Study on the accumulative fatigue damage rules under multiaxial two‐stage step spectra constructed by loadings with similar lives

In this paper, the influence on the multiaxial fatigue damage accumulation caused by loading path variation was studied. For 2024‐T4 aluminium alloy, the damage evolution during the entire life was first observed. On the basis of the observation, the stage I of fatigue damage evolution was further divided into two sub‐stages, and the dominant stress parameters of these two sub‐stages were proposed. Taking the dominant stress parameters into account, a phased accumulative fatigue damage model was proposed. Then, 12 multiaxial two‐stage step spectra constructed by loadings with approximately identical fatigue lives were carried out on 2024‐T4 aluminium alloy. The accumulative fatigue damage was calculated by the proposed model, and another five commonly used models and the calculated results were compared. According to the comparison, the newly proposed model had the most accurate results with the smallest scatter.     

A general regression model for lifetime evaluation and prediction

A particular form of a probabilistic model for materials under fatigue which embodies Weibull features and the size effect in a weakest-link framework is derived. The parametric and functional form of the model arises from a certain set of assumptions, as the weakest-link principle, stability, limit behavior, limited range and compatibility, which can be justified as being consistent with experimental features of fatigue (mainly of highly drawn steel wires) and the mathematics of extreme value theory. These assumptions, which are discussed, can be used to rule out other possible forms as being fundamentally inconsistent. The authors also discuss estimation procedures for the parameters based on two steps: a non-linear regression step, in which the threshold lifetime and stress range values are determined, and a second step in which the Weibull parameters are estimated by pooling data from different stress levels and using a probability-weighted moments approach or the Castillo-Hadi estimators. Next, the damage accumulation problem is dealt with and two different proposals for the damage index are given. The model, originally developed to handle a fixed load parameter (such as the stress range in cyclic fatigue), is extended to handle a block load sequence involving many load levels, as well as random load programs. Some formulas for calculating the accumulated damage index for constant, block and random loading are given. Finally, the model and methods are applied to a particular fatigue program on concrete to illustrate all concepts and the practical use of formulas.     

A NOTE ON MODELLING SHORT FATIGUE CRACK BEHAVIOUR

Based upon experimental short fatigue crack growth data and adopting the Brown–Hobson model, new crack growth equations have been derived in an attempt to describe more precisely short fatigue crack growth behaviour that separates the physically small crack regime from the long crack regime. An empirical model for physically small crack growth was developed by employing elastic–plastic fracture mechanics parameters.
By considering the proposed approach to short fatigue crack modelling, a new second 'microstructural' threshold condition has been established using only short fatigue crack growth data. In the case of fatigue in an aggressive environment it is suggested that three transition (threshold) conditions can be identified representing: (i) a stress-assisted pitting/pit-to-crack transition; (ii) a microstructurally short shear crack/physically small tensile crack transition; and (iii) a physically small crack/long crack transition.
A comparison of this approach with that of existing models has been made, and predictions of total fatigue lifetime using the model have been presented. A reasonable agreement has been observed between predicted and experimental crack growth rates.     

A comparative study of fatigue estimation methods for single‐spot and multispot welds

Fatigue life and load data of spot‐welded samples were obtained by performing tensile‐shear fatigue tests on single‐spot‐welded samples, and by collecting published data on tensile‐shear fatigue tests of multispot‐welded samples. Finite element models of the spot‐welded samples were then constructed, and their accuracy was validated by comparing their results with those of static loading tests. Methods to estimate fatigue in spot‐welded joints proposed by Sheppard, Rupp, and Swellam were used to predict the fatigue life of each sample, and their results were compared. The sensitivity of each method to spot‐welding parameters, as well as the arrangement and number of welded spots, was analyzed to obtain their scope of applicability. Finally, the Sheppard and Rupp methods were used to obtain fitted fatigue curves of each spot‐welded sample, and the equivalent life method was used to generate P‐S‐N curves of the single‐spot‐ and multispot‐welded samples. This method can serve as a useful reference for fatigue reliability analyses of mechanical parts with spot‐welded joints.     

Parameter uncertainty effects on variance-based sensitivity analysis

In the past several years there has been considerable commercial and academic interest in methods for variance-based sensitivity analysis. The industrial focus is motivated by the importance of attributing variance contributions to input factors. A more complete understanding of these relationships enables companies to achieve goals related to quality, safety and asset utilization. In a number of applications, it is possible to distinguish between two types of input variables—regressive variables and model parameters. Regressive variables are those that can be influenced by process design or by a control strategy. With model parameters, there are typically no opportunities to directly influence their variability. In this paper, we propose a new method to perform sensitivity analysis through a partitioning of the input variables into these two groupings: regressive variables and model parameters. A sequential analysis is proposed, where first an sensitivity analysis is performed with respect to the regressive variables. In the second step, the uncertainty effects arising from the model parameters are included. This strategy can be quite useful in understanding process variability and in developing strategies to reduce overall variability. When this method is used for nonlinear models which are linear in the parameters, analytical solutions can be utilized. In the more general case of models that are nonlinear in both the regressive variables and the parameters, either first order approximations can be used, or numerically intensive methods must be used.     

Improved test method and analytical modelling for fatigue crack growth in coarse‐grain titanium alloy with rough fatigue surfaces

Fatigue crack growth rate properties are typically determined by experimental methods in accordance with ASTM Standard E647. These traditional methods use standard notched specimens that are precracked under cyclic tensile loads before the main test. The data that are produced using this approach have been demonstrated elsewhere to be potentially adversely affected by the test method, particularly in the threshold region where load reduction (LR) methods are also required. Coarse‐grained materials that exhibit rough and tortuous fatigue surfaces have been observed to be strongly affected by the tensile precracking and LR, in part because the anomalies caused by crack closure and roughness‐induced closure become more important. The focus of the work reported in this paper was to further develop methods to determine more accurate fatigue crack growth rate properties from threshold through to fracture for coarse‐grained, β‐annealed, titanium alloy Ti‐6Al‐4V extra low interstitial thick plate material. A particular emphasis was put upon the threshold and near threshold region, which is of strong importance in the overall fatigue life of components. New approaches that differ from the ASTM Standard included compression precracking, LR starting from a lower load level and continuing the test beyond rates where crack growth would otherwise be considered below threshold. For the threshold regime, two LR methods were also investigated: the ASTM method and a method where the load is reduced with crack growth such that the crack mouth opening displacement is held constant, in an attempt to avoid remote closure. Constant amplitude fatigue crack growth rate data were produced from threshold to fracture for the titanium alloy at a variety of stress ratios. Spike overload tests were also conducted These data were then used to develop an improved analytical model to predict crack growth under spectrum loading and the predictions were found to correlate well with test results.     

Evaluation of the Fatemi‐Socie damage parameter for the fatigue life calculation with application of the Chaboche plasticity model

This paper presents an approach to the evaluation of the Fatemi‐Socie parameter applied to the lifetime calculation of specimens made of CuZn37 brass. In particular, two factors affecting the calculated fatigue lives are analysed: (i) the influence of stresses calculated by applying the Chaboche plasticity model on the computed lifetime and (ii) the influence of a variability of parameter k of material sensitivity to normal stress on the calculated lifetime. The novelty of the presented research is associated with the fatigue life calculation according to the Fatemi‐Socie model with the introduced k dependence accounting for the lifetime. Underestimation of the calculated stresses results in the higher calculated fatigue lives but with acceptable scatter band. The parameter of material sensitivity to normal stress for the CuZn37 brass varies insignificantly having little impact on the calculated fatigue lives.     

Optimal Design of Step‐stress Accelerated Degradation Test with Multiple Stresses and Multiple Degradation Measures

Products with high reliability and long lifetimes undergo different types of stresses in use conditions. Often there are multiple performance indicators for products that gradually degrade over time. An accelerated degradation test (ADT) with multiple stresses and multiple degradation measures (MSMDM) may provide a more accurate prediction of the lifetime of these products. However, the ADT requires a moderate sample size, which is not practical for newly developed or costly products with only a few available test specimens on hand. Therefore, in this study, a step‐stress ADT (SSADT) with MSMDM is developed. However, it is a difficult endeavor to design SSADT with MSMDM to predict accurate reliability estimation under several constraints. Previous methods are used only for cases with a single stress or degradation measure, and are not suitable for SSADT with MSMDM. In this paper, an approach of optimal design is proposed for SSADT with MSMDM and its steps for a rubber sealed O‐ring are demonstrated to illustrate its validity. Results of the sensitivity analysis for the optimal test plan indicate robustness when the deviation of model parameters is within 10% of the estimated values. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

Non‐destructive evaluation of fatigue damage and fatigue crack initiation in type 316 stainless steel by positron annihilation line‐shape and lifetime analyses

Rotating bending fatigue tests were conducted using type 316 stainless steel. The fatigue tests were periodically terminated, and fatigue damage and fatigue crack initiation were non‐destructively and sequentially evaluated by positron annihilation line‐shape and lifetime analyses. The counter‐jig and anticoincidence methods were used for positron annihilation line‐shape and lifetime analyses, respectively, to enhance the analytical precision. The fatigue crack lengths were monitored by a plastic replication technique, and related to the parameters in both analyses. S‐parameter obtained in the line‐shape analysis increased with increasing fatigue damage, while it was difficult to detect fatigue crack initiation and subsequent small fatigue crack growth. That was because the precision of line‐shape analysis was limited. On the other hand, both fatigue damage and fatigue crack initiation were successfully detected by lifetime analysis. Positron annihilation lifetime also increased with increasing fatigue damage, and lifetime was longer at the notch root with fatigue crack than at the smooth section without crack. It was considered that the precision of lifetime analysis was high enough to detect high dislocation density areas at the fatigue crack tips.     

Condition‐based Maintenance Optimization Using Neural Network‐based Health Condition Prediction

Artificial neural network (ANN)‐based methods have been extensively investigated for equipment health condition prediction. However, effective condition‐based maintenance (CBM) optimization methods utilizing ANN prediction information are currently not available due to two key challenges: (i) ANN prediction models typically only give a single remaining life prediction value, and it is hard to quantify the uncertainty associated with the predicted value; (ii) simulation methods are generally used for evaluating the cost of the CBM policies, while more accurate and efficient numerical methods are not available, which is critical for performing CBM optimization. In this paper, we propose a CBM optimization approach based on ANN remaining life prediction information, in which the above‐mentioned key challenges are addressed. The CBM policy is defined by a failure probability threshold value. The remaining life prediction uncertainty is estimated based on ANN lifetime prediction errors on the test set during the ANN training and testing processes. A numerical method is developed to evaluate the cost of the proposed CBM policy more accurately and efficiently. Optimization can be performed to find the optimal failure probability threshold value corresponding to the lowest maintenance cost. The effectiveness of the proposed CBM approach is demonstrated using two simulated degradation data sets and a real‐world condition monitoring data set collected from pump bearings. The proposed approach is also compared with benchmark maintenance policies and is found to outperform the benchmark policies. The proposed CBM approach can also be adapted to utilize information obtained using other prognostics methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Reliability assessment of high‐quality and long‐life products based on zero‐failure data

For a period of mission time, only zero‐failure data can be obtained for high‐quality long‐life products. In the case of zero‐failure data reliability assessment, the point estimates and confidence interval estimates of distribution parameters cannot be obtained simultaneously by the current reliability assessment models, and the credibility of the assessment results may be reduced if they are obtained at the same time. A new model is proposed for consistency problem in this paper. In the proposed model, the point estimates of reliability can be obtained by the lifetime probability distribution derived from matching distribution curve method, while the confidence interval estimates of reliability can be obtained by using new samples generated from the lifetime probability distribution according to parameter bootstrap method. By analyzing the zero‐failure data of the torque motors after real operation, the results show that the new model not only meets the requirements of reliability assessment but also improves the accuracy of reliability interval estimation.     

Reliability inference for VGA adapter from dual suppliers based on contaminated type‐I interval‐censored data

Type‐I interval‐censoring scheme only documents the number of failed units within two prespecified consecutive exam times at the larger time point after putting all units on test at the initial time schedule. It is challenging to use the collected information from type‐I interval‐censoring scheme to evaluate the reliability of unit when not all admitted units are operated or tested at the same initial time and a majority of units are randomly selected to replace the failed test units at unrecorded time points. Moreover, the lifetime distribution of all pooled units from dual resources usually follows a mixture distribution. To overcome these two problems, a two‐stage inference process that consists of a data‐cleaning step and a parameter estimation step via either Markov chain Monte Carlo (MCMC) algorithm or profile likelihood method is proposed based on the contaminated type‐I interval‐censored sample from a mixture distribution with unknown proportion. An extensive simulation study is conducted under the mixture smallest extreme value distributions to evaluate the performance of the proposed method for a case study. Finally, the proposed methods are applied to the mixture lifetime distribution modeling of video graphics array adapters for the support of reliability decision.     

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.     

A unified fractal approach for the interpretation of the anomalous scaling laws in fatigue and comparison with existing models

In this paper, a critical reexamination of the fractal models for the analysis of crack-size effects in fatigue is proposed. The enhanced ability to detect and measure very short cracks has in fact pointed out the so-called anomalous behavior of short cracks with respect to their longer counterparts. The crack-size dependencies of both the fatigue threshold and the Paris’ constant C are only two notable examples of these anomalous scaling laws. In this context, a unified theoretical model seems to be missing and the behavior of short cracks can still be considered as an open problem. A new generalized theory based on fractal geometry is herein proposed, which permits to consistently interpret the short crack-related anomalous scaling laws within a unified theoretical framework. The proposed model is used to interpret relevant experimental data related to the crack-size dependence of the fatigue threshold in metals. As a main result, the model gives an explanation to the experimentally observed variability in the slope of the asymptote of the scaling law for the fatigue threshold in the short crack regime.     

Damage mechanics based probabilistic high‐cycle fatigue life prediction for Al 2024‐T3 using non‐intrusive polynomial chaos

This paper proposes a low‐cost method for predicting probabilistic high‐cycle fatigue life for Al 2024‐T3 based on continuum damage mechanics and non‐intrusive polynomial chaos (NIPC). To randomize Lemaitre's two scale fatigue damage model, parameters S and s are regarded as random variables. Based on small sample of test life, inverse analysis is performed to obtain samples of the two parameters. Statistic characteristics of the two parameters are calculated analytically through coefficients of NIPC. Fatigue test of aluminum alloy 2024‐T3 standard coupon and plate with hole under different spectrum loading shows that the proposed method is effective.     

随机荷载作用下参数不确定结构的疲劳损伤估计

基于改进区间分析和频域疲劳计算方法,对参数不确定结构在平稳高斯荷载作用下的疲劳损伤进行研究,提出完全混合和简化计算两种方法。采用区间变量模型定义结构的不确定参数,功率谱密度描述外荷载的随机性;利用有理级数显式表示结构区间频响函数及在平稳高斯荷载作用下不确定结构的应力响应区间。通过数值方法验证疲劳损伤期望率关于不确定参数的单调性后,将应力响应中不确定参数的界限完全组合提出完全混合方法,准确估计参数不确定结构的疲劳损伤期望率区间;简化计算方法则将不确定参数的界限适当组合,由显式表达式近似计算结构的疲劳损伤期望率区间。算例表明,两种方法均具有较高计算精度,且大幅减少计算量。     

Probabilistic cumulative damage model to estimate fatigue life

This paper introduces a numerical model to estimate fatigue life under step‐stress conditions, using the Weibull and lognormal distributions. The maximum likelihood method was used to estimate the free parameters of the distributions. The model was fitted to an experimental data on fatigue life in the specimens of steel SAE 8620, by using evolutionary computation to optimize the likelihood function. Results are reported on the values of the parameters and their confidence interval. Also, a validation of the model is discussed using analysis of residuals.