Analysis of crack interactions at adjacent holes and onset of multi-site fatigue damage in aging airframes

Focusing on the geometry of one hot spot in airframes, this paper discusses the onset of the interaction of two collinear cracks at adjacent holes and defines the onset as a criterion for multi-site fatigue damage failure. The finite element method is used to calculate the stress intensity factors at the tips of two collinear cracks at adjacent holes growing towards each other. The stress intensity factor is found to increase rapidly at the onset of interaction. Since a rapid increase in stress intensity factor results in a rapid and unstable growth of the crack, the onset of the interaction is proposed as the point where the multi-site fatigue damage starts. A criterion to avoid multi-site fatigue damage locally is then established based on the separation distance of two crack tips at the onset of the interaction. To speed up the simulation of crack growth under multi-site fatigue damage with the finite element method, a semi-empirical criterion is derived to determine the time at which the stress intensity factors at the tips of the cracks correlate. The numerical examples show that the proposed criterion saves simulation time while incurring negligible relative error in the computation of the final crack length.     

Fatigue crack growth prediction in nuclear piping using Markov chain Monte Carlo simulation

In this paper, we present and demonstrate a methodology to improve probabilistic fatigue crack growth (FCG) predictions by using the concept of Bayesian updating using Markov chain Monte Carlo simulations. The methodology is demonstrated on a cracked pipe undergoing fatigue loading. Initial estimates of the FCG rate are made using the Paris law. The prior probability distributions of the Paris law parameters are taken from the tests on specimen made of the same material as that of pipe. Measured data on crack depth over number of loading cycles are used to update the prior distribution using the Markov chain Monte Carlo. The confidence interval on the predicted FCG rate is also estimated. In actual piping placed in a plant, the measured data can be considered equivalent to the data received from in-service inspection. It is shown that the proposed methodology improves the fatigue life prediction. The number of observations used for updating is found to leave a significant effect on the accuracy of the updated prediction.     

Quantitative methods for structural health management using in situ acoustic emission monitoring

This paper presents an end-to-end approach for structural health management using acoustic emission (AE) monitoring. Three quantitative methods are proposed to utilize the information obtained from in situ AE monitoring to improve structural integrity assessment. Fatigue crack growth tests with real-time acoustic emissions monitoring are conducted on CT specimens made of 7075-T6 aluminum. Proper filtration of the resulting AE signals reveals a log-linear relationship between fracture parameters (e.g. crack growth rate) and select AE features; a flexible statistical model is developed to describe the relationship between these parameters. Bayesian inference is used to estimate the model parameters from experimental data. The model is then used to calculate two important quantities that can be used for structural health management: (a) an AE-based instantaneous damage severity index, and (b) an AE-based estimate of the crack size distribution at a given point in time, assuming a known initial crack size distribution. Finally, recursive Bayesian estimation is used for online integration of the structural health assessment information obtained from AE monitoring, with crack size estimates obtained from empirical crack growth model. The data used in Bayesian updating includes observed crack sizes and/or crack growth rate observations.     

A Bayesian evaluation of simulation models of multiple-site fatigue cracks

The rivet holes along the longitudinal top row of the outer skin of the fuselage over a two-bay length are considered as the independent structural unit for the simulated multiple-site fatigue cracks. Models of multiple-site fatigue cracks are proposed. The models are divided into several phases with some uncertain parameters. These phases are incorporated sequentially into a computer code with the Monte Carlo simulation method. The Bayesian estimation of uncertain parameters in the model can be identified on visual inspections by the Bayesian procedure from in-service inspection data measuring crack lengths of each rivet hole. In summary, this study evaluates effects of differences in the simulation models for the crack coalescence and failure phase for the distribution of inspection data measuring crack lengths with the Bayesian estimation of uncertain parameters from simulated in-service inspection data.     

数据驱动下孪生贝叶斯理论非齐次泊松过程的结构损伤评估方法

以结构件裂纹扩展过程中的损伤状态评估为研究对象,提出了一种孪生贝叶斯理论非齐次泊松过程的结构损伤评估方法.首先,结合基于裂尖场能量的可靠度序化策略与非齐次泊松过程,运用贝叶斯理论对试验信息及总体过程参数的渐进关系进行组合,获得过程参数先验分布.同时,基于裂尖场能量递进因子与似然函数的概念,通过先验信息、序化策略及后验信...     

Fatigue behavior of concrete subjected to biaxial loading in the compression region

Concrete hollow cylinders subjected to combined compression and torsion were used to simulate concrete airport pavements subjected to biaxial fatigue loading in the compression region. It was found that the increase in the compliance in the post-peak period is due to the damage evolution of the specimen. The static failure mechanisms was explained by fracture mechanics. Similar failure was observed in fatigue loading. It was found that with the crack growth as a parameter, the static response acts as an envelope for the fatigue failure response. The rate of the crack growth under fatigue loading follows a two-stage process: a deceleration stage followed by an acceleration stage up to failure. In the deceleration stage, the growth is governed by the R-curve of the specimen. In the acceleration stage, it is governed by the Paris Law. The previously proposed model in the biaxial tension region was extended to the biaxial compression region. In the biaxial compression region, static and fatigue behaviors under pure compressive loading were modelled in terms of inelastic displacement, rather than crack length.     

The effect of crack tunneling on crack growth: experiments and CTOA analyses

This paper compares experimental crack-front shapes recorded at various stages of crack growth with area-average crack growth values during fracture tests conducted on 2024-T351 aluminum alloy plate. Crack-front shapes were determined by fracturing the specimen to a predetermined amount of crack growth and fatigue cycling the specimen for about 4000 cycles at a high stress ratio (P_min/P_max) to mark the crack-front location. For each shape, the area-average crack length was determined. The evolution of tunneling was used to create a calibration curve that could be used to adjust surface measured crack-length values, for a more representative comparison with analyses that use a straight crack-front approximation. The analysis compares much more favorably with the average crack growth than with the surface measured values near maximum load. However, the area-average technique tends to over correct crack growth near the crack initiation load. Crack tunneling results show that the area-average technique produces more representative crack-length measurements compared to optical based surface measurements.     

Effect of small cycles and load spectrum truncation on the fatigue life scatter in 7050 Al alloy

This work examines the effect of dynamic buffet loads (small cycles) on the scatter in the fatigue life of aircraft aluminum. Current life cycle management of fighter airframes assumes, without engineering evidence, that buffet loads cause an increase in the scatter factor used in safe-life calculations. Hence, the role of small cycles in spectra representative of the CF-188 aileron inboard hinge was examined in this study. The base load spectrum with the dynamic content was filtered to remove specified amounts of dynamic damage as determined by the CI89 strain-based cumulative fatigue damage program. The effect of this filtering on the scatter in crack initiation life and total fatigue life of double edge notched fatigue coupons of 7075-T7451 aluminum alloy were examined. The results indicate that inclusion of the dynamic loading caused the distribution of the crack initiation life to become bimodal. Each mode could be described with a log-normal distribution, the standard deviation of which was lower than the standard deviation obtained for the filtered load spectra. There was no evidence that the standard deviation increased with small cycle content, once the true nature of the distribution was taken into account. In fact, the standard deviation associated with the truncated spectrum was considerably larger. The bimodal distribution is positted to be a result of included particles near the surface on the fatigue limit of individual specimens.     

Microstructure-dependent fatigue damage process zone and notch sensitivity index

The development of simulation methods for calculating notch root parameters for purposes of estimating the fatigue life of notched components is a critical aspect of designing against fatigue failures. At present, however, treatment of the notch root stress and plastic strain field gradients, coupled with intrinsic length scales of grains or other material attributes, has yet to be developed. Ultimately, this approach will be necessary to form a predictive basis for notch size effects in forming and propagating microstructurally small cracks in real structural materials and components. In this study, computational micromechanics is used to clarify and distinguish process zone for crack formation and microstructurally small crack growth, relative to scale of notch root radius and spatial extent of stress concentration at the notch. A new nonlocal criterion for the fatigue damage process zone based on the distribution of a shear-based fatigue indicator parameter is proposed and used along with a statistical method to obtain a new microstructure-sensitive fatigue notch factor and associated notch sensitivity index, thereby extending notch sensitivity to explicitly incorporate microstructure sensitivity and attendant size effects via probabilistic arguments. The notch sensitivity values obtained for a range of notch root radii using the new statistical approach presented in this study predict the general trends obtained from experimental results available in literature.     

A novel accumulative fatigue damage model for multiaxial step spectrum considering the variations of loading amplitude and loading path

In this paper, based on the process of the fatigue crack initiation and the critical plane theory, a continuous stress parameter was proposed to quantify the driving force of the fatigue crack initiation for the fully reversed multiaxial fatigue loading. In this stress parameter, the shear stress amplitude and normal stress amplitude on the critical plane were combined with the variable coefficients which were affected by the normalized fatigue life and the loading non‐proportionality. Owing to these coefficients, for the multiaxial loadings with different non‐proportionalities, the driving force of the fatigue crack initiation during the whole life could be described. After that, a novel accumulative fatigue damage model was established for the multiaxial two‐stage step spectrum. In this model, the accumulative damage was calculated according to the variation of the proposed stress parameter on the critical plane. Considering the directionality of the multiaxial fatigue damage, for the spectrum in which the loading path was variable, the damage accumulation was carried out on the critical planes of the both loadings, and the larger one was chosen as the final accumulative fatigue damage. In order to verify the new model, up to 41 different multiaxial two‐stage step spectrum loading tests on 2024‐T4 aluminium alloy were collected. The new model, as well as other five commonly used models, was applied to calculate the accumulative fatigue damage. The final results showed that, compared with other commonly used models, the new model had the most accurate results with the smallest scatters.     

Incorporation of risk and updating in inspection of fatigue-sensitive details of ship structures

Fatigue cracks, as a structural deterioration mechanism, may lead to unanticipated out of service of naval ships. Consequently, risk assessment and effective inspection planning of naval ships under fatigue damage are needed to achieve economic and sustainable performance of these structures. This paper presents a probabilistic framework for fatigue risk and updating assessment and updating through inspection events. The computation associated with fatigue damage is performed using fracture mechanics and uncertainties are considered within this process. Furthermore, a quantitative risk assessment model using rating functions is presented to identify inspection priority among multiple fatigue-sensitive details. Bayesian techniques are adopted for reliability and risk updating of both inspected and uninspected fatigue-sensitive details at component and system levels. Additionally, correlation of fatigue damage among different critical details is considered and incorporated within risk assessment and updating. A number of analyses are performed to investigate the fatigue risk ranking assessment and updating. Applications are presented on an existing tanker with multiple fatigue-sensitive details.     

Fatigue crack initiation and propagation under cyclic contact loading

A computational model for contact fatigue damage analysis of gear teeth flanks is presented in this paper. The model considers the conditions required for the surface fatigue crack initiation and then allows for proper simulation of the fatigue crack propagation that leads to the appearance of small pits on the contact surface. The fatigue process leading to pitting is divided into crack initiation and a crack propagation period.The model for prediction of identification of critical material areas and the number of loading cycles, required for the initial fatigue crack to appear, is based on Coffin-Manson relations between deformations and loading cycles, and comprises characteristic material fatigue parameters. The computational approach is based on continuum mechanics, where a homogenous and elastic material model is assumed and results of cyclic loading conditions are obtained using the finite element method analysis.The short crack theory together with the finite element method is then used for simulation of the fatigue crack growth. The virtual crack extension (VCE) method, implemented in the finite element method, is used for simulating the fatigue crack growth from the initial crack up to the formation of the surface pit. The relationship between the stress intensity factor K and crack length a, which is needed for determination of the required number of loading cycles N_p for a crack propagation from the initial to the critical length, is shown.     

Bridge fatigue assessment and management using reliability-based crack growth and probability of detection models

This paper focuses on conducting lifetime performance assessment and management of aging steel bridges under fatigue by integrating three prediction models: fatigue reliability model (FRM), crack growth model (CGM), and probability of detection (PoD) model. A novel approach using these models is proposed for planning interventions on fatigue sensitive structures. Based on information from field monitoring and/or non-destructive evaluation, prediction models are developed to (a) estimate the time-dependent fatigue performance using FRM, (b) provide the time-dependent crack growth using CGM, and (c) quantify the detection capability associated with fatigue cracks using PoD model. In order to assess and manage bridge fatigue life, the three models are combined based on two parameters (i.e., number of cycles, crack size). As an illustration, the combined approach is used for fatigue assessment and management of an existing bridge.     

An efficient analytical Bayesian method for reliability and system response updating based on Laplace and inverse first-order reliability computations

This paper presents an efficient analytical Bayesian method for reliability and system response updating without using simulations. The method includes additional information such as measurement data via Bayesian modeling to reduce estimation uncertainties. Laplace approximation method is used to evaluate Bayesian posterior distributions analytically. An efficient algorithm based on inverse first-order reliability method is developed to evaluate system responses given a reliability index or confidence interval. Since the proposed method involves no simulations such as Monte Carlo or Markov chain Monte Carlo simulations, the overall computational efficiency improves significantly, particularly for problems with complicated performance functions. A practical fatigue crack propagation problem with experimental data, and a structural scale example are presented for methodology demonstration. The accuracy and computational efficiency of the proposed method are compared with traditional simulation-based methods.     

Damage tolerance approach for analyzing a helicopter main rotor blade

In this article, damage tolerance approach is used for life estimation of the main rotor blade of a helicopter under random loading. At first, fatigue crack growth properties and threshold stress intensity range of the spar is obtained based on ASTM E647 test method. Then, crack growth analysis is done using Zencrack software. In order to calculate the length of the smallest growing cracks and their fatigue crack growth life, no crack growth and slow crack growth approaches were used. A comprehensive investigation was carried out on the effect of initial crack length on growth or no growth of cracks.     

The evolution of short fatigue crack lengths and crack density: two approaches

The density and size of short cracks on the surface of 1Cr18Ni9Ti stainless steel smooth specimens during low cycle fatigue are investigated using a replica technique. The density and size data are analysed from two different observation policies, i.e. Policy I pays attention to the whole specimen test piece and Policy II is related to an ‘effective short fatigue crack criterion’, which pays attention to the dominant crack (DC) initiation zone and the zones ahead of the DC tips. The results reveal that both the crack density and crack size evolution exhibit a specific character during the microstructural short crack (MSC) and physical short crack (PSC) stages. The Policy I‐based observations exhibit an increasing density and little scatter of the density data. The increasing density violates the general test observation of decreasing collective crack effects in the PSC stage. The little scatter is too small to reflect the intrinsic scatter of fatigue properties. Both the crack density and crack size evolution from this policy show little relationship with the intrinsic localization of fatigue damage. However, Policy II‐based observations show an increasing crack density and an increasing density scatter in the MSC stage. The density and scatter reach their maximum values at the transition point between the MSC and PSC stages. Then, they decrease with fatigue cycling in the PSC stage and tend to their saturation values when the DC size is above about 500 μm. This behaviour shows a good agreement with the general test observations of decreasing collective crack effects and growth rate scatter in the PSC stage. Further, both approaches exhibit an evolutionary positively skewed crack size distribution, and an increasing difference between the average crack length and the DC length in the PSC stage, indicative of decreasing collective crack effects. A three‐parameter Weibull distribution (3‐PWD) is appropriately used to describe the crack sizes and a 6.5 to 7.6 μm value of location parameter of the distribution is obtained to reflect a minimum value for the initial cracks. It is worth noting that Policy I‐based observations show an increasing positively skewed crack size distribution, an increasing scatter of the size data and a decreasing shape parameter of the 3‐PWD. This represents an increasing collective crack effect and an increasing irregularity of interactive cracks, which violates the general test observations. In contrast, Policy II‐based observations exhibit a decreasing positively skewed size distribution shape and an increasing (from <1 gradually to >1) shape parameter of the 3‐PWD that is in agreement with the general test observations. The increasing shape parameter indicates that the collective crack effects act as an evolutionary process from an initial non‐ordered (chaotic) random state gradually to an independent random state at the transition point between the MSC and PSC stages and then, to a loading history‐dependent random state. This behaviour is in accordance with the evolutionary DC growth behaviour. Therefore, the evolutionary short crack behaviour associated with the intrinsic localization of fatigue damage should be appropriately revealed from the ‘effective short fatigue crack criterion’‐based observations.     

基于贝叶斯理论的钢筋混凝土柱受剪承载力计算

现行混凝土结构设计规范中钢筋混凝土柱的受剪承载力公式为半经验半理论计算公式,由于试验数据的有限性和钢筋混凝土材料离散性较大的本质特性,规范建议公式缺乏明确的理论模型。该文以贝叶斯动态信息更新思路,根据主观经验信息选定现行规范中钢筋混凝土柱受剪承载力计算公式作为贝叶斯先验模型,通过已完成试验研究的柱受剪承载力数据,应用贝叶斯方法综合这两类信息进行推断,建立钢筋混凝土柱在反复荷载作用下受剪承载力的概率模型,对未知参数进行估计,修正先验模型并建立后验模型,以达到对先验模型的更新。通过先验模型计算值、后验模型计算值及试验值相互间的对比分析可知:贝叶斯方法继承了先验信息的完备性和大量试验数据的准确性,能够更准确地预测钢筋混凝土柱的受剪承载力。     

A RELIABILITY-BASED MODEL TO PREDICT SCATTER IN FATIGUE CRACK NUCLEATION LIFE

This paper investigates the scatter inherent in the early stages of fatigue life. A probabilistic fatigue model is proposed which relates the microstructural heterogeneity to the scatter in crack nucleation life. The crack nucleation life is defined as the number of cycles necessary to develop a crack with a length equal to the grain size. The model assumes homogeneity at the level of the grain size. A fracture mechanics-based microstructural model is used to describe the response of the grains. The primitive random variables which drive crack nucleation are identified and recent developments recorded in the literature are used to describe their statistical characteristics. First order reliability methods are used to predict the statistical distribution of fatigue crack nucleation life. Comparisons are made with trends in experimental observations.     

基于Gibbs抽样的马尔科夫蒙特卡罗方法在结构物理参数识别及损伤定位中的研究

通过对结构动力特征方程进行的一系列变化,得到了线性结构识别模型,并由贝叶斯更新理论得到其后验分布形式.利用结构的模态参数,并考虑其随机性,应用基于Gibbs抽样的马尔科夫蒙特卡罗方法对线性结构识别模型中各参数的条件后验分布进行了抽样,成功地实现了结构物理参数识别及损伤定位.数值算例表明:Gibbs抽样结果可以以不同的方...