Fatigue reliability evaluation using probability density evolution method

Probability density evolution method is extended to analysis of fatigue reliability. The joint probability density evolution equation of random parameters and fatigue damage is derived based on the principle of preservation of probability, and a finite difference algorithm in terms of TVD theory is presented. For a given damage threshold, cycle-dependent fatigue reliability can be calculated by the proposed method without assuming the probabilistic distribution of fatigue damage in advance. Two validation examples indicate that the proposed method is able to give reasonable results for constant-amplitude loading and variable-amplitude loading. The predicted fatigue reliability under constant-amplitude loading shows a considerable accuracy. In addition, reliability isolines of fatigue damage can be used to predict the fatigue life with a specified failure probability.     

Fatigue life prediction under variable loading based on a new damage model

To examine the performance of nonlinear models proposed in the estimation of fatigue damage and fatigue life of components under random loading, a batch of specimens made of 6082 T 6 aluminium alloy has been studied and some of the results are reported in the present paper. The paper describes an algorithm and suggests a fatigue cumulative damage model, especially when random loading is considered. This paper contains the results of mono-axial random load fatigue tests with different mean and amplitude values performed on 6082 T 6 aluminium alloy specimens. Cycles were counted with rainflow algorithm and damage was cumulated with a new model proposed in this paper and with the Palmgren–Miner model. The proposed model has been formulated to take into account the damage evolution at different load levels and it allows the effect of the loading sequence to be included by means of a recurrence formula derived for multilevel loading, considering complex load sequences. It is concluded that a ‘damaged stress interaction damage rule’ proposed here allows a better fatigue damage prediction than the widely used Palmgren–Miner rule, and a formula derived in random fatigue could be used to predict the fatigue damage and fatigue lifetime very easily. The results obtained by the model are compared with the experimental results and those calculated by the most fatigue damage model used in fatigue (Miner’s model). The comparison shows that the proposed model, presents a good estimation of the experimental results. Moreover, the error is minimized in comparison to the Miner’s model.     

混凝土双轴拉压、三轴拉压压变幅疲劳性能研究

利用大型多轴疲劳试验机,进行了拉压双轴和拉压压三轴荷载作用下混凝土两级、三级变幅疲劳试验研究,重点分析了残余应变的变化规律。试验结果表明:混凝土在拉压和拉压压加载工况下的残余应变主要与相对疲劳次数和侧压应力比有关,基本不受加载历程因素的影响。定义相对残余应变为损伤变量,建立了损伤演变方程,并进行了疲劳损伤分析和剩余疲劳寿命预测,为混凝土在多轴变幅疲劳试验研究及疲劳损伤评价提供参考。     

混凝土三轴变幅拉-压疲劳性能试验研究

进行了最小应力水平为0.20fc,最大应力水平为0.20ft~0.55ft,定侧压为0.30fc的变截面混凝土试件三轴拉-压等幅和变幅疲劳试验,分析了混凝土三轴拉-压疲劳最大和最小纵向总应变的三阶段演变规律和级间相似性,给出了疲劳损伤演化规律。进一步验证了Miner线性损伤累积理论的不适用性,提出了非线性损伤累积模型,并进行了疲劳剩余寿命预测,通过与试验结果的比较表明该模型具有较高的精度和适用性。     

Fatigue life under variable-amplitude loading according to the cycle-counting and spectral methods

We compare the values for the fatigue life of 12010.3 steel determined experimentally under variable-amplitude tension-compression and calculated by two methods in time and frequency ranges. The first method is based on the schematization of the loading history and uses the rainflow algorithm. The fatigue life was calculated according to the Serensen-Kogaev linear hypothesis of damage accumulation wit the use of the Manson-Coffin dependence. The second method is based on power spectral density functions. These methods differ in the approaches used for the determination of the probability density of amplitude distribution from the deformation history. It is established that, in the case considered, the values of fatigue life calculated by the cycle-counting method and by the spectral method are close to the values determined experimentally. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 3, pp. 121–128, May–June, 2006.     

Multiaxial fatigue life assessment of welded structures

Welded structures, such as welded pressure vessel components subjected to multiaxial cyclic loading, are particularly susceptible to fatigue damage. In this paper, a new path-length-based effective stress range is proposed to assess the fatigue life of weld joints under multiaxial fatigue loading. The path-length measure, a function of both normal and shear components on a critical crack plane, has a solid root in classic fracture mechanics and its application is validated by correlating nominal fatigue data including pure-bending, pure-torsion, in-phase, and out-of-phase loading. Path-Dependent Maximum Range (PDMR), a unique general-purpose fatigue life assessment package for multiaxial variable-amplitude loading, is introduced in this paper. Finally, the application of PDMR to multiaxial fatigue life assessment of complex loading cases is also discussed.     

BIMODAL CONCEPT OF HIGH-CYCLE FATIGUE LIFE PREDICTION FOR CONSTANT AND VARIABLE AMPLITUDE FATIGUE

A bimodal concept for the prediction of the high-cycle fatigue life of structural details subjected to constant- or variable-amplitude loading is considered in this paper. The total fatigue life was separated into two phases: crack initiation and crack propagation. The portion of life spent in crack initiation was estimated by using S–N data obtained on smooth specimens. A fracture mechanics concept was used to calculate the portion of life spent in crack propagation, and the S–N curve, including the fatigue limit of a structural detail, was determined by using material properties and the geometry of the detail. The bimodal concept was applied to a welded stiffener and the results are compared with experimental data reported in the literature.     

A fatigue damage model of composite materials

The mechanical properties of composite materials degrade progressively with the increasing of the number of cyclic loadings. Based on the stiffness degradation rule of composites, a phenomenological fatigue damage model is presented in this paper, which contains two material parameters. They are proportional to the fatigue life of materials and inversely proportional to the fatigue loading level. Thirteen sets of experimental data of composite stiffness degradation were employed to verify the presented model, and the statistical results showed that this model is capable of describing the damage evolution of composite materials. The characteristics of damage development and accumulation of composite materials subjected to variable loading were studied in this paper. Four sets of two-level loading experimental data were cited to verify the damage model, and the results showed that the predicted life is in good agreement with the experimental ones.     

Residual life, linear fatigue damage accumulation and optimal stopping

An optimal stopping procedure is proposed for the operation of a component subjected to constant-amplitude cyclic loading. Prediction of a residual life distribution is based on the successive re-estimation of the density function of a component life only by raising the density curve. As in the case of Miner's rule, damage accumulation is assumed to be linear, with a simple treatment using a random variable that gives the explicit interpretation of a probability space in terms of fatigue failures of components under cyclic loading. The cost of stopping is given as a sequence of the random variables which are the costs of losses per unit time in consequence of possible stopping at every inspection period or failure. It is shown that the optimal stopping problem may be solved in the class of monotonic cases. The inferred decision rule has a very simple structure, and its other possible usages are discussed. Throughout the paper the idea of close interconnection between damage accumulation and decision rules is traced for the problem of optimal operation of a component in which a degradation process is developing.     

Multiaxial fatigue life prediction method based on path‐dependent cycle counting under tension/torsion random loading

A path‐dependent cycle counting method is proposed by applying the distance formula between two points on the tension‐shear equivalent strain plane for the identified half‐cycles first. The Shang–Wang multiaxial fatigue damage model for an identified half‐cycle and Miner's linear accumulation damage rule are used to calculate cumulative fatigue damage. Therefore, a multiaxial fatigue life prediction procedure is presented to predict conveniently fatigue life under a given tension and torsion random loading time history. The proposed method is evaluated by experimental data from tests on cylindrical thin‐walled tubes specimens of En15R steel subjected to combined tension/torsion random loading, and the prediction results of the proposed method are compared with those of the Wang–Brown method. The results showed that both methods provided satisfactory prediction.     

An experimental approach to estimate damage and remaining life of metals under uniaxial fatigue loading

An experimental procedure to estimate damage evolution and remaining fatigue life of metals associated with fatigue loading is presented. Experimental phase involves uniaxial tension–compression fatigue tests performed with solid API 5L X52 and tubular carbon steel 1018 specimens subjected to both constant and variable amplitude loading. A correlation between the so-called damage parameter and the thermal response of a material at different damage levels is proposed. Results demonstrate that the correlation can estimate damage evolution with reasonable accuracy in both constant and variable amplitude fatigue processes. It is shown that under the conditions tested the evolution of damage parameter with respect to the normalized fatigue life is independent of the load amplitude, load ratio, loading sequence, material properties, and specimen geometry. The proposed correlation and the relationship between the damage parameter and the normalized fatigue life are employed to develop a non-destructive method to predict the remaining fatigue life of metallic specimens with prior fatigue damage. The method is applied to both constant and variable amplitude loading and the predicted results are found to be in good agreement with those obtained from the experiments.     

The influence of mode mixity and adhesive system on the fatigue life of adhesive joints

In real applications, adhesive joints are commonly subjected to fatigue and mixed mode loading conditions. The aim of the current work is to experimentally analyse the influence of mode mixity on the fatigue strength of joints with an epoxy‐based adhesive. Different adhesive systems (acrylic and epoxies) were considered for pure mode I fatigue loading conditions. To achieve this, Arcan joints with an epoxy adhesive were manufactured and tested at different mode mixities. Based on stiffness degradation, monitored during the tests, damage evolution was calculated for different loading conditions and for all the tested adhesives. Finally, fatigue envelopes were constructed for different fatigue life regimes. Results show that a shear loading component reduces both the static strength and fatigue life of the joints. A small reduction rate of the stiffness was found throughout the most part of the life until a sudden drop was observed, indicating a smooth damage evolution.     

Fatigue of welded steel joints under wideband loadings

Fatigue tests were conducted on high-strength welded steel cruciform-shaped specimens subjected to random loadings to investigate the effects of loading intensity, nonnormality and frequency bandwidth on the rate of fatigue damage accumulation. The test result are compared with predictions made using the Rayleigh approximation and rainflow analysis in terms of cycles and times to failure. Results indicate that nonnormality can significantly increase the rate of fatigue damage accumulation and result in nonconservative fatigue life estimates if it is effect is not accounted for properly. Likewise, frequency content was also found to influence the rate of fatigue damage accumulation, but to a lesser extent than nonnormality.     

An improved neural computing method for describing the scatter of S–N curves

The reliability evaluation of structural components under random loading is affected by several uncertainties. Proper statistical tools should be used to manage the large amount of causalities and the lack of knowledge on the actual reliability-affecting parameters. For fatigue reliability prediction of a structural component, the probability distribution of material fatigue resistance should be determined, given that the scatter of loading spectra is known and a suitable damage cumulating model is chosen. In the randomness of fatigue resistance of a material, constant amplitude fatigue test results show that at any stress level the fatigue life is a random variable. In this instance fatigue life is affected by a variety of influential factors, such as stress amplitude, mean stress, notch factor, temperature, etc. Therefore a hybrid neural computing method was proposed for describing the fatigue data trends and the statistical scatter of fatigue life under constant loading conditions for an arbitrary set of influential factors. To support the main idea, two examples are presented. It can be concluded that the improved neural computing method is suitable for describing the fatigue data trends and the scatter of fatigue life under constant loading conditions for an arbitrary set of influential factors, once the optimal neural network is designed and trained.     

Fatigue crack growth with overloads/underloads: Interaction effects and surface roughness

The generalization of damage tolerance to variable amplitude fatigue is of prime importance in order to maintain the reliability of structures and mechanical components subjected to severe loading conditions. Engineering spectra usually contain overloads and underloads which distribution may not be random. However for predicting the life of a structure, a simplified spectrum is usually determined from the real one, in order to reduce testing periods on prototypes. Therefore it is thus important to know which cycles can contribute to crack growth and which can be neglected. This paper presents an analysis of fatigue crack growth on M (T) specimens made of a medium carbon steel DIN Ck45. The specimens are subjected to repeated blocks of cycles made up of one or several (1, 2, 6 or 10) overloads (or underloads) separated by a variable number (10, 1000 or 10 000) of baseline cycles. The main objective of this study is to better understand the mechanisms at the origin of interactions effects due to the presence of overloads (or underloads) at different locations of each block loading. Under constant amplitude loading, single variables ΔK and K_max are required in crack growth relationships. The transferability of fatigue laws, obtained under constant amplitude loading to variable amplitude fatigue, requires at least an additional variable, whose evolution with crack length accounts for the interactions effects between cycles of different types. Results have shown that the interaction effects in fatigue crack growth are closely related to the mechanisms of crack growth: cyclic plastic behaviour of the material and fracture surface roughness. Measurements of roughness of the surface fracture were carried out in both constant amplitude and variable amplitude tests. The roughness characterization helped to determine the importance of the mechanisms on variable amplitude fatigue crack growth and determine the influence of overloads/underloads on fatigue crack growth.     

Fatigue crack growth in fibre metal laminates under selective variable-amplitude loading

To extend the predictive capability of existing crack growth models for fibre metal laminates under constant amplitude fatigue loading to variable-amplitude loading, further research on variable-amplitude fatigue mechanisms in fibre metal laminates is necessary. In response to this need, an experimental study into the effects of multiple overloads, underloads and various block-loading sequences on crack growth in the fibre metal laminate Glare was investigated. Crack growth retardation effects were observed in the tests; however, the magnitude of these effects was lower than seen in monolithic aluminium because of fibre bridging. As a result, predictions of the observed behaviour were attempted using an existing constant-amplitude fatigue crack growth model for Glare in combination with a linear damage accumulation law.     

Multiaxial fatigue and life prediction of elastomeric components

Elastomeric components have wide usage in many industries. The typical service loading for most of these components is variable amplitude and multiaxial. In this study a general methodology for life prediction of elastomeric components under these typical loading conditions was developed and illustrated for a passenger vehicle cradle mount. Crack initiation life prediction was performed using different damage criteria. The methodology was validated with component testing under different loading conditions including constant and variable amplitude in-phase and out-of-phase axial–torsion experiments. The optimum method for crack initiation life prediction for complex multiaxial variable amplitude loading was found to be a critical plane approach based on maximum normal strain plane and damage quantification by cracking energy density on that plane. Rainflow cycle counting method and Miner’s linear damage rule were used for predicting fatigue life under variable amplitude loadings. The fracture mechanics approach was used for total fatigue life prediction of the component based on specimen crack growth data and FE simulation results. Total fatigue life prediction results showed good agreement with experiments for all of the loading conditions considered.     

Crack propagation of CCT foam specimen under low strain rate fatigue

The objective of this study is to investigate the effect of holes on the low strain rate fatigue properties of the nickel foam material and to understand the lifetime of this material which is subjected to the repeated loads. Failures of foam materials under single and repeated loads analogous to fatigue are essential to designers and users in military and aerospace structures. The material failure induced by repeated low strain rate loading becomes a critical issue because of significant loss of stiffness and compressive strength in the foam material. Testing methods to study low strain rate (that is, strain rate) fatigue are quite numerous; no single standard testing procedure is defined for studying the low strain rate fatigue property of a material. The increasing application of foam material in aerospace structures, owing to high specific stiffness and strength has attracted a great concern about the high sensitivity to low strain rate damage introduced during manufacture or in service, and the effects of such damage on structural degradation. To investigate this issue, this study sets up an experimental procedure to determine the low strain rate fatigue properties of nickel foam material. This study performs both experimental and numerical investigations to catch the low strain rate fatigue behavior of nickel foam with open-cell type. The experiments are conducted by rod up and down at the strain rate fatigue of loading. The crack length at the specific cycles are measured experimentally by taking pictures with a paper ruler attached on the surface of specimen and these values are apply to the computer simulations as crack seam model. The simulation result of stress intensity factors are compared with a well known theoretical calculation. Design life and probability of failure or survival at specified life can be calculated so that the fatigue life of nickel core material subjected to repeated low strain rate loading is predicted.