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.     

Assurance of reliable time limits in fatigue depending on choice of failure simulation: Energy density versus stress intensity

The principle of least variance is applied to evaluate the reliability of the design conditions of the Runyang cable-stayed bridge. Monitored fatigue load in service data are analyzed in conjunction with the specimen fatigue crack growth data for bridge steel. Aside from size differences, the interactive effects of material behavior with load amplitude and frequency would vary with the depicted physical model for the reliability of life prediction. Based on the same crack growth history in time or cycle, the two choice selected for comparison are stress intensity factor (SIF) range, and the strain energy density (SED) range. Reliability is found to depend on the trade off between load amplitude and frequency. Considered are high-amplitude; low-frequency and low-amplitude; high-frequency. In each case, the chances are the reliable time span of fatigue crack growth will not coincide with the useful portion of bridge life, simply because the load frequency must be anticipated as an educated estimate. It is subject to change. Conversion of the crack length fatigue cycle history to the corresponding time history requires the specification of load frequency that can set the time span of the useful life. This is demonstrated for the Runyang bridge, where approximately 30 MPa and 8 MPa would correspond to the high and low fatigue load, respectively.Significant variances were found for the SIF and SED models. The difference can be attributed to the inclusion of the mean stress in the SED that is more forgiving since it accounts for both the stress and strain effects, in contrast to the SIF model that leaves out the strain and the mean stress. Since the principle of least variance refers to the average of the R-integrals, the results based on the linear sum (LS) and root mean square (RMS) will differ quantitatively, but not qualitatively. The obvious mismatch of the fatigue load used to determine the material property and that for the bridge design can be adjusted and absorbed into the appropriate choice for the load frequency, a compensating factor not realized up to now. To this end, the weighted functions in the R-integrals further emphasize long run effects of the least variance reliability analysis. Attention is called to Changeability in addition to determinability and probability for predicting the time to failure. That is to better anticipate the change in the fatigue load frequency, to which the assistance of health monitoring should provide.     

A stochastic theory of cumulative fatigue damage

A stochastic theory for the cumulative fatigue damage of structural components with random fatigue strength under random loading is proposed on the basis of Stratonovich-Khasminskii theorem. The analytical solutions for the probability densities of the cumulative fatigue damage and fatigue life and for the reliability function are given for steel and reinforced concrete components with constant fatigue strength subject to a narrow band stationary Gaussian stress process with zero mean. The results agree very well with those of digital simulation. It is noted that the theory can be applied, in principle, to both metallic and non-metallic materials, narrow band and wide band stress process, and adapted to a sequence ofn, stationary stress processes or quasi-stationary stress process. The scatter and degradation of fatigue strength and the inspection maintenance can also be incorporated into the theory.     

应变倍增器研制及应用

设计了一种结构独特、机械放大率高的应变倍增器,从而使工程结构表面应变放大到疲劳寿命计门槛值以上,满足了大型工程结构长寿命、低应力工作特点的寿命检测要求。该元件采用了弓形弹性元件与硅橡胶预应力组合结构,它具有简单紧凑、刚度低、可靠性好,使用方便的特点。并可同时利用其上安装的疲劳寿命计进行倍增系数标定和疲劳寿命检测。静载试验和理论分析表明,这种应变倍增器具有良好的线性响应和重复稳定性。疲劳试验研究表明,在疲劳寿命计工作寿命内,器件无疲劳破坏情况,且其疲劳响应性能可用已有的标定数据放大相应的倍增系数得到,能满足各种大型工程结构疲劳损伤监测的要求。     

The influence of strain-hardening and grain size on early fatigue damage based on a micromechanics theory

Early fatigue damage is assumed to correspond to the build-up of local plastic shear strain. The influence of strain-hardening and grain size on the early stage of fatigue damage of a polycrystal subjected to fluctuating stress is considered. The calculations are based on a micromechanics theory proposed recently by the authors. It is shown that the increase of the strain-hardening rate and/or the decrease of the grain size decreases the rate of early fatigue damage. In order to produce 100 per cent local plastic shear strain for a given number of loading cycles, the range of the alternating stress decreases with increasing amounts of mean stress. This result is shown to be rather insensitive to the rate of strain-hardening and is found to lie between the values predicted by Gerber's parabolic law and by the modified Goodman linear law for fatigue failure.     

Development of a multiaxial fatigue theory by considering constraint effects on small mixed-mode cracks

The effects of the transverse strain (the normal strain in the crack-line direction) on the near-tip fields of small shallow surface cracks (Case A cracks) in power-law hardening materials are investigated by finite element analyses. The small Case A cracks are under plane stress, general yielding, and mixed mode I and II conditions. Constant effective stress contours representing the intense straining zones near the tip, deformed crack-tip profiles and near-tip mode mixity factors are presented for different transverse strains in the crack-line direction. Based on the concept of characterization of fatigue crack growth by the cyclic J-integral, the effects of the transverse strain on J are investigated. The results suggest that the fatigue life prediction based on multiaxial fatigue theories and the critical plane approach should include the constraint effects due to the transverse strain. Consequently, the concept of constant fatigue life contour on the Γ-plane in multiaxial fatigue theories is generalized to the constant fatigue life surface in the Γ-space where the shear strain and the two normal strains are the three axes. Finally, a damage parameter as a function of the shear strain and the two normal strains is proposed for evaluation of fatigue damage under multiaxial loading conditions.     

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.     

基于疲劳损伤和倒塌事故的导管架平台结构风险分析

基于风险的检验技术已成为海洋工程领域的研究热点,其优势在于优化检验范围,减少检验成本。通过有限元方法对导管架平台结构的疲劳损伤和倒塌失效进行数值计算,并基于可靠性理论对平台结构关键构件的疲劳失效概率以及该构件疲劳破坏后平台结构的整体倒塌失效概率进行确定,形成风险矩阵,以制定相应的检验计划。在此基础上,对南海某导管架平台结构进行了定量风险评估,形成关键节点和构件的风险矩阵,并给出了相应的检验目标以指导制定检验计划。本文工作可为导管架平台结构制定合理高效的检验计划,在保障平台结构安全作业的同时降低运行费用。     

薄壁圆管空间结构的热疲劳可靠性分析

针对薄壁圆管的空间结构,分析其在交变热载荷下的疲劳可靠性问题。为同时考虑由截面平均温度和截面温差造成的疲劳损伤,提出了综合利用剩余强度和疲劳累积损伤模型的分析方法。首先根据疲劳累积损伤相等原理,将截面温差造成的多级扰动应力载荷作用频次等效为平均温度下的常幅应力载荷作用次数,从而将两者产生的热应力载荷统一为一常幅载荷,再利用剩余强度模型基于动态应力-强度干涉理论对疲劳可靠度进行分析,得到了结构在综合考虑两种热疲劳状态下的动态可靠度。本方法可避免直接利用疲劳累积损伤理论临界损伤值难以确定的问题,且能体现金属疲劳损伤的真实情况。最后以哈勃望远镜为例,分析了其主梁随疲劳热载荷循环作用下的动态可靠度,得出了一些有意义的结论。     

Post-buckled propagation model for compressive fatigue of impact damaged laminates

An analytical model for prediction of compressive fatigue threshold strains in composite plates with barely visible impact damage (BVID) is presented. The model represents the complex damage morphology as a single circular delamination at a critical level and calculates the strain at which thin-film buckling of the circular delaminated region occurs. The threshold strain is defined as the strain at which the strain energy release rate for the fracture of post-buckled delaminated plies along the delamination is equal to the critical Mode I value (G_1C) for the resin. The model predicts the critical through-thickness level for delamination, the stability of delamination growth and also the sensitivity to experimental error in geometric measurements of the damage area. Results obtained using the model show an agreement of fatigue strain to within 4% of experimental values for four sets of data reported in the literature.     

Simulated microstructure-sensitive extreme value probabilities for high cycle fatigue of duplex Ti-6Al-4V

A newly developed microstructure-sensitive extreme value probabilistic framework to characterize the performance/variability for damage evolution processes is exercised to compare the driving forces for fatigue crack formation (nucleation and early growth) at room temperature for four different microstructure variants of a duplex Ti-6Al-4V alloy. The aforementioned probabilistic framework links certain extreme value fatigue response parameters with microstructure attributes at fatigue critical sites through the use of marked correlation functions. By applying this framework to study the driving forces for fatigue crack formation in these microstructure variants of Ti-6Al-4V, these microstructures can be ranked in terms of relative high cycle fatigue (HCF) performance and the correlated microstructure attributes that have the most influence on the predicted fatigue response can be identified. Nonlocal fatigue indicator parameters (FIPs) based on the cyclic plastic strain averaged over domains on the length scale of the microstructure attributes (e.g., grains, phases) are used to estimate the driving force(s) for fatigue crack formation at the grain scale. By simulating multiple statistical volume elements (SVEs) using crystal plasticity constitutive relations, extreme value distributions of the predicted driving forces for fatigue crack formation are estimated using these FIPs. This strategy of using multiple SVEs contrasts with simulation based on a single representative volume element (RVE), which is often untenably large when considering extreme value responses. The simulations demonstrate that microstructures with smaller relative primary α grain sizes and lower volume fractions of the primary α grains tend to exhibit less variability and smaller magnitudes of the driving forces for fatigue crack formation. The extreme value FIPs are predicted to most likely occur at clusters of primary α grains oriented for easy basal slip. Additionally, surrounding grains/phases with soft orientation shed load to less favorably oriented primary α grains, producing extreme value FIPs.     

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为降低用来确定疲劳极限的升降法试验的工作量，以热力学为基础，引入损伤驱动力，构建 损伤演化方程. 积分此方程得到疲劳寿命与应力或应变的理论关系. 对光滑试件，根据成组 法疲劳试验结果利用最小二乘法拟合包括疲劳极限在内的材质参数. 利用损伤力学方法求得 高应力区的疲劳寿命曲线，由此递推得到低应力区寿命值和疲劳极限. 所得理论疲劳极限值 与升降法疲劳试验结果十分吻合. 节约了疲劳试验的机时、费用与人力.     

Cumulative damage evaluation of steel using infrared thermography

Following the first damage models proposed by Palmgren and Miner, numerous researchers have focused on the problem of predicting the residual life of a material from its load history. Every component dynamically loaded, particularly over the fatigue limit, shows an increase in temperature. The higher the temperature, the higher the load applied. Therefore, in an undamaged material or mechanical component, it is possible to associate each loading stress over the fatigue limit with a temperature value at the hottest point of the surface during the first phase of the test trough a thermo-mechanical characterization (TMC) map. Using the thermoanalysis of steel specimen data, this paper shows that the energetic effect (as a different temperature increments for equal loading uniaxial stress) can be used to evaluate the cumulative damage caused by previous loading. The tests were performed using C40 steel for which traditional fatigue curves in literature are reported.     

复杂应力状态镍基单晶合金低周疲劳损伤模型

根据连续介质损伤力学理论,采用应变能释放率作为热力学广义力描述正交异性材料的疲劳损伤过程,引入取向函数考虑镍基单晶合金晶体取向对疲劳损伤的非线性影响,提出了一个各向异性疲劳损伤模型。应用多元线性回归分析方法,拟合疲劳试验数据可确定模型参数。从应变能释放率的应变空间表达式出发,导出了含有3个弹性常数的单晶合金应变三轴性因子,它既反映了材料性能的晶体取向相关性,又反映了正应力和剪应力的相互作用,并可退化为各向同性材料的应变三轴性因子。利用该模型对CMSX-2镍基单晶合金在应力控制对称循环拉-扭载荷作用下的低周疲劳寿命进行预测,预测值与试验值吻合的相当好,试验所得数据均落在2.2倍偏差的分布带内。     

Determination of effective stress range and its application on fatigue stress assessment of existing bridges

This paper presents a unified approach on determination of the effective stress range based on equivalent law of strain energy and fatigue damage model, so as to provide an efficient approach for accurately assessing effective fatigue stress of existing bridge under traffic loading. A new theoretical framework to relate variable- and constant-amplitude fatigue is proposed in this paper. Different formulation for calculating effective stress range can be derived by the proposed theory, which include the effective stress range by the root mean square, by Miner's law and a new effective stress range based on the nonlinear fatigue damage model. Comparison of the theoretical results of fatigue damage under the effective stress range of the variable-amplitude stress spectrum and experimental data of fatigue damage under realistic traffic loading has confirmed the validity of the proposed theory. As a way to relate variable-amplitude fatigue data with constant-amplitude data, the effective stress range provides the most convenient way for evaluating fatigue damage under variable-amplitude loading. The proposed theory is then applied to provide an efficient approach for accurately assessing fatigue damage of existing bridges under traffic loading, in which online strain history data measured from bridge structural health monitoring system is available. The proposed approach is applied to evaluate the effective stress range for the purpose of the fatigue analysis of a deck section of a long-span steel bridge––the Tsing Ma Bridge in Hong Kong.     

Frequency-dependent random fatigue of panel-type structures made of ceramic matrix composites

The panel-type structures used in aerospace engineering can be subjected to severe highfrequency acoustic loadings in service. This paper evaluates the frequency-dependent random fatigue of panel-type structures made of ceramic matrix composites(CMCs) under acoustic loadings. Firstly, the high-frequency random responses from the broadband random excitation will result in more stress cycles in a deinite period of time. The probability density distributions of stress amplitudes will be different in different frequency bandwidths, though the peak stress estimations are identical. Secondly, the fatigue properties of CMCs can be highly frequency-dependent. The fatigue evaluation method for the random vibration case is adopted to evaluate the fatigue damage of a representative stiffened panel structure. The frequency effect through S-N curves on random fatigue damage is numerically veriied. Finally, a parameter is demonstrated to characterize the mean vibration frequency of a random process, and hence this parameter can further be considered as a reasonable loading frequency in the fatigue tests of CMCs to obtain more reliable S-N curves.Therefore, the inluence of vibration frequency can be incorporated in the random fatigue model from the two perspectives.     

A statistical theory of fatigue crack growth at damage cumulation

Summary A statistical theory of the fatigue crack growth at damage cumulation is proposed. The theory gives the average of fatigue crack length at any time t, and deduces the evolution of failure probability with time varying. Furthermore, the variance and relative error of fatigue crack length at any time t are acquired. The Paris equation for the average of the crack length at any time t is derived from the statistical theory. Therefore, the prediction of the probability distribution of the crack length can be given for any time t. Actual applications of the theory are given, which conform to the experiments. Accepted for publication 17 June 1996     

Statistical correlation of fatigue life of 15MnVN steel notched bar under variable amplitude tension-tension block loading

Variable amplitude tension-tension block loading is repeated and applied to test 15MnVN steel notched bars. The block loading consists of three steps of load increase reaching a peak at the fourth step followed by three steps of load decrease returning to the initial level. The results are presented in terms of the probability distribution function. One of the objectives of this work is to show that the probability distribution correlates well with the fatigue life data of the high-strength low-alloy steel which exhibits the discontinuous strain hardening characteristics and does not have any overload effect. It is shown that the fatigue life and critical accumulated damage data flow the log-normal distribution.     

腐蚀环境下结构系统疲劳主要失效模式识别

疲劳主要失效模式识别是结构系统疲劳可靠性理论研究的主要内容之一。本文研究了腐蚀环境下结构系统疲劳主要失效模式识别方法:(1)建立了腐蚀环境下结构元部件损伤随机模型,对该模型的适用性作了讨论;(2)研究了识别结构系统疲劳主要失效模式的全局分枝约界法,与结构元部件损伤随机模型结合,实现腐蚀环境下结构系统疲劳主要失效模式识别,并对算法执行过程作了调整;(3)引入了一种安全裕量方程确定方法。理论分析和数值算例表明,本文所提算法可实现腐蚀环境下结构系统疲劳主要失效模式识别。