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Crack Problems (crack + problem)
Selected AbstractsFretting fatigue limit as a short crack problem at the edge of contactFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 5 2004Y. KONDO ABSTRACT This paper proposes a local stress concept to evaluate the fretting fatigue limit for contact edge cracks. A unique S,N curve based on the local stress could be obtained for a contact edge crack irrespective of mechanical factors such as contact pressure, relative slip, contact length, specimen size and loading type. The analytical background for the local stress concept was studied using FEM analysis. It was shown that the local stress uniquely determined the ,K change due to crack growth as well as the stress distribution near the contact edge. The condition that determined the fretting fatigue limit was predicted by combining the ,K change due to crack growth and the ,Kth for a short crack. The formation of a non-propagating crack at the fatigue limit was predicted by the model and it was experimentally confirmed by a long-life fretting fatigue test. [source] Dynamic non-planar crack rupture by a finite volume methodGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2007M. Benjemaa SUMMARY Modelling dynamic rupture for complex geometrical fault structures is performed through a finite volume method. After transformations for building up the partial differential system following explicit conservative law, we design an unstructured bi-dimensional time-domain numerical formulation of the crack problem. As a result, arbitrary non-planar faults can be explicitly represented without extra computational cost. On these complex surfaces, boundary conditions are set on stress fluxes and not on stress values. Prescribed rupture velocity gives accurate solutions with respect to analytical ones depending on the mesh refinement, while solutions for spontaneous propagation are analysed through numerical means. An example of non-planar spontaneous fault growth in heterogeneous media demonstrates the good behaviour of the proposed algorithm as well as specific difficulties of such numerical modelling. [source] Hypersingular integral equation method for three-dimensional crack problem in shear modeINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2004Y. Z. ChenArticle first published online: 19 APR 200 Abstract This paper presents the use of the hypersingular integral equation method for solving the flat crack problem in shear mode. In the method, the crack opening displacement (COD) functions are assumed to be polynomials with several undetermined coefficients. The involved hypersingular integral can be reduced into a repeat integral in a particular polar co-ordinate, and further integrated by a known quadrature rule. This technique considerably reduces the effort of derivation and computation to obtain the final solution. The undetermined coefficients in the COD functions are obtained from an algebraic equation. The stress intensity factors (SIF) along the boundary of the flat crack can then be easily calculated. Numerical examples are given to demonstrate the efficiency of the proposed method. Copyright 2004 John Wiley & Sons, Ltd. [source] An enriched element-failure method (REFM) for delamination analysis of composite structuresINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2009X. S. Sun Abstract This paper develops an enriched element-failure method for delamination analysis of composite structures. This method combines discontinuous enrichments in the extended finite element method and element-failure concepts in the element-failure method within the finite element framework. An improved discontinuous enrichment function is presented to effectively model the kinked discontinuities; and, based on fracture mechanics, a general near-tip enrichment function is also derived from the asymptotic displacement fields to represent the discontinuity and local stress intensification around the crack-tip. The delamination is treated as a crack problem that is represented by the discontinuous enrichment functions and then the enrichments are transformed to external nodal forces applied to nodes around the crack. The crack and its propagation are modeled by the ,failed elements' that are applied to the external nodal forces. Delamination and crack kinking problems can be solved simultaneously without remeshing the model or re-assembling the stiffness matrix with this method. Examples are used to demonstrate the application of the proposed method to delamination analysis. The validity of the proposed method is verified and the simulation results show that both interlaminar delamination and crack kinking (intralaminar crack) occur in the cross-ply laminated plate, which is observed in the experiment. Copyright © 2009 John Wiley & Sons, Ltd. [source] An extended finite element method with analytical enrichment for cohesive crack modelingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2009James V. CoxArticle first published online: 28 NOV 200 Abstract A recent approach to fracture modeling has combined the extended finite element method (XFEM) with cohesive zone models. Most studies have used simplified enrichment functions to represent the strong discontinuity but have lacked an analytical basis to represent the displacement gradients in the vicinity of the cohesive crack. In this study enrichment functions based upon an existing analytical investigation of the cohesive crack problem are proposed. These functions have the potential of representing displacement gradients in the vicinity of the cohesive crack and allow the crack to incrementally advance across each element. Key aspects of the corresponding numerical formulation and enrichment functions are discussed. A parameter study for a simple mode I model problem is presented to evaluate if quasi-static crack propagation can be accurately followed with the proposed formulation. The effects of mesh refinement and mesh orientation are considered. Propagation of the cohesive zone tip and crack tip, time variation of the cohesive zone length, and crack profiles are examined. The analysis results indicate that the analytically based enrichment functions can accurately track the cohesive crack propagation of a mode I crack independent of mesh orientation. A mixed mode example further demonstrates the potential of the formulation. Copyright © 2008 John Wiley & Sons, Ltd. [source] Numerical simulation of the non-linear crack problem with non-penetrationMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2004Victor A. Kovtunenko Abstract Here the numerical simulation of some plane Lamé problem with a rectilinear crack under non-penetration condition is presented. The corresponding solids are assumed to be isotropic and homogeneous as well as bonded. The non-linear crack problem is formulated as a variational inequality. We use penalty iteration and the finite-element method to calculate numerically its approximate solution. Applying analytic formulas obtained from shape sensitivity analysis, we calculate then energetic and stress characteristics of the solution, and describe the quasistatic propagation of the crack under linear loading. The results are presented in comparison with the classical, linear crack problem, when interpenetration between the crack faces may occur. Copyright © 2004 John Wiley & Sons, Ltd. [source] T-stress solutions for two-dimensional crack problems in anisotropic elasticity using the boundary element methodFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 5 2006P. D. SHAH ABSTRACT The importance of a two-parameter approach in the fracture mechanics analysis of many cracked components is increasingly being recognized in engineering industry. In addition to the stress intensity factor, the T stress is the second parameter considered in fracture assessments. In this paper, the path-independent mutual M - integral method to evaluate the T stress is extended to treat plane, generally anisotropic cracked bodies. It is implemented into the boundary element method for two-dimensional elasticity. Examples are presented to demonstrate the veracity of the formulations developed and its applicability. The numerical solutions obtained show that material anisotropy can have a significant effect on the T stress for a given cracked geometry. [source] Stress intensity factors for cracked triangular cross-section thin-walled tubesFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 12 2004Y. J. XIE ABSTRACT For one kind of finite-boundary crack problems, the cracked equilateral triangular cross-section tube, an analytical and very simple method to determine the stress intensity factors has been proposed based on a new concept of crack surface widening energy release rate and the principle of virtual work. Different from the classical crack extension energy release rate, the crack surface widening energy release rate can be defined by the G*-integral theory and expressed by stress intensity factors. This energy release rate can also be defined easily by the elementary strength theory for slender structures and expressed by axial strains and loads. These two forms of crack surface widening energy release rate constitute the basis of a new analysis method for cracked tubes. From present discussions, a series of stress intensity factors are derived for cracked equilateral triangular cross-section tubes. Actually, the present method can also be applied to cracked polygonal tubes. [source] An appropriate quadrature rule for the analysis of plane crack problems in the boundary-element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2001E. E. Theotokoglou Abstract An hypersingular integral equation of a three-dimensional elastic solid with an embedded planar crack subjected to a uniform stress field at infinity is derived. The solution of the boundary-integral equation is succeeded taking into consideration an appropriate Gauss quadrature rule for finite part integrals which is suitable for the numerical treatment of any plane crack with a smooth-contour shape and permit the fast convergence for the results. The problem of a circular and of an elliptical crack in an infinite body subjected to a uniform stress field at infinity is confronted; and the stress intensity factors are calculated. Copyright © 2001 John Wiley & Sons, Ltd. [source] Applications of numerical eigenfunctions in the fractal-like finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004D. K. L. Tsang Abstract The fractal-like finite element method is an accurate and efficient method to determine the stress intensity factors (SIF) around crack tips. The use of a self-similar mesh together with the William's eigenfunctions reduce the number of unknowns significantly. The SIFs are the primary unknowns and no post-processing is required. In all previous studies, we used the analytic eigenfunction expression to perform the global transformation. However, the eigenfunction cannot be found analytically in general crack problems. Two-dimensional axisymmetrical cracks are considered here. The resulting static equilibrium equations in local co-ordinates are non-homogeneous ordinary differential equations, for which the analytic eigenfunction cannot be found completely. We use a finite difference method to determine all the eigenfunctions needed numerically. Our evaluated SIF values show very close agreement with published results. Copyright © 2004 John Wiley & Sons, Ltd. [source] Meshfree point collocation method for elasticity and crack problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004Sang-Ho Lee Abstract A generalized diffuse derivative approximation is combined with a point collocation scheme for solid mechanics problems. The derivatives are obtained from a local approximation so their evaluation is computationally very efficient. This meshfree point collocation method has other advantages: it does not require special treatment for essential boundary condition nor the time-consuming integration of a weak form. Neither the connectivity of the mesh nor differentiability of the weight function is necessary. The accuracy of the solutions is exceptional and generally exceeds that of element-free Galerkin method with linear basis. The performance and robustness are demonstrated by several numerical examples, including crack problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] Boundary element formulation for 3D transversely isotropic cracked bodiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004M. P. Ariza Abstract The boundary traction integral representation is obtained in elasticity when the classical displacement representation is differentiated and combined according to Hooke's law. The use of both traction and displacement integral representations leads to a mixed (or dual) formulation of the BEM where the discretization effort for crack problems is much smaller than in the classical formulation. A boundary element analysis of three-dimensional fracture mechanics problems of transversely isotropic solids based on the mixed formulation is presented in this paper. The hypersingular and strongly singular kernels appearing in the formulation are regularized by using two terms of the displacement series expansion and one term of the traction expansion, at the collocation point. All the remaining integrals are analytically evaluated or transformed by means of Stokes' theorem into regular or weakly singular integrals, which are numerically computed. The method is general and can be used for elements of any shape including quarter-point crack front elements. No change of co-ordinates is required for the integration. The formulation as presented in this paper is something as clear, general and easy to handle as the classical BE formulation. It is used in combination with three-dimensional quadratic and quarter-point elements to obtain accurate results for several different crack problems. Cracks in boundless and finite transversely isotropic domains are studied. The meshes are simple and include only discretization of the crack and the external boundary. The obtained results are in good agreement with those existing in the literature. Copyright © 2004 John Wiley & Sons, Ltd. [source] Dual boundary element method for anisotropic dynamic fracture mechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2004E. L. Albuquerque Abstract In this work, the dual boundary element method formulation is developed for effective modelling of dynamic crack problems. The static fundamental solutions are used and the domain integral, which comes from the inertial term, is transformed into boundary integrals using the dual reciprocity technique. Dynamic stress intensity factors are computed from crack opening displacements. Comparisons are made with quasi-isotropic as well as anisotropic results, using the sub-region technique. Several examples are presented to assess the accuracy and efficiency of the proposed method. Copyright © 2004 John Wiley & Sons, Ltd. [source] Partition of unity enrichment for bimaterial interface cracksINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2004N. Sukumar Abstract Partition of unity enrichment techniques are developed for bimaterial interface cracks. A discontinuous function and the two-dimensional near-tip asymptotic displacement functions are added to the finite element approximation using the framework of partition of unity. This enables the domain to be modelled by finite elements without explicitly meshing the crack surfaces. The crack-tip enrichment functions are chosen as those that span the asymptotic displacement fields for an interfacial crack. The concept of partition of unity facilitates the incorporation of the oscillatory nature of the singularity within a conforming finite element approximation. The mixed-mode (complex) stress intensity factors for bimaterial interfacial cracks are numerically evaluated using the domain form of the interaction integral. Good agreement between the numerical results and the reference solutions for benchmark interfacial crack problems is realized. Copyright © 2004 John Wiley & Sons, Ltd. [source] Development of the DYNA3D simulation code with automated fracture procedure for brick elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2003Ala Tabiei Abstract Numerical simulation of cracked structures is an important aspect in structural safety assessment. In recent years, there has been an increasing rate of development of numerical codes for modelling fracture procedure. The subject of this investigation is implementing automated fracture models in the DYNA3D non-linear explicit finite element code to simulate pseudo 3D crack growth procedure. The implemented models have the capabilities of simulating automatic crack propagation without user intervention. The implementation is carried on solid elements. The methodology of implementing fracture models is described. An element deletion-and-replacement remeshing procedure is proposed for updating the explicit geometric description of evolving cracks. Fracture parameters such as stress intensity factors, energy release rates and crack tip opening angle are evaluated. The maximum circumferential stress criterion is used to predict the direction of crack advancement. Seven crack problems are presented to verify the effectiveness of the methodology. Mesh sensitivity and loading rate effects are studied in the validation of the presented procedure. Copyright © 2003 John Wiley & Sons, Ltd. [source] | ||||||||||