distance for Mode I in order to investigate cracks interaction problem. Using the theory of Cauchy's integral and the numerical analysis, the fields in the vicinity of the crack tips were determined.
A Boundary Elements Numerical Procedure Applied to Effective Crack Approach
Annuaire de L'universite D'architecture, de Genie …, 2002
The methods of linear elastic fracture mechanics (LEFM) are well developed when one deals with ideally brittle materials such as ceramics and glass - see references [1], [2]. The existing powerful numerical techniques such as FEM (Finite Element Method) and BEM (Boundary Element Method) enable researchers to perform the best linear static analysis in order to calculate the stress intensity factors (SIF) – the basic fracture mechanics parameters of LEFM. It was shown in paper [3], how using a specially developed singular boundary element such an analysis can be performed on a structure containing general corners.
Fracture response of cracked orthotropic plates
2008
The solution of the elastostatic problem of an orthotropic body having a central inclined crack and subjected at infinity to a uniform biaxial load has been employed. It is assumed that the crack line does not coincide with an axis of elastic symmetry of the body. The stress filed is reported. The topic of the present paper is the extension of the maximum Circumferential Tensile Stress Criterion to orthotropic materials, in order to obtain the crack initiation angle, pointing out the effects of orthotropy and load biaxiality. The influence of ...
International Journal of Fracture, 1996
A new formulation of the boundary element method (BEM) is proposed in this paper to calculate stress intensity factors for cracked 2-D anisotropic materials. The most outstanding feature of this new approach is that the displacement and traction integral equations are collocated on the outside boundary of the problem (no-crack boundary) only and on one side of the crack surfaces only, respectively. Since the new BEM formulation uses displacements or tractions as unknowns on the outside boundary and displacement differences as unknowns on the crack surfaces, the formulation combines the best attributes of the traditional displacement BEM as well as the displacement discontinuity method (DDM). Compared with the recently proposed dual BEM, the present approach doesn't require dual elements and nodes on the crack surfaces, and further, it can be used for anisotropic media with cracks of any geometric shapes. Numerical examples of calculation of stress intensity factors were conducted, and excellent agreement with previously published results was obtained. The authors believe that the new BEM formulation presented in this paper will provide an alternative and yet efficient numerical technique for the study of cracked 2-D anisotropic media, and for the simulation of quasi-static crack propagation.
Update: Application of the Finite Element Method to Linear Elastic Fracture Mechanics
Applied Mechanics Reviews, 2010
Since the previous paper was written (Banks-Sills, 1991, “Application of the Finite Element Method to Linear Elastic Fracture Mechanics,” Appl. Mech. Rev., 44, pp. 447–461), much progress has been made in applying the finite element method to linear elastic fracture mechanics. In this paper, the problem of calculating stress intensity factors in two- and three-dimensional mixed mode problems will be considered for isotropic and anisotropic materials. The square-root singular stresses in the neighborhood of the crack tip will be modeled by quarter-point, square and collapsed, triangular elements for two-dimensional problems, respectively, and by brick and collapsed, prismatic elements in three dimensions. The stress intensity factors are obtained by means of the interaction energy or M-integral. Displacement extrapolation is employed as a check on the results. In addition, the problem of interface cracks between homogeneous, isotropic, and anisotropic materials is presented. The purp...
Stress analysis of orthotropic planes weakened by cracks
Applied Mathematical Modelling, 2007
The stress fields in an orthotropic infinite plane containing Volterra type climb and glide edge dislocations are derived. The dislocation solutions are utilized to formulate integral equations for dislocation density functions on the surfaces of smooth cracks. The integral equations are of Cauchy singular type and are solved for several different cases of crack configurations and arrangements. The results are used to evaluate modes I and II stress intensity factors for multiple smooth cracks.
Modelling and experimental study of parallel cracks propagation in an orthotropic elastic material
Computational Materials Science, 2012
The analysis of parallel cracks in an elastic orthotropic material, representing a fibre reinforced elastic composite is important from practical point of view. Such a case takes place in many engineering problems, particularly in operation of aircrafts, where local parallel cracks in structural parts of airplane can appear. The most important is to investigate if the cracks are stable or become suddenly unstable under certain level of loading.