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。     

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。     

On the stress state of a piezoceramic body with a flat crack under symmetric loads

A static-equilibrium problem is solved for an electroelastic transversely isotropic medium with a flat crack of arbitrary shape located in the plane of isotropy. The medium is subjected to symmetric mechanical and electric loads. A relationship is established between the stress intensity factor (SIF) and electric-displacement intensity factor (EDIF) for an infinite piezoceramic body and the SIF for a purely elastic material with a crack of the same shape. This allows us to find the SIF and EDIF for an electroelastic material directly from the corresponding elastic problem, not solving electroelastic problems. As an example, the SIF and EDIF are determined for an elliptical crack in a piezoceramic body assuming linear behavior of the stresses and the normal electric displacement on the crack surface __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 67–77, November 2005.     

A generalized Paris’ law for fatigue crack growth

An extension of the celebrated Paris law for crack propagation is given to take into account some of the deviations from the power-law regime in a simple manner using the Wöhler SN curve of the material, suggesting a more general “unified law”. In particular, using recent proposals by the first author, the stress intensity factor K(a) is replaced with a suitable mean over a material/structural parameter length scale Δa, the “fracture quantum”. In practice, for a Griffith crack, this is seen to correspond to increasing the effective crack length of Δa, similarly to the Dugdale strip-yield models. However, instead of including explicitly information on cyclic plastic yield, short-crack behavior, crack closure, and all other detailed information needed to eventually explain the SN curve of the material, we include directly the SN curve constants as material property. The idea comes as a natural extension of the recent successful proposals by the first author to the static failure and to the infinite life envelopes. Here, we suggest a dependence of this fracture “quantum” on the applied stress range level such that the correct convergence towards the Wöhler-like regime is obtained. Hence, the final law includes both Wöhler's and Paris’ material constants, and can be seen as either a generalized Wöhler's SN curve law in the presence of a crack or a generalized Paris’ law for cracks of any size.     

Fatigue life prediction of out-of-plane gusset welded joints using strain energy density factor approach

Fatigue growth behavior of out-of-plane gusset welded joints is studied using the strain energy density factor approach. Fatigue tests on two types of specimens with curvatures of ρ = 0 and ρ = 30 were performed in order to estimate fatigue strength under tension. Fatigue crack growth analysis is carried out to show the effects of initial crack shape, initial crack length and stress ratio. Fatigue crack growth parameters were obtained from crack growth curves assuming constant crack shapes. The results of analysis for the assumed crack shapes agreed well with the experimental data. Fatigue propagation life of the ρ = 30 specimen was larger than that of the ρ = 0 specimen.     

Fatigue life prediction of in-plane gusset welded joints using strain energy density factor approach

Fatigue crack growth behavior of in-plane gusset welded joints is studied using the strain energy density factor approach. Fatigue tests were performed in order to estimate fatigue strength under tension. Fatigue crack growth analysis was carried out to show the effects of the initial crack shape, the initial crack length, and the stress ratio on the crack types of in-plane gusset welded joints. The assumed crack types were edge crack, semi-elliptical crack, and corner crack. Fatigue crack growth parameters were obtained from crack growth curves assuming constant crack shapes for the given crack types. The results of analysis for the assumed crack types agreed well with the experimental data. The fatigue life did not change as initial crack shape varied for a given initial crack length.     

焊趾表面裂纹的形态发展曲线与疲劳寿命预测

以作者建立的焊地椭圆表面裂纹应力强度因子数据库以及复杂应力场中焊践半随圆表面裂纹前缘应力强度因子分布计算的基本模式法为基础上,给出了复杂应力场中焊践表面表纹在疲劳扩展过程中形态变化规律及寿命的工程分析方法。     

One, no one, and one hundred thousand crack propagation laws: A generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth

Barenblatt and Botvina with elegant dimensional analysis arguments have elucidated that Paris’ power-law is a weak form of scaling, so that the Paris’ parameters C and m should not be taken as material constants. On the contrary, they are expected to depend on all the dimensionless parameters of the problem, and are really “constants” only within some specific ranges of all these. In the present paper, the dimensional analysis approach by Barenblatt and Botvina is generalized to explore the functional dependencies of m and C on more dimensionless parameters than the original Barenblatt and Botvina, and experimental results are interpreted for a wider range of materials including both metals and concrete. In particular, we find that the size-scale dependencies of m and C and the resulting correlation between C and m are quite different for metals and for quasi-brittle materials, as it is already suggested from the fact the fatigue crack propagation processes lead to m=2-5 in metals and m=10-50 in quasi-brittle materials. Therefore, according to the concepts of complete and incomplete self-similarities, the experimentally observed breakdowns of the classical Paris’ law are discussed and interpreted within a unified theoretical framework. Finally, we show that most attempts to address the deviations from the Paris’ law or the empirical correlations between the constants can be explained with this approach. We also suggest that “incomplete similarity” corresponds to the difficulties encountered so far by the “damage tolerant” approach which, after nearly 50 years since the introduction of Paris’ law, is still not a reliable calculation of damage, as Paris himself admits in a recent review.     

The effect of the sheet rigidity on strength of the spot weld tension shear joint

This paper presents some test and analysis results for a spot welded joint subjected to tensile and alternate load. The effect of sheet rigidity on the tensile strength and fatigue life of the spot welded joint is studied by using the stress intensity factorsK _I,K _II,K _III and an effective stress intensity factor K_max calculated by the finite element method for crack around the nugget. The results show that the effective stress intensity factor K_max is an essential parameter for estimating the fatigue life of the spot welded joint.     

双轴载荷作用下源于椭圆孔的分支裂纹的一种边界元分析

利用一种边界元方法来研究双轴载荷作用下无限大板中源于椭圆孔的分支裂纹．该边界元方法由Crouch与Starfied建立的常位移不连续单元和笔者提出的裂尖位移不连续单元构成．在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其它边界,文中算例说明本数值方法对计算平面弹性裂纹的应力强度因子是非常有效的。该文对双轴载荷作用下无限大板中源于椭圆孔的分支裂纹的数值结果进一步证实本数值方法对计算复杂裂纹的应力强度因子的有效性,同时该数值结果可以揭示双轴载荷及裂纹体几何对应力强度因子的影响。     

Fatigue life estimate of C---Mn steel welded cruciform joints

The fatigue life of a manual metal arc welded cruciform joint failing from a root lack of the penetration region is estimated by the application of crack growth relations. A two-parameter relation was used. The initiation life and propagation life of the joint were taken into account to obtain the total fatigue life of the joint from the crack growth parameters. To test the accuracy of the method, the predicted data was compared with the experimental data for a C---Mn type steel welded joints. The results were in good agreement with the experimental data.     

软夹硬力学不均匀焊接接头疲劳裂纹闭合行为的实验研究

力学性能不均匀是焊接接头的三大待征之一，本文采用柔度法研究了不同硬夹层宽度的软夹硬力学不均匀焊接接头疲劳裂纹的闭俣行为。研究结果表明，裂纹尖端附近软区的局部屈服在疲劳载荷卸载过程中促使裂纹闭合。随着硬夹层宽度的减小，这一影响越来越明显。     

Fatigue based three-dimensional structural design optimisation studies implementing the generalised Frost–Dugdale crack growth law

Experimental studies of fatigue crack growth in aluminium alloys have shown that, at the low-to-mid stress intensity factor range, there is often a log-linear relationship between the crack length and the fatigue life. These observations have led to the development of the generalised Frost–Dugdale crack growth law, which allowed the accurate prediction of fatigue crack growth from Region I. For this research paper the ‘generalised Frost–Dugdale’ law was used to perform an optimisation study of 7050-T7451 Aluminium structures. The structural optimisation procedure proposed integrates geometrical modelling, structural analysis and optimization into one complete and automated computer-aided design process. The results from the structural optimisation study compared the ‘generalised Frost–Dugdale’ law and the traditional Paris law. Gradient-less, gradient-based optimisation algorithm and an enumeration scheme were considered in this investigation. The enumeration scheme takes advantage of a cluster computer architecture which enables a visualisation of the solution space allowing verification and validation of the optimisation algorithm. The results indicated that the optimal geometrical shape and predicted fatigue life depended on the crack sizes, structural geometry, boundary conditions and fatigue crack growth law. As a result, this procedure illustrates that for the design of light weight structures, a fatigue based optimisation used in conjunction with visualisation of the solution space may provide a viable design methodology. The importance of non-destructive inspection (NDI) and its role in determining optimal structural geometries is also revealed. Furthermore, the possibility of the application of the generalised Frost–Dugdale model in design optimisation has been demonstrated. This procedure has the potential to be applied to structures with complex structural configurations taking into account crack propagation in Region I.     

Fatigue crack growth of cable steel wires in a suspension bridge: Multiscaling and mesoscopic fracture mechanics

Intrinsically, fatigue failure problem is a typical multiscale problem because a fatigue failure process deals with the fatigue crack growth from microscale to macroscale that passes two different scales. Both the microscopic and macroscopic effects in geometry and material property would affect the fatigue behaviors of structural components. Classical continuum mechanics has inability to treat such a multiscale problem since it excludes the scale effect from the beginning by introducing the continuity and homogeneity assumptions which blot out the discontinuity and inhomogeneity of materials at the microscopic scale. The main obstacle here is the link between the microscopic and macroscopic scale. It has to divide a continuous fatigue process into two parts which are analyzed respectively by different approaches. The first is so called as the fatigue crack initiation period and the second as the fatigue crack propagation period. Now the problem can be solved by application of the mesoscopic fracture mechanics theories developed in the recent years which focus on the link between different scales such as nano-, micro- and macro-scale.On the physical background of the problem, a restraining stress zone that can describe the material damaging process from micro to macro is then introduced and a macro/micro dual scale edge crack model is thus established. The expression of the macro/micro dual scale strain energy density factor is obtained which serves as a governing quantity for the fatigue crack growth. A multiscaling formulation for the fatigue crack growth is systematically developed. This is a main contribution to the fundamental theories for fatigue problem in this work. There prevail three basic parameters μ^∗, σ^∗ and d^∗ in the proposed approach. They can take both the microscopic and macroscopic factors in geometry and material property into account. Note that μ^∗, σ^∗ and d^∗ stand respectively for the ratio of microscopic to macroscopic shear modulus, the ratio of restraining stress to applied stress and the ratio of microvoid size ahead of crack tip to the characteristic length of material microstructure.To illustrate the proposed multiscale approach, Hangzhou Jiangdong Bridge is selected to perform the numerical computations. The bridge locates at Hangzhou, the capital of Zhejiang Province of China. It is a self-anchored suspension bridge on the Qiantang River. The cables are made of 109 parallel steel wires in the diameter of 7 mm. Cable forces are calculated by finite element method in the service period with and without traffic load. Two parameters α and β are introduced to account for the additional tightening and loosening effects of cables in two different ways. The fatigue crack growth rate coefficient C₀ is determined from the fatigue experimental result. It can be concluded from numerical results that the size of initial microscopic defects is a dominant factor for the fatigue life of steel wires. In general, the tightening effect of cables would decrease the fatigue life while the loosening effect would impede the fatigue crack growth. However, the result can be reversed in some particular conditions. Moreover, the different evolution modes of three basic parameters μ^∗, σ^∗ and d^∗ actually have the different influences on the fatigue crack growth behavior of steel wires. Finally the methodology developed in this work can apply to all cracking-induced failure problems of polycrystal materials, not only fatigue, but also creep rupture and cracking under both static and dynamic load and so on.     

A numerical analysis of cracks emanating from a surface elliptical hole in infinite body in tension

This paper deals with such a kind of surface crack problem with an approximately same depth, which is called a liked-plane crack problem. Based on the previous investigations on internal rectangular crack and surface rectangular crack in infinite solid in tension and a hybrid displacement discontinuity method (a boundary element method) proposed recently by Yan, a numerical approach for the liked-plane crack problem in hand is presented. Numerical examples are given to illustrate the numerical approach is simple, yet accurate for calculating the SIFs of a liked-plane crack. Specifically, a pair of cracks emanating from a surface elliptical hole in infinite body in tension are investigated in detail.     

基于多因素的焊接结构疲劳裂纹扩展速率分析

以Donahue等提出的疲劳裂纹扩展速率计算模型为基础,通过引入形状系数、张开比和残余应力等参数,建立了适用于焊接结构的疲劳裂纹扩展速率计算模型,分析了多种因素对焊接结构疲劳裂纹扩展速率的影响规律。结果表明,焊板厚度和焊缝余高的变化均会对焊接结构疲劳裂纹的扩展速率产生影响,在对焊接结构表面形状进行设计时应保有一定的焊缝余高;有效应力比的增大会降低焊接结构疲劳裂纹的扩展速率,且裂纹深度的变化不会改变有效应力比对焊接结构疲劳裂纹扩展速率的影响;残余应力的增大会提高焊接结构疲劳裂纹的扩展速率,且残余应力对疲劳裂纹扩展速率的促进作用随着裂纹深度的增加而增大,在对焊接结构的疲劳性能进行设计时须考虑残余应力对结构性能的影响。     

Fatigue life evaluation by weight functions for orthotropic bridge decks

This paper is concerned with the prediction of fatigue crack propagation in welded orthotropic decks for road and railway steel bridges. The analysis makes use of a weight function (WF), that provides effective evaluation of the stress intensity factor (SIF) for any crack length and loading condition. The WF was determined by a hybrid (numerical/analytical) technique and verified with numerical results. The fatigue life were estimated for different initial crack lengths and loading cycles. Endurance limits were obtained to establish in-service inspection schedule of the structure. The effect of weldment residual stress on the fatigue life was also analyzed. It was shown that the WF technique provides an expedient evaluation of these effects, also accounting for non-linear (contact) phenomena.     

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.     

具有半边裂纹导电薄板放电瞬间的温度场数值模拟

采用数值模拟方法 ,模拟计算了具有半边裂纹的导电薄板在放电瞬间的温度场分布。计算结果表明 :在裂纹尖端附近由于电磁热的集中效应 ,可使材料熔化形成焊口 ,裂纹尖端处的曲率半径显著增大 ,并且焊口的温度分布与形状是不完全对称的。裂纹尖端焊口形状的模拟计算结果与试验结果非常吻合。从温度梯度的分布结果可知 ,裂纹前缘附近在放电过程中将产生很大的压应力 ,可显著减少甚至是消除裂纹前缘处的扩展应力数值 ,抑制了裂纹主干线的形成 ,可达到遏制裂纹扩展的目的     

内部压力作用下矩形板中源于椭圆孔的分支裂纹应力强度因子的一种数值分析

应用一种边界元方法来研究内部压力作用下矩形板中源于椭圆孔的分支裂纹。该边界元方法由Crouch与Starfied建立的常位移不连续单元和笔者最近提出的裂尖位移不连续单元构成。在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其它边界。本数值结果进一步证实这种数值方法对计算有限大板中复杂裂纹的应力强度因子的有效性,同时该数值结果可以揭示裂纹体几何对应力强度因子的影响。