Strain-life Models Research Articles

Strain-based running-reliability characterisation in time-domain for risk monitoring under various load conditions

This aim of this paper is to characterise the strain-based fatigue life data in time-domain using the newly modelled running-reliability technique that considers the load sequence effect. Current established conventional strain life models do not consider dependence for fatigue life of low or high amplitudes, on which with occur first in the load history. Finite element analysis is carried out to ensure the strain signals are captured at the most critical region during road test at various conditions. Fatigue life of 2.74 × 104 to 6.07 × 105 cycle/block with mean cycle to failure of 4.32 × 106 to 7.00 × 106 cycle/block is predicted based on the cycle sequence effect using cycle-counting method. The newly modelled running-reliability technique is formulated to extract the features of high amplitude excitation obtained from the strain signals for characterising the fatigue reliability features under load sequence effect. Hence, the reliability-hazard relationship for fatigue reliability characterisation of strain-based approach in time-domain using running-reliability technique.

Fatigue Life Modelling of Steel Suspension Coil Springs Based on Wavelet Vibration Features Using Neuro-Fuzzy Methods

This study proposed wavelet-based approaches to characterise random vibration road excitations for durability prediction of coil springs. Conventional strain-life approaches require long computational time, while the accuracy of the vibration fatigue methods is unsatisfactory. It is therefore a necessity to establish an accurate fatigue life prediction model based on vibrational features. Wavelet-based methods were applied to determine the low-frequency energy and multifractality of road excitations. Strain-life models were applied for fatigue life evaluation from strain histories. ANFIS modelling was subsequently adopted to associate the vibration features with the fatigue life of coil springs. Results showed that the proposed wavelet-based methods were effective to determine the signal energy and multifractality of vibration signals. The established vibration-based models showed good fatigue life conservativity with a data survivability of more than 90%. The highest Pearson coefficient of 0.955 associated with the lowest RMSE of 0.660 was obtained by the Morrow-based model. It is suggested that the low-frequency energy and multifractality of the vibration signals can be used as fatigue-related features in life predictions of coil springs under random loading. Finally, the proposed model is an acceptable fatigue life prediction method based on vibration features, and it can reduce the dependency on strain data measurement.

Fatigue Reliability Characterisation of Effective Strain Damage Model Using Extreme Value Distribution for Road Load Conditions

The aim of this paper is to characterise the fatigue reliability for various random strain loads under extreme value distribution while considering the cycle sequence effect condition in fatigue life prediction. The established strain-life models, i.e., Morrow and Smith-Watson-Topper, considered a mean stress effect and strain amplitude; nevertheless, it excluded the load sequence effect, which involves the fatigue crack closure that is subjected to overload or underload. A FESEM-EDX analysis is conducted to characterise the failure features that occurred on the leaf spring. A finite element is simulated to determine the critical region in order to obtain the strain load behaviour. In addition, the strain signal is captured experimentally at 500 Hz for 100 s under operating conditions for three different road loads based on the critical location obtained from the finite element analysis. The fatigue life correlation shows that the Pearson correlation coefficients are greater than 0.9, which indicates the effective strain damage model is linearly correlated with the strain-life models. The fatigue life data are modelled using extreme value distribution by considering the random strain loads as extreme data. The reliability rate for the fatigue life is reported to be more than 0.59 within the hazard rate range of 9.6 × 10-8 to 1.2 × 10-7 based on the mean cycle to the failure point. Hence, the effective strain damage model is proposed for a fatigue reliability assessment under extreme conditions with higher reliability and provides fatigue life prediction when subjected to cycle sequence effects.

On the need to evaluate the probabilistic of fatigue life assessment of random strain loading considering load sequence effects

This study presents a probabilistic method of fatigue life assessment for random strain signals that consider the effect of load cycle sequences. The Effective-Strain-Damage (ESD) model was utilised to calculate the fatigue life of coil spring. The probabilistic approach was used to evaluate the reliability properties of the fatigue life data, indicating that the ESD model estimated lower fatigue life than conventional strain-life models as the load sequence effect encouraged rapid crack propagation. Furthermore, a lower mean-cycle-to-failure (McTF) of 4.53 × 104 blocks to failure was estimated from the ESD-based fatigue life, as it was 7.5–8.1% lower than the McTFs computed from the fatigue life predicted by other models. The results indicated that the coil springs had lower fatigue reliability when the load cycle sequence was included. The McTF can be used as a representation of the reasonable service cycle of the coil spring since the uncertainties of the random loading were considered. Finally, this approach suggested a more appropriate assessment of the life cycle of coil springs subjected to random loading conditions with many uncertainties.

An improved strain-life model based on the Walker equation to describe tensile and compressive mean stress effects

Strain-life models that include Walker-like products can reproduce the higher mean stress effects in fatigue crack initiation observed in high-strength materials. These models are able to improve Smith-Watson-Topper’s strain-life predictions, at the cost of additional data-fitting exponents. This work reviews and compares several such models using 34 metallic alloy data sets from the literature that include non-zero mean stresses, totaling 1,355 uniaxial fatigue specimens. This comprehensive evaluation suggests that two different calibrations of Walker’s exponent are required to properly fit data measured under tensile and compressive mean stresses. Hence, an equivalent strain amplitude is proposed based on these two exponents, as well as on the ratio between the stress peak and amplitude. The new strain-life model resulting from this equivalent strain amplitude is able to describe uniaxial fatigue data under all stress ratios R < 1. Estimates for both exponents are provided as a function of the ultimate tensile strength of the material, which could be used in the absence of fatigue data under non-zero mean stresses, an asset for practical applications. A modified version of the proposed strain-life model, which considers mean stress effects only in the elastic damage term, is evaluated as well. Explicit equations are presented for the optimal calibration of all parameters from both models.

Low-cycle fatigue modelling supported by strain energy density-based Huffman model considering the variability of dislocation density

The fatigue crack initiation and propagation phases have been widely studied by the scientific community. There are several models to describe low-cycle fatigue behaviour based on strain damage criteria, but the most widely used is the Coffin-Manson-Morrow relationship, normally used for the fatigue crack initiation modelling. In addition, strain-life models based on hardness measurements and monotonic properties of metals have also been suggested. There are also integrated fatigue models that describe both the fatigue crack initiation and propagation phases, such as the UniGrow, Huffman, Peeker, among others, where the concept of successive crack re-initializations (increments) based on local approaches is adopted. In this paper, the low-cycle fatigue modelling based on Huffman approach using the strain energy density and considering dislocations density is investigated and discussed. For this, various methodologies to evaluating low-cycle fatigue strength based on Huffman approach and exploring different dislocation density parameters are suggested: (i) critical dislocation density driven by the highest strain amplitude; (ii) the mean value of the dislocation density of the available experimental fatigue data and, (iii) Monte Carlo (MC) stochastic prediction considering the variability of dislocation density and the cyclic strain hardening coefficient. Besides, the Monte Carlo stochastic simulations for obtaining the strain-life parameters, fatigue strength and ductility coefficients, it allows the generation of probabilistic fields for the low-cycle fatigue behaviour of metals. In this research, the experimental fatigue data of 1050, 6061-T651, and AlMgSi0.8 aluminium alloys are used to apply the suggested methodologies. A comparison between the experimental fatigue data and strain-life curves based on various suggested methodologies is made.

Acceptability of the effective strain damage model for fatigue life assessment considering the load sequence effect for automotive coil spring

This paper aims to assess the effective strain damage (ESD) model with a durability analysis of an automobile coil spring under consideration of the load sequence effect. Conventional strain-life models such as Coffin-Manson, Morrow and Smith-Watson-Topper are insufficient in predicting fatigue life under the consideration of the load sequence effect. Strain time histories of coil springs were captured based on three types of road conditions: highway, campus and industrial roads. In order to determine the fatigue life, the ESD and conventional strain-life models were employed. The strain-life models predicted lower fatigue life values for campus and industrial roads, which contained many high amplitude events. Similar fatigue life predictions for ESD and conventional strain-life models were found on the highway due to the absence of high amplitude events, which led to a minimal load sequence effect. The suitability of the ESD model was verified through the Weibull probability plot, in which the ESD model fitted well to the distribution compared to conventional strain-life models. The main contribution is that load interactions have a significant influence on predicting fatigue life within the random strain histories of the fatigue properties of a coil spring.

A Nonstationary Uncertainty Model and Bayesian Calibration of Strain-Life Models

Abstract The Coffin–Manson–Basquin–Haford (CMBH) model is a well-accepted strain-life relationship to model fatigue life as a function of applied strain. In this paper, we propose a nonstationary uncertainty model for the CMBH model, alongside a Bayesian framework for model calibration and estimation of confidence and prediction intervals. Using Inconel 617 coupon test data, we compared our approach to traditional stationary variance models. The proposed uncertainty model successfully captures the fact that the variance of strain amplitude decreases with increasing fatigue life. Additionally, a discussion on how to use the proposed Bayesian framework to compensate for the lack of data by using prior information coming from similar alloys is also presented considering Hastealloy-X and Inconel 617 coupon data.

The needs of power spectral density in fatigue life prediction of heavy vehicle leaf spring

This study characterized the properties of random strain loading data for using power spectral density (PSD) in frequency domain of a heavy vehicle leaf spring. This is due to missing data caused by the sensitivity of the strain gauges in capturing strain signal. Strain signal was captured from a leaf spring component for 100 s at a sampling rate of 200 Hz using strain gauge. Fatigue life prediction was computed using strain-life models: Coffin-Manson, Morrow and Smith-Watson-Topper (SWT). The fatigue strain data showed that downhill data produces the lowest fatigue life prediction at 3.42 × 102 cycles/block with high energy of 3.6 × 104μɛ2.Hz-1; then it was followed by curve and highway data. This was supported by the root-mean-square (RMS) value at 324.24 μɛ as it is directly related towards the PSD based on the energy contained for each captured signal. The correlation of fatigue life and strain amplitude was calculated to identify the distribution of fatigue strain data of leaf spring. Thus, the fatigue strain loading data can be characterized properly based on the energy content in PSD, the statistical parameter in the form of RMS value and the correlation with strain amplitude for random strain loading of leaf spring.

Durability assessment of suspension coil spring considering the multifractality of road excitations

This study presents the characterisation of multifractality of road excitation time series under different road conditions for prediction of the durability of a suspension coil spring. Road excitation acceleration signals and strain signals were acquired from the suspension system of a vehicle travelling under different road conditions. Multifractal analysis revealed a higher tendency to multifractality in road excitations with more surface irregularities. With the fatigue lives predicted by different strain-life models (Coffin-Manson, Morrow, and Smith-Watson-Topper), fatigue life prediction linear models based on road multifractality were established. It was found that the Morrow-based linear model gave the most accurate estimation of fatigue life, with the highest R2 of 0.8762. In conclusion, the models for the prediction of coil springs’ fatigue life based on road multifractality provide an accurate and faster alternative for durability assessment of coil springs. This can significantly facilitate the design process of coil springs to meet industry requirements.

Fatigue Reliability Assessment of an Automobile Coil Spring under Random Strain Loads Using Probabilistic Technique

This paper presents a mathematical model to estimate strain-life probabilistic modeling based on the fatigue reliability prediction of an automobile coil spring under random strain loads. The proposed technique was determined using a probabilistic method of the Gumbel distribution for strain-life models of automobile suspension systems. Strain signals from different road excitations in experimental tests were measured. The probability density function of the Gumbel distribution was considered to estimate model parameters using maximum likelihood estimation (MLE). The Akaike information criterion (AIC) method was performed to specify which model can estimate the best fit model parameters. Results demonstrated a good agreement between the predicted fatigue lives of the proposed probabilistic model and the measured strain fatigue life models. The root-mean-square errors (RMSE) based on the Coffin–Manson, Morrow, and Smith–Watson–Topper strain-life models were approximately 0.00114, 0.00107, and 0.00509, respectively, indicating a high correlation with the proposed model and experimental data. The results demonstrated that the proposed probabilistic model is effective for the fatigue life prediction of automobile coil springs using strain and stress fatigue life approaches.

Comprehensive investigation of fatigue behavior and a new strain-life model for CP-Ti under different loading conditions

This paper investigates symmetric strain, stress and asymmetric stress-controlled fatigue behavior of prestrained and non-prestrained CP-Ti. The effects of stress ratio, mean stress, prestrain on stress/strain life were carefully analyzed. Stress-life of CP-Ti shows non-monotonic variation with stress ratio, as compressive ratcheting resulted by tension-compression asymmetry accumulates under symmetric stress cycling. Stress-life can be improved by prestrain, regardless of loading condition, due to the decrease of responded strain amplitude. Stress fatigue resistance of the material is actually deteriorated by prestrain at the stress level identical to that of non-prestrained CP-Ti. Strain-life of prestrained sample shows little variation at high strain amplitude due to mean stress relaxation and significant reduction at low strain amplitude. By introducing asymmetry factor, it is further found that strain-life of the material is insensitive to prestrain if the applied mean stress level keeps constant. Finally, current strain-life models with different mean stress correction terms are discussed to evaluate their application ability in fatigue life prediction of CP-Ti under different loading conditions. Though two additional parameters are introduced into the mean stress correction term with power law form, there are still few data points beyond the scatter bounds of two. Therefore, a new strain-life model with exponential mean stress correction term is proposed and verified by fatigue life data of different materials, which has more advantage than existing strain-life models at a wide range of mean stress level.

Optimization of spring fatigue life prediction model for vehicle ride using hybrid multi-layer perceptron artificial neural networks

Abstract In this study, hybrid multi-layer perceptron artificial neural network (HMLP ANN) models were developed to predict the fatigue life of automotive coil springs with high accuracy based on the vertical vibrations of the vehicle and natural frequencies of the vehicle suspension system. The design and development of vehicle suspension systems involve numerous steps from conceptual design to prototyping and testing, including fatigue life evaluation and vehicle ride analysis. Optimizing HMLP ANN models will significantly simplify the design and development process, which forms the motivation of this study. Simulations were conducted on a quarter car model to extract the loading signals using the measured acceleration signals and artificial road profiles as inputs. The fatigue life was predicted based on the Coffin-Manson, Morrow, and Smith-Watson-Topper strain-life models whereas the comfort ride index was assessed according to the ISO 2631-1:1997 standard. Various HMLP ANN models were trained using the Levenberg-Marquardt backpropagation algorithm to determine the optimum architectures. The lowest mean square error (0.0117) is obtained for the Morrow HMLP ANN model with three hidden layers. The coefficient of determination values are more than 0.9559, indicating that there is good fit between the training/testing datasets and the data predicted by the optimum HMLP ANN models. These models were validated using the conservative correlation approach and there is good agreement between the targeted and predicted fatigue life values. It can be concluded that the optimum HMLP ANN models are capable of predicting the fatigue life of automotive coil springs with acceptable accuracy.

Probabilistic-Based Analysis for Damaging Features of Fatigue Strain Loadings

This paper presents the behaviour of fatigue damage extraction in fatigue strain histories of automotive components using the probabilistic approach. This is a consideration for the evaluation of fatigue damage extraction in automotive components under service loading that is vital in a reliability analysis. For the purpose of research work, two strain signals data are collected from a car coil spring during a road test. The fatigue strain signals are then extracted using the wavelet transform in order to extract the high amplitude segments that contribute to the fatigue damage. At this stage, the low amplitude segments are removed because of their minimal contribution to the fatigue damage. The fatigue damage based on all extracted segments is calculated using some significant strain-life models. Subsequently, the statistics-based Weibull distribution is applied to evaluate the fatigue damage extraction. It has been found that about 70% of the probability of failure occurs in the 1.0 x 10-5 to 1.0 x 10-4 damage range for both signals, while 90% of the probability of failure occurs in the 1.0 x 10-4 to 1.0 x 10-3 damage range. Lastly, it is suggested that the fatigue damage can be determined by the Weibull distribution analysis

Development of multiple linear regression-based models for fatigue life evaluation of automotive coil springs

Abstract This paper discusses the establishment of multiple linear regression (MLR)-based spring durability models for predicting the fatigue life of automotive coil springs based on the vertical vibrations of the vehicle and natural frequencies of the vehicle suspension system. These models were developed in order to simplify the design and development process of vehicle suspension systems, which is both time-intensive and cost-intensive. The simulated force-time histories were processed to obtain the fatigue life of the automotive coil spring based on the strain-life models whereas the acceleration-time histories were weighted according to the ISO-2631-1:1997 standard to determine the vertical vibrations of the vehicle. MLR was used to establish the spring durability models and the goodness of fit, linearity, normality, and homoscedasticity of the models were assessed. The highest coefficient of determination at 0.8820 was obtained for the Morrow MLR-based spring durability model, with the mean square error of 0.5855. The models were validated by comparing the fatigue life values predicted by the models with those predicted from strain measurements. The results show a good agreement between the predicted and experimental values, indicating the suitability of these models in predicting the fatigue life of automotive coil springs.

Substructure-based distributed collaborative probabilistic analysis method for low-cycle fatigue damage assessment of turbine blade–disk

A numerical simulation-based probabilistic analysis methodology, substructure-based distributed collaborative probabilistic analysis method (SDCPAM), is proposed for accurate and efficient fatigue prognosis based on distributed collaborative response surface method (DCRSM) and substructure analysis method. This paper focuses on the low-cycle fatigue (LCF) damage assessment for turbine blade–disk system. Based on the established probabilistic strain–life models and fatigue reliability model for tandem system, the LCF damage principle of turbine blade–disk system is proposed and integrated with SDCPAM. Following that, the LCF life prediction of the turbine blade–disk is completed, and probabilistic sensitivity analyses of blade and disk to the LCF life of the turbine blade–disk system are achieved. According to the above efforts, the feasibility and effectiveness of SDCPAM is verified. Finally, the LCF damage assessment for the blade–disk system is accomplished, and the influences of applied cycle and reliability level on the LCF damage are investigated. Through the comparisons of the proposed with traditional fatigue reliability model, it is illustrated that the proposed fatigue reliability model is reasonable. The results show that blade and disk almost have the same great influence on the blade–disk LCF life. In addition, applied cycles under normal and lognormal distributions produce the same LCF damage reliability that decreases with increasing applied cycle and reliability level. The efforts of this study indicate the reasonability of the proposed method and models in describing the LCF damage reliability of the blade–disk system, and enrich the reliability theory and method for the complex structure with multi-component and multi-failure mode.

On the need to adopt strain-based probabilistic approach in predicting fatigue life

This paper presents a comparison of fatigue life prediction capabilities among three deterministic and one probabilistic strain–life models. Most existing life prediction models are deterministic even though the fatigue process is stochastic in nature. Therefore, variability in experimental fatigue life data is not statistically justified when the deterministic approach is adopted. In this study, the Coffin–Manson, Smith–Watson–Topper, Morrow, and Weibull regression models through the use of Miner’s rule for damage accumulation process are each compared with the experimental data. Both available in the literature, two sets of experimental data for variable amplitude loading and random loading spectrum were used to explore the prediction accuracies of the models. Simulations were based on models to obtain additional results for different levels of maximum strain. They were conducted to investigate the maximum strain–life behaviour under random loading. Fatigue life comparisons were then performed, and the scatter band for type of load, level of strain amplitude, and each model separately were used for evaluations. The results show that the difference percentage in comparison with experimental data varies, but all the predictions are within the acceptable limit, that is, 50% when the factor of 2 was used. Weibull regression model has the lowest normalized-root-mean square error value (0.07) and thus has highest prediction capability among the models. Therefore, the probabilistic model is a better alternative for strain–life prediction compared with deterministic models.

High-cycle fatigue life prediction of reinforced concrete deep beams

Concrete elements deteriorate as a result of continuous application of compressive fatigue loads. Irreversible deformation accumulates; hence, the effect on embedded steel reinforcing bars capacity and concrete resistance should be accounted for in the fatigue analysis of concrete structures. Experimental investigations were conducted to study the fatigue behaviour of eight small-scale reinforced concrete deep beams with a shear span to effective depth ratio of 1.25. Percentages of the diagonal cracking load from monotonic tests were used as fatigue loads. The deformation evolution within the shear spans of the deep beams were obtained by estimating the average principal and shear strain evolutions from the strain transformation analysis of LVDT (Linear Variable Displacement Transformer) data. Mid-span deflections and reinforcement strain evolutions with proximity to a major concrete crack location were obtained. In all beams, failure occurred with fracture of the longitudinal reinforcement at the intersection with the major concrete crack. Maximum strain evolutions for shear reinforcement measured at regions around the bends were observed to be lower than the strain evolutions observed in the longitudinal reinforcement. This was attributed to the governing arch mechanism common with deep beams.The strut and tie method was modified to predict the fatigue life of the deep beams tested by modifying the constitutive models and effectiveness factor of concrete with fatigue damage models. To achieve this, the irreversible compressive fatigue strain in concrete is considered as a pseudo-load. The crack initiation life and the progressive crack growth of steel reinforcement are accounted for using strain-life models and linear elastic fracture mechanics, respectively. Within the developed algorithm, failure will occur when one of the evolving forces in either the concrete strut or steel reinforcement approaches the corresponding residual resistance capacity.

Probabilistic Scatter Band with Error Distribution for Fatigue Life Comparisons

This paper presents a new probabilistic evaluation technique of fatigue life based on the adaptation of control chart concept incorporated in a scatter band. Conventionally, scatter band is a tool for visual evaluation of fatigue life accuracy. Such band is also used as an evaluation criterion for the estimation methods of fatigue strain–life equation. However, the current scatter band technique provides no probabilistic interpretation of the deviation that occurred during comparison. This technique is only used as a comparison tool considering whether the data points fall within or outside the predefined accuracy band. Therefore, a new framework of probabilistic scatter band is introduced in this study. The symmetrical tolerance interval with normal distribution is used to characterise the probabilistic field with upper and lower tolerance limit according to two standard deviations or a 95% tolerance limit. Using this technique, the comparison between fatigue life prediction and experimental data is provided in regions according to conservatism. The probability of error and rejection index values according to the statistical distribution of fatigue life is also presented. The proposed technique is applied in fatigue life evaluation between strain–life models and experimental data available in literature. The new technique is practically informative in probabilistic interpretation of fatigue life results with scatter and uncertainty factors included.

Strain-based approach for fatigue crack propagation simulation of the 6061-T651 aluminium alloy

Fatigue crack growth models based on elastic-plastic stress-strain histories, at the crack tip vicinity, and strain-life damage models have been proposed. The UniGrow model is a particular case of fatigue crack propagation models. The residual stresses developed at the crack tip play a central role in these models, since they are used to assess the actual fatigue crack driving force, taking into account mean stress and loading sequential effects. The performance of the UniGrow model is assessed based on available experimental constant amplitude crack propagation data, derived for the 6061-T651 aluminium alloy. Key issues in fatigue crack growth prediction, using the UniGrow model, in particular the residual stresses evolution, are discussed. Using available strain-life data, it was possible to model the fatigue crack propagation behaviour for the AA6061-T651, taking into account the stress R-ratio effects. A satisfactory agreement was found, between the predictions and the experimental crack propagation data.