INTERACTION OF THREE PARALLEL CRACKS IN RECTANGULAR PLATE UNDER CYCLIC LOADS

This paper presents a numerical approach for modeling the interaction between multiple cracks in a rectangular plate under cyclic loads. It involves the formulation of fatigue growth of multiple crack tips under ruixed-mode loading and an extension of a hybrid displacement discontinuity method （a boundary element method） to fatigue crack growth analyses. Because of 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, remeshing of existing boundaries is not necessary for each increment of crack extension. Crack extension is conveniently modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. As an example, the numerical approach is used to analyze the fatigue growth of three parallel cracks in a rectangular plate. The numerical results illustrate the validation of the numerical approach and can reveal the effect of the geometry of the cracked plate on the fatigue growth.     

STUDY ON THE SURFACE CRACK GROWTH BEHAVIOR IN 14MnNbq BRIDGE STEEL

Three-dimensional crack closure correction methods are investigated in this paper.The fatigue crack growth tests of surface cracks in 14MnNbq steel for bridge plate subjected to tensile and bending loadings are systematically conducted.The experimentally measured fatigue crack growth rates of surface cracks are compared with those of through-thickness cracks in detail.It is found that the crack growth rates of surface cracks are lower than those of through-thickness cracks.In order to correct their differences in fatigue crack growth rates, a dimensionless crack closure correction model is proposed.Although this correction model is determined only by the experimental data of surface cracks under tensile loading with a constant ratio R=0.05, it can correlate the surface crack growth rates with reasonable accuracy under tensile and bending loadings with various stress ratios ranging from 0 to 0.5.Furthermore, predictions of fatigue life and crack aspect ratio for surface cracks are discussed, and the predicted results are also compared with those obtained from other prediction approaches.Comparison results show that the proposed crack closure correction model gives better prediction of fatigue life than other models.     

表面裂纹疲劳扩展的数值模拟(Ⅱ)

根据Paris疲劳裂纹扩展规律,对拉伸和纯弯曲疲劳载荷下表面裂纹扩展进行了数值模拟。数值模型中,用三次样条函数曲线拟合裂纹尖端,在裂纹扩展增量计算中考虑了裂纹闭合影响。裂纹形状演化的模拟结果与Newman和Raju经验公式预测结果进行了比较,表明了所采用的数值模拟方法的实用性。研究发现,裂纹闭合对疲劳裂纹扩展过程中的裂纹形状演化以及裂纹尖端的应力强度因子(SIF)分布都有明显影响。同裂纹形状演化一样,疲劳裂纹扩展过程中裂纹尖端的SIF分布表现出明显的特征。最后,建议了一个简单函数来统一描述表面裂纹尖端的SIF分布。     

基于局域分析的疲劳短裂纹群体演化随机模型

采用局域裂纹数密度描述金属材料中不同局部区域的疲劳短裂纹群体损伤的发展情况通过考虑在不同局域存在的材料性质的随机涨落及局部损伤对损伤总量发展的影响，建立了局域裂纹数密度演化随机方程对方程数值求解从而模拟了材料的疲劳短裂纹损伤过程结果显示出主裂纹出现的随机性，并讨论了裂纹总数与最大裂纹尺度在统计意义上的演化特征     

拉压循环载荷下正交异性钢桥面板肋-面板焊缝裂纹扩展分析

采用四步法计算了考虑循环载荷中压应力影响的正交异性钢桥面板的肋-面板焊缝表面裂纹扩展。第一步是基于正交异性钢桥面板的疲劳分析模型,计算肋-面板焊缝处的应力,第二步是通过肋-面板焊缝的三维局部模型,用Schwartz-Neumann交替法计算焊缝表面裂纹的应力强度因子分布,第三步是用二维断裂力学模型和增量塑性损伤模型,计算循环载荷中的压应力对裂纹扩展的影响,第四步是用第二步中的三维裂纹分析结果和第三步中的二维断裂力学模型得到的裂纹扩展公式,计算钢桥面板的肋-面板焊缝表面裂纹扩展。计算结果表明,对应于正交异性钢桥面板肋-面板焊缝处的循环应力,本文所用模型的裂纹尖端反向塑性区导致裂纹扩展率增加50%以上。研究结果为正交异性钢桥面板肋-面板焊缝裂纹的疲劳寿命分析提供了研究基础。     

Micromechanical model of stage I to stage II crack growth transition for aluminium alloys

Stage I to Stage II crack growth transition is a kinetic process that is particularly studied in this work. Crack growth transition is modelled to occur when small fatigue crack growth is deterred by an effective barrier that reduces the crack growth rate to a minimum. Effective blockage of small crack growth due to barriers is characterised by pile-up of dislocations. Crack tip pile-up sliding displacement is formulated by adopting a continuous configuration of dislocation pile-up. Transition condition is quantitatively determined when a crack tip sliding displacement of Stage I cracks just meets a crack tip opening displacement of Stage II cracks. As a result, a dislocation-based micromechanical model is systematically developed that enables kinetic predictions of crack growth transition and growth rates of small fatigue cracks. Moreover, the concept of microstructurally-affected-zone is further interpreted in terms of local microstructure and load levels, leading to good explanations for scatters of small crack growth. All model-based growth rate predictions show a good coincidence with experimental results.     

Fatigue cracking and its influence on dynamic response characteristics of spot welded specimens

X-ray imaging has been used to determine the fatigue crack growth behavior and failure mechanisms of spot welded specimens. Cracks critical to final failure of the tensileshear specimens studied are through-thickness plate cracks, which are usually initiated about 0.2–1.0 mm away from the edge of the nugget. In addition, frequency response functions (FRFs), obtained by impact hammer-accelerometer experiments throughout the fatigue process, show that the natural frequencies of these joints nonlinearly decrease with the growth of fatigue cracks. The three-dimensional finite-element analysis results for FRFs of uncracked and cracked spot welded joints are shown to be in good agreement with the experimental data. It is also shown that the fatigue cracks have different degrees of influence on different natural frequencies because of the location of cracks and vibrating modes. The results by both experiment and finite element analysis indicate that analysis of the variation of natural frequencies and vibrating modes may be used to study the fatigue crack propagating shape and the location of the fatigue crack.     

CTOA and crack-tunneling measurements in thin sheet 2024-T3 aluminum alloy

The stable tearing behavior of 2.3-mm thick sheets of 2024-T3 aluminum alloy was experimentally investigated for middle crack tension specimens having initial flaws that were: (a) flat fatigue cracks (low fatigue stress) and (b) 45-deg through-thickness slant cracks (high fatigue stress). The critical CTOA values during stable tearing were measured by two independent methods, optical microscopy and digital-image correlation. Results from the two methods agree well.The CTOA measurements and observations of the fracture surfaces have shown that the initial stable tearing behavior of low and high fatigue stress tests is significantly different. The cracks in the low fatigue stress tests underwent a transition from flat-to-slant crack growth, during which the CTOA values were high and significant crack tunneling occurred. After crack growth equal to about the thickness (a>B), CTOA reached a constant value of 6 deg and after crack growth equal to about twice the thickness (a>2B), crack tunneling stabilized. The cracks in the high fatigue stress tests reach the same constant CTOA value after crack growth equal to about the thickness, but produced only slightly higher CTOA values during initial crack growth. The amount of tunneling in the high fatigue stress tests was about the same as that in the low fatigue stress tests after the flat-to-slant transition.This study indicates that stress history has an influence on the initial portion of the stable tearing behavior. The initial high CTOA values, in the low fatigue crack tests, coincided with large three-dimensional crack front shape changes due to a variation in the through-thickness crack-tip constraint. The measured CTOA reached a constant value of 6 deg for crack growth of about the specimen thickness. This coincided with the onset of 45-deg slant crack growth and a stabilized, slightly tunneled (about 20 percent of the thickness) crack-front shape. For crack growth on the 45-deg slant, the crack front and local field variables are still highly three dimensional.     

Limitations of growth regimes for cracks initiated in smooth fatigue specimens

The stages of the growth of small cracks initiating at natural flaws in smooth specimens subjected to fatigue loading are characterized and the dominant propagation mechanisms and corresponding fracture paths are described. Characteristic crack lengths are introduced to assess the transition between the regimes of microstructurally small cracks, physically small cracks and long cracks. A log Δσ-log a-diagram is used to derive estimates of these crack lengths. It is shown that simple formulate can be found which relate these characteristic crack lengths to mechanical and material parameters that can be measured using standard fracture mechanics specimens and fatigue tests.     

Predicting the fatigue life and crack aspect ratio evolution in complex structures

This paper discusses a computationally efficient method for determining the behaviour of complex structures containing three-dimensional cracks. A simple method is presented for calculating the mode I stress intensities for semi-elliptical cracks emanating from the saddle point of two intersecting tubular members. This method, which gives results in good agreement with published values, uses the finite element technique, but does not require the crack to be modelled explicitly. The technique is then used, in conjunction with FASTRAN II, to study fatigue crack growth and the results are compared to experimental data. Good agreement is achieved between both the predicted and measured fatigue crack growth and the evolution of the crack aspect ratios.     

Particle impact on metal substrates with application to foreign object damage to aircraft engines

Foreign object damage (FOD) occurs when hard, millimeter-sized objects such as gravel or sand are ingested into aircraft jet engines. Particles impacting turbine blades at velocities up to about 300 m/s produce small indentation craters which can become sites for fatigue crack initiation, severely limiting the lifetime of the blade. A framework for analyzing FOD and its effect on fatigue cracking is established in this paper. Finite element analysis is used to determine the residual stresses and geometric stress concentration resulting from FOD. The roles of material rate sensitivity and inertia are delineated. The most important non-dimensional parameters governing impact indents are identified, significantly reducing the set of independent parameters. The second step in the analysis focuses on the potency of cracks emerging from critical locations at the indents. The results have been used to address the question: When and to what extent do the residual stresses and stress concentration caused by FOD reduce the critical crack size associated with threshold fatigue crack growth? For deep indents, it is found that elastic stress concentration is the dominant factor in reducing critical crack threshold when the applied cyclic load ratio, R, is large, otherwise the residual stresses are also important. Comparisons with a set of experiments conducted in parallel with the theory show that the numerical approach can account for various phenomena observed in practice.     

Fatigue growth modeling of cracks emanating from a circular hole in infinite plate

This paper presents a numerical approach of fatigue growth analysis of cracks emanating from a hole in infinite elastic plate subjected to remote loads. It involves a generation of Bueckner’s principle and a hybrid displacement discontinuity method (a boundary element method) proposed recently by the senior author of the paper. Because of an intrinsic feature of the boundary element method, a general crack growth problem 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 modeled conveniently by adding new boundary elements on the incremental crack extension to the previous crack boundaries. As an example, fatigue growth process of an inclined crack in an infinite plate under uniaxial cycle load is modeled to illustrate the effectiveness of the numerical approach. In addition, fatigue growth of cracks emanating from a circular hole in infinite elastic plate subjected to remote loads is investigated by using the numerical approach. Many numerical results are given     

含缺口试件疲劳全寿命预测一种建议的方法

传统的研究含缺口构件的疲劳的方法是将疲劳启裂和疲劳裂纹扩展两个过程完全独立起来,用不同的方法来模拟,相互间并没有定量的关系。本文是基于最新发展的多轴疲劳损伤理论,建立了一种适用于各种载荷条件下的疲劳启裂和裂纹扩展的普适方法。根据从弹塑性分析中得到的应力应变,确定疲劳损伤模型,建立能够预测疲劳启裂、裂纹扩展速率和扩展方向的新方法。整个模拟可以分为两步:弹-塑性应力分析得到材料的应力应变分布;再运用一个通用的疲劳准则预测疲劳裂纹启裂和裂纹扩展。通过对1070号钢含缺口试件的疲劳全寿命预测,得到了与实验非常吻合的模拟结果。     

Growth of part-through and through-thickness fatigue cracks in sheet glassy plastics

Linear-elastic fracture mechanics is used to interpret observations of through-thickness fatigue crack growth in sheet specimens of polymethylmethacrylate, polycarbonate and an unfilled epoxy, and to correlate measurements of the growth of part-through and through-thickness fatigue cracks in sheet polymethylmethacrylate. It is shown that at least one of these materials may be useful for model studies of the growth of part-through thickness fatigue cracks in metallic components.     

Thermal fatigue crack networks: an computational study

Various components of nuclear reactors experience various thermo-mechanical loading. Thermal fatigue cracking has been clearly detected in reactor heat removal system (RHRS) of Pressurized Water Reactors (PWRs). The study presented here is focused on the AISI 304L stainless steel used in PWRs. The thermal fatigue behavior of this steel has been investigated using a specific thermal fatigue facility called “SPLASH test”. This test equipment allows the reproduction of multiple cracking networks similar to those detected during inspections. The present study deals with the modeling of cracking network development. It is structured in two parts: (i) experimental results and main characteristics of the crack networks, and (ii) numerical simulation on the multiple crack growth problem, using a modified stress intensity factor, and a generalized Paris’ law. In spite of simplified assumptions, the model predictions are in good agreement with observations, as far as the evolution of the mean and deepest cracks during cycling are concerned.     

接管内拐裂纹K_I的光弹测定

接管内拐角部位裂纹的断裂力学分析是很有实际意义的.本文利用三维光弹性冻结切片法对K_I沿平板—接管及圆柱—接管二种模型内拐角裂纹前缘的分布进行了测定,同时,利用所得的实验结果对某些疲劳裂纹扩展现象进行了定性的解释.     

Strain energy density prediction of fatigue crack growth from hole of aging aircraft structures

Fatigue crack growth rate depends not only on the load amplitude, but also on the morphology of crack path. The strain energy density theory has the ability to analyze crack growth rate. A strain energy density crack growth model is proposed. It can predict the lifetime of fatigue crack growth for mixed mode cracks while an equation for mode I crack is also obtained. The validity of the model is established with two cases: a center-crack panel and cracks emanating from the edge of a hole. The stress intensity factor expression for the former case is analytical while that of the latter is calculated numerically using finite elements. The results are compared with the testing data. Good agreement shows that the proposed model is useful.     

On the development of the strip yield model for the assessment of multiple site damage

The strip yield model is used to assess the link-up of multiple fatigue cracks in a simple open hole configuration. This analysis is based upon the complex stress function formulation of the problem of multiple straight collinear cuts in an infinite sheet. The predictions of link-up and fracture are compared to results from a fatigue crack propagation test on an open hole specimen, and are shown to be in very close agreement.     

Crack growth of through and part-through thickness cracks under cyclic loading

Stress intensity factor expressions corrected for crack front curvature are used to derive the corrosion fatigue growth data for through and part-through thickness cracks subjected to cyclic loading. Results are obtained by application of the boundary element method for solving three-dimensional crack problems. Different radius of curvature is assumed using the open literature cyclic crack growth parameters for air and sea water. As is to be expected, crack growth increased with decreasing crack front curvature and in sea water environment when compared with that in air.     

Crack Patching: Analysis and Design

Bonded composite patches are frequently used to retard crack growth. This repair procedure is usually referred to as crack patching. The present paper outlines the various methods for the analysis and design of fiber composite patches in thin and thick structures. As illustrative examples the repair of fatigue cracks in the wing skins of Mirage III aircraft, of surface flaws in Macchi landing wheels, and of cracks in a truss is considered.