Three-dimensional mixed mode analysis of a cracked body by fractal finite element method

A semi-analytical method namely fractal finite element method is presented for the determination of stress intensity factor for the straight three-dimenisonal plane crack. Using the concept of fractal geometry, infinite many of finite elements are generated virtually around the crack border. Based on the analytical global displacement function, numerous DOFs are transformed to a small set of generalised coordinates in an expeditious way. No post-processing and special finite elements are required to develop for extracting the stress intensity factors. Examples are given to illustrate the accuracy and efficiency of the present method. Very good accuracy (with less than 3% errors) is obtained for the maximum value of SIFs for different modes.     

裂纹面荷载作用下多裂纹应力强度因子计算

该文基于比例边界有限元法计算了裂纹面荷载作用下平面多裂纹应力强度因子.比例边界有限元法可以给出裂纹尖端位移场和应力场的解析表达式,该特点可以使应力强度因子根据定义直接计算,同时不需要对裂纹尖端进行特殊处理.联合子结构技术可以计算多裂纹问题的应力强度因子.数值算例表明该文方法是有效且高精确的,进而推广了比例边界有限元法的...     

Numerical solution of cracked thin plates subjected to bending, twisting and shear loads

A semi-analytical method namely fractal finite element method is presented for the determination of mode I and mode II moment intensity factors for thin plate with crack using Kirchhoff's theory. Using the concept of fractal geometry, infinite many of finite elements is generated virtually around the crack border. Based on the analytical global displacement function, numerous degrees of freedom (DOF) are transformed to a small set of generalised coordinates in an expeditious way. The stress intensity factors can be obtained directly from the generalized coordinates. No post-processing and special finite elements are required to develop for extracting the stress intensity factors. Examples of cracked plate subjected to bending, twisting and shear loads are given to illustrate the accuracy and efficiency of the present method. The influence of finite boundaries on the calculation of the moment intensity factors is studied in details. Very accuracy results when compare with the theoretical and numerical counterparts are found.     

A numerical analysis of cracks emanating from a square hole in a rectangular plate under biaxial loads

This note concerns with stress intensity factors of cracks emanating from a square hole in rectangular plate under biaxial loads by means of the boundary element method which consists of the non-singular displacement discontinuity element presented by Crouch and Starfied and the crack tip displacement discontinuity elements proposed by the author. In the boundary element implementation the left or the right crack tip displacement discontinuity element is placed locally at corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundary. The present numerical results illustrate that the present approach is very effective and accurate for calculating stress intensity factors of complicated cracks in a finite plate and can reveal the effect of the biaxial load and the cracked body geometry on stress intensity factors.     

Stress intensity factors for functionally graded solid cylinders

This paper presents the mode I stress intensity factors for functionally graded solid cylinders with an embedded penny-shaped crack or an external circumferential crack. The solid cylinders are assumed under remote uniform tension. The multiple isoparametric finite element method is used. Various types of functionally graded materials and different gradient compositions for each type are investigated. The results show that the material property distribution has a quite considerable influence on the stress intensity factors. The influence for embedded cracks is quite different from that for external cracks.     

轮轨摩擦接触下钢轨多裂纹相互作用研究

利用热机耦合有限元法,建立了轮轨摩擦接触时钢轨表面多裂纹的热弹性平面应变有限元模型。数值模型中,考虑轮轨摩擦温升对轮轨材料参数的影响,通过移动载荷和热源来模拟运动车轮对钢轨的作用。分析了轮轨滑动接触时多裂纹相互作用和表面裂纹数量对钢轨疲劳裂纹扩展特性的影响。计算结果表明:与单个裂纹相比,多裂纹有降低钢轨疲劳裂纹扩展的作用;钢轨裂纹尖端应力强度因子K1和应力强度因子范围?K2均随裂纹数的增多而减小;钢轨表面裂纹数为5条时可以反映更多裂纹时的裂纹扩展特性。     

Stress intensity factors and crack propagation in a single crystal nickel-based superalloy

A three-dimensional finite element method was used to calculate the stress intensity factors for corner cracked specimens of a single crystal nickel-based superalloy. The anisotropic material properties and inclinations of the cracks were shown to have significant effects on the stress intensities. Then the two-dimensional resolved shear stress approach for predicting the crack planes and crack growth directions in single crystals was extended to the three-dimensional case. Using this approach, the fatigue crack growth behaviour in single crystal corner cracked specimens could be explained.     

Computation of mode I stress intensity factors for three-dimensional bodies using displacements at an arbitrary location

An approach is developed to determine stress intensity factors using the displacements due to a crack increment in a three-dimensional body. By computing displacements for both the actual loading and a virtual force some distance from the crack, stress intensity factors may be obtained by the finite element method without using special crack elements. Numerical results obtained using coarse meshes for several crack configurations are found to be in good agreement with those available in the literature. This revised version was published online in July 2006 with corrections to the Cover Date.     

A brief note on elastic T-stress for centred crack in anisotropic plate

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). The FFEM combines an exterior finite element model and a localized inner model near the crack tip. The mesh geometry of the latter is self-similar in radial layers around the tip. A higher order displacement series derived from Laurent series and Goursat functions is used to condense the large numbers of nodal displacements at the inner model near the crack tip into a small set of unknown coefficients. In this study, the variations of the SIFs and the T-stress with material properties and orientations of a crack are presented. The separation of the analytical displacement series into four fundamental cases has shown to be necessary in order to cover all the material variations and the orientations of a crack in the plate with general rectilinear anisotropic materials.     

Stress intensity factors of a central interface crack in a bonded finite plate and periodic interface cracks under arbitrary material combinations

Although a lot of interface crack problems were previously treated, few solutions are available under arbitrary material combinations. This paper deals with a central interface crack in a bonded finite plate and periodic interface cracks. Then, the effects of material combination and relative crack length on the stress intensity factors are discussed. A useful method to calculate the stress intensity factor of interface crack is presented with focusing on the stress at the crack tip calculated by the finite element method.     

A complex variable boundary element method for solving interface crack problems

The problem of finite bimaterial plates with an edge crack along the interface is studied. A complex variable boundary element method is presented and applied to determine the stress intensity factor for finite bimaterial plates. Using the pseudo-orthogonal characteristic of the eigenfunction expansion forms and the well-known Bueckner work conjugate integral and taking the different complex potentials as auxiliary fields, the interfacial stress intensity factors associated with the physical stress-displacement fields are evaluated. The effects of material properties and crack geometry on stress intensity factors are investigated. The numerical examples for three typical specimens with six different combinations of the bimaterial are given. This revised version was published online in July 2006 with corrections to the Cover Date.     

Multiple penny-shaped cracks interaction in a finite body and their effect on stress intensity factor

In this paper we investigate the stress intensity factors (SIFs) of multiple penny-shaped cracks in an elastic solid cylinder under mode I (axial tension) loading. The cracks are located symmetrically and in parallel to one another in the isotropic cylinder. The fractal-like finite element method (FFEM) is employed to study the interaction of multiple cracks and to demonstrate the efficiency of the FFEM for multiple crack problems. The results show that the SIF values of the inner cracks, which are denoted as crack number 1,2,3,…,(n+1)/2 of a stack of n parallel cracks, are lower than the SIF values of a single crack by between 16% and 48%. Also, the outermost crack, that is the crack closest to the boundaries of a multiple cracked body, has the highest SIF values and is, therefore, likely to fail first.     

Dislocation-based semi-analytical method for calculating stress intensity factors of cracks: Two-dimensional cases

Determination of the stress intensity factors of cracks is a fundamental issue for assessing the performance safety and predicting the service lifetime of engineering structures. In the present paper, a dislocation-based semi-analytical method is presented by integrating the continuous dislocation model with the finite element method together. Using the superposition principle, a two-dimensional crack problem in a finite elastic body is reduced to the solution of a set of coupled singular integral equations and the calculation of the stress fields of a body which has the same shape as the original one but has no crack. It can easily solve crack problems of structures with arbitrary shape, and the calculated stress intensity factors show almost no dependence upon the finite element mesh. Some representative examples are given to illustrate the efficacy and accuracy of this novel numerical method. Only two-dimensional cases are addressed here, but this method can be extended to three-dimensional problems.     

Stress intensity factor calculation of steel-lined hoop-wrapped cylinders with internal semi-elliptical circumferential crack

The purpose of this paper is to present mode I stress intensity factor for a circumferential semi-elliptical crack on the inner surface of a hoop-wrapped steel-lined CNG cylinder. The stress intensity factors along the crack front are directly computed by 3D finite element method for a wide range of variations of the crack geometry. Also influence of many parameters such as cylinder internal pressure, composite layer thickness, composite material properties and undertaking Auto-Frettage pressure are studied on the stress intensity factor of the crack and some conclusive results are drawn. For the sake of validation of the results and because of lack of the results for a circumferential semi-elliptical crack in the literature, a semi-elliptical axial crack in a composite hoop-wrapped cylinder has been modeled and the results have been compared with those in the literature showing a good agreement.     

Computation of the stress intensity factors for repaired cracks with bonded composite patch in mode I and mixed mode

In this study, the finite element method is used to analyse the behaviour of repaired cracks with bonded composite patches in mode I and mixed mode by computing the stress intensity factors at the crack tip. The effects of the patch size and the adhesive properties on the stress intensity factors variation were highlighted. The plot of the stress intensity factors according to the crack length in mode I, shows that the stress intensity factor exhibits an asymptotic behaviour as the crack length increases. In mixed mode, the obtained results show that the Mode I stress intensity factor is more affected by the presence of the patch than that of mode II.     

STRESS INTENSITY FACTORS AND WEIGHT FUNCTIONS FOR SEMI-ELLIPTICAL SURFACE CRACKS IN FINITE-THICKNESS PLATES UNDER TWO-DIMENSIONAL STRESS DISTRIBUTION

Abstract— A Fourier series approach is proposed to calculate stress intensity factors using weight functions for semi-elliptical surface cracks in flat plates subjected to two-dimensional stress distributions. The weight functions were derived from reference stress intensity factors obtained by three-dimensional finite element analyses. The close form weight functions derived are suitable for the calculation of stress intensity factors for semi-elliptical surface cracks in flat plates under two-dimensional stress distributions with the crack aspect ratio in the range of 0.1 ≤ a/c ≤ 1 and relative depth in the range of 0 ≤ a/t ≤ 0.8. Solutions were verified using several two-dimensional non-linear stress distributions; the maximum difference being 6%.     

An interaction integral method for computing mixed mode stress intensity factors for curved bimaterial interface cracks in non-uniform temperature fields

In finite element analysis the interaction integral has been a useful tool for computing the stress intensity factors for fracture analysis. This work extends the interaction integral to account for non-uniform temperatures in the calculation of stress intensity factors for three dimensional curvilinear cracks either in a homogeneous body or on a bimaterial interface. First, the derivation of the computational algorithm, which includes the additional terms developed by the non-zero gradient of the temperature field, is presented in detail. The algorithm is then implemented in conjunction with commercial finite element software to calculate the stress intensity factors of a crack undergoing non-uniform temperatures on both a homogeneous and a bimaterial interface. The numerical results displayed path independence and showed excellent agreement with available analytical solutions.     

Stress intensity factor analyses of interface cracks between dissimilar anisotropic materials using the finite element method

Delamination along an interface between dissimilar materials is the primary cause of failure in microstructures like electronic packages, micro-electro-mechanical systems (MEMS), and so on. Fracture mechanics is a powerful tool for the evaluation of delamination. However, many materials used in microstructures such as composite materials and single crystals are anisotropic materials. Stress intensity factors of an interface crack between dissimilar anisotropic materials, which were proposed by Hwu, are useful for evaluating the reliability of microstructures. However, numerical methods that can analyze the stress intensity factors of an interface crack between anisotropic materials have not been developed. We propose herein a new numerical method for the analysis of an interface crack between dissimilar anisotropic materials. The stress intensity factors of an interface crack are based on the generalized plane strain condition. The energy release rate is obtained by the virtual crack extension method in conjunction with the finite element method for the generalized plane strain condition. The energy release rate is separated into individual modes of the stress intensity factors K_I, K_II, and K_III, using the principal of superposition. The target problem to be solved is superposed on the asymptotic solution of displacement in the vicinity of an interface crack tip, which is described using the Stroh formalism. Analyses of the stress intensity factors of center interface cracks between semi-infinite dissimilar anisotropic media subjected to concentrated self-balanced loads on the center of crack surfaces and to uniform loads are demonstrated. The present method accurately provides mode-separated stress intensity factors using relatively coarse meshes for the finite element method.     

An analytical method for mixed-mode propagation of pressurized fractures in remotely compressed rocks

An analytical method for mixed-mode (mode I and mode II) propagation of pressurized fractures in remotely compressed rocks is presented in this paper. Stress intensity factors for such fractured rocks subjected to two-dimensional stress system are formulated approximately. A sequential crack tip propagation algorithm is developed in conjunction with the maximum tensile stress criterion for crack extension. For updating stress intensity factors during crack tip propagation, a dynamic fictitious fracture plane is used. Based on the displacement correlation technique, which is usually used in boundary element/finite element analyses, for computing stress intensity factors in terms of nodal displacements, further simplification in the estimation of crack opening and sliding displacements is suggested. The proposed method is verified comparing results (stress intensity factors, propagation paths and crack opening and sliding displacements) with that obtained from a boundary element based program and available in literatures. Results are found in good agreements for all the verification examples, while the proposed method requires a trivial computing time.     

Stress intensity factors for three‐dimensional weld toe cracks using weld toe magnification factors

In welded components, particularly those with complex geometrical shapes, evaluating stress intensity factors is a difficult task. To effectively calculate the stress intensity factors, a weld toe magnification factor is introduced that can be derived from data obtained in a parametric study performed by finite element method (FEM). Although solutions for the weld toe magnification factor have been presented, these are applicable only to non‐load‐carrying cruciform or T‐butt joints, due possibly to the requirement of very complicated calculations. In the majority of cases for various welded joints, the currently used weld toe magnification factors do not adequately describe the behaviour of weld toe cracks. In this study, the weld toe magnification factor solutions for the three types of welded joints such as cruciform, cover plate and longitudinal stiffener joints were provided through a parametric study using three‐dimensional finite elements. The solutions were formed with exponents and fractions that have polynomial functions in terms of a/c and a/t – that is, crack depths normalised by corresponding half crack lengths and specimen thickness. The proposed weld toe magnification factors were applied to evaluate the fatigue crack propagation life considering the propagation mechanisms of multiple‐surface cracks for all welded joints. It showed good agreement within a deviation factor of two between the experimental and calculated results for the fatigue crack propagation life.