Closed form solution of stress intensity factors for cracks emanating from surface semi-spherical cavity in finite body with energy release rate method

In this paper, a new semi-analytical and semi-engineering method of the closed form solution of stress intensity factors （SIFs） of cracks emanating from a surface semi-spherical cavity in a finite body is derived using the energy release rate theory. A mode of crack opening displacements of a normal slice is established, and the normal slice relevant functions are introduced. The proposed method is both effective and accurate for the problem of three-dimensional cracks emanating from a surface cavity. A series of useful results of SIFs are obtained.

Simulation Research on Stress Intensity Factors of Different Crack Aspect Ratios on Hollow Axles

Because of the wicked service environment of the high speed train, it is possible that the hollow axle of the train may encounter the foreign object damage and form a sharp notch. Under the fatigue loading a crack can initiate from the notch and propagate to failure. It is noted that the stress intensity factor is the control parameter of the crack propagating, for the purpose of getting the more exact propagation characteristics, the stress intensity factor is studied mainly. The service loads of hollow axles are defined, and the stress distribution of hollow axles is obtained according to the load spectrum. The semi-ellipse crack configuration is defined with three parameters： the aspect ratio, the relative depth and the relative location along the crack front. Quarter point 20-node isoparametric degenerate singular elements are used for the region near the crack tip. The finite element model of crack extension of hollow axle is created, and the crack front is dispersed which can realize orthogonal extension. Based on this the stress intensity factors of crack front were calculated, and the distribution rules of the stress intensity factors of different initial crack shapes are obtained. The conclusions are compared with that of the analytic method and they agree with each other very well, and the calculating results show that there is a close relationship between the stress intensity factor and the initial crack shape. For a round crack the stress intensity factor at the surface point increases faster than the one at the center point with the crock propagation. However, for a narrow crack, the results are in contrast with that of a round one. So, all the cracks with different shapes propagate toward to a similar shape, and they grow at this shape to end. The study may contribute to the crack propagate characteristics research.

Weight Function Method for Stress Intensity Factor of Internal Surface Semi-elliptical Crack in Elliptical Holes

The hatches for inspecting are usually designed with elliptical holes in airplane structures, so computation of the stress intensity factor of three dimensional crack at elliptical holes is pivotal for damage tolerance analysis of these structures. In this paper, weight function is derived for a two dimensional through cracks at elliptical holes by applying a compounding method. Stress intensity factor formulas for an internal surface semi-elliptical crack in elliptical holes are obtained wing the three dimensional weight function method. Stress intensity factors for an internal surface semi-elliptical crack in elliptical holes under remote tension are computed. At the same time, research on how radius of curvature for elliptical holes affect stress intensity factors was conducted. Stress intensity factors decrease when radius of curvature increases. Some results and conclusions which are of practical value are given.

SCATTERING OF SH-WAVE BY CRACKS ORIGINATING AT AN ELLIPTIC HOLE AND DYNAMIC STRESS INTENSITY FACTOR

The method of complex function and the method of Green's function are used to investigate the problem of SH-wave scattering by radial cracks of any limited length along the radius originating at the boundary of an elliptical hole, and the solution of dynamic stress intensity factor at the crack tip was given. A Green's function was constructed for the problem, which is a basic solution of displacement field for an elastic half space containing a half elliptical gap impacted by anti-plane harmonic linear source force at any point of its horizontal boundary. With division of a crack technique, a series of integral equations can be established on the conditions of continuity and the solution of dynamic stress intensity factor can be obtained. The influence of an elliptical hole on the dynamic stress intensity factor at the crack tip was discussed.

Closed-Form Solutions of Stress Intensity Factors for Semi-elliptical Surface Cracks in a Cylindrical Bar Under Pure Tension

In this work,the stress intensity factors(SIFs)for a wide range of semi-elliptical surface cracks with different inclination angles in a cylindrical bar subjected to pure tension were investigated numerically.The main parameters considered to evaluate the SIFs were the crack size ratio(a/d),the crack aspect ratio(a/c),and the crack inclination angle(0).The dual-boundary element met hod implemented in software BEASY was used to compute the SIF values for cracks.Furt her more,the general closed-form solutions were proposed to evaluate the corresponding SIFs for Mode I,Mode II and Mode III types of fracture through curve fitting approaches.These solutions can provide accurate and reliable values of stress intensity factors for a crack on a cylindrical bar under pure tension in a rapid way compared to those obtained using computational models.In addition,these results can be used as inputs for failure studies and life evaluations of cracked cylinder under working conditions.

SEMI-ELLIPTIC SURFACE CRACK IN AN ELASTIC SOLID WITH FINITE SIZE UNDER IMPACT LOADING

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.

A NEW METHOD OF ANALYZING SURFACE CRACKS

The authors have developed a new line-spring boundary element method in the present paper, which combines the advantage of the line-spring model with that of the boundary element method. This method reduces the three-dimension problem of the surface cracks into a quasi-one-dimension problem and can be used to analyze the surface cracked plate under various loading conditions. In this paper theoretical analyses and numerical verifications are carried out. The calculated results are reported, which indicate that the present method is efficient and can be used to analyze the surface crack problem on a personal computer.

Interacting Stress Intensity Factors of Multiple Elliptical-Holes and Cracks Under Far-Field and Arbitrary Surface Stresses

Calculating interacting stress intensity factors(SIFs)of multiple ellipticalholes and cracks is very important for safety assessment,stop-hole optimization design and resource exploitation production in underground rock engineering,e.g.,buried tunnels,deep mining,geothermal and shale oil/gas exploitation by hydraulic fracturing technology,where both geo-stresses and surface stresses are applied on buried tunnels,horizontal wells and natural cracks.However,current literatures are focused mainly on study of interacting SIFs of multiple elliptical-holes(or circularholes)and cracks only under far-field stresses without consideration of arbitrary surface stresses.Recently,our group has proposed a new integral method to calculate interacting SIFs of multiple circular-holes and cracks subjected to far-filed and surface stresses.This new method will be developed to study the problem of multiple elliptical-hole and cracks subjected to both far-field and surface stresses.In this study,based on Cauchy integral theorem,the exact fundamental stress solutions of single elliptical-hole under arbitrarily concentrated surface normal and shear forces are derived to establish new integral equation formulations for calculating interacting SIFs of multiple elliptical-holes and cracks under both far-field and arbitrary surface stresses.The new method is proved to be valid by comparing our results of interacting SIFs with those obtained by Green’s function method,displacement discontinuity method,singular integral equation method,pseudo-dislocations method and finite element method.Computational examples of one elliptical-hole and one crack in an infinite elastic body are given to analyze influence of loads and geometries on interacting SIFs.Research results show that whenσ_(xx)^(∞)≥σ^(yy′)^(∞),there appears a neutral crack orientation angle b0(without elliptical-hole’s effect).Increasing s¥xx/s¥yy and b/a(close to circularhole)usually decreases b0 of KI and benefits to the layout of stop-holes.The surface compressive stresses applied onto elliptical-hole(n)and crack(p)have significant influence on interacting SIFs but almost no on b0.Increasing n and p usually results in increase of interacting SIFs and facilitates crack propagation and fracture networks.The elliptical-hole orientation angle(a)and holed-cracked distance(t)have great influence on the interacting SIFs while have little effect on b0.The present method is not only simple(without any singular parts),high-accurate(due to exact fundamental stress solutions)and wider applicable(under far-field stresses and arbitrarily distributed surface stress)than the common methods,but also has the potential for the anisotropic problem involving multiple holes and cracks.

Investigation on 3D fatigue crack propagation in surface-cracked specimens

In the present work the fatigue crack growth in AISI304 specimens is investigated experimentally. In 3D finite element analysis the virtual crack closure technique is applied to calculate distributions and variations of the stress intensity factor along the surface crack front. It is confirmed that the stress intensity factor along the surface crack front varies non-uniformly with crack growth. Crack growth rate is proportional to the stress intensity factor distribution in the 3D cracked specimen. The fatigue crack growth in surface cracked specimens can be described by the Forman model identified in conventional compact tension specimens. For crack growth in the free specimen surface the arc length seems more suitable to quantify crack progress. Geometry and loading configuration of the surface cracked specimen seem to not affect the fatigue crack growth substantially.

STUDY ON CRACKED PLATES WITH BONDED PATCHES UNDER IN PLANE BIAXIAL LOADINGS

Based on the finite element method, a numerical investigation into the bonded repair efficiency of cracked plates under in plane biaxial loadings is presented. The main considerations are: reduction in stress intensity factor (SIF) at the crack tip, the maximum tensile stress in the composite patch and the maximum shear stress in the adhesive bond between the patch and the plate. Without the patch, a tensile or compressive stress parallel to the crack has no effect on the SIF at the crack tip. While with a composite patch, there exists coupling effect between the normal stress parallel to the crack and the SIF, and the coupling effect depends significantly on ply orientation of the patch and the biaxial stress ratio of the plate.

Analytic model of non-uniform corrosion induced cracking of reinforced concrete structure

In order to perfectly reflect the dynamic corrosion of reinforced concrete (RC) cover in practical engineering,an analytic model of non-uniform corrosion induced cracking was presented based on the elastic-plastic fracture mechanics theory.Comparisons with the published experimental data show that the predictions given by the present model are in good agreement with the results both for natural exposed experiments and short-time indoor tests (the best difference is about 2.7%).Also it obviously provides much better precision than those models under the assumption of uniform corrosion (the maximal improved precision is about 48%).Therefore,it is pointed out that the so-called uniform corrosion models to describe the cover cracking of RC should be adopted cautiously.Finally,the influences of thickness of local rusty layer around the reinforcing steel bar on the critical corrosion-induced crack indexes were investigated.It is found that the thickness of local rusty layer has great effect on the critical mass loss of reinforcing steel,threshold expansion pressure,and time to cover cracking.For local rusty layer thickness with a size of a=0.5 mm,the time to cover cracking will increase by about one times when a/b (a,semi-minor axis;b,semi-major axis) changes from 0.1 to 1 mm.

Multi‑Crack Interaction and Influence on the Spherical Pressure Hull for a Deep‑Sea Manned Submersible

This study investigates the interaction and influence of surface cracks on the spherical pressure hull of a deep-sea manned submersible.The finite element model of the spherical hull is established,and a semi-elliptical surface crack is inserted in the welding toe of the spherical hull as the main crack.Considering the combined effect of external uniform pressure and welding residual stress at the weld toe,the stress intensity factor(SIF)is obtained based on the M-integral method.Inserting disturbing cracks at different positions on the spherical hull surface,the interaction and influence between multi-cracks are revealed by numerical calculation.The results show that the existence of the disturbing crack has a great influence on the stress intensity factor of the main crack,and the influence is different with the different location of disturbing crack.The study of the interaction of multiple cracks under different interference factors and the influence of disturbing cracks on the main crack can provide some reference for future engineering applications.

Stress intensity factors under combined bending and torsion moments

This paper discusses stress intensity factor （SIF） calculations for surface cracks in round bars subjected to combined torsion and bending loadings. Different crack aspect ratios, a/b, ranging from 0.0 to 1.2 and relative crack depths, a/D, ranging from 0.1 to 0.6 were considered. Since the loading was non-symmetrical for torsion loadings, a whole finite element model was constructed. Then, the individual and combined bending and torsion loadings were remotely applied to the model. The equivalent SIF method, F＊EQ, was then used explicitly to combine the individual SIFs from the bending and torsion loadings. A comparison was then carried out with the combined SIF, F＊FE, obtained using the finite element analysis （FEA） under similar loadings. It was found that the equivalent SIF method successfully predicted the combined SIF for Mode I. However, discrepancies between the results determined from the different approaches occurred when Fm was involved. It was also noted that the predicted F＊ EE using FEA was higher than the F＊EQ predicted through the equivalent SIF method due to the difference in crack face interactions.

起重机械损伤方钢管CFRP胶粘修复技术研究

起重机械的方管构件在使用中易出现裂纹等损伤,采用碳纤维增强复合材料(CFRP)补片胶粘可修复损伤的方管构件。利用ABAQUS软件对两种不同裂纹的损伤钢管进行了三点弯曲模拟试验,以极限承载力、胶层应力和裂纹尖端应力强度因子作为判断依据,分析CFRP补片长度、厚度和方管壁厚对损伤方管修复效果的影响。模拟试验结果表明,在脱粘风险较低的情况下,合理的CFRP补片长度和厚度可以有效阻止裂纹的扩展,并提升构件的抗弯能力,方管壁厚越大,CFRP补片脱粘的风险越大。

三维表面裂纹应力强度因子参数敏感性有限元分析

三维表面裂纹是许多工程结构中普遍存在的一种缺陷,无论是在损伤容限设计或缺陷评估阶段,人们都要求对裂纹的应力强度因子进行精确的估计,这一参量对裂纹的预测和剩余疲劳寿命的估计起到至关重要的作用。借助有限元软件Abaqus和断裂力学软件Franc3d建立三维半椭圆表面裂纹实体模型,依据断裂力学相关知识,采用M-积分法,对含有表面裂纹的模型进行数值模拟,研究了模型在不同裂纹形状比(a/b=1.5、1.36、1.25和1.15)以及裂纹倾角(θ=0°、15°、30°和45°)下的裂纹扩展情况和应力强度因子参数敏感性。主要研究内容与结论如下:裂纹形状比a/b越大,应力强度因子越小,应力强度因子分布形貌由“凹”向“凸”转变;裂纹倾角达到0°时,裂纹深处应力强度因子最大,裂纹更容易扩展,随着裂纹倾角(0°、15°、30°和45°)的增大,应力强度因子逐渐减小。

管路外表面裂纹应力强度因子研究

油气管道裂纹会降低管路的承载能力甚至会带来危险,因而研究带内压的有裂纹管道的安全性成为迫切需要解决的问题。以椭圆表面裂纹的管道为研究对象,通过对裂纹体进行有限元软件和三维裂纹分析软件联合仿真,研究裂纹体的应力云图和裂纹应力强度因子变化。研究结果表明:径向裂纹若增大倾斜角与深度,将增加裂纹前缘的应力集中;增加裂纹倾斜角度,Ⅰ型裂纹应力强度因子和J积分会小,Ⅱ型和Ⅲ型裂纹应力强度因子会增加;椭圆裂纹的深度加大会让裂纹前缘的Ⅰ型裂纹应力强度因子和J积分变大,但两端处值的增长速度大于尖端处;裂纹长度的增加会让裂纹尖端附近Ⅰ型裂纹应力强度因子和J积分增长速率大于裂纹两端处。研究结果为管道裂纹扩展与控制提供技术支撑。

脆性材料在压缩载荷作用下的断裂破坏准则

目前多裂隙材料在压缩载荷作用下的力学行为问题已成为当前断裂力学及岩石力学等学科的重要课题。选取位于同一直线上的多裂隙体,考虑裂隙(纹)表面间的摩擦力并应用复变应力函数,推出了裂纹应力强度因子的解析表达式。当只有两个裂纹或一个裂纹存在时,给出了准确的应力强度因子解析解。最后依据共线双裂纹模型和单裂纹模型及传统的裂纹断裂准则,建立了脆性材料在压缩载荷作用下的断裂破毁准则。在一些特殊情况下,这个准则可以简化,并且其简化后的准则具有应用价值,特别是当材料不含有宏观裂纹时,这个准则就和著名的库伦-摩尔准则相一致。

T型接头焊趾表面裂纹应力强度因子的简化计算方法

T型接头是船舶与海洋结构物的典型结构形式之一,其焊趾处常常是疲劳热点区域。T型接头焊趾表面裂纹的应力强度因子是船舶与海洋结构的、基于断裂力学安全评定和疲劳寿命预测的基础。本文对T型接头表面裂纹应力强度因子的计算方法,尤其是Bow ness等人提出的T型接头焊趾表面裂纹应力强度因子的计算公式进行了分析,在此基础上导出了形式简单,物理意义明确的T型接头焊趾表面裂纹应力强度因子的简化计算公式,并和相关的应力强度因子的计算结果进行了比较,证明了本文简化方法的可行性。

CRC+AC复合式路面结构中AC层的裂缝扩展

针对CRC+AC复合式路面结构的特点和现有研究的不足,运用断裂力学理论和有限元法,对AC层的受力进行了计算和分析,对AC层裂缝的产生和扩展机理进行了研究。计算了AC层荷载型和温度型裂缝的尖端应力强度因子,研究了裂缝扩展时期、裂缝长度、结构层厚度、模量等因素对AC层裂缝扩展的影响规律。研究结果表明:AC层裂缝的扩展时期对扩展强度有一定的影响;增加AC层的厚度对裂缝扩展尤其是对AC层底面裂缝的扩展能起到很好的延缓作用;CRC层厚度对AC层裂缝扩展的影响很小或基本没有影响;随着AC层模量的增加,AC层温度裂缝的扩展强度线性增加,荷载裂缝的扩展强度变化不大;其他结构层的厚度和模量对AC层裂缝的扩展强度基本没有影响。研究结果可为CRC+AC复合式路面的合理设计提供参考依据。

压力容器开孔接管处表面斜裂纹应力强度因子数值分析

通过在裂纹前沿设置奇异单元,建立了圆筒形压力容器开孔接管处表面斜裂纹断裂力学有限元分析模型;运用可视化编程语言VB编制了压力容器开孔接管处表面斜裂纹应力强度因子参数化分析软件,实现了与有限元分析软件ANSYS的连接与调用;根据内压作用时多种几何参数情况下应力强度因子的计算值,绘制了裂纹前沿应力强度因子随裂纹相对深度、裂纹对应弧度、支管与主管直径比及裂纹倾斜角的变化曲线。