Surface Crack Problem Research Articles

Numerical Aspects of Isogeometric Boundary Element Methods: (Nearly) Singular Quadrature, Trimmed NURBS and Surface Crack Modeling

This work presents some numerical aspects of isogeometric boundary element methods (IGABEM). The behavior of hyper-singular and nearly-singular integration is first explored on the distorted NURBS surface. Several numerical treatments are proposed to enhance the quadrature in the framework of isogeometric analysis. Then a numerical implementation of IGABEM on the trimmed NURBS is detailed. Based on this idea, the surface crack problem is modeled incorporation with the phantom element method. The proposed method allows the crack to intersect with the boundary of the body while preserving the original parametrization of the NURBS-based CAD geometry.

Fatigue Crack Growth Analysis of Semielliptical Surface Crack

The aim of this paper is to present the simulation technique and experimental work for surface crack in a structure. For the sake of test apparatuss feasibility, a semielliptical surface crack in a structure was converted into small specimen size. The specimens represented semielliptical surface crack problem in real application of engineering structure. The specimens with semielliptical surface crack were tested by experiment and simulation. The S-version Finite Element Model (S-FEM) was implemented in simulation, and verification was performed through experimental works. The S-FEM consists of virtual crack closure method and Paris law as a crack growth criterion for 3-dimensional problem with hexahedron elements was used. Auto-mesh generation technique with a fully automatic crack growth simulation system was employed in S-FEM simulation. Specimens with 0oof crack surface angle were prepared and analysed for the modeIloading. A four-point bending fatigue test was conducted and simulated in order to gain crack path, fatigue crack growth and stress intensity factors value. Results from simulation and experiment showed good agreement with a certain condition. The implications from the results were discussed through the analysis of fatigue crack growth.

Stress intensity factors of cracks emanating from a surface square hole in infinite body in tension

ABSTRACTThis paper deals with such a kind of surface crack problem with a same depth (called a liked‐plane crack problem for short). Based on the previous investigations on an internal rectangular crack and a surface rectangular crack in an infinite solid in tension and the hybrid displacement discontinuity method, a numerical approach for the liked‐plane crack problem is presented. Numerical examples are given to illustrate the numerical approach is simple, yet accurate for calculating the stress intensity factors (SIFs) of the liked‐plane crack problem. Specifically, SIFs of a pair of cracks emanating from a surface square hole in an infinite body in tension are investigated in detail.

A numerical analysis of cracks emanating from a surface elliptical hole in infinite body in tension

This paper deals with such a kind of surface crack problem with an approximately same depth, which is called a liked-plane crack problem. Based on the previous investigations on internal rectangular crack and surface rectangular crack in infinite solid in tension and a hybrid displacement discontinuity method (a boundary element method) proposed recently by Yan, a numerical approach for the liked-plane crack problem in hand is presented. Numerical examples are given to illustrate the numerical approach is simple, yet accurate for calculating the SIFs of a liked-plane crack. Specifically, a pair of cracks emanating from a surface elliptical hole in infinite body in tension are investigated in detail.

重合メッシュ法を用いた疲労き裂進展シミュレーション : 第3報,三次元表面き裂進展シミュレーション

Fatigue crack growth under mixed mode loading conditions is simulated using S-FEM. By using S-FEM technique, only local mesh should be re-meshed and it becomes easy to simulate crack growth. By combining with re-meshing technique, local mesh is re-meshed automatically, and curved crack path is modeled easily. Fully automatic crack growth simulation system in 3-dimensional problem is developed. At first, a basic slant surface crack problem is solved, and it is shown that surface crack grows under pure mode I conditions, which is similar in 2-dimensional problem. It is also shown that this system is available for complicated structure, for example, surface crack at inner surface of pipe. Finally, interaction effect of two surface cracks is evaluated.

Fracture analysis of a surface through-thickness crack in PZT thin film under a continuous laser irradiation

In this paper, the surface crack problem in PZT thin films under a continuous laser irradiation has been investigated by the superposition principle. Using commercial (FEM) software ANSYS 9.0, the piezoelectric fields near the crack tip were solved for surface crack in the finite PZT thin film. The SIFs for crack-tip fields were obtained by using the limited stress extrapolation technique (LSET) and then the energy release rates were calculated by the relation to the intensity factors. When the irradiation time and crack location were changed, the energy release rates G, G I, and G e for total, mechanical terms (mode I) and electric contribution were investigated. The results show that the mechanical opening mode I is the main mode for the surface crack under a continuous laser irradiation. However, electric mode IV has inhibiting effect on crack growth. At the beginning of laser irradiation, the surface tiny crack which is close to the centre of film will propagate more easily. During the laser irradiation, the crack which is far from the centre of film will propagate more easily.

Surface crack problem for functionally graded magnetoelectroelastic coating–homogeneous elastic substrate system under anti-plane mechanical and in-plane electric and magnetic loading

A functionally graded magnetoelectroelastic material layer bonded to a homogeneous elastic substrate is investigated. The functionally graded magnetoelectroelastic layer contains a surface crack that is perpendicular to the surface of the medium. The structure is subjected to anti-plane mechanical and in-plane electric and magnetic loads, the crack problem involves the anti-plane elastic field coupled with the in-plane electric and magnetic field. The elastic layer can be an ideal insulator or an ideal conductor. Integral transform and dislocation density functions are employed to reduce the problem to the solution of a system of singular integral equations. Numerical results show the influences of the material gradient parameter and crack configuration on field intensity factors and energy release rates of the functionally graded magnetoelectroelastic coating–homogeneous elastic substrate structure.

Semi-elliptic surface crack in an elastic solid with finite size under impact loading

ABSTRACT In this paper a semi-elliptic surface crack problem in an elastic solid of finite size under impact loading is investigated. An analysis is performed by means of fracture dynamics and the finite element method, and a three-dimensional finite element program is developed to compute the dynamic stress intensity factor. The results reveal that the effects of the solid's boundary surface, crack surface, material inertia and stress wave interactions play significant roles in dynamic fracture.

2010 X-FEMによる三次元弾塑性破壊解析(S04-1 FEM/メッシュフリー法/粒子法とその関連技術(1),S04 FEM/メッシュフリー法/粒子法とその関連技術)

In this study, numerical procedures for thee-dimensional elastic-plastic X-FEM analysis including selections of the near-tip enrichment functions are examined. The utilized enrichment functions approximate the asymptotic displacement field near the crack tip obtained by the HRR solution. As a numerical example, a surface crack problem of elastic-plastic materials is solved to evaluate the crack opening displacement and the J-integrals along the crack front, which is evaluated using the domain integral method. Obtained results are compared with those obtained using conventional finite element analysis.

The Surface Crack Problem for a Piezoelectric Slab with Functionally Graded Properties

The Surface Crack Problem for a Piezoelectric Slab with Functionally Graded Properties

The Surface Crack Problem for a Layered Elastic Medium with a Functionally Graded Nonhomogeneous Interface

The plane elasticity solution is presented in this paper for the crack problem of a layered medium. A functionally graded interfacial region is assumed to exist as a distinct nonhomogeneous transitional layer with the exponentially varying elastic property between the dissimilar homogeneous surface layer and the substrate. The surface layer contains a crack perpendicular to the surface. Fourier transforms are used to formulate the problem in terms of a singular integral equation. The main results presented are the variations of the stress intensity factors as functions of geometric and material parameters of the layered medium.

The Surface Crack Problem for a Layered Elastic Medium With a Functionally Graded Nonhomogeneous Interface.

The plane elasticity solution is presented in this paper for the crack problem of a layered medium. A functionally graded interfacial region is assumed to exist as a distinct nonhomogeneous transitional layer with the exponentially varying elastic property between the dissimilar homogeneous surface layer and the substrate. The surface layer contains a crack perpendicular to the surface. Fourier transforms are used to formulate the problem in terms of a singular integral equation. The main results presented are the variations of the stress intensity factors as functions of geometric and material parameters of the layered medium.

The surface crack problem for a layered plate with a functionally graded nonhomogeneous interface

The plane elasticity solution is presented in this paper for the crack problem of a layered plate. A functionally graded interfacial region is assumed to exist as a distinct nonhomogeneous transitional layer with the exponentially varying elastic property between the dissimilar homogeneous surface layer and the substrate. The surface layer contains a crack perpendicular to the boundaries. The Fourier transform technique is used to formulate the problem in terms of a singular integral equation. The main results presented are the variations of stress intensity factors as functions of geometric and material parameters of the layered plate.

Non-linear surface crack analysis by three dimensional boundary element with mixed boundary conditions

In this paper, an effective three dimensional boundary element method with mixed boundary conditions is prescribed for nonlinear surface crack analyses. The line spring model originally proposed by Rice and Levy is used to form the non-linear mixed boundary conditions of the 3D crack problem in a continuum manner, which is then combined with the three dimensional boundary element method to compute the fracture parameter J integral of non-linear surface crack. A predictor–corrector method is presented for the nonlinear compliance matrix of the mixed boundary so that a more accurate result can be reached. Two numerical examples are discussed to show the effectiveness of the method. Especially, the surface crack problem is addressed in which the non-linear region only happens at the mixed boundary condition area, and most of the remaining area is still elastic.

Fracture analyses of surface-cracked pipes and elbows using the line-spring/shell model

The line-spring/shell model proposed by Rice and Levy (1972) and further modified by Parks and co-workers (1981, 1982, 1995) provides an attractive and inexpensive alternative to analyzing surface-cracked structures. This model idealizes the complex three-dimensional surface crack problem in a plate- or shell-like structure as a more tractable two-dimensional problem. Though used in some previous studies, this model has largely been ignored in the study of surface-cracked nuclear piping components. While it is true that the line-spring method has some restrictions, it can provide reasonably accurate predictions of important fracture parameters of cracked components within the domain of its applicability. Through some detailed studies of surface-cracked pipes and elbows, the predictive nature of the line-spring model is demonstrated by comparing its predictions with that of a three-dimensional finite element model as well as with experimental measurements. Excellent comparisons between the predictions of the line-spring/shell and three-dimensional finite element models are shown not only using the three-dimensional finite element calculations performed by the author, but also using the three-dimensional calculations performed by two other independent investigators. It is hoped that the results shown in this paper invalidate the criticisms and reestablish the usefulness and reasonable accuracy of the line-spring mode, within its domain of applicability, in the analyses of surface-cracked structures.

The Surface Crack Problem for a Plate With Functionally Graded Properties

In this study the plane elasticity problem for a nonhomogeneous layer containing a crack perpendicular to the boundaries is considered. It is assumed that the Young’s modulus of the medium varies continuously in the thickness direction. The problem is solved under three different loading conditions, namely fixed grip, membrane loading, and bending applied to the layer away from the crack region. Mode I stress intensity factors are presented for embedded as well as edge cracks for various values of dimensionless parameters representing the size and the location of the crack and the material nonhomogeneity. Some sample results are also given for the crack-opening displacement and the stress distribution.

Numerical modeling of the surface crack problem in welded connections : Liejun, H.; Bozhen, C. 9th International Conference on Nondestructive Evaluation in the Nuclear Industry, Tokyo (Japan), 25–28 Apr. 1988, pp. 667–672. Edited by K. lida, J.E. Doherty and X. Edelmann. ASM (1988)

Numerical modeling of the surface crack problem in welded connections : Liejun, H.; Bozhen, C. 9th International Conference on Nondestructive Evaluation in the Nuclear Industry, Tokyo (Japan), 25–28 Apr. 1988, pp. 667–672. Edited by K. lida, J.E. Doherty and X. Edelmann. ASM (1988)

Surface cracks in toroidal shells

Toroidal shells containing a surface crack and subjected to various symmetric and antisymmetric loading conditions are considered. A singular integral formulation of a through crack located along a principal line of curvature of a shell is used along with the line spring model to treat the surface crack problem. Transverse shear deformations are taken into account in the shell theory. Locating the crack along a line or principal curvature uncouples the symmetric mode I deformations from the antisymmetric mode II and III deformations, which are inherently coupled. Mode I loadings considered include membrane loading and bending, while the mode II and III cases include in plane shear, twisting and transverse shear. In addition to these loadings, residual stresses resulting in mode I deformations are considered. Stress intensity factors for the various loadings are given for shell geometries representative of spherical caps, cylindrical pipes and pipe elbows for a number of crack locations.

Stress-Intensity Factors for an Internal Semi-Elliptical Surface Crack in Cylindrical Pressure Vessels

Abstract In this paper, the surface crack problem in a cylinder subjected to internal pressure is solved. The analysis is based on the body force method, but it is different from the conventional body force method in the following point. That is, the body forces to be distributed continuously on the assumed boundaries in an infinite body are approximated by some discrete point forces acting on the outside of the assumed boundaries. By using this method combined with the resultant force boundary conditions, solutions with high accuracy are obtained.

Fracture mechanics of functionally graded materials

In this paper, after a brief discussion of the elementary concepts of fracture mechanics in nonhomogeneous materials, a number of typical problem areas relating to the fracture of functionally gradient materials (FGMs) are identified. The main topics considered are the investigation of the nature of stress singularity near the tip of a crack fully embedded in a nonhomogeneous medium, the general problem of debonding of an FGM coating from a homogeneous substrate, the basic surface crack problem in FGMs and cracking perpendicular to the interfaces, periodic surface cracking and the associated problem of stress and energy relaxation, and the problem of stress concentration at and the initiation and growth of delamination cracks from the stress-free ends of FGM-coated homogeneous substrates under residual or thermal stresses. Each topic is very briefly reviewed, some sample results are presented and comparisons with the corresponding results obtained from homogeneous materials are made.