Fatigue crack growth model for assessing reliability of box-girders for cable-stayed bridge combining SHMS with strain data

Enhancement of the computer algorithm developed for the Runyang cable-stayed bridge (RYCB) in China is made by incorporating the fatigue crack growth analysis in contrast to the SN curve approach. Strain data obtained from the structural health monitoring system (SHMS) and finite element calculations are used. This provides the application of a deterministic method in addition to the probabilistic approach with the added feature of crack growth. The choice of selecting the two-parameter fatigue crack growth criterion was based on the definition of reliability index β such that the new results can be compared with those using the SN curves. A gradual drop of the reliability index β with time with an upper limit was obtained for the crack growth model in contrast to the linear time relation for the SN curve model that had no upper limit. This difference is significant and reveals the importance for selecting the fatigue failure criterion. Deterministic and probabilistic crack growth models are used to assess the differences. The results are based on the box-girder component strain history data of the Runyang Cable-stayed Bridge (RYCB) in China, stress history recorded by structural health monitoring system (SHMS) is analyzed using the monitored stress amplitude, mean stress and stress ratio. Finite element calculations are used to supplement data at locations not accessible for measurements. Additional improvement with reference to damage accumulation and the physical meaning of the reliability index will be studies in relation to the fatigue damage of box-girder of long cable-stayed bridges.     

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.     

Fatigue damage in polycrystals – Part 2: Intrinsic scatter of fatigue life

Part 2 deals with the evolution of plastic flow resistance with crack growth from its minimum value (fatigue limit) towards its saturated bulk value (cyclic yield stress). The far-field stress level, the geometry of the crack and the grain size distribution of the material are those parameters that control the area of crack tip plasticity and hence the rate towards saturation. The implication of the far-field stress is held responsible for the violation of the similitude concept and the failure of the stress intensity factor to describe conditions of short cracking. However, an engineering tool based on the stress intensity factor and being able to predict the fatigue life of short cracks can be constructed, considering that the distribution of crack growth rates is intrinsically defined by the material itself. The above allows the development of a set of equations able to construct the fatigue life scatter of the material.     

Fatigue criteria for integrity assessment of long-span steel bridge with health monitoring

A structural health assessment (SHA) methodology is developed using data acquired from structural health monitoring (SHM) system installed on long-span bridges. A set of fatigue criteria has been proposed for pre-determining the global state of the bridge structure failure due to fatigue. This involves finding the threshold of fatigue initiation, below which the rate of fatigue damage may be undetectable under current technology or it is economically unfeasible. The state-of-art for large structures corresponds to the initiation of macro-cracks caused by the accumulation of damage generated by actual service loads for the case of bridges. In what follows, consideration is given to developing fatigue crack growth criterion based on the concept of the continuum damage mechanics (CDM). Fatigue accumulative is included in the model where a fatigue limit for multi-axial stress state is considered. The proposed criterion advocates the evolution of micro-crack growth up to the stage of macro-crack formulation. Considered are the loading histories that correspond to normal traffic loading for highways and railways, incidental or accident loadings such as those caused by typhoons and effective environmental loadings. The potential sites of damage are determined are discussed. The proposed criterion is applied to analyze the fatigue damage of the Tsing Ma Bridge with online strain history data acquired by the SHM system that is permanently installed in the bridge.     

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。     

Fatigue crack growth simulation in coated materials using X-FEM

In the present work, the eXtended Finite Element Method (XFEM) is used to study the effect of bi-material interfaces on fatigue life in galvanised panels. X-FEM and Paris law are implemented in ABAQUS software using Python code. The XFEM method proved to be an adequate method for stress intensity factor computation, and, furthermore, no remeshing is required for crack growth simulations. A study of fatigue crack growth is conducted for several substrate materials, and the influence of the initial crack angle is ascertained. This study also compares the crack growth rate between three types of bi-materials alloys zinc/steel, zinc/aluminium, and zinc/zinc. The interaction between two cracks and fatigue life, in the presence of bi-material interface, is investigated as well.     

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.     

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 growth prediction of elliptical cracks in welded joint structure: Hybrid and energy density approach

A hybrid weight function approach (HWFM) is presented for the fatigue life prediction of infinite body and welded joint structure containing elliptical cracks. A self-containing computer code has been developed for this purpose. Numerical computations were first conducted on cracked infinite body showing a physical fact, that the elliptical shape of the crack becomes circular during its evolution. The prediction of the fatigue crack growth shows that the present results are in perfect concordance with those reported in the literature. Then, numerical tests were carried out on two types of specimens of welded joint structure. The present results were compared to the experimental and predicted ones of other authors, demonstrating that the hybridization method is a powerful numerical technique, and that the SEDF approach (using the Sih’s law) is more valid for the critical cases of welded joints than the SIF approach (using the Paris law). A parametric study has been conducted on the stress ratio “R” showing that the fatigue life to failure decreases with the increase of “R”.     

基于子模型法的带有表面裂纹钢丝应力强度因子研究

钢丝裂纹应力强度因子是进行钢丝疲劳断裂寿命评估、疲劳裂纹扩展分析和钢丝断裂强度评估等工作的重要参数。本文首先介绍了裂纹扩展分析软件FRANC3D,然后基于子模型法模拟研究了拉伸荷载作用下带有表面裂纹钢丝的应力强度因子,裂纹种类包括直线形裂纹和半圆形裂纹,最后拟合得到拉伸荷载作用下带表面裂纹钢丝的应力强度因子形状修正系数表达式,分析了利用该公式进行承载力评估时产生误差的原因。研究结果表明,利用子模型模拟分析拉伸荷载作用下带有表面裂纹的钢丝应力强度因子时计算精度高,计算速度快,对计算机硬件要求低;利用该方法得到的钢丝裂纹应力强度因子,在进行索承式桥梁吊索安全性能评估时,评估结果更精确。     

Three-dimensional structure optimal design for extending fatigue life by using biological algorithm

This paper presents some applications of a new structural shape optimization procedure for maximizing fatigue life or inspection intervals for damage tolerant structures. In this approach, a new and simple method, which we termed FAST (Failure Analysis of Structures), for estimating the stress intensity factor for cracks at a notch, as well as an extension of the biological algorithm was employed to study the problem of optimization with fatigue life as the design objective. Research by the authors has demonstrated that the optimum shape for minimizing stress is not necessarily the optimum shape for static strength or fatigue life of a damage tolerant structure. The examples are presented that highlight this difference. The optimal shapes for stress are compared with optimized shapes found for static strength with different crack lengths. These are also compared with optimized shapes found for maximum fatigue life. The choice of initial crack size was found to have a significant effect on the optimal shapes for the structures presented.     

Evolution of fatigue damage using the fatigue damage map method

Using only readily available material properties and the concept of the fatigue damage map the work attends to develop a methodology able to predict crack tip propagation rates characterising each of the fatigue stages, namely crack arrest, microstructurally and physically short crack (Stage I), long crack growth (Stage II) and Stage III growth. Crack tip propagation rates are predicted through the combination of an Elasto-Plastic crack tip opening displacement model and the crack blunting theory. The methodology provides a theoretical framework for a 3D version of the fatigue damage map for damage tolerance design. In addition, the work attends to explain a number of fundamental problems starting from crack tip propagation discrepancies, found in the short cracking stage, as well as to provide an insight towards the effect of grain size on the fatigue limit/threshold stress intensity factor.     

A model for predicting the retardation effect following a single overload

Many engineering components are subjected to variable amplitude loading history. It is well known that retardation in fatigue crack growth occurs due to application of single overloads in a constant amplitude loading block. Many models have been proposed to capture this counter intuitive phenomenon which has resulted in improved understanding of retardation effect following tensile overloads and consequently resulting in better life prediction models. The proposed study is focused on to evaluation of retardation in fatigue life due to application of a single overload. A model for prediction of crack growth and crack growth rate following single overloads is presented. Several modifications to Wheeler’s growth idea are proposed, which incorporate a consideration for effective stress intensity factor, based on Elber’s concept of crack closure, relationship between overload ratio and the Wheeler’s exponent, and fatigue growth rate calculations. The results presented here show that plastic zone interaction following overload and the consideration of crack closure explain retardation effect following a single overload. Correlation between analysis and experimental data obtained from several sources in literature show that the scheme, is robust and provides an insight into the nonlinear aspect of crack growth results. The model has been tested for 2024-T3 aluminum alloy and 6061-T6 aluminum alloy and thorough calibrations performed, established the fidelity of the program.     

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。     

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。     

Intergranular strain evolution near fatigue crack tips in polycrystalline metals

The deformation field near a steady fatigue crack includes a plastic zone in front of the crack tip and a plastic wake behind it, and the magnitude, distribution, and history of the residual strain along the crack path depend on the stress multiaxiality, material properties, and history of stress intensity factor and crack growth rate. An in situ, full-field, non-destructive measurement of lattice strain (which relies on the intergranular interactions of the inhomogeneous deformation fields in neighboring grains) by neutron diffraction techniques has been performed for the fatigue test of a Ni-based superalloy compact tension specimen. These microscopic grain level measurements provided unprecedented information on the fatigue growth mechanisms. A two-scale model is developed to predict the lattice strain evolution near fatigue crack tips in polycrystalline materials. An irreversible, hysteretic cohesive interface model is adopted to simulate a steady fatigue crack, which allows us to generate the stress/strain distribution and history near the fatigue crack tip. The continuum deformation history is used as inputs for the micromechanical analysis of lattice strain evolution using the slip-based crystal plasticity model, thus making a mechanistic connection between macro- and micro-strains. Predictions from perfect grain-boundary simulations exhibit the same lattice strain distributions as in neutron diffraction measurements, except for discrepancies near the crack tip within about one-tenth of the plastic zone size. By considering the intergranular damage, which leads to vanishing intergranular strains as damage proceeds, we find a significantly improved agreement between predicted and measured lattice strains inside the fatigue process zone. Consequently, the intergranular damage near fatigue crack tip is concluded to be responsible for fatigue crack growth.     

DETERMINATION OF CRACK SURFACE DISPLACEMENTS FOR A RADIAL CRACK EMANATING FROM A SEMI-CIRCULAR NOTCH USING WEIGHT FUNCTION METHOD

A radial crack emanating from a semi-circular notch is of significant engineering importance. Accurate determination of key fracture mechanics parameters is essential for damage tolerance design and fatigue crack growth life predictions. The purpose of this paper is to provide an efficient and accurate closed-form weight function approach to the calculation of crack surface displacements for a radial crack emanating from a semi-circular notch in a semi-infinite plate.Results are presented for two load conditions: remote applied stress and uniform stress segment applied to crack surfaces. Based on a correction of stress intensity factor ratio, highly accurate analytical equations of crack surface displacements under the two load conditions are developed by fitting the data obtained with the weight function method. It is demonstrated that the WuCarlsson closed-form weight functions are very efficient, accurate and easy-to-use for calculating crack surface displacements for arbitrary load conditions. The method will facilitate fatigue crack closure and other fracture mechanics analyses where accurate crack surface displacements are required.     

随机车辆冲击作用下简支梁桥疲劳可靠度评估

为了研究考虑随机车辆冲击效应的简支梁桥疲劳安全水平,提出了基于车-桥耦合振动与随机车流的桥梁疲劳应力谱模拟方法,并应用于疲劳可靠度评估。基于某高速公路桥梁动态称重数据建立随机车流模型,采用小样本车辆数据拟合桥梁等效疲劳应力范围的插值响应函数,最后由高斯混合模型拟合大样本随机车流作用于桥梁构件的疲劳应力谱。分析了25 m标准跨径简支T梁桥底部普通钢筋的疲劳应力谱,评估了考虑路面劣化与交通量增长的桥梁疲劳可靠度。数值分析结果表明,基于随机车流模拟的疲劳应力谱具有典型的多峰分布特征,包含了超载车辆产生的疲劳应力;车辆对桥梁的冲击效应致使等效疲劳应力放大系数略大于冲击系数,当路面等级为一般时,采用规范冲击系数将低估车辆冲击效应的疲劳损伤;路面劣化与交通量增长均会导致桥梁运营期内的疲劳可靠指标显著降低,由路面劣化导致车辆对简支梁桥的冲击效应不可忽略。     

Fatigue damage evolution in silicon films for micromechanical applications

In this paper we examine the conditions for surface topography evolution and crack growth/fracture during the cyclic actuation of polysilicon microelectromechanical systems (MEMS) structures. The surface topography evolution that occurs during cyclic fatigue is shown to be stressassisted and may be predicted by linear perturbation analyses. The conditions for crack growth (due to pre-existing or nucleated cracks) are also examined within the framework of linear elastic fracture mechanics. Within this framework, we consider pre-existing cracks in the topical SiO₂ layer that forms on the Si substrate in the absence of passivation. The thickening of the SiO₂ that is normally observed during cyclic actuation of Si MEMS structures is shown to increase the possibility of stable crack growth by stress corrosion cracking prior to the onset of unstable crack growth in the SiO₂ and Si layers. Finally, the implications of the results are discussed for the prediction of fatigue damage in silicon MEMS structures.     

Fatigue crack growth analysis of adhesively repaired panel using perfectly and imperfectly composite patches

Fatigue crack behavior of cracked aluminum panel repaired with the imperfectly bonded composite patch is analyzed. The imperfection is in the form of debond which could result during the bonding of patch or the service life of the repaired structure. Debonds, of various sizes and at different locations with respect to the crack front, are investigated. An analytical procedure, involving two-dimensional finite element method having three layers to model cracked plate, adhesive and composite patch, is used to compute the stress intensity factors of test coupons. From the computed stress intensity factors, the crack growth rates are obtained analytically by assuming that the relationship between the stress intensity factor and the crack growth rate after repair is the same as the fatigue crack growth relationship for cracked panel material. The fatigue crack growth rates obtained experimentally and analytically are in good agreement with each other and they vary linearly with crack length inside the patch. The experimental results are bounded between its analytical counterparts at the mid-plane and free edge surfaces of the cracked panel. The present analytical procedure can, thus, be used to characterize the effects of imperfectly and perfectly bonded composite patch repairs on the durability and damage tolerance of the repaired structure.