Quadratic damage rule in random loading case

The simple mathematical structure of the quadratic damage rule (QDR) enables mathematical expression of the failure condition in the case of random loading. Random loading after modified rainflow analysis is considered as a random marked point process. Moments of the damage distribution can be expressed by use of ensemble averages. A condition for validity of the first damage moment solution is formulated. The QDR damage first moment solution involves failure predictions for both stationary and non‐stationary loadings. In these cases, final fracture conditions suitable for practical use are derived. QDR predicts fatigue lives that are always shorter than the linear damage rule (LDR) in the case of stationary loading with short interval of statistical dependence of random variables. QDR appears to be a suitable additional engineering tool for random loading fatigue life predictions considering loading sequence and loading level interactions.     

Fatigue damage of medium carbon steel under sequential application of axial and torsional loading

Fatigue tests were conducted on S45C steel under fully reversed strain control conditions with axial/torsional ( at ) and torsional/axial ( ta ) loading sequences. The linear damage value (n₁/N₁+n₂/N₂) was found to depend on the sequence of loading mode ( at or ta ), sequence of strain amplitude (low/high or high/low) and life fraction spent in the first loading. In general, at loading yields larger damage values than ta loading and the low–high sequence of equivalent strain leads to larger damage values than the high–low sequence. The material exhibits cyclic softening under axial cyclic strain. Cyclic hardening occurs in the torsion part of ta loading, which elevates the axial stress in the subsequent loading, causing more damage than in pure axial fatigue at the same strain amplitude. Fatigue life is predicted based on the linear damage rule, the double linear damage rule, the damage curve approach and the plastic work model of Morrow. Results show that overly conservative lives are obtained by these models for at loading while overestimation of life is more likely for ta loading. A modified damage curve method is proposed to account for the load sequence effect, for which predicted lives are found to lie in the factor‐2 scatter band from experimental lives.     

1Cr15Ni4Mo3N不锈钢表面显微硬度演化与疲劳性能研究

目的 研究1Cr15Ni4Mo3N高强不锈钢服役过程中表面硬度演化规律及其疲劳极限。方法 采用疲劳拉伸试样,在应力比为0.1条件下对不锈钢开展0、2 000、10⁴、10⁵、10⁶、5×10⁶、10⁷次循环的疲劳试验,使用显微硬度计测试试件表面显微硬度;采用逐级载荷加载法测试不锈钢疲劳极限并用统计学方法验证试验结果的可靠性;使用扫描电镜观察分析疲劳断口形貌特征。结果 在0~10⁴次循环下,硬度由433.39HV1提高至459.43HV1,当循环至10⁷次时,硬度下降至326.11HV1,试验得到不锈钢疲劳极限为765.7 MPa。断口宏观形貌表明,裂纹源位于试件表面层,断面具备裂纹源区、扩展区、瞬断区3个典型疲劳特征,扩展区表面比较平整,微观下扩展区呈河流状花样向四周放射扩展,伴随有大量二次裂纹发生和少量二相粒子析出,有明显的疲劳辉纹。瞬断区相对粗糙,有大范围等轴韧窝,且韧窝内存在大量二相粒子析出。结论 在疲劳加载过程中,低循环周期表现为循环硬化,高循环周期表现为循环软化。疲劳极限统计结果具有可靠性。在不锈钢塑性变形时,第二相粒子周围出现裂纹形成微孔并不断扩大聚集最终导致韧性断裂。     

A high-cycle fatigue accumulation model based on electrical resistance for structural steels

For high-cycle fatigue of metals, the DC electrical resistance is a more sensitive parameter to the initiation of micro-cracks during the irreversible fatigue damage accumulation process. This implies that the electrical resistance is a suitable parameter that can be consistent with the fatigue damage physical mechanism. The relation between the ratio of electrical resistance changes and the cyclic fraction of the fatigue specimen may reasonably represent deterioration in mechanical properties of structural steels during the high-cycle fatigue process. The high-cycle fatigue damage accumulation model based on electrical resistance for structural steels was proposed. The model was verified by some experimental data for three structural steels; normalized 45C steel, 20 Mn steel and 16 Mn steel, and good agreement was obtained. The corresponding fatigue lifetime on the basis of the electrical resistance model was also performed. The results show that the approach to fatigue lifetime prediction and failure based on the electrical resistance is a good non-destructive technique.     

A critical plane-strain energy density criterion for multiaxial low-cycle fatigue life under non-proportional loading

A series of multiaxial low-cycle fatigue experiments was performed on 45 steel under non-proportional loading. The present evaluations of multiaxial low-cycle fatigue life were systematically analysed. A combined energy density and critical plane concept is proposed that considers different failure mechanisms for a shear-type failure and a tensile-type failure, and from which different damage parameters for the critical plane-strain energy density are proposed. For tensile-type failures in material 45 steel and shear-type failures in material 42CrMo steel, the new damage parameters permit a good prediction for multiaxial low-cycle fatigue failure under non-proportional loading. The currently used critical plane models are a special and simple form of the new model.     

考虑电阻率变化的电阻法预测金属材料剩余寿命

 推导了考虑电阻率变化的用电阻表征的损伤变量公式,并对不考虑电阻率变化的均匀损伤和考虑电阻率变化的不均匀损伤两种模型进行了比较,结果表明电阻的预测值与实验数据相符合.并讨论了损伤对金属材料电阻率的影响.给出了金属材料疲劳损伤的剩余寿命预测公式.     

Fatigue life estimation under random loading using the energy criterion

A procedure for estimating the useful life of a component for a given (admissable) probability of fatigue fracture origination under random loading is presented. The method uses material constants obtained from the S/N and cyclic stress/strain curves, standard deviation and probability density distribution of the loading process and a macroblock of harmonic cycles obtained by applying the rainflow cycle counting method to the random loading process. Theoretical and experimental lives are found to exhibit good agreement.     

Cumulative fatigue damage dynamic interference statistical model

After studying in depth the statistical characteristics of cumulative fatigue damage D(t) and its critical value D_c, a new dynamic interference statistical model for fatigue reliability analysis is presented in this paper. Because the non-linearity of fatigue damage accumulation has been taken into account, this model is able to predict the fatigue reliability for random spectrum loading. To verify the predicted results, two fatigue experiments were conducted in which the numbers of specimens were more than 100, using fighter spectrum loading (FALSTAFF spectrum) and constant-amplitude loading respectively. It is shown that the new model is reliable, practicable and better than existing models.     

A fracture mechanics analysis on the fatigue behaviour of cruciform joints of duplex stainless steel

The paper presents the results of an experimental and numerical study on the fatigue behaviour of cruciform load carrying joints made from the duplex stainless steel and failing from the weld root through the weld metal. Fatigue crack growth (FCG) data, obtained in specimens of the weld metal, are presented, as well as threshold data, both obtained for R= 0 and 0.5. The influence of stress ratio is discussed, and the FCGR results are compared with data for low carbon structural steels. S–N data were obtained in the joints, both for R= 0.05 and 0.5, and the fatigue cracking mechanisms were analysed in detail with the SEM. It was found that the cracks propagated very early in the lifetime of the joints, under mixed mode conditions (I + II), but the mode I component was found to be predominant over mode II. The geometries of the cracks were defined in detail from measurements taken in the fracture surfaces. A 2D FE analysis was carried out for the mixed mode inclined cracks obtained at the weld root, and the J‐integral formulations were obtained as a function of crack length and crack propagation angle. The values of the crack propagation angle, θ_i, were obtained for the J_max conditions, and it was found that, in the fatigue tests, the cracks propagated in directions very close to the predicted directions of maximum J. K_I and K_II formulations were obtained, and the K_I data were compared with the formulations given in the PD6493 (BS7910) document, and some differences were found. A more general formulation for K under mixed mode conditions was derived. The derived K solutions were applied to predict the fatigue lives of the joints under crack propagation, and an extremely good agreement was found with the experimental results obtained in the fatigue tests.     

船体结构疲劳寿命的评估

船舶事故分析表明，疲劳破坏是其结构破坏的主要形式。由于船体中节点的多样性以及节点荷载的复杂性，使得船体结构的疲劳校核计算也相当复杂，所以工程中提出了一些简化方法。介绍了船体结构疲劳强度校核的基本原理，疲劳载荷和疲劳累积损伤计算方法；编写了船体结构疲劳强度校核程序，并用其评估了大型油轮(VLCC)在典型节点处的疲劳寿命。     

渗碳Cr-Ni高强硬度合金钢超高周疲劳寿命预测

为了给渗碳合金钢提供一种有效可行的超高周疲劳寿命预测方法,在应力比为0和0.3两种情况下,对渗碳Cr-Ni高强硬度合金钢展开疲劳试验研究.通过对试样断口的微观组织观测,发现渗碳层与基体材料中均有非金属夹杂的存在;通过对裂纹萌生位置和疲劳断口形貌的观察,将疲劳失效分为带有细晶粒区(Fine Granular Area,F...     

Fatigue analysis of offshore platforms subject to sea wave loadings

The fatigue damage calculation for random loading on offshore platforms takes the form of a rainflow analysis of the dynamic response of individual members to various sea states. This procedure is lengthu and consequently this paper attempts to provide a theoretical method for determining random load fatigue damage. This dynamic response for many joints leads to a broad band random loading but despite this, previous theoretical methods have simplified the loading to narrow band. This has not been done in the present case; instead, an analysis based on broad band random loading has been produced. This theoretical approach gives a fatigue life estimate which is slightly (6.6%) more conservative, for a typical example, than a rainflow analysis.     

On the application of the stochastic approach in predicting fatigue reliability using Miner's damage rule

The present paper investigates the application of the stochastic approach when the commonly adopted Miner's linear damage rule is implemented, both in its traditional and modified forms to include the presence of a random stress threshold (random fatigue limit), below which the rate of damage accumulation is reduced. Main steps are provided to obtain the simulated distribution of the accumulated damage under variable amplitude loading. When the stochastic approach is applied in the presence of a random fatigue limit, an additional correlation structure, which takes into account the fatigue limit value, must be introduced in the analysis. If the number of cycles to failure under constant amplitude loading is Weibull (Log‐Normal) distributed, then the corresponding accumulated damage is Fréchet (Log‐Normal) distributed. The effects of the correlation structure on reliability prediction under variable amplitude loading are also investigated. To this aim, several experimental datasets are taken from the literature, covering various metallic materials and variable amplitude block sequences. The results show that the choice of the damage accumulation model is a key factor to value the improvement in the accuracy of reliability predictions introduced by the stochastic approach. Comparison of the predicted number of cycles to failure with experimental data shows that larger errors are non‐conservative, regardless of the adopted correlation structure. When the analysis is limited to reliability levels above 80%, for these large non‐conservative errors, it is the quantile approach to be closer to actual experimental data, thus limiting the overestimation of component's life. For the experimental datasets considered in the paper, adoption of a stochastic approach would improve the accuracy of Miner's predictions in 10% of cases.     

A curvilinear integral method for multiaxial fatigue life computing under non-proportional, arbitrary or random stressing

Some popular concepts for reducing three variable stress components σ_x(t), σ_y(t), τ_xy(t) to one equivalent amplitude spectrum, and the use of the linear damage accumulation hypothesis, have been evaluated as not fully correct when these components vary non-proportionally and arbitrarily. A different approach is suggested: computing damage accumulation by means of an integral directly on the non-radial arbitrary path, called the ‘trajectory’, described in the σ_x−σ_y plane when τ_xy(t) = 0, in the σ_x−τ_xy plane when σ_y(t) = 0, or in a special coordinate space where this trajectory is invariant of stress directions x, y. If the trajectory is random, it may be replaced by a statistical two-dimensional density of distribution. The integrand, called the R-function, is derived from various S−N fatigue curves under different determined loadings. Thus the traditional S−N function is replaced by the R-function for direct damage summation with differential analysis, which allows the loading to be arbitrary (non-cyclic, multiaxial and non-proportional). The method works by means of computer programs and is applicable to real structures.     

Two-stage fatigue loading of woven carbon fibre reinforced laminates

A brief review of the models used to predict the cumulative fatigue damage in FRP composites is presented. Two‐stage fatigue loading of a [0/90,± 45₂,0/90]_s quasi‐ isotropic woven carbon fibre/epoxy resin laminate was evaluated at stress ratio R = 0.05 and the failure mechanisms investigated using x‐radiography after each loading stage. The results are presented in terms of fatigue strength and damage growth and are compared with those in the literature. A low‐to‐high loading sequence is more damaging than a high‐to‐low one and the Palmgren‐Miner linear damage rule may no longer be valid for this kind of material, as previously reported.     

Life prediction for fatigue of T800/5245 carbob-fibre composites: II. Variable-amplitude loading

This is the second of two papers describing the fatigue response of a [(±45,0₂)₂]_s laminate of the T800/5245 composite system, a modern aerospace material consisting of high-failure-strain, intermediate-modulus carbon fibres in a toughened bismaleimide resin system. In the first paper, the fatigue response in repeated tension, repeated compression, and mixed tension-compression was determined at constant stress levels over a wide range of R values. The results of those constant-amplitude experiments were then used to define a programme of four- and two-block variable-loading experiments in an attempt to derive predictive methods for such loading conditions. Formulae have been developed to predict life under non-linear cumulative damage conditions and empirical data derived to validate the procedures.     

A stochastic theory of cumulative fatigue damage

A Stochastic theory for the cumulative fatigue damage of structural component with random fatigue strength under random loading is proposed on the basis of the 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 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 metallic and some nonmetallic materials, to both narrow band and wide band stress process, and can be adapted to a sequence of n stationary stress process or quasi-stationary stress process. The scatter and degradation of fatigue strength can also be incorporated into the theory.