The Crack Extension Force of a Curved Crack Derived from the Principle of Virtual Work

A general method to determine the crack extension force F related to a finite segment of a curved crack is presented. A path independent integral expression that holds in curvilinear coordinates is derived from the principle of virtual work. An appropriate virtual displacement field allows variation of the position of a crack tip. F is related to the path independent integral expression through variation of a total energy expression. To illustrate the applicability of the method F is derived for the conical crack in axisymmetric loading. For a plane crack with a straight front F is identical to the J-integral, Rice (1968).     

Correction to the Crack Extension Direction in Numerical Modelling of Mixed Mode Crack Paths

In order to avoid introduction of an error when a local crack growth criterion is used in an incremental crack growth formulation, each straight crack extension would have to be infinitesimal or have its direction corrected. In this paper a new procedure to correct the crack extension direction is proposed in connection with crack growth analyzed by the Dual Boundary Element Method (DBEM). The proposed correction procedure and a reference correction procedure already described in the literature are evaluated by solving two different computational crack growth examples. In the two examples it is found that analyses of the crack paths performed with the proposed crack correction procedure using big increments of crack extension are in excellent agreement with analyses of the crack paths performed by using very small increments of crack extension. Furthermore, it is shown that the reference correction procedure has a tendency to overcorrect the crack growth direction if the stop criterion for the iterative correction procedure is not calibrated in each new crack growth analysis.     

裂缝悬臂梁的振动特性及其裂缝参数识别

结构中裂缝的存在使其局部刚度减小、阻尼增大、固有频率降低。本文利用扭曲弹簧模型，对裂缝悬臂梁前三阶固有频率的变化与裂缝位置和深度的关系进行了计算和分析，并且利用特征方程以及前三阶固有频率，通过作图法对裂缝参数进行识别。并以悬臂梁为例证明了这种识别方法精度较高，可以作为进一步研究无损诊断的理论基础。     

Determination of Crack Bridging Stresses from Crack Opening Displacement Profiles

This paper discusses the development of an optimization procedure to deduce the bridging stress from the crack opening displacements (COD) measured during fatigue crack growth. Finite element analysis was conducted using the center-cracked geometry to verify the optimization procedure. The proposed procedure successfully predicted the bridging stress distributions with zero stresses at the crack tip and the bridging stress distributions with non-zero stresses at the crack tip. The results also showed that COD measurements spaced at ≈ 0.8-1.0 mm are sufficient for reliable prediction of bridging stresses. Accurate prediction of bridging stresses near the crack tip required COD data within ≈ 0.1 mm from the crack tip. The application of the proposed procedure to a metal matrix composite (SCS-6/TIMETAL®21S) is also discussed.     

Plane Problem of a Crack on the Interface of Orthotropic Plates with Friction of Crack Lips

We consider a plane problem of a crack on the interface of different orthotropic arbitrarily oriented semiinfinite spaces subjected to the action of uniform tensile and shear forces applied at infinity. In the vicinity of the crack tip, the crack lips smoothly close up to form a contact zone of a priori unknown length in the presence of constant friction between the lips. A transcendental equation for the length of the contact zone is deduced and analyzed. As a result, we obtain the dependences of the relative length of the contact zone and the stress intensity factors on the orientation of the principal directions of orthotropy for different values of the external load and boundary friction.     

疲劳载荷下工业纯铁表面与内部裂纹长度的研究初探

疲劳裂纹扩展试验中,采用表面裂纹长度作为疲劳裂纹长度进行疲劳裂纹扩展计算和疲劳裂纹扩展模型建立的过程中,会导致计算的最终结果和模型产生一定的误差。对工业纯铁板材试样进行疲劳裂纹扩展试验,分析疲劳裂纹扩展过程中裂纹长度与裂纹扩展速率的关系,以及对疲劳裂纹扩展断口形貌特征进行观察。结果表明,上述2种方法均可来确定表面裂纹长度和内部裂纹长度之间的关系。     

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.     

传动箱体的裂纹扩展

某特种车辆的传动箱体是个易损件.在实测载荷的基础上,用断裂力学原理和疲劳强度理论,计算了在程序载荷作用下,箱体危险部位稳定扩展和失稳扩展的启裂裂纹长度和临界裂长度及裂纹扩展寿命占总寿命的比例,为其损伤容限设计和耐久性设计提供了基本依据.     

Crack interaction modelling

The growth characteristics of short fatigue cracks under axial loading were investigated using specimens of the ferritic–martensitic steel F82H-mod. Interest focused on crack propagation due to coalescence, which proved to be the dominant mechanism of crack growth. Crack propagation due to coalescence under a certain loading state is strongly influenced by the microstructure of the material on the one hand and by the interaction of cracks on the other. This study deals with an elasto-plastic fracture mechanics analysis of two interacting cracks neglecting the microstructural influence. Finite element calculations based on a Ramberg–Osgood model for the material properties were performed to quantify the interaction of two cracks in terms of an interaction function Y depending on the material and crack configuration. Finally, a neural network was trained to determine the interaction function for two cracks within the range of interest.     

On the Plastic Zone Size and the Crack Tip Opening Displacement of an Interface Crack Between two Dissimilar Materials

In the paper, the elastic-plastic fracture behavior of an interface crack between two dissimilar materials is investigated. The mixed-mode Dugdale model is applied to examine the plastic zone size and the crack tip opening displacement. In numerical examples, the plastic zone size and the crack tip opening displacement of an interface crack under uniform loads are studied in detail. Two formulae are proposed to calculate the plastic zone size and the crack tip opening displacement of an interface crack under small scale yielding conditions.     

Modelling Crack Closure for an Interface Crack Under Harmonic Loading

The paper is devoted to a linear crack located between two dissimilar elastic half-spaces under normally incident harmonic tension-compression loading. The system of boundary integral equations for displacements and tractions is derived from the dynamic Somigliana identity. The dynamic stress intensity factors (the opening and the transverse shear modes) are computed as functions of the loading frequency taking the contact interaction of the opposite crack faces into account. The results are compared with those obtained neglecting the crack closure.     

Mode-I Elliptical Crack in an Infinite Elastic Body. Part 2. Contact of the Crack Faces

Interaction between the faces of an elliptical crack, which is in a partially negative external-stress field, is considered. The problem consists in finding both the region where the faces are in contact and the contact stresses that arise in this case. These stresses are represented as a finite polynomial series with unknown coefficients, which are determined with the proviso that the squared deviations of displacements in the contact region from zero and squared deviations of total stresses from the given ones in the rest of the region are minimal. This contact region itself is found as a result of search for the absolute minimum of these deviations. Concrete results are given for a crack, which is in a linear stress field.     

低合金高强钢的延迟裂纹和应力腐蚀裂纹

本文介绍了低合金高强钢制的球罐在定期检验时发现的焊接接头裂纹。作者从应力腐蚀裂纹和氢致裂纹的机理、影响因素、形貌、发生区域、发生时间来论证球罐的应力腐蚀裂纹和氢致裂纹的内在机理是一样的,属于氢致开裂机理。理论分析和检验检测实践证明在球罐的焊接加工阶段采取措施防止氢致裂纹就能大大降低应力腐蚀裂纹敏感性。     

Effect of Closure of the Tip of a Fatigue Crack on the Asymmetry of Loading Cycles and on the Thresholds of Crack Resistance

On the basis of the experimental data, it is shown that, in the presence of closure of the tip of a fatigue crack, the imaginary influence of the positive load ratio R on the kinetics of crack growth and on the thresholds of crack resistance expressed via the threshold range of stress intensity factors K _th,R is actually the quantitative representation of changes in the characteristic of crack closure K _cl ^op provided that we use the nominal range of stress intensity factors K.     

A Continuum Mechanics Approach for Crack Initiation and Crack Growth Predictions

Very often, different approaches are used for crack initiation and crack growth predictions. The current article introduces a recently developed approach that can be used for the predictions of both crack initiation and crack propagation. A basic assumption is that both crack nucleation and crack growth are governed by the same fatigue damage mechanisms and a single fatigue damage criterion can model both stages. A rule is that any material point fails to form a fresh crack if the total accumulated fatigue damage reaches a limit. For crack initiation predictions, the stresses and strains are obtained either directly from experiments or though a numerical analysis. For the prediction of crack growth, the approach consists of two steps. Elastic‐plastic stress analysis is conducted to obtain the detailed stress‐strain responses. A general fatigue criterion is used to predict fatigue crack growth. Compact specimens made of 1070 steel were experimentally tested under constant amplitude loading with different R‐ratios and the overloading influence. The capability of the approach to predict both crack initiation and the crack growth under these loading conditions was demonstrated by comparing the predictions with the experimental observations.     

裂纹闭合与疲劳裂纹扩展力的测试方法

介绍了一种在近十年里发展的裂纹扩展力测量方法，这种方法将裂纹扩展的门槛值行为与直流电位法结合起来，可以测量某一载荷下裂纹开始扩展的应力强度因子Ｋｐｒ，并由此计算有效应力强度因子范围ΔＫｅｆｆ＝Ｋｍａｘ－Ｋｐｒ。