Determination of crack tip asymptotic stress field by fractal finite element method

Introduction many 2d and 3d electrical field problems can be considered as being of the exterior form, that is the problem domain is unbounded. There are many investigators who have studied the stress distribution around the notches, groove, and other irregularities of various machine components. A finite element method for determining the angular. The use of finite element method in the stress analysis of an. The mesh geometry of the latter is selfsimilar in radial layers around the tip. Determination of stress concentration factor in stone. In analysis, the ratio of crack length and width also define the critical stress field, if the path independent radius of jintegral for both crack tips are overlapped, the calculation of j value might be overestimated and the stress behavior is equal to behavior of single edge crack in finite body. Asymptotic boundary conditions for finite element analysis.

Orhan erol august 20, 81 pages the behaviour of stone columns in soft cohesive soil is investigated by finite element analyses. Prediction of crack propagation using finite element method. Element library for threedimensional stress analysis by. Relative performance of three meshreduction methods in. In the specific case of a cracktip, asymptotic expressions for the stress field in a. The maximum strain on crack tip and far field stress on plate were used to validate the finite element modeling of ten sile test. The stress at any discontinuity is higher than the normal stress in the machine element. A finite element technique for determination of elastic crack tip stress intensity factors is presented. New anisotropic cracktip enrichment functions for the. Finite element investigation on the stress state at crack. Finite element method for analyzing stress intensity factor. The radial dependence of the fields is assumed known. The stress intensity factor for edge crack in finite plate can be achieved by the formula 3 when 1 h b. Nonlinear finite element models using elasticperfectly plastic material strength formulations have been used to determine factors of safety.

A complete set of series form solutions of stress and displacement functions, including all higher order terms, around the crack tip for anisotropic crack problems have been newly derived by eigenfunction expansion approach. Experimental finite element approach for stress analysis. Stress strain analysis by the finite element method duration. Analytical determination of coefficients in cracktip stress expansions. The method, based on the energy release rate, requires no special crack tip elements.

Determination of crack tip asymptotic stressfield by fractal finite element method r. Finite element method analysis of stress intensity factor in. This problem is chosen as the coefficients of the crack tip elastic field up to n 5 have been calculated and presented in the literature. Leung department of civil engineering, the university of hong kong, pokfulam road, hong kong, china department of building and construction engineering, city university of hong kong, tat chee avenue, kowloon, hong kong, china abstract a semianalytical method is used for the. Finite element investigation on the stress state at crack tip. An explicit stabilization scheme is employed to suppress the spurious kinematic modes of the subintegrated lagrangian element. Determination of coefficients of the crack tip asymptotic field by fractal hybrid finite elements article in engineering fracture mechanics 7410. Analytical determination of coefficients in cracktip stress. A semianalytical method is used for the determination of stress intensity factors sif as well as the crack tip asymptotic stress field of a crack in elastic body. Stress concentration analysis using finite element method. Determination of crack tip asymptotic stress field by.

How to enhance efficiency and accuracy of the over. Xfem was used in this thesis as a numerical solution method that is very well suited for reliability analysis of crack propagation problems. The determination of failure criteria is very important for the proper. Finite element method for analyzing stress intensity factor of a surface crack in tubular joints y. On the calculation of derivatives of stress intensity. Numerical solutions of twodimensional anisotropic crack.

In particular, in this work, a parametric 3d finite element model has been carried out in order toshow the influence of the crack size and of the component thickness on pzs. Stress analysis around crack tips in finite strain problems. Finite element mesh representation of one half of the cracked plate. Then, we indicate the enrichment functions to be usedinthexfemtomodelaninterfacecrack. Based on linear elastic fracture mechanics lefm, the sifs and energy of cracked media may be estimated. Iterated function system to model fractal boundaries and fractal bodies, obtaining asymptotic. Further, the solution for only a single crack length is required, and the crack is advanced by moving nodal points rather than by removing nodal tractions at the crack tip and. Then, the node is split into two nodes and the tip of the crack is assumed to propagate to the next node. There are 15 equations 6 geometrical equations, 3 differential equilibrium equations, 6 constitutional equations to find 15 searched functions 3 displacement functions, 6 functions of the component of strain tensor, 6 functions of the component of stress tensor in continuum mechanics. Further, the solution for only a single crack length is required, and the crack is advanced by moving nodal points rather than by removing nodal tractions at the crack tip and performing a second. Cracks occur in many structural parts due to various causes. Determination of sharp vnotch stress intensity factors using the extended finite element method. The stress singularity is modelled by the superelement and the williams es, hence refining the finite element meshes near the singular point and creation of crack faces can be avoided. The finite element method for the analysis of nonlinear and.

Determination of sharp vnotch stress intensity factors using. For the method to be applicable, the asymptotic fields must admit a separable form in polar coordinates. Finite element method and standards for which the test is recommended by the national agency u. Finite element modeling fem for evaluation of stress intensity factor for a crack at an angle and for vnotch specimen 164 finite element modeling fem for evaluation of. Determination of coefficients of the crack tip asymptotic. Stressstrain analysis by the finite element method duration.

This paper applies the fractal finite element method ffem together with 9node lagrangian hybrid elements to the calculation of linear elastic crack tip fields. A novel modification of decouple scaled boundary finite. The ffem combines an exterior finite element model and a localized inner model near the crack tip. Numerical solutions of twodimensional anisotropic crack problems. Introduction many 2d and 3d electrical field problems can be considered as being of the exterior form, that is the problem domain is.

Strain on crack tip to evaluate xfem result in abaqus, a stress intensity factor comparison was made against benchmark case. He showed that the stress at the crack tip of a fractal crack under uniform. Stress intensity factors for cracks in anisotropic materials. Figure 7 shows the average of strain on crack tip from three times test. The extended finite element method xfem is an extension of the conventional finite element method based on the concept of partition unit. Finite element analysis of prediction of crack growth has been cited in many the literature. Determination of sharp vnotch stress intensity factors. Hu school of civil engineering, yantai university, yantai, 264005 china email. A finite element method for computing the angular variation of asymptotic singular solutions is presented. Convergence study on application of the overdeterministic. It was shown that the results of the experimental and the numerical studies were in good agreement. Super singular element method for twodimensional crack. Finite element method for analyzing stress intensity. Stress intensity factors for cracks in anisotropic.

Determination of geometry factor of crack in dented api 5l. This study presents the novel modification of decoupled scaled boundary finite element method dsbfem to. It was not successfully identified until weibull in 1939 recognized that the tail is a power law. Asymptotic analysis of the stress field at a crack tip in a linearly elastic material. This is achieved by enriching the finite element approximation of the nodes surrounding the notch tip with the first term of the notch tip asymptotic field and the nodes that intersect the notch faces with a jump enrichment function using a partition of unity method. The finite element method has become the preferred tool for analyzing a wide variety of physical problems. The stress intensity factors sifs and the tstress for a planar crack with anisotropic materials are evaluated by the fractal finite element method ffem. The introduction describes the systematic design and stress calculation of the constituent parts of the industrial operation machine. The analytical solutions of displacement functions were classified into four cases with respect to different types of complex parameters.

The derivative of displacement in the tangential direction can be calculated for the assumed linear displacement field, from. In fracture mechanics and failure analysis, cracked media energy and consequently stress intensity factors sifs play a crucial and significant role. Williams expansion terms and their importance for accurate stress. On the other hand, the extended finite element method xfemavoids remeshing and o. When the tensile strength criterion is violated at this node, it is split and the procedure is repeated. The asymptotic limit obtained here differs from the singularity degrees. The stress intensity factor, t stress, and the higher order coefficients can be obtained directly from the global variables without any postprocessing. The stress intensity factors sifs and the t stress for a planar crack with anisotropic materials are evaluated by the fractal finite element method ffem. Accurate closed form solution of the sif at each crack tip is obtained by conducting asymptotic analysis. This method was introduced by ted belytschko and his colleagues in 1999 24. Stress analysis of slab and wall using finite element method. A finite element method for determining the angular variation. For the sake of the symmetries about the centrelines of the specimen, only a. The analytical solutions of displacement functions were classified into four cases with respect to different types of complex parameters and different corresponding.

Denoting the tail exponent as m \displaystyle m, one can then show that, if the structure is sufficiently larger than one rve i. This paper presents an example of a stress analysis of the arm of an industrial operation machine. The result of finite element modelling agrees well with that obtained by the first approach. Stability analysis of rock slopes using the finite element. Calculation of dynamic stresses using finite element method. The advantages of the finite element method over other numerical techniques, such as the finite difference method and the bound ary element method, include efficient and accurate mod. The advantages of the finite element method over other numerical techniques, such as the finite difference method and the bound ary element.

For stress analysis, the finite element method was chosen, whereby a brief description of the method and the finite elements is given. Index termsasymptotic boundary conditions, finite element method, open boundary problems, static fields. A fractal model of the stress field around a rough crack. Dynamic stress intensity factors for cracks using the enriched finite element method 2005. Dec, 2008 stress analysis of slab and wall using finite element method. A novel modification of decouple scaled boundary finite element method in fracture mechanics problems. In this thesis, numerical calculation of stress intensity factors of cracks in. Determination of coefficients of the crack tip asymptotic field by fractal hybrid finite elements rkl su, sl fok engineering fracture mechanics 74 10, 16491664, 2007.

A brief note on elastic tstress for centred crack in. On the calculation of derivatives of stress intensity factors. The geometry of the single edge crack specimen is shown in fig. The use of finite element method in the stress analysis of. The main goal is to determine an accurate approximation of the nearcracktip. Jan 08, 2014 stress concentration analysis using finite element method.

Stress analysis around crack tips in finite strain. A stiffness derivative finite element technique for. Dynamic stress intensity factors for cracks using the enriched finite element method murat saribay lehigh university. The stress singularity is modelled by the superelement and the williams es, hence refining the finiteelement meshes near the singular point and creation of crack faces can be avoided. Calculation of dynamic stresses using finite element. Experimental and numerical investigation of fracture parameters for. We attempt an asymptotic expansion of the crack tip stress field cr of the form.

Abstract fatigue failure is very common for tubular joints used in offshore engineering because they are frequently. The finite element analysis was carried out with ansys. Calculation of the stress intensity factor for arbitrary. Xfem models a crack as an enriched feature by adding degrees of freedom in elements with special displacement functions. The analytical solution around the crack tip in the near field is solved and. There are many investigators who have studied the stress distribution around the notches, groove. Determination of crack tip asymptotic stress field by fractal.

Determination of stress intensity factors by the finite element. Element library for threedimensional stress analysis by the. Cubic crack tip element 32noded hexahedron, showing orientation oflocal. Fok, determination of coefficients of the crack tip asymptotic field by fractal hybrid finite elements, engineering fracture mechanics 74 2007 16491664. High stress is created through the notch, in turn notch tip easily moved, the displacement field or stress is to be known in the vicinity of crack tip. Stress concentrations at the crack tips and crack propagation due to tensile stresses are active areas of research in the past many decades. The difficulties encountered to describe the stressstrain state at the crack tip through the parameter of. Mukhtar relative performance of three meshreduction methods in predicting mode iii cracktip singularity latin american journal of solids and structures 14 2017 12261250 ential quadrature element method, which is similar to the fem in principle, has been used by liao. Asymptotic boundary conditions for finite element analysis of.

The fractal twolevel finite element method has been proved to be very efficient and accurate for determining the stress intensity factor sif for modei. Determination of crack tip asymptotic stress field by fractal finite element method. Another formulation of integral equation method for mode iii crack. Finite element investigation on the stress state at crack tip by using epfm parameters. Leung department of civil engineering, the university of hong kong, pokfulam road, hong kong, china department of building and construction engineering, city university of hong kong, tat chee avenue, kowloon, hong kong, china abstract a semianalytical method. In a real fracture, the finite limits of fractal scales are always compatible with the. The quarterpoint quadratic isoparametric element at the crack tip. Calculation of the crack tip parameters in the holed wiley online. Dynamic stress intensity factors for cracks using the. Interacting cracks analysis using finite element method. Determination of stress intensity factors using finite element method derivatives in eq. Finite element method analysis of stress intensity factor. Sep 01, 2003 a complete set of series form solutions of stress and displacement functions, including all higher order terms, around the crack tip for anisotropic crack problems have been newly derived by eigenfunction expansion approach. The purpose ofthis study is to extend this special computational technique to the case ofanisotropic crack problems.