Cracks emanating from a square hole in rectangular plate in tension

A numerical analysis of cracks emanating from a square hole in a rectangular plate in tension is performed using a hybrid displacement discontinuity method (a boundary element method). Detailed solutions of the stress intensity factors (SIFs) of the plane elastic crack problem are given, which can reveal the effect of geometric parameters of the cracked body on the SIFs. By comparing the calculated SIFs of the plane elastic crack problem with those of the centre crack in a rectangular plate in tension, in addition, an amplifying effect of the square hole on the SIFs is found. The numerical results reported here also prove that the boundary element method is simple, yet accurate, for calculating the SIFs of complex crack problems in finite plate.     

Stress intensity factors for corner cracks in single‐edge notch bend specimen by a three‐dimensional weight function method

A three‐dimensional (3D) weight function method is employed to calculate stress intensity factors of quarter‐elliptical corner cracks at a semi‐circular notch in the newly developed single‐edge notch bend specimen. Corner cracks covering a wide range of geometrical parameters under pin‐loading and remote tension conditions are analysed. Stress intensity factors from the 3D weight function analysis agree well with ABAQUS‐Franc3D finite element results. An engineering similitude approach previously developed for the half‐elliptical surface crack in single‐edge notch bend specimen is also applied to the present corner crack configuration. The results compare well with those from the present weight function analysis.     

Stress intensity factors for surface fatigue crack in a round bar under cyclic axial loading

In this paper, the surface fatigue crack growth shape for an initial straight-fronted edge crack in an elastic bar of circular cross-section is determined through experiments under pure fatigue axial loading. Three different initial notch depths are discussed. The relations of the aspect ratio (b/c) and relative crack depth (b/D) are obtained, and it is shown that there is a great difference in the growth of cracks with different initial front shapes and crack depths. Further, using the three-dimensional finite element method, the stress intensity factors (SIFs) are determined under remote uniform tension loading. Since the relationship of b/c and b/D changes during the fatigue crack growth, the SIFs are determined for different surface crack configurations.     

A general weight function for inclined kinked edge cracks in a semi-plane

A general method for evaluating the Stress Intensity Factors (SIFs) of an inclined kinked edge crack in a semi-plane is presented. An analytical Weight Function (WF) with a matrix structure was derived by extending a method developed for an inclined edge crack. The effects of the principal geometrical parameters governing the problem were studied through a parametric Finite Element (FE) analysis, carried out for different reference loading conditions. The WF can be used to produce efficient and accurate evaluations of the SIFs for cracks with initial inclination angle in the range −60° to +60° and kinked angle in the range from −90° to +90°. The agreement between the results with those obtained by accurate FE solutions suggests that the proposed WF can be used as a general tool for evaluating the fracture mechanics parameters of an inclined kinked crack.     

压电弹性体中光滑顶点的正三角形孔边裂纹的反平面问题分析

通过构造新的保角映射,利用复变函数的方法,研究了含光滑顶点的正三角形孔边裂纹的横观各向同性的压电弹性体的反平面问题。在电可穿透和电不可穿透裂纹、孔周及裂纹面为自由表面的假设下,充分利用Cauchy积分公式和复变函数方法,得到了裂纹尖端的场强度因子和能量释放率的表达式。数值算例显示了在不同边界条件下裂纹的几何尺寸、机电载荷对能量释放率和机械应变能释放率的影响规律。结果表明:在电可通和电不可通边界条件下,裂纹长度和三角形边长的增加会导致能量释放率增加,机械载荷则总是促进裂纹的扩展。在电不可通边界条件下电位移可以促进或抑制裂纹的扩展,而在电可通边界条件下电位移对裂纹扩展没有影响。     

Evaluating MTS criterion in predicting mixed-mode crack extension under different loading conditions

The maximum tangential stress (MTS) criterion is one of the most widely used criteria for predicting the direction of crack extension. The suitability of this criterion is examined under different loading conditions using the extended finite element method (XFEM). Experimental and numerical results reported in the literature are considered to evaluate the validity and accuracy of the criterion. The results demonstrate that the MTS criterion evaluated by stress intensity factors (SIFs) can accurately predict the direction of crack propagation in specimens under direct tensile loading. This criterion overestimates the angle of crack initiation in the specimen under indirect tensile loading but underestimates the angle in the specimen subjected to 3-point bending. It is concluded that the MTS criterion based on SIFs could not accurately predict the direction of the crack initiation, which could, however, be determined properly based on the stress distribution around the crack tip obtained by the XFEM numerical models.     

Numerical and experimental applications of the least-squares method to determine mode-II stress intensity factors for double fillet welded lap joints

Due to its simplicity, the least-squares method provides an efficient means to evaluate the stress intensity factors (SIFs) of cracks in complicated structures. This paper demonstrates numerical and experimental applications of the least-squares method to study mode-II SIFs of double fillet welded lap joints. In the numerical application, double fillet welded lap joints with different geometric parameters, including overlap length, weld leg size, plate thickness and plate length, were systematically analysed by the finite-element method combined with the least-squares method. The computed SIF results were then employed to develop the general formulae of the shearing fracture mode (mode-II) stress intensity factors. To validate the numerical results, three double fillet welded lap joint specimens were tested by a non-contact optical experiment using a common digital camera and a proposed image processing scheme. The measured crack shearing displacements near the crack tip were substituted into the least-squares procedure to obtain the SIFs of the specimens. The numerical and experimental results were in good agreement with the existing numerical results for double fillet welded lap joints provided in the handbook (Murakami, 1987). The non-contact optical experiment makes the field measurement of SIFs possible, which is very useful for fracture analysis or fatigue evaluation of structures like steel bridges, naval structures and offshore structures.     

The interface crack problem under a concentrated load for a functionally graded coating–substrate composite system

The plane crack problem for a functionally graded coating–substrate system under a concentrated load is studied in this paper. The medium consists of a functionally graded coating bonded to a homogeneous substrate of finite thickness, containing an interface crack of finite length. With use of the integration transform and differential factor methods, the displacement form can be obtained. By introducing auxiliary functions, the present problem can be turned into solving a group of singular integral equations. The mixed-mode stress intensity factors (SIFs) and strain energy release rates (SERRs) are obtained. The influences of the parameters such as the load location, nonhomogeneity constants and the geometry parameters on the SIFs and SERRs are studied.     

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.     

Three-Dimensional Static and Dynamic Analysis of a Composite Cruciform Structure Subjected to Biaxial Loading: A Discontinuum Approach

A three-dimensional structural integrity analysis using the eXtended Finite Element Method (XFEM) is considered for simulating the crack behaviour of a chopped fibre-glass-reinforced polyester (CGRP) cruciform specimen subjected to a quasi-static tensile biaxial loading. This is the first time this problem is accomplished for computing the stress intensity factors (SIFs) produced in the biaxially loaded area of the cruciform specimen. A static crack analysis for the calculation of the mixed-mode SIFs is carried out. SIFs are calculated for infinite plates under biaxial loading as well as for the CGRP cruciform specimens in order to review the possible edge effects. A ratio relating the side of the central zone of the cruciform and the crack length is proposed. Additionally, the initiation and evolution of a three-dimensional crack are successfully simulated. Specific challenges such as the 3D crack initiation, based on a principal stress criterion, and its front propagation, in perpendicular to the principal stress direction, are conveniently addressed. No initial crack location is pre-defined and an unique crack is developed. Finally, computational outputs are compared with theoretical and experimental results validating the analysis.     

Quantitative evaluation of the fatigue limit of a metal with an arbitrary crack under a stress controlled condition – Stress Ratio R=−1

The static crack problem of a functionally graded coating-substrate structure with an internal or edge crack perpendicular to the interface is investigated under an in-plane load. The structure is made up of a functionally graded coating with an internal or edge crack and a homogeneous substrate of finite thickness. The material properties are assumed to vary continuously from the coating to the substrate. By use of Fourier transform method, the mixed boundary value problem is reduced to a singular integral equation which can be solved numerically. During the analysis, a higher-order term is obtained in the asymptotic analysis of the singular kernel to improve the convergence efficiency of numerical integrals. The influences of material constants and the geometry parameters on the stress intensity factors (SIFs) are studied. In Part II of this paper, the transient response of the structure subjected to an in-plane impact is investigated.     

J-Q characterization of propagating cracks

An investigation is performed to determine to what extent the state at a growing crack tip vicinity can be characterised by J and Q calculated from FE analyses of successively stationary crack tip positions. FE models in two-dimensionals of single edge notch bend and double edge cracked panel specimens with several different crack lengths are used to cover a range of load and constraint levels. The stress and strain fields are compared between different specimens keeping J- and Q-values equal. A remeshing technique in the commercial FE-code ABAQUS is used to enhance the efficiency of the analysis. The results show that the J-Q-theory provides reasonably accurate crack tip characterization also for growing cracks. This leads to the conclusion that FE analyses of successive stationary cracks rather than full FE propagation analyses are sufficient. The limit of validity for propagation is similar to the validation limit for the stationary case, although somewhat more restrictive.     

Fracture behaviors for a functionally graded superconducting cylinder with a cylindrical crack

In this study, a double exponential model is proposed to investigate the cylindrical crack problem for a functionally graded superconducting cylinder. The stress intensity factors (SIFs) are analytically obtained by transforming the corresponding crack problem into dual integral equations. The effects of applied magnetic field, model parameters, and crack configuration on the SIFs are analyzed. Some important phenomena are observed. Among others, both decreasing the graded index of Young's modulus and increasing the introduced nondimensional exponent parameter in the critical current model can inhibit crack propagation. This study should be useful for the application of superconducting devices.     

碳纤维复合材料破坏的超声波检测

本文对碳纤维增强复合材料O°、±45°和0°/90°铺层的无缺口、有直边缺口、有中心圆孔和有中心缺口层板,作了静态拉伸试验研究。采用超声波扫描成象检测方法,检测了碳/环氧复合材料在不同加载区域内的损伤分布及损伤程度,得到了载荷—损伤程度曲线和材料内部缺陷分布的分层图象。结果表明:带有垂直于载荷方向直边缺口的试件在受静态拉伸时,裂缝不是沿缺口长度方向作自相似扩展,而是沿纤维方向的界面扩展,缺口基本上不影响试件无缺口部分的承载能力;对于带中心缺口的试件,首先出现缺口尖端的界面分离;带中心圆孔的试件,损伤从孔周开始,逐渐沿纤维方向扩展。本文还分析了试件的损伤和破坏机理。     

Radial locations of strain gages for accurate measurement of mode I stress intensity factor

Strain gage methods are popular in experimental determination of stress intensity factors (SIFs). Radial location of gages with respect to the crack tip plays an important role in accuracy of strain measurements and thus accurate determination of SIFs. The present work proposes a finite element based simple, accurate and consistent method for determination of the limiting value of the radial distance (r_max) of a strain gage. This parameter is in turn useful in deciding the valid strain gage location for accurate measurement of opening mode SIF. The results obtained from the present investigation agree well with the theoretical predictions and could be used for experimental determination of SIFs for both single ended and double ended cracked specimens. The r_max values of center cracked and edge cracked plates with different crack length to width ratio are estimated. The results of the present investigation show that the relative size of the crack length and net ligament length strongly influences the r_max value and the effect of Poisson’s ratio is marginal on the r_max value.     

A computational strategy for damage‐tolerant design of hollow shafts under mixed‐mode loading condition

Three‐dimensional numerical analyses, using the finite element method (FEM), have been adopted to simulate fatigue crack propagation in a hollow cylindrical specimen, under pure axial or combined axial‐torsion loading conditions. Specimens, made of Al alloys B95AT and D16T, have been experimentally tested under pure axial load and combined in‐phase constant amplitude axial and torsional loadings. The stress intensity factors (SIFs) have been calculated, according to the J‐integral approach, along the front of a part through crack, initiated in correspondence of the outer surface of a hollow cylindrical specimen. The crack path is evaluated by using the maximum energy release rate (MERR) criterion, whereas the Paris law is used to calculate crack growth rates. A numerical and experimental comparison of the results is presented, showing a good agreement in terms of crack growth rates and paths.     

弯扭组合载荷下圆管半椭圆表面裂纹应力强度因子的有限元分析

对表面裂纹复合型应力强度因子的研究一直是线弹性断裂力学中的重要课题,例如弯扭组合载荷下圆管半椭圆表面裂纹应力强度因子的计算,到现在也没有一个正确的分析解。考虑到裂尖的应力奇异性,在裂纹前沿手动设置三维奇异单元,用三维有限元法中的1/4点位移法计算弯扭组合载荷下圆管表面椭圆裂纹前沿的Ⅰ型、Ⅱ型和Ⅲ型应力强度因子,并分析其随裂纹深度增加时的变化规律。运用该方法计算了有关模型的应力强度因子,并与该模型的实验值进行了比较,计算结果和实验结果吻合良好。     

Evaluating stress intensity factors of a surface crack in lubricated rolling contacts

The three-dimensional finite element method and the least-squares method were used to find the stress intensity factors (SIFs) of a surface crack in a lubricated roller. A steel roller on a rigid plane was modeled, in which a semi-elliptical surface crack is inclined at an angle ψ to the vertical axis. A distance c is set between the crack base and the roller edge. The results indicate that the mode-I SIF reaches the maximum value when the angle θ is equal to 0° (on the roller surface), and the mode-II SIF reaches the absolute maximum value when the angle θ is near or equal to 90° (inside the roller), where θ is the angle of the semi-ellipse from 0° to 180°. The influence of mode-III SIFs in this model is minor since they are much smaller than the mode-I and mode-II SIFs. The SIFs increase greatly when the crack location approaches the uncrowned edge. At this time, a crowned profile can be used to significantly reduce the SIFs near the roller edge. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effects of CFRP bond locations on the Mode I stress intensity factor of centre‐cracked tensile steel plates

The fatigue life of cracked steel members can be greatly extended by externally attached carbon fibre reinforced plastics (CFRP), which reduces the stress intensity factors (SIFs) at the crack tip. Access to cracks is sometimes limited and the CFRP has to be attached away from the cracks. There is a lack of knowledge on SIFs for such strengthening scheme. This paper presents the effects of CFRP bond locations on the Mode I SIF of centre‐cracked tensile (CCT) steel plate. The Mode I SIF at the crack tip is calculated using the finite element (FE) models. A correction factor is introduced as a function of CFRP bond location and crack length. The FE results are compared and agree well with experimental tests conducted by the authors. By combining with another two factors (one considering CFRP mechanical properties and the other considering CFRP bond width) derived previously by the authors, SIF formulae are proposed for CFRP reinforced CCT steel plates.     

MODE I STRESS INTENSITY FACTOR EQUATIONS FOR CRACKS AT NOTCHES AND CAVITIES

Abstract— In this paper, the notch-crack problem is treated in two different ways: if the non-dimensional crack length l /ρ ( l = crack length; ρ= notch root radius) is smaller than the transition crack length l _T/ρ, it is treated as an edge crack lying within the local stress field around the notch tip; if l/ ρ is larger than l _T/ρ, the notch-crack is considered as a simple flat crack problem subjected to remote loading, the flat crack size being the sum of notch depth and the real crack length. Based on currently available numerical data, expressions for the transition crack length, l _T, and for the geometric factor F = K _I/(1.1215K_tσ√π l ) are developed for various notch problems for the crack length range l ≦ l _T. It is found that the stress (σ_yy) normalized by the peak stress (σ_peak), σ_yy/σ_peak, for the pre-cracked component is very similar to the geometric factor for short cracks.