Multiaxial fatigue reliability analysis of railroad wheels

A general methodology for fatigue reliability degradation of railroad wheels is proposed in this paper. Both fatigue crack initiation and crack propagation life are included in the proposed methodology using previously developed multiaxial fatigue models by the same authors. A response surface method in conjunction with design of experiments is used to develop a closed form approximation of the fatigue damage accumulation with respect to the input random variables. The total fatigue life of railroad wheels under stochastic loading is simulated, accounting for the spatial and temporal randomness of the fatigue damage. The field observations of railroad wheel fatigue failures are compared with the numerical predictions using the proposed methodology.     

有限板共线多孔MSD疲劳裂纹扩展有限元模拟

介绍了二维断裂分析有限元软件FRANC2D/L在疲劳裂纹扩展模拟方面的基本步骤．利用该软件对有限板中心孔边对称裂纹的疲劳裂纹扩展进行模拟计算,对比模拟结果和试验数据,发现两者吻合良好,证明了利用该方法模拟疲劳裂纹扩展的可靠性．将FRANC2D/L应用到有限板共线多孔MSD疲劳裂纹扩展的有限元模拟上,得到了各孔边裂纹的长度和疲劳扩展寿命之间的关系曲线．模拟计算结果表明,在相同条件下,有限板中心孔边对称裂纹的裂纹扩展寿命要远远高于MSD结构中中心孔边裂纹的疲劳扩展寿命;由于MSD结构中影响各孔边裂纹的因素有所差异,各条裂纹的疲劳扩展寿命也会有所不同．另外,还给出了不含主裂纹的MSD和含主裂纹的MSD两种情况下的疲劳裂纹扩展历程,通过比较得知,含主裂纹的MSD结构更容易发生裂纹的合并和贯穿致使结构发生破坏．     

A probabilistic-based airframe integrity management model

This paper proposes a lognormal distribution model to relate crack-length distribution to fatigue damage accumulated in aging airframes. The fatigue damage is expressed as fatigue life expended (FLE) and is calculated using the strain-life method and Miner's rule. A two-stage Bayesian updating procedure is constructed to determine the unknown parameters in the proposed semi-empirical model of crack length versus FLE. At the first stage of the Bayesian updating, the crack closure model is used to simulate the crack growth based upon generic but uncertain physical properties. The simulated crack-growth results are then used as data to update the uninformative prior distributions of the unknown parameters of the proposed semi-empirical model. At the second stage of the Bayesian updating, the crack-length data collected from field inspections are used as evidence to further update the posteriors from the first stage of the Bayesian updating. Two approaches are proposed to build the crack-length distribution for the fleet based on individual posterior crack distribution of each aircraft. The proposed distribution model of the crack length can be used to analyze the reliability of aging airframes by predicting, for instance, the probability that a crack will reach an unacceptable length after additional flight hours.     

Three‐dimensional fatigue crack growth modelling in a helical gear using extended finite element method

In this paper, the fatigue crack growth in helical gear tooth root has been simulated using linear elastic fracture mechanics. The extended finite element method has been used to simulate 3D fatigue crack growth and obtain growth path. Paris equation has been used to calculate the fatigue life of the gear. The modelling time has reduced considerably compared to previous works carried out on 3D crack growth in gears. Some verifications have been carried out to ensure the reliability of the results.     

Circumferential inner fatigue crack growth and penetration behaviour in pipe subjected to a bending moment

Surface defects in most pipe components under cyclic stress tend to be origins of fatigue crack growth, which may cause serious failure of the whole structure. An analysis of crack growth and penetration behaviour from these defects may therefore be one of the most important subjects on the reliability of the LBB (leak before break) design philosophy. However, studies on fatigue crack growth and COD (crack opening displacement) behaviour in a complex through-wall crack are relatively rare. To that purpose, a series of fatigue tests has been carried out at room temperature on carbon steel pipe which has an inner surface crack. Before crack penetration, leak-life, fatigue crack growth behaviour, e.g. aspect ratios and d a /d N versus Δ K were evaluated successfully by using a proposed plate model. After crack penetration, a new formula to evaluate K is proposed. For the complex crack created after through-wall penetration, fatigue life and fatigue crack growth behaviour were evaluated quantitatively by using the new formula and the model proposed in this study.     

考虑结构裂纹扩展的振动疲劳寿命计算方法

工程实践中任何结构都存在不同程度的裂纹损伤,振动激励下动响应与疲劳裂纹扩展之间互相耦合,直接影响结构振动疲劳寿命.为了考虑结构振动疲劳耦合效应对疲劳寿命的影响,提出了一种考虑结构裂纹扩展的振动疲劳寿命计算方法.分析时,通过建立若干个含不同长度裂纹的结构有限元模型模拟结构裂纹扩展,采用Paris方程分段计算结构振动疲劳裂纹扩展寿命,通过试验确定的固有频率降变化规律反推结构裂纹萌生寿命,最后累计得到结构疲劳总寿命.结论表明,仿真计算结果与试验结果比较吻合.     

Fatigue life prediction for boom structure of concrete pump truck

Frequent premature fatigue failure of construction machinery has spurred the demand for fatigue life prediction of such equipment. In this study, fatigue cracks were investigated in a concrete pump truck boom typically a high-strength steel plate welded box girder structure. The focus was two-tip corner cracks which frequently initiate at the weld toe between the top flange plate and the web plate because these are commonly observed in the field. A fatigue crack growth numerical approach for three-dimensional shell problems was proposed to simulate fatigue crack growth in cracked structures. Fatigue experiments were performed on a full-scale cracked boom to validate the effectiveness of this approach. The influence of the initial crack length was examined using the proposed approach. Numerical results revealed that variation in the initial crack length can affect the remaining fatigue life. For engineering convenience, an interpolation method was employed to determine the remaining fatigue life of a cracked boom with an arbitrary initial crack length. The comparisons between interpolation and numerical results demonstrate that the interpolation method can be used to guide repair decisions with reasonable precision.     

Fatigue crack initiation assessment of welded joints accounting for residual stress

The impact of residual stresses on the fatigue crack initiation life of welded joints is evaluated by the finite element method. The residual stresses of nonload‐carrying cruciform joints, induced by welding and ultrasonic impact treatment, are modelled by initial stresses, using the linear superposition principle. An alternative approach of using modified stress‐strain curves in the highly stressed zone is also proposed to account for the residual stress effect on the local stress‐strain history. An evaluation of the fatigue crack initiation life of welded joints based on the local strain approach is carried out. The predicted results show the effect of residual stresses and agree well with published experimental results of as‐welded and ultrasonic impact treated specimens, demonstrating the applicability of both approaches. The proposed approaches may provide effective tools to evaluate the residual stress effect on the fatigue crack initiation life of welded joints.     

A study of fatigue crack growth from artificial corrosion pits at welded joints under complex stress fields

The paper studies the effects of artificial corrosion pits and complex stress fields on the fatigue crack growth of full penetration load‐carrying fillet cruciform welded joints with 45° inclined angle. Parameters of fatigue crack growth rate of welded joints are obtained from S‐N curves under different levels of corrosion. A numerical method is used to simulate fatigue crack growth using different mixed mode fatigue crack growth criteria. Using polynomial regression, the crack shape correction factor of welded joints is fitted as a function of crack depth ratios. Because the maximum circumferential stress criterion is simple and easy to use in practice, fatigue crack growth rate is modified using this criterion. The relationship of effective stress intensity factor, crack growth angle and crack depth is studied under different corrosion levels. The simulated crack growth path obtained from the numerical method is compared with the actual crack growth path observed by fatigue tests. The results show that fatigue cracks do not initiate at the edge or bottom of pits but at the weld toes where the maximum stress occurs. The artificial corrosion pits have little effect on the effective stress intensity factor ranges and crack growth angle. The fatigue crack growth rates of welded joints with pits 1 and 2 are 1.15 times and 1.40 times larger than that of the welded joint with no pit, respectively. The simulated crack growth path agrees well with the actual one. The fatigue life prediction accuracy using the modified formulation is improved by about 18%. The crack shape correction factor obtained using the maximum circumferential stress criterion is recommended being used to calculate fatigue life.     

钢桥面板纵肋与横隔板焊接细节表面缺陷及疲劳效应研究

初始焊接缺陷是影响结构件疲劳性能的关键因素之一。在断裂力学评估框架下引入特征化初始焊接缺陷,结合相互作用积分法与复合断裂准则解决由表面缺陷所导致的复合型疲劳裂纹扩展问题,在此基础上编写裂纹扩展模拟程序,建立表面焊接缺陷效应评价方法,通过分析揭示了不同形态和尺度的初始焊接缺陷对于钢桥面板纵肋与横隔板构造细节裂纹扩展关键性度量指标和疲劳寿命预测的影响。结果表明:所建立的方法可有效用于评估焊趾部位表面焊接缺陷对于疲劳性能的效应;面状缺陷对于裂纹扩展度量指标和疲劳寿命预测结果的影响更为显著,其初始缺陷深度和形态均是影响疲劳性能的关键因素,体积型缺陷对于疲劳寿命的影响主要由深度方向的缺陷尺寸决定;焊接缺陷的形态和几何参数取值应根据工程实际和规范建议值共同确定,直接简化为面状缺陷会低估结构件的疲劳寿命;考虑焊接缺陷不确定性的可靠度评估方法尚需进一步研究。     

钢箱梁桥焊接细节的疲劳断裂可靠性分析

联合线弹性断裂力学和长期监测数据提出了大跨桥梁焊接细节疲劳可靠度评估方法, 并以润扬大桥钢箱梁的焊接细节为对象开展了应用研究。首先, 采用长期监测数据建立了疲劳荷载效应的概率模型;其次, 推导了焊接细节疲劳断裂抗力的表达式, 分析了初始裂纹深度和极限裂纹深度对断裂抗力的影响规律, 采用随机数值模拟的方法得到了断裂抗力的概率模型;最后研究了交通荷载增长条件下焊接细节疲劳可靠度的时变规律。研究表明:断裂抗力服从对数正态分布, 且对初始裂纹深度极为敏感;当考虑交通荷载增长, 桥梁的服役期还未满设计基准期时, 焊接细节的可靠度就将低于目标可靠度水平。     

Curvilinear fatigue crack reliability analysis by stochastic boundary element method

In this paper, the stochastic boundary element method, which combines the mixed boundary integral equations method explored in Reference 1 with the first-order reliability method, is developed to study probabilistic fatigue crack growth. Due to the high degree of complexity and non-linearity of the response, direct differentiation coupied with the response-surface method is employed to determine the response gradient. Three random processes, the mode I and mode II. stress intensity factors and the crack direction angle, are included in the expression of the response gradient. The sensitivity of these random processes is determined using a first-order response model. An iteration scheme based on the HL-RF method² is applied to locate the most probable failure point on the limit-state surface. The accuracy and efficiency of the stochastic boundary element method are evaluated by comparing the cumulative distribution function of the fatigue life obtained with Monte Carlo simulation. The reliability index and the corresponding probability of failure are calculated for a fatigue crack growth problem with randomness in the crack geometry, defect geometry, fatigue parameters and external loads. The response sensitivity of each primary random variable at the design point is determined to show its role in the fatigue failure. The variation of each primary random variable at the design point with the change of probability of failure is also presented in numerical examples.     

DFR based fatigue reliability assessment of riveted lap joint accounting for correlations

The objective of this paper is to analyse the effect of correlation on the fatigue reliability of a riveted lap joint with multiple rivets using a fast reliability assessment approach based on the detail fatigue rating method. The detail fatigue rating method, DFR method, is based on the nominal stress fatigue approach. The DFR represents the inherent characteristic of fatigue capacity of a structure independent from the applied fatigue load. The fatigue reliability assessment model of a structure is proposed based on the relations of fatigue loading, characteristic fatigue life and DFR. The upper and lower bounds of fatigue reliability of a riveted lap joint structure with multiple rivets subjected to fatigue loading is analysed using the DFR and Ditlevsen approaches accounting for the correlations between rivet holes failures.     

Modeling of fatigue crack propagation using dual boundary element method and Gaussian Monte Carlo method

This paper studies the modeling of fatigue crack propagation on a multiple crack site of a finite plate using deterministic and probabilistic methods. Stress intensity factor has been calculated by the combined deterministic approach of the dual boundary element method (DBEM) and the probabilistic approach of the Gaussian Monte Carlo method. The Gaussian Monte Carlo method has been incorporated to simulate the random process of the fatigue crack propagation. A finite plate of aluminum alloy 2024-T3 with a thickness of 1.6 mm and 14 holes is analyzed and the fatigue life of the plate is predicted by following a linear elastic law of fracture mechanics. The results of fatigue life predicted by DBEM-Monte Carlo method are in good agreement with experimental ones. The same approach is also applied to two other engineering applications of a gear tooth and a bracket.     

Reliability assessment of structures based upon probabilistic fracture mechanics

The stochastic fatigue crack growth model (termed the Tsurui-Ishikawa model) based upon the Markov approximation method introducing the notion of death point has been proposed, and a great deal of its practical usefulness in the reliability assessment of structures has been demonstrated for those cases where the fatigue crack propagation process plays a crucial role toward their failure. By performing the reliability analysis, based upon the model, in consideration of uncertainties of both initial crack length and their number, the effect of such uncertainties has been clarified on the reliability degradation of a structural component. This result is of much interest from a practical viewpoint because it gives a guideline to determine the safe life (design life or inspection interval) to assure the prescribed level of reliability for random loadings with a variety of correlation times. Further, studies have been made on which parameter is the most significant according to the problem through parameter sensitivity study. With the aid of the proposed model, reliability assurance or reliability-based design can be performed properly against fatigue failure of structures subjected to random loading.     

基于模态频率的缺口梁疲劳裂纹扩展寿命预测

从试验出发,研究了含V型缺口悬臂梁在循环载荷作用下的疲劳裂纹扩展特性及其模态频率变化规律,分析了模态频率与裂纹扩展增量间的关联性。将裂纹扩展增量作为损伤参量,建立了基于模态频率下降率与损伤参量的关系。基于损伤力学,建立了裂纹损伤与循环加载次数的演化模型。结合模态频率下降率与裂纹损伤参量的关系,提出了一种基于模态频率下降率的缺口梁疲劳裂纹扩展寿命预测方法,实现了基于当前裂纹损伤和对应循环次数的疲劳裂纹扩展剩余寿命预测。结果表明,模态频率下降率对缺口梁的疲劳裂纹扩展寿命敏感,该方法预测的疲劳裂纹扩展寿命与实测的疲劳裂纹扩展寿命基本吻合。     

A crack propagation criterion based on ΔCTOD measured with 2D‐digital image correlation technique

The fatigue cracks growth rate of a forged HSLA steel (AISI 4130) was investigated using thin single edge notch tensile specimen to simulate the crack development on a diesel train crankshafts. The effect of load ratio, R, was investigated at room temperature. Fatigue fracture surfaces were examined by scanning electron microscopy. An approach based on the crack tip opening displacement range (ΔCTOD) was proposed as fatigue crack propagation criterion. ΔCTOD measurements were carried out using 2D‐digital image correlation techniques. J‐integral values were estimated using ΔCTOD. Under test conditions investigated, it was found that the use of ΔCTOD as a fatigue crack growth driving force parameter is relevant and could describe the crack propagation behaviour, under different load ratio R.     

Fatigue crack nucleation and growth in filled natural rubber

Rubber components subjected to fluctuating loads often fail due to nucleation and the growth of defects or cracks. The prevention of such failures depends upon an understanding of the mechanics underlying the failure process. This investigation explores the nucleation and growth of cracks in filled natural rubber. Both fatigue macro‐crack nucleation as well as fatigue crack growth experiments were conducted using simple tension and planar tension specimens, respectively. Crack nucleation as well as crack growth life prediction analysis approaches were used to correlate the experimental data. Several aspects of the fatigue process, such as failure mode and the effects of R ratio (minimum strain) on fatigue life, are also discussed. It is shown that a small positive R ratio can have a significant beneficial effect on fatigue life and crack growth rate, particularly at low strain range.     

EIFS-based crack growth fatigue life prediction of pitting-corroded test specimens

Corrosive environment causes corrosion pits at material surface and reduces the fatigue strength significantly. Fatigue crack usually initiates at and propagates from these locations. In this paper, a general methodology for fatigue life prediction for corroded specimens is proposed. The proposed methodology combines an asymptotic stress intensity factor solution and a power law corrosion pit growth function for fatigue life prediction of corroded specimens. First, a previously developed asymptotic interpolation method is proposed to calculate the stress intensity factor (SIF) for the crack at notch roots. Next, a growing semi-circular notch is assumed to exist on the specimen’s surface under corrosive environments. The notch growth rate is different under different corrosion conditions and is assumed to be a power function. Fatigue life can be predicted using the crack growth analysis assuming a crack propagating from the notch root. Plasticity correction is included into the proposed methodology for medium-to-low cycle fatigue analysis. The proposed methodology is validated using experimental fatigue life testing data of aluminum alloys and steels. Very good agreement is observed between experimental observations and model predictions.     

基于开裂能密度及裂纹扩展特性的橡胶隔振器疲劳特性预测

基于开裂能密度的连续介质力学参数及橡胶材料裂纹扩展特性(裂纹扩展速率与撕裂能之关系),获得橡胶部件多轴疲劳特性计算公式,并计算某汽车动力总成橡胶隔振器的疲劳特性。计算与试验对比表明,橡胶隔振器疲劳特性预测(寿命、开裂位置及开裂方向)与实测较一致。预测疲劳寿命分布在实测疲劳寿命的1/2倍分散因子内,满足工程疲劳寿命预测要求。提出的橡胶隔振器多轴疲劳特性预测方法,可用试验效率较高、投入较少的材料裂纹扩展试验代替耗时较多的材料疲劳破坏试验,不仅能为橡胶部件前期疲劳设计提供参考,亦能大幅缩短产品疲劳设计周期。