金属材料疲劳裂纹扩展曲线的拟合方法研究

提出了一种金属材料疲劳裂纹扩展曲线(a~N曲线)的拟合方法,即修正的双曲函数拟合方法。为检验这种曲线拟合方法的适用性,利用2024-T42铝合金CCT试样的疲劳裂纹扩展试验数据,对该铝合金的疲劳裂纹扩展曲线进行了拟合分析,并给出了疲劳裂纹扩展速率和扩展寿命。通过疲劳裂纹扩展寿命计算结果和试验结果的对比分析,证明这种拟合方法具有较高的拟合精度。     

A statistical model for fatigue crack growth under random loads including retardation effects

A model for the statistical analysis of crack growth under random loading that includes the loading sequence effect is presented. The model defines and incorporates an equivalent closure stress that is included in the fatigue crack growth law via the effective stress intensity factor. The equivalent closure stress for each loading process is obtained from the probability density function of peaks p(S) in the random loading process, the properties of the material and the specimen geometry. The model was applied to the analysis of crack growth life under random loading on sheets of two different aluminum alloys: 2024-T351 and 2219-T851. The crack-growth lifetimes thus obtained were consistent with experimental data and with the results obtained by using a cycle-by-cycle simulation scheme.     

THE EFFECTS OF STRESS RATIO, COMPRESSIVE PEAK STRESS AND MAXIMUM STRESS LEVEL ON FATIGUE BEHAVIOUR OF 2024-T3 ALUMINIUM ALLOY

Abstract— Fatigue crack growth behaviour of 2024-T3 aluminium alloy is investigated as a function of stress ratio, compressive peak stress and maximum stress level. It is found that as the stress ratio and the magnitude of the compressive peak stress are increased, the threshold stress intensity range decreased linearly. Intermediate and near threshold growth rate data are analysed with different formulae for effective stress intensity range. The data covered different values of stress ratio, compressive peak stress and maximum stress level. A formula for the crack opening stress level is introduced as a function of stress ratio, compressive peak stress and maximum stress level. The formula permitted a good correlation between crack growth data for both positive stress ratio and negative compressive peak stress values. Using the new formula, intermediate and near threshold crack growth data for the 2024-T3 aluminium alloy yielded a unique crack growth rate vs effective stress intensity range curve for all stress ratio and compressive peak stress values investigated. This suggests that for the 2024-T3 aluminium alloy the crack growth rate vs effective stress intensity range curve does not depend on stress ratio, compressive peak stress, or maximum stress level. The significance of the new equation and the crack growth rate versus effective stress intensity range curve is that they allow a designer to find crack growth rate vs stress intensity range data for the 2024-T3 aluminium alloy in both intermediate and near threshold regions for the particular stress ratio, compressive peak stress and maximum stress level conditions of the component under investigation.     

A model of fatigue crack growth based on Dugdale model and damage accumulation

The modified Dugdale model given by Budiansky-Hutchinson and a Coffin-Manson type damage law are used to calculate the cumulative fatigue damage of material elements at the tip of a fatigue crack. From this analysis a fatigue crack growth equation is obtained which gives predicted crack growth rates in reasonable agreement with experimental data for two aluminium alloys 7075-T6 and 2024-T81, two titanium alloys Ti-8A1-1Mo-1V and Ti-6A1-6V and a PH13-8Mo stainless steel. Limitations of this new fatigue crack growth model are also discussed.     

Growth characteristics for fatigue cracks embedded in fastener hole walls

A unique method for producing either single or double fatigue cracks embedded in fastener hole walls is described. The method repeatedly produces small semielliptical fatigue cracks and is valuable for basic experimental evaluations dealing with crack growth from fastener holes. Test specimens were prepared from 7075-T651 aluminum alloy plate for collecting constant amplitude embedded crack growth data for open and filled hoies without load transfer. Fractographic data are presented to show crack front shape and growth rates. Crack shape data correlated well with similar data derived from naturally induced embedded cracks. Analytical predictions were made for the same cases evaluated experimentally. Good correlations between the analytical and experimental results were obtained.     

Three-dimensional finite element simulations of mixed-mode stable tearing crack growth experiments

Mixed-mode stable tearing crack growth events in Arcan plate specimens made of aluminum alloy 2024-T3 are simulated using three-dimensional (3D) finite element methods. A modeling/simulation procedure utilizing a mixed-mode CTOD fracture criterion and the custom 3D crack growth simulation software, CRACK3D, with an automatic local re-meshing option is demonstrated. Simulation predictions of the load-crack extension curve and the in-plane curvilinear crack growth path are compared with experimental measurements for various mixed-mode loading cases. Issues such as the effects of near-tip finite element size and crack extension increment size on simulation predictions are investigated.     

A predictive fatigue life model for anodized 7050 aluminium alloy

The objective of this study is to predict fatigue life of anodized 7050 aluminum alloy specimens. In the case of anodized 7050-T7451 alloy, fractographic observations of fatigue tested specimens showed that pickling pits were the predominant sites for crack nucleation and subsequent failure. It has been shown that fatigue failure was favored by the presence of multiple cracks. From these experimental results, a fatigue life predictive model has been developed including multi-site crack consideration, coalescence between neighboring cracks, a short crack growth stage and a long crack propagation stage. In this model, all pickling pits are considered as potential initial flaws from which short cracks could nucleate if stress conditions allow. This model is built from experimental topography measurements of pickled surfaces which allowed to detect the pits and to characterize their sizes (depth, length, width). From depth crack propagation point of view, the pickling pits are considered as stress concentrator during the only short crack growth stage. From surface crack propagation point of view, machining roughness is equally considered as stress concentrator and its influence is taken into account during the all propagation stage. The predictive model results have been compared to experimental fatigue data obtained for anodized 7050-T7451 specimens. Predictions and experimental results are in good agreement.     

Fatigue crack growth in residual stress fields

A fatigue crack growth (FCG) model for specimens with well-characterized residual stress fields has been studied using experimental analysis and finite element (FE) modeling. The residual stress field was obtained using four point bending tests performed on 7050-T7451 aluminum alloy rectangular specimens and consecutively modeled using the FE method. The experimentally obtained residual stress fields were characterized using a digital image correlation technique and a slitting method, and a good agreement between the experimental residual stress fields and the stress field in the FE model was obtained. The FE FCG models were developed using a linear elastic model, a linear elastic model with crack closure and an elastic–plastic model with crack closure. The crack growth in the FE FCG model was predicted using Paris–Erdogan data obtained from the residual stress free samples, using the Harter T-method for interpolating between different baseline crack growth curves, and using the effective stress intensity factor range and stress ratio. The elastic–plastic model with crack closure effects provides results close to the experimental data for the FCG with positive applied stress ratios reproducing the FCG deceleration in the compressive zone of the residual stress field. However, in the case of a negative stress ratio all models with crack closure effects strongly underestimate the FCG rates, in which case a linear elastic model provides the best fit with the experimental data. The results demonstrate that the negative part of the stress cycle with a fully closed crack contributes to the driving force for the FCG and thus should be accounted for in the fatigue life estimates.     

A stochastic model of fatigue crack propagation under variable-amplitude loading

This paper presents a stochastic model of fatigue crack propagation in ductile alloys that are commonly encountered in mechanical structures and machine components of complex systems (e.g. aircraft, spacecraft, ships and submarines, and power plants). The stochastic model is built upon a deterministic state-space model of fatigue crack propagation under variable-amplitude loading. The (non-stationary) statistic of the crack growth process for center-cracked specimens is obtained as a closed form solution of the stochastic differential equations. Model predictions are in agreement with experimental data for specimens fabricated from 2024-T3 and 7075-T6 aluminum alloys and Ti-6Al-4 V alloy subjected to constant-amplitude and variable-amplitude loading, respectively. The stochastic model of crack propagation can be executed in real time on an inexpensive platform such as a Pentium processor.     

Experimental approach to dimple fracture mechanisms under short pulse loading

Dimple fracture mechanisms are discussed for three kinds of aluminum alloys on the basis of an experimental approach and a finite element (FEM) analysis. The void growth and coalescence process was observed by an optical microscope and a scanning electron microscope. The fractographic observation for aluminum alloys 7075-T651 and 6061-T651 showed that several large voids called a dominant void are nucleated at inclusion sites or the second-phase particles ahead of the crack tip and followed by fine voids initiation leading coalescence of the dominant voids with the crack tip. On the other hand, in aluminum alloy 2017-T3, voids are nucleated very close to the crack tip and directly coalesce with the crack tip. FEM computation results suggested that the void nucleation and growth process is closely related to the triaxial stress state ahead of the crack tip.     

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.     

腐蚀环境下2024-T3铝合金疲劳裂纹扩展和剩余强度实验研究

对2024-T3铝合金在5种典型实验室环境和3种组合环境下的疲劳裂纹扩展和剩余强度进行了实验研究.通过实验获得的裂纹扩展数据,对Paris公式进行条件拟合,得到各种环境下的裂纹扩展常数,并作了对比分析.结果表明,腐蚀环境的参与使2024-T3铝合金的疲劳裂纹扩展速率明显加快,不同腐蚀环境对疲劳裂纹扩展速率的影响程度不同,其影响的严重程度由重到轻依次为:油箱结构区、厨房与厕所、油箱积存水、盐水、潮湿空气、高空环境、干燥空气.实验数据还进一步表明,腐蚀介质对临界裂纹长度的影响很小,说明环境对剩余强度能力无直接影响.     

Estimation of the effects of plasticity and resulting crack closure during small fatigue crack growth

On the basis of a plastic-strip model and the method of singular integral equations, a closed-form analytical solution of the problem of an elastic-plastic plate containing a rectilinear fatigue crack is considered. The solution is used for the prediction of fatigue growth of `mechanically-small' crack by accounting for reverse plastic yielding and plasticity-induced crack closure in the material. The main effects of these factors on the crack-growth rate are analyzed, and the predicted results are compared with experimental data on small fatigue-crack growth in a aluminum-lithium alloy 2091-T351 and Fe-3% Si alloy.     

A study of stochastic fatigue crack growth modeling through experimental data

To capture the statistical nature of fatigue crack growth, many stochastic models have been proposed in the literature. These models may have been verified by only one data set, and therefore not appreciated by other fellow researchers. Part of the reason is the difficulty and time-consuming in obtaining the statistically meaningful fatigue crack growth data. In the present study, experimental work is carried out to obtain the fatigue crack growth data of a batch of 2024-T351 aluminum alloy specimens. A rather universal stochastic fatigue crack growth model proposed by Yang and Manning is employed to analyze the data. The solution of the stochastic differential equation associated with the stochastic model gives us the crack exceedance probability as well as the probability of random time to reach a specified crack size. Through comparison between the analytical and experimental results, it is found the model with a minor modification can fit the experimental data rather well. Once the appropriate stochastic model is established, it can be used for the fatigue reliability prediction of structures made of the tested material. In the present study, in particular, it can be used for the reliability assessment of aging aircraft made of 2024-T351 aluminum alloy.     

STRESS STATE-RELATED FATIGUE CRACK GROWTH UNDER SPECTRUM LOADING

Abstract— The fatigue crack growth behaviour in aluminium alloy sheets of 2024-T3 and 7475-T761, subjected to standardized spectra (TWIST and FALSTAFF), was investigated using centre-cracked specimens. A strip crack closure model was used to interpret experimental data, and to make predictions for the crack growth.
The strip model is based on the Dugdale concept, but modified to keep plastically-stretched materials on the crack surface so that the crack opening load can be determined, and the fatigue crack growth can be analysed according to Elber's crack growth assumption. Differing from other models of the same kind, a variable constraint factor was introduced to account for the gradual transition of stress state at the crack tip resulting from the crack growth. It has been shown that the transition of stress state at the crack tip causes the unusual behaviour of the fatigue crack growth in sheets. Both experiments and predictions show that a crack may grow faster at a low load than at a higher one in a certain applied load range due to the crack tip stress state transition. The crack tip stress state also contributes to the thickness effect observed for the crack growth in sheets. In agreement with experimental results, it has been shown that a plane stress state will prevail at the crack tip in a thin sheet compared to that in a thick sheet. The plane stress state results in a higher crack opening level which leads to a longer fatigue life for thin sheets.     

Comparison of the simulation and experimental fatigue crack behaviors in the nanoseconds laser shocked aluminum alloy

This investigation was performed to compare the simulation and experimental results of the fatigue crack growth rates and behaviors of the 7050-T7451 aluminum alloy by nanoseconds laser shock processing (LSP). Forman–Newman–deKoning (FNK) model embedded in the Franc2D/L software was utilized to predict fatigue crack growth rate, which was conducted to weigh the stress intensity factor (SIF) changing on the surface cracks. LSP induced high compressive residual stresses that served to enhance fatigue properties by improving the resistance against fatigue crack initiation and propagation. The circulating times of crack growth obtained from the simulation and experimental values indicated a slower fatigue crack growth rates after LSP. The relationships between the elastic–plastic materials crack growth rates and the SIF changing after LSP are resolved.     

Predicting corner crack fatigue propagation from cold worked holes

We predict the fatigue propagation of corner cracks from cold worked holes using three dimensional finite element models. The models account for the through thickness variation in residual stress left after cold working. The predictions are compared to experimental results in aluminum 2024-T351 and 7075-T651. The models show the evolution of P-shaped crack fronts similar to those observed in experiments. Predictions based on the initial residual stress field left after cold working were nonconservative, predicting either slower than experimental crack growth or crack growth that arrests. Predictions based on an estimate of the stable relaxed residual stress field near the hole were conservative, and predicted 5-10 times greater life than the current Department of Defense reduced initial flaw size approach.     

CRACK CLOSURE IN SMALL FATIGUE CRACKS—A COMPARISON OF FINITE ELEMENT PREDICTIONS WITH IN-SITU SCANNING ELECTRON MICROSCOPE MEASUREMENTS

Abstract— A three dimensional, elastic-plastic, finite element analysis of fatigue crack growth and plasticity-induced crack closure has been performed for a range of small, semi-circular cracks. Predicted crack opening displacements have been compared with data obtained from in-situ SEM measurements for a coarse-grained aluminium alloy 2024-T351. The magnitude of fatigue crack closure measured from in-situ SEM measurements was consistently higher than that predicted from the finite element analysis. It is deduced that the higher closure stresses obtained from in-situ SEM measurements are due to the contact of asperities on the fatigue crack surfaces. A simple mathematical model is suggested to describe the fatigue crack closure stress caused by the combination of both a plastic wake and asperities on the fatigue crack surfaces. The predicted fatigue crack closure stresses and their dependence on crack size are consistent with experimental measurement.     

Microstructurally-dependent model for predicting the kinetics of physically small and long fatigue crack growth

Based on the proposed concept of the fatigue threshold stress intensity factor ranges, a model has been developed that describes the kinetics of physically small fatigue crack and long fatigue crack growth. The model allows the calculation of the crack growth rate under the regular fully-reversed uniaxial loading from the data on the static characteristics of mechanical properties and the microstructure of the initial material. The crack depth at which the cyclic plastic zone size ahead of the crack tip will exceed the grain size should be considered as a criterion of the small-to-long crack transition. Under high-cycle fatigue conditions physically small fatigue crack growth will be divided into two phases of growth: the first phase is when the crack propagates along the slip planes of individual grains, and the second one is when the crack changes the mechanism of growth and propagates in the plane perpendicular to the loading direction. The model validity has been tested using the experimental data on the growth of the long cracks in specimens of titanium alloy VT3-1 in seven microstructural states and the small cracks in specimens of titanium alloy Ti–6Al–4V and aluminum alloy 2024-T3. Good agreement between the calculated and experimental results is obtained.     

Method of analysis and prediction for variable amplitude fatigue crack growth

Fatigue crack growth behavior of structure subjected to variable amplitude loading is very complex. Both the truncation and the load sequence have been shown to have a significant influence on the test results because of the load level interaction effects. To understand these interaction effects and the possible influence they can have on the results obtained a test program was performed. Fatigue crack growth tests were conducted on the program using 7075-T6 and 2024-T3 aluminum and titanium 6A1-4V mill anneal.

Using the test data, an analysis method was developed. In this analysis method the crack growth rate is evaluated for each load cycle using a modification of the fracture mechanics correlation technique. The crack growth for each cycle was evaluated as a function of the stress intensity factor excursion with a correction factor for the maximum and minimum peak stress levels in the test spectrum. The fatigue crack growth correction for the peak stresses in the spectrum is given as a growth rate correction factor r. The relationship for r, is termed the ‘fatigue crack growth rate interaction model’.

For verification, the interaction model was applied to test data from spectrum loading tests. The correlation obtained for the example, indicated that the model properly predicts the interaction effects and its use could significantly improve the accuracy of crack growth life calculations for programmed spectrum tests.