Calculation of dynamic stresses using finite element method. Based on linear elastic fracture mechanics lefm, the sifs and energy of cracked media may be estimated. Dynamic stress intensity factors for cracks using the enriched finite element method 2005. The geometry of the single edge crack specimen is shown in fig. In this thesis, numerical calculation of stress intensity factors of cracks in. The quarterpoint quadratic isoparametric element at the crack tip. Interacting cracks analysis using finite element method. 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. The finite element analysis was carried out with ansys. Determination of geometry factor of crack in dented api 5l. It was not successfully identified until weibull in 1939 recognized that the tail is a power law. Index termsasymptotic boundary conditions, finite element method, open boundary problems, static fields.
Cubic crack tip element 32noded hexahedron, showing orientation oflocal. Finite element analysis of prediction of crack growth has been cited in many the literature. Numerical solutions of twodimensional anisotropic crack problems. A brief note on elastic tstress for centred crack in. 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. The finite element method for the analysis of nonlinear.
Dec, 2008 stress analysis of slab and wall using finite element method. The finite element method has become the preferred tool for analyzing a wide variety of physical problems. Xfem models a crack as an enriched feature by adding degrees of freedom in elements with special displacement functions. In the specific case of a cracktip, asymptotic expressions for the stress field in a. Determination of sharp vnotch stress intensity factors. Stress analysis of slab and wall using finite element method. 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. Introduction many 2d and 3d electrical field problems can be considered as being of the exterior form, that is the problem domain is unbounded. A stiffness derivative finite element technique for. The derivative of displacement in the tangential direction can be calculated for the assumed linear displacement field, from. How to enhance efficiency and accuracy of the over. This paper presents an example of a stress analysis of the arm of an industrial operation machine. The advantages of the finite element method over other numerical techniques, such as the finite difference method and the bound ary element. In a real fracture, the finite limits of fractal scales are always compatible with the.
For the sake of the symmetries about the centrelines of the specimen, only a. Abstract fatigue failure is very common for tubular joints used in offshore engineering because they are frequently. The use of finite element method in the stress analysis of an. Dynamic stress intensity factors for cracks using the enriched finite element method murat saribay lehigh university. The stress at any discontinuity is higher than the normal stress in the machine element. Calculation of the stress intensity factor for arbitrary. Calculation of the crack tip parameters in the holed wiley online. The determination of failure criteria is very important for the proper. Asymptotic boundary conditions for finite element analysis. Determination of stress concentration factor in stone. Determination of sharp vnotch stress intensity factors using. This study presents the novel modification of decoupled scaled boundary finite element method dsbfem to. 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 analytical solution around the crack tip in the near field is solved and.
Jan 08, 2014 stress concentration analysis using finite element method. 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. Relative performance of three meshreduction methods in. Iterated function system to model fractal boundaries and fractal bodies, obtaining asymptotic. The stress intensity factor, t stress, and the higher order coefficients can be obtained directly from the global variables without any postprocessing. The result of finite element modelling agrees well with that obtained by the first approach. 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. Orhan erol august 20, 81 pages the behaviour of stone columns in soft cohesive soil is investigated by finite element analyses. On the calculation of derivatives of stress intensity factors. The maximum strain on crack tip and far field stress on plate were used to validate the finite element modeling of ten sile test. Williams expansion terms and their importance for accurate stress.
Experimental and numerical investigation of fracture parameters for. 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. Analytical determination of coefficients in cracktip stress expansions. Stressstrain analysis by the finite element method duration. 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. Finite element investigation on the stress state at crack tip by using epfm parameters. 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 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. A finite element technique for determination of elastic crack tip stress intensity factors is presented. An explicit stabilization scheme is employed to suppress the spurious kinematic modes of the subintegrated lagrangian element. Strain on crack tip to evaluate xfem result in abaqus, a stress intensity factor comparison was made against benchmark case.
Calculation of dynamic stresses using finite element. Nonlinear finite element models using elasticperfectly plastic material strength formulations have been used to determine factors of safety. Then, we indicate the enrichment functions to be usedinthexfemtomodelaninterfacecrack. The stress intensity factor for edge crack in finite plate can be achieved by the formula 3 when 1 h b. The difficulties encountered to describe the stressstrain state at the crack tip through the parameter of. Determination of crack tip asymptotic stress field by fractal. The purpose ofthis study is to extend this special computational technique to the case ofanisotropic crack problems. Determination of crack tip asymptotic stressfield by fractal finite element method r. In fracture mechanics and failure analysis, cracked media energy and consequently stress intensity factors sifs play a crucial and significant role. Finite element investigation on the stress state at crack tip. A fractal model of the stress field around a rough crack. For the method to be applicable, the asymptotic fields must admit a separable form in polar coordinates. Determination of coefficients of the crack tip asymptotic field by fractal hybrid finite elements article in engineering fracture mechanics 7410. 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.
Finite element method analysis of stress intensity factor. A novel modification of decouple scaled boundary finite element method in fracture mechanics problems. 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. Introduction many 2d and 3d electrical field problems can be considered as being of the exterior form, that is the problem domain is. Finite element investigation on the stress state at crack. Finite element method and standards for which the test is recommended by the national agency u. Finite element method for analyzing stress intensity factor of a surface crack in tubular joints y. The ffem combines an exterior finite element model and a localized inner model near the crack tip. He showed that the stress at the crack tip of a fractal crack under uniform. On the calculation of derivatives of stress intensity. For stress analysis, the finite element method was chosen, whereby a brief description of the method and the finite elements is given. A novel modification of decouple scaled boundary finite. Convergence study on application of the overdeterministic.
Another formulation of integral equation method for mode iii crack. Stress intensity factors for cracks in anisotropic. Figure 7 shows the average of strain on crack tip from three times test. The asymptotic limit obtained here differs from the singularity degrees.
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. Determination of stress intensity factors by the finite element. Asymptotic analysis of the stress field at a crack tip in a linearly elastic material. 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. 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. Stress intensity factors for cracks in anisotropic materials. The introduction describes the systematic design and stress calculation of the constituent parts of the industrial operation machine. 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. Stress analysis around crack tips in finite strain. The mesh geometry of the latter is selfsimilar in radial layers around the tip.
The analytical solutions of displacement functions were classified into four cases with respect to different types of complex parameters. There are many investigators who have studied the stress distribution around the notches, groove. On the other hand, the extended finite element method xfemavoids remeshing and o. Finite element method for analyzing stress intensity. Stress concentration analysis using finite element method. A finite element method for determining the angular.
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. Stress concentrations at the crack tips and crack propagation due to tensile stresses are active areas of research in the past many decades. Stability analysis of rock slopes using the finite element. When the tensile strength criterion is violated at this node, it is split and the procedure is repeated. There are many investigators who have studied the stress distribution around the notches, groove, and other irregularities of various machine components. It was shown that the results of the experimental and the numerical studies were in good agreement. 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. This paper applies the fractal finite element method ffem together with 9node lagrangian hybrid elements to the calculation of linear elastic crack tip fields. Analytical determination of coefficients in cracktip stress. The extended finite element method xfem is an extension of the conventional finite element method based on the concept of partition unit.
Accurate closed form solution of the sif at each crack tip is obtained by conducting asymptotic analysis. New anisotropic cracktip enrichment functions for the. The use of finite element method in the stress analysis of. The main goal is to determine an accurate approximation of the nearcracktip. We attempt an asymptotic expansion of the crack tip stress field cr of the form.
The fractal twolevel finite element method has been proved to be very efficient and accurate for determining the stress intensity factor sif for modei. 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. Hu school of civil engineering, yantai university, yantai, 264005 china email. The finite element method for the analysis of nonlinear and. Finite element method for analyzing stress intensity factor. Stress strain analysis by the finite element method duration. Then, the node is split into two nodes and the tip of the crack is assumed to propagate to the next node. Denoting the tail exponent as m \displaystyle m, one can then show that, if the structure is sufficiently larger than one rve i. Experimental finite element approach for stress analysis. Determination of coefficients of the crack tip asymptotic. Numerical solutions of twodimensional anisotropic crack. Xfem was used in this thesis as a numerical solution method that is very well suited for reliability analysis of crack propagation problems. Determination of crack tip asymptotic stress field by. Super singular element method for twodimensional crack.
Asymptotic boundary conditions for finite element analysis of. A finite element method for computing the angular variation of asymptotic singular solutions is presented. Fok, determination of coefficients of the crack tip asymptotic field by fractal hybrid finite elements, engineering fracture mechanics 74 2007 16491664. 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.
A finite element method for determining the angular variation. The finite element method is one of the efficient and wellknown. 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. The method, based on the energy release rate, requires no special crack tip elements. Prediction of crack propagation using finite element method. Element library for threedimensional stress analysis by. Element library for threedimensional stress analysis by the. Finite element mesh representation of one half of the cracked plate. Finite element method analysis of stress intensity factor in.
Determination of sharp vnotch stress intensity factors using the extended finite element method. Dynamic stress intensity factors for cracks using the. Determination of stress intensity factors using finite element method derivatives in eq. The radial dependence of the fields is assumed known.
165 337 831 1060 1159 1546 1325 660 208 699 739 101 38 408 1339 1435 1432 706 974 582 241 1016 1400 975 933 990 1314 521 633 215 952 1246 1380 401 1394 415 903 334 1418 1290 963 127 279 1311