Cracks emanating from circular hole or square hole in rectangular plate in tension

A numerical analysis of cracks emanating from a circular hole (Fig. 1) or a square hole (Fig. 2) in rectangular plate in tension is performed by means of the displacement discontinuity method with crack-tip elements (a boundary element method) presented recently by the author. Detail solutions of the stress intensity factors (SIFs) of the two plane elastic crack problems are given, which can reveal the effect of geometric parameters of the cracked bodies on the SIFs. By comparing the SIFs of the two crack problems with those of the center crack in rectangular plate in tension (Fig. 3), in addition, an effect of the circular hole or the square hole on the SIFs of the center crack is discussed in detail. The numerical results reported here also illustrate that the boundary element method is simple, yet accurate for calculating the SIFs of complex crack problems in finite plate.     

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

This 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.     

Rectangular tensile sheet with single edge crack or edge half-circular-hole crack

By using the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author, this note presents the stress intensity factors (SIFs) of a rectangular tensile plate with single edge crack. Further this note studies the SIFs of crack emanating from an edge half-circular hole. By comparing the calculated SIFs of the single edge half-circular-hole crack with those of the single edge crack, a shielding effect of the half-circular hole on the SIFs of the single edge crack is discussed. It is found that the boundary element method is simple, yet accurate for calculating the SIFs of complex crack problems in finite plate.     

Boundary element analysis of three‐dimensional cracks in anisotropic solids

This paper presents a boundary element analysis of linear elastic fracture mechanics in three‐dimensional cracks of anisotropic solids. The method is a single‐domain based, thus it can model the solids with multiple interacting cracks or damage. In addition, the method can apply the fracture analysis in both bounded and unbounded anisotropic media and the stress intensity factors (SIFs) can be deduced directly from the boundary element solutions. The present boundary element formulation is based on a pair of boundary integral equations, namely, the displacement and traction boundary integral equations. While the former is collocated exclusively on the uncracked boundary, the latter is discretized only on one side of the crack surface. The displacement and/or traction are used as unknown variables on the uncracked boundary and the relative crack opening displacement (COD) (i.e. displacement discontinuity, or dislocation) is treated as a unknown quantity on the crack surface. This formulation possesses the advantages of both the traditional displacement boundary element method (BEM) and the displacement discontinuity (or dislocation) method, and thus eliminates the deficiency associated with the BEMs in modelling fracture behaviour of the solids. Special crack‐front elements are introduced to capture the crack‐tip behaviour. Numerical examples of stress intensity factors (SIFs) calculation are given for transversely isotropic orthotropic and anisotropic solids. For a penny‐shaped or a square‐shaped crack located in the plane of isotropy, the SIFs obtained with the present formulation are in very good agreement with existing closed‐form solutions and numerical results. For the crack not aligned with the plane of isotropy or in an anisotropic solid under remote pure tension, mixed mode fracture behavior occurs due to the material anisotropy and SIFs strongly depend on material anisotropy. Copyright © 2000 John Wiley & Sons, Ltd.     

Rectangular Tensile Sheet with Double Edge Notch Cracks

This paper deals with the rectangular tensile sheet with symmetric double edge notch cracks. Such a crack problem is called an edge notch crack problem for short. By using a hybrid displacement discontinuity method (a boundary element method), two edge notch models are analyzed in detail. By changing the geometrical forms and parameters of the edge notch, and by comparing the stress intensity factors (SIFs) of the edge notch crack problem with those of the double edge cracked plate tension specimen (DECT), which is a model frequently used in fracture mechanics, the effect of the geometrical forms and parameters of the edge notch on the SIFs of the DECT specimen, is revealed. Some geometric characterestic parameters are introduced here, which are used to formulate the notch length and the branch crack length, which are to be determined in mechanical machining of the DECT specimen So we can say that the geometric characterestic parameters and the formulae used to determine the notch length and the branch crack length presented in this paper perhaps have some guidance role for mechanical machining of the DECT specimen.     

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.     

Cracks emanating from a rhombus hole in infinite and finite plate subjected to internal pressure

This note deals with the stress intensity factors (SIFs) of cracks emanating from a rhombus hole in a rectangular plate subjected to internal pressure by means of the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author. Moreover, an empirical formula of the SIFs of the crack problem is presented and examined. It is found that the empirical formula is very accurate for evaluating the SIFs of the crack problem.     

Fatigue growth prediction of center slant crack in rectangular plate

This paper presents a numerical prediction model of mixed‐mode crack fatigue growth in a plane elastic plate. It involves a formulations of fatigue growth of multiple crack tips under mixed‐mode loading and a displacement discontinuity method with crack‐tip elements (a boundary element method) proposed recently by Yan is extended to analyse the fatigue growth process of multiple crack tips. Due to an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single‐region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is conveniently modelled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the present numerical approach is used to analyse the fatigue growth of a centre slant crack in a rectangular plate. The numerical results illustrate the validation of the numerical prediction model and can reveal the effect of the geometry of the cracked plate on the fatigue growth.     

An effective method of stress intensity factor calculation for cracks emanating from a triangular or square hole under biaxial loads

This paper is concerned with stress intensity factors for cracks emanating from a triangular or square hole under biaxial loads by means of a new boundary element method. The boundary element method consists of the constant 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 the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The method is called a Hybrid Displacement Discontinuity Method (HDDM). Numerical examples are included to show that the method is very efficient and accurate for calculating stress intensity factors for plane elastic crack problems. In addition, the present numerical results can reveal the effect of the biaxial loads on stress intensity factors.     

An empirical formula for stress intensity factors of cracks emanating from a circular hole in a rectangular plate in tension

An empirical formula of the SIFs of cracks emanating from a circular hole in a rectangular plate in tension is presented and examined. It is found that the empirical formula is simple, yet accurate for evaluating the SIFs of the crack problem.     

SGBEM analysis of crack-particle(s) interactions due to elastic constants mismatch

The effects of elastic constants mismatch on the interaction between a propagating crack and single or multiple inclusions in brittle matrix materials are investigated using numerical simulations. The simulations employ a quasi-static crack-growth prediction tool based upon the symmetric-Galerkin boundary element method (SGBEM) for multiregions, a modified quarter-point crack-tip element, the displacement correlation technique for evaluating stress intensity factors (SIFs), and the maximum principal stress criterion for crack-growth direction. It is shown that, even with this simple method for calculating SIF, the crack-growth prediction tool is both highly accurate and computationally effective. This is evidenced by results for the case of a single inclusion in an infinite plate, where the SGBEM results for the SIFs show excellent agreement with known analytical solutions. The simulation results for crack growth and stress intensity behaviors in particulate media are very stable. The crack-tip shielding and amplification behaviors, as seen in similar studies using other numerical approaches, can be clearly observed.     

Stress intensity factors for cracks emanating from a triangular or square hole in an infinite plate by boundary elements

This paper concerns stress intensity factors of cracks emanating from a triangular or square hole in an infinite plate subjected to internal pressure calculated by means of a boundary element method, which consists of constant displacement discontinuity element presented by Crouch and Starfied and 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 boundaries. Numerical examples are included to show that the method is very efficient and accurate for calculating stress intensity factors of plane elasticity crack problems. Specifically, the numerical results of stress intensity factors of cracks emanating from a triangular or square hole in an infinite plate subjected to internal pressure are given.     

T-stress Solutions for Cracks Emanating from a Circular Hole in a Finite Plate

The boundary element method is employed to obtain T-stress solutions for cracks emanating from a circular hole in finite rectangular plates. Numerical values of the T-stress are obtained using the M-contour integral approach. A range of crack lengths are analyzed for two hole sizes, and the cases of a single crack and double-cracks emanating from the hole in the plate under both uniform remote tension and simple bending are considered. For completeness, stress intensity factor solutions are also presented. These results will be useful for failure assessments using two-parameter linear elastic fracture mechanics.     

正交各向异性孔板的材料参数识别

结合优化技术和边界元分析,针对正交各向异性孔板进行了材料参数的识别。材料参数识别的问题转化为极小化目标函数的问题,其中目标函数定义为测量位移与边界元计算相应的位移之差的平方和。采用Levenberg-Marquardt方法解极小化目标函数的问题,其中灵敏度的计算是基于离散的边界元代数矩阵方程对识别材料参数的求导。数值算例中,首先把边界元计算正交各向异性圆孔方板位移的结果与解析解进行比较,两者符合良好;然后采用本文提出的方法识别正交各向异性圆孔方板的材料参数。数值算例表明本文提出的方法是有效的。     

Stress intensity factors of square crack inclined to interface of transversely isotropic bi-material

This paper analyzes a square crack in a transversely isotropic bi-material solid by using dual boundary element method. The square crack is inclined to the interface of the bi-material. The fundamental solution for the bi-material solid occupying an infinite region is incorporated into the dual boundary integral equations. The square crack can have an arbitrary angle with respect to the plane of isotropy of the bi-material occupying either finite or infinite regions. The stress intensity factor (SIF) values of the modes I, II, and III associated with the square crack are calculated from the crack opening displacements. Numerical results show that the properties of the anisotropic bi-material have evident influences on the values of the three SIFs. The values of the three SIFs are further examined by taking into account the effect of the external boundary of the internally cracked bi-material.     

Integral formulation for elastodynamic T-stresses

In this paper, a path independent integral formulation is presented for the computation of dynamic T-stresses in a two-dimensional body with a stationary crack. The mutual M-integral expressed through dynamic Ĵ-integrals provides sufficient information for determining T-stresses on the basis of the relationship found between the M-integral and T-stresses. The elastodynamic fields required for the evaluation of the Ĵ-and M-integrals are obtained by the boundary element method. The time-domain approach is used for the solution of the boundary value crack problem and numerical results for two crack problems are presented. In the first a rectangular plate with a central crack is considered and in the second two cracks at a hole in an infinite sheet. A comparison is made with the results obtained by the boundary layer and displacement field methods based on the asymptotic expansions of stresses and displacements at a crack tip vicinity. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the computation of the pure Neumann problem in 2-dimensional elasticity

The accurate computation of stress intensity factors (SIFs) plays a decisive role in the determination of crack paths. The calculation of SIFs with the help of singular weight functions leads to pure Neumann problem for anisotropic elasticity in a plane domain with a crack. Here a method is presented to overcome the specific numerical difficulties which arises while calculating these solutions with Finite Element methods. The accuracy and advantage of this method are shown by a numerical example, the calculation of SIFs of a compact tension specimen.      

Free out-of-plane vibration of cracked curved beams on elastic foundation by estimating the stress intensity factor

Abstract

This paper is concerned with evaluating stress intensity factors (SIFs), for a cracked curved beam of rectangular cross section, applying an approach which allows us to estimate the strain energy release rate. The beam is located on an elastic foundation. The out-of-plane vibration of the beam is investigated. This approach requires an additional factor namely correction factor, on the basis of the energy release zone slope to approximate the SIFs. The initial curvature of the beam, however, adds some complication in using this factor. The second part of this study is investigating a numerical approach, namely differential quadrature element method (DQEM), to gain the natural frequencies of the cracked beam. This method is applied to show the application of the SIFs to calculate the compliance of the cracked section for modeling the crack. The other method which is used to obtain the natural frequencies is the finite element method (FEM). The results of these two methods are found to be in good agreement, which shows the precision of the stress intensity factors of the cracked beam.     

BIEM solution of piezoelectric cracked finite solids under time-harmonic loading

The time-harmonic behavior of cracked finite piezoelectric 2D solids of arbitrary shape is studied by the nonhypersingular traction boundary integral equation method (BIEM). Plane strain and generalized traction free boundary conditions along the crack are assumed. The system may be loaded at the external boundary by arbitrary mechanical or electrical loads. As numerical example a center cracked rectangular piezoelectric plate under time-harmonic tension and electrical displacement is investigated in detail. The accuracy of the proposed numerical algorithm is checked by comparison with available results obtained by other methods for special cases. Parametric studies revealing the sensitivity of the stress intensity factors (SIFs) on the frequency of the applied mechanical and electrical load, on its coupled and uncoupled character and on the piezoelectric properties of the material are presented.     

Stress intensity factors evaluation for through-transverse crack in slab track system under vehicle dynamic load

The stress intensity factors (SIFs) for through-transverse crack in the China Railway Track System (CRTS II) slab track system under vehicle dynamic load are evaluated in this paper. A coupled dynamic model of a half-vehicle and the slab track is presented in which the half-vehicle is treated as a 18-degree-of-freedom multi-body system. The slab track is modeled as two continuous Bernoulli–Euler beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The model is applied to calculate the vertical and lateral dynamic wheel–rail forces. A three-dimensional finite element model of the slab track system is then established in which the through-transverse crack at the bottom of concrete base is created by using extended finite element method (XFEM). The wheel–rail forces obtained by the vehicle-track dynamics calculation are utilized as the inputs to finite element model, and then the values of dynamic SIFs at the crack-tip are extracted from the XFEM solution by domain based interaction integral approach. The influences of subgrade modulus, crack length, crack angle, friction coefficient between cracked surfaces, and friction coefficient between faces of concrete base and subgrade on dynamic SIFs are investigated in detail. The analysis indicates that the subgrade modulus, crack length and crack angle have great effects on dynamic SIFs at the crack-tip, while both of the friction coefficients have negligible influences on variations of dynamic SIFs. Also the statistical characteristics of varying SIFs due to random wheel–rail forces are studied and results reveal that the distributions of dynamic SIFs follow an approximately Gaussian distribution with different mean values and standard deviations. The numerical results obtained are very useful in the maintenance of the slab track system.