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.     

椭圆裂纹的权函数和应力强度因子

本文推导了承受作用在同心椭圆周上法向均匀分布力拉伸的无限大体椭圆裂纹的权函数,并用它计算了一些应力强度因子K_1。对于椭圆裂纹的特殊情况——圆盘裂纹,则相应的应力强度因子K_1与文献[1]完全相同。本文所提出的方法具有计算简便的优点。     

型材中裂纹应力强度因子计算方法

本文应用分区广义变分原理,提出了求解含有裂纹的型材应力强度因子的计算方法。并对角材中含有边缘裂纹和槽形型材中含有中心裂纹的应力强度因子进行了数值计算,计算结果绘成了曲线。     

Stress Intensity Factor of an Edge Crack in Composite Media

A solution to the 2-D problem of a rigid circular inclusion squeezed by two semi-infinite elastic planes is presented. The size of the contact zone and the length of the opened area as a function of the applied stress, material properties and radius of the inclusion are calculated. The results demonstrate a strong non-linearity of the solution.     

A Simple Method for Calculating the Stress Intensity Factor of a One-Sided Reinforced Crack

A simple method is suggested to calculate the stress intensity factor for a one-sided reinforced crack using the spring constant as a function of the through-thickness coordinate z. The present results coincide very well with three-dimensional finite element results( Wang, et al., 1998).     

Stress Intensity Factor of an Edge Crack in Bonded Orthotropic Materials

The article presents the problem of an edge crack under normal point loading terminating perpendicular to the surface of an orthotropic strip of finite thickness which is bonded to another orthotropic half plane. Expressing the displacements and stresses in plane strain condition in terms of harmonic functions, the problem is reduced to a pair of simultaneous integral equations with Cauchy type singularities, which are finally been solved by the Hilbert transform technique. The analytical expression of stress intensity factor (SIF) at the crack tip for large thickness of the strip is calculated, which corresponds to the weight function of a crack under normal loading. The influences of elastic constants of two different orthotropic materials, distinct arbitrary locations of normal point loading on the crack surface and length of the crack on the dynamic SIF are depicted through graphs.     

Stress Intensity Factor Variations near the Edge Crack Tip upon Its Stepwise Growth

Calculation results to evaluate time variations of the stress intensity factor near the tip of the edge crack upon its stepwise growth are presented. The crack pop-in in a thick plate under tensile loading is shown to result in cyclic K ₁ variations with a period and amplitude that are dependent on the initial crack length, pop-in length and plate dimensions. Time-average K ₁ values correspond to those calculated for the stationary crack.__________Translated from Problemy Prochnosti, No. 2, pp. 66 – 71, March – April, 2005.     

双轴弯曲载荷下表面裂纹应力强度因子的数值计算

本文通过FRANC3D软件计算双轴弯曲载荷下表面裂纹前缘的应力强度因子,数值计算和理论计算结果基本吻合;通过等裂纹面积不同纵横比的表面裂纹前缘应力强度因子的分析可知:当表面裂纹为浅裂纹时,等裂纹面积下a/c=1/3时椭圆表面裂纹最为危险;当表面裂纹为深裂纹时,等裂纹面积下a/c=2时椭圆表面裂纹最为危险。     

Ultrasonic Measurement of the Crack Depth and the Crack Opening Stress Intensity Factor Under a No Load Condition

This paper describes a new methodology for evaluating the crack depth and the crack opening stress intensity factor of small closed cracks using an ultrasonic technique. Surface connected back-wall cracks of depth ranging from 0.4 to 4.0 mm in steel specimens are considered. The crack corner echo amplitude of an ultrasonic shear wave, SW, beam of 50° incidence in material is used. First, the ultrasonic echo response of an open crack is determined as a function of crack depth. Next, based on changing the crack closure stress, an empirical relation between the crack closure stress and the crack-echo response is formulated. The crack depth and the crack closure stress of an unknown closed crack based on these relations are determined by inverse analysis of the ultrasonic response of the crack. From the evaluated crack depth and crack closure stress, the crack opening stress intensity factor is determined. The accuracy and reliability of this new nondestructive evaluation (NDE) method is verified by comparing the evaluated crack depth with the actual one. The latter is measured on the fractured surface obtained after carrying out ultrasonic testing. The ultrasonic method developed is proved to be a powerful tool for quantitative and nondestructive evaluation of the crack depth as well as the crack closure stress.     

Experimental Evaluation of Mixed Mode Stress Intensity Factor for Prediction of Crack Growth by Phoelastic Method

Determination of stress intensity factors K _I, K _II, and constant stress term, σ _ox is investigated. A theory of determining the stress intensity factors using photo-elastic method is formulated taking three stress terms. Three-parameter method of fracture analysis for determining the mixed mode stress intensity factors under biaxial loading conditions from photo-elastic isochromatic fringe data is used. A special biaxial test rig is designed and fabricated for loading the specimen biaxially. A simplified and accurate method is proposed to collect the data from isochromatic fringes. Taking specimen geometry and boundary conditions into account, regression models are developed for estimation of fracture parameters.     

The Stress Intensity Factor of an Edge Dislocation Near an Elliptically Blunted Crack Tip

The stress field around the tip of an elliptically blunted crack induced by an edge dislocation has been obtained in closed form, from which the mode I and mode II stress intensity factors induced by the edge dislocation are obtained. The solutions apply to the edge dislocation either emitted from crack-tip surface or originated elsewhere, and for the dislocation located anywhere around the crack tip. The effects of the crack length, the crack-tip bluntness, the origination and position of the dislocation on the stress intensity factors are examined.     

A Residual Stress Intensity Factor Solution for Knoop Indentation Cracks

The residual stress intensity factors at the surface and at the deepest point of the semi-elliptical Knoop indentation crack is determined from the stresses in the damaged zone below the indenter. For this purpose, the weight function approach by Cruse and Besuner was used and wide-range expressions of the geometric function are given. The solution is then applied to a commercial silicon nitride for which all relevant geometrical data are available.     

Three-dimensional Correction of the Stress Intensity Factor for Plate with a Notch

The 3D effects of the 2D mode I stress intensity factor for the plate with a V-shaped straight through-thickness notch are investigated by the finite element method and three-dimensional thicknessdependent correction of SIF is suggested. The correction relies on the assumed relationship between the SIF and the constraint factor (out-of-plane degree of freedom). The 3D finite element mesh generator combining the 2D in-plane adaptive unstructured mesh with the structured through-thickness mesh Is developed and applied for the analysis purposes. Three-dimensionality was examined by using two independent indicators, namely, stress- or strain-based constraint factors. The three-point bend and tensile center-cracked plates are investigated. The results demonstrated that the developed 3D corrections may be treated as upper bound estimates of the SIF for three-point bend plate,while directly obtained numerical values are considered as lower bound estimates. Analysis of the tensile center-cracked plate demonstrated a different nature of the 3D SIF profile, which cannot be simply explained as a transitional state between plain strain and plain stress. Therefore, the suggested 3D correction concept is of a particular character.     

焊接桥梁结构的断裂驱动力分析

对焊接桥梁结构的典型单元H型构件进行了简化分析 ,同时考虑了焊接残余应力的影响 ,估计了临界裂纹的长度 ,并将构件按设计应力进行了分类 ,计算出各类应力构件的驱动力。临界裂纹长度 2aC=6 0mm ;H型构件中基体的驱动力KBI=1.12 (α +β1)σs πaC,焊缝的驱动力KWI =1.12 (α +β2 )σs πaC     

An Isolated Mode I Three-Dimensional Planar Crack: The Stress Intensity Factor is Independent of The Elastic Constants

It is demonstrated that for an isolated Mode I planar crack embedded in an infinite body, the stress intensity factor along the crack front is a function independent of the elastic constants.     

纤维－金属胶结层板的桥接应力与应力强度因子研究

在国内外首次建立了纤维－金属结层板（ＦＲＭＬｓ）裂纹桥接应力分布的计算模型，本模型考虑了分层形状与尺寸、分层前沿胶黏剂的剪切变形、层板的残余温度应力以及有限板宽等因素的影响。在正确计算裂纹桥接应力的基础上，用权函数方法得到了纤维－金属胶结层板在桥接机理下的应力强度因子。     

冲击载荷作用下动态应力强度因子的迭加积分法

介绍利用线性时不变系统求响应的迭加积分法(杜阿美尔积分)求解带裂纹构件的线弹性动态应力强度因子。即先求出结构的单位冲激响应,再与载荷做卷积求得总的响应;或者先计算出单位阶跃响应,再与载荷的微分做卷积来求得总的响应。理论和计算都证明了这两种迭加积分法的精度。在动态起裂韧度测试实验中,特别是用实验-数值法要处理同一组试样的大量实验数据,应用迭加积分法可以有效的避免数值求解的重复计算,减少计算量。     

Analytical Solutions for Stress Intensity Factor,T-Stress and Weight Function for the Edge-Cracked Half-Space

An analytical solution for the linear-elastic problem of an edge-cracked semi-infinite body was given already in 1957. For the numerical evaluation of this solution an iteration procedure had to be applied. This might be the reason why the related analysis was not commonly used. By means of powerful mathematical tools developed in the last years it is now possible to evaluate highly-precise stress intensity factors, T-stress terms, weight functions etc. This will be shown in this paper in detail.     

Stress Intensity Controlled Kinetic Crack Growth and Stress History Dependent Life Prediction with Statistical Variability

Consistent with viscoelastic behavior, a power law form in terms of the stress intensity factor is used to specify crack kinetics (growth rate) in the central crack problem under Mode I conditions. The crack growth rate is integrated to obtain the crack size and thereby the stress intensity factor as a function of time. The crack is allowed to grow in a controlled, load dependent manner until it reaches the size at which it becomes unstable. The corresponding time at which this occurs is taken as the lifetime of the material under the specified load history. The special cases of constant load (creep rupture) and constant strain rate to failure are found to have a very simple relationship with each other. This lifetime relationship is verified through the comparison with corresponding data upon a polymeric composite. Finally the creep rupture case is generalized to a probabilistic formalism. The theoretically predicted lifetime distribution functions are verified with data, also upon a polymeric composite. Possible extension of the entire formalism to cyclic fatigue in metals is discussed. Dedicated to Professor Z.P. Bažant for his many contributions.