Fatigue Life Of Rubber Research Articles

Prediction of Rubber Fatigue Life Using an Assimilation‐based Learning Approach and Incremental Crack Propagation Model

ABSTRACTAccurately and efficiently predicting the fatigue life of rubber materials has been a long‐standing challenge due to limited understanding of the fatigue mechanism. In this study, a variational assimilation‐based machine learning method assisted with incremental crack propagation model is proposed to predict the fatigue life of rubber materials. Firstly, according to the fracture mechanics theory, a new rubber fatigue life prediction model based on incremental crack propagation and sparse experimental data is established, which owns higher accuracy than the classical crack energy density model. Further, a rubber fatigue life solver coupled incremental crack propagation model and nonlinear finite element method is introduced to generate a dense fatigue life dataset of rubber materials with high accuracy. Finally, the artificial neural network model is trained, cross‐validated, and tested using the dense dataset, and the three‐dimensional variational assimilation model is employed to merge the predicted values of artificial neural network with experimental data. By comparing against the experimental data, the effectiveness of the proposed method was verified; thereby, we offer an accurate and efficient approach to predict the rubber fatigue life.

Modeling the thermo-oxidative aging effects on fatigue life of natural rubber using a continuum damage mechanics approach

Thermo-oxidative aging (TOA) significantly impacts the fatigue life of rubbers by reducing the fatigue strength and modifying the slope of the Wöhler curve, rendering traditional time-temperature superposition methods inadequate. In this work, we aim to develop a model capable of predicting the effect of TOA on the fatigue properties of rubbers. For this purpose, dumbbell specimens of natural rubber (NR) were subjected to aging in an air-vented oven at different temperatures prior to mechanical testing. Tensile tests were conducted to quantify the aging effects on a microscale network parameter known as elastically active chains (EAC) density, along with determining ultimate properties such as the stress and strain at break. By using a time-temperature equivalence and the Arrhenius shift factor, master curves were constructed for both EAC density and ultimate properties. Subsequently, the fracture properties of the aged material were predicted using an energy limiter approach whose evolution follows that of EAC density. Furthermore, a relationship between the parameters of the continuum damage mechanics (CDM) approach (specifically, the power law parameters of the Wöhler curve) and the fracture properties was proposed, resulting in accurate estimates of the fatigue life regardless of the aging conditions. Satisfactory agreement was observed between the model predictions and the data for nine aging conditions encompassing four different temperatures. The CDM approach also allows assessing the evolution of mechanical damage within the material influenced by TOA. The novelty of this approach lies in establishing a direct relationship between fatigue and fracture properties. Moreover, this is the first time to the best of our knowledge that TOA has been explicitly incorporated into a fatigue life prediction model via the evolution of the EAC density.

Accelerated fatigue bench test method for rubber vibration isolators based on load spectrum compilation

The present study is focused on the development of a novel method for compiling load blocks to accelerate the fatigue bench test of rubber vibration isolators. This approach involves three main steps: Firstly, a uniaxial tensile fatigue test is conducted on rubber specimens under a constant amplitude load. According to the fatigue test data, a rubber fatigue life prediction model is established. Secondly, the mount load spectrum is statistically analyzed, and the fatigue damage distribution of the mount is calculated using the rubber fatigue life prediction model. Lastly, following the principle of damage equivalence, the load spectrum is compiled into load blocks. The fatigue bench test of the mount is then conducted using both the load spectrum and the load block as loading data, respectively. The test results demonstrate that the fatigue failure locations of the mounts are essentially identical under both loading data types, verifying the effectiveness of the proposed load block compilation method.

A simple fatigue methodology for filled natural rubbers under positive and negative R ratios

This paper suggests a simple methodology to optimize the uniaxial fatigue predictions for filled natural rubbers. In this study, the stress ratio R effect on rubber fatigue life is investigated numerically. For this purpose, a Finite Element model is developed to determine both amplitude and mean stress values in the critical zone of the considered specimen. The suggested model incorporates the R ratio effect using an equivalent stress amplitude. It is proven that the new model can efficiently describe the fatigue life for a large R -value interval with higher accuracy.

Intelligent prediction of fatigue life of natural rubber considering strain ratio effect

AbstractAn intelligent prediction model of rubber fatigue life considering strain ratios based on the support vector regression (SVR) and an improved sparrow search algorithm (ISSA) is proposed. In order to solve the problem that traditional methods may lead to unsatisfactory prediction results, we establish a prediction model based on SVR. To further improve the prediction accuracy, we utilize the ISSA algorithm to optimize various hyper‐parameters in the model. Fatigue tests of filled natural rubber on dumbbell‐type specimens are performed and applied to verify the effectiveness of the proposed model. The results show that the ISSA optimized SVR (ISSA‐SVR) model is superior in terms of prediction accuracy, convergence speed, and stability compared with SVR models using the grid search or some standard optimization algorithms. Furthermore, comparisons of some published related models demonstrate that the ISSA‐SVR has the most accurate predictive results, which gather within 1.5 times the dispersion lines.

Residual fatigue life prediction of natural rubber components under variable amplitude loads

In the present study, the residual fatigue life (RFL) of natural rubber (NR) components under variable amplitude loads is predicted. To this end, a support vector machine (SVM) model is established to estimate the fatigue life of NR specimens under a constant amplitude load. Here, the strain amplitude and strain mean of NR specimens are used as input variables while the rubber fatigue life is considered as the output variable of the SVM model. It is found the regression results and predicted life distribution of the SVM model are promising. Then the load sequence and load interaction are considered in the calculations and a nonlinear fatigue cumulative damage (NFCD) model is developed. Finally, the RFL of rubber specimens under variable amplitude load is predicted using the Miner criterion and the NFCD model. The performed experiments demonstrate that the prediction accuracy of the NFCD model is higher than that of the Miner criterion.

Effect of Nanoclay Filler on Fatigue Life of Natural Rubber/Styrene-Butadiene Blend

In this paper, the fatigue life of natural rubber (NR)/styrene-butadiene rubber (SBR) compound is evaluated experimentally. The parameters investigated are the NR, SBR, and nanoclay loading in the composition, strain amplitude, and the frequency of the fatigue test. Fracture surfaces of NR/SBR/nanoclay compound are investigated using scanning electron microscopy (SEM). The results show that by increasing NR and the nanoclay loading in the rubber composition, the fatigue life of the rubber increases. For the nanoclay, a threshold value exists beyond which the fatigue life of the rubber compound decreases. It is also observed that by increasing the test frequency, the fatigue life of the rubber compound decreased. Tensile, hardness, and dynamic mechanical thermal analysis (DMTA) tests were also performed to evaluate the mechanical and thermal properties of the compound. SEM results show that by increasing the strain amplitude, the test specimens fail softly, and the addition of nanoparticles roughens the fracture surface and increases the fatigue life.

Probabilistic fatigue life prediction model of natural rubber components based on the expanded sample data

A novel method for determine the probabilistic distribution model of natural rubber (NR) fatigue life is proposed. Uniaxial tension fatigue tests are carried out on dumbbell-shaped cylindrical specimens. According to the fatigue test data, a support vector machine (SVM) model is established, in which the empirical reliability and the rubber fatigue life are considered as input and output variables, respectively. The SVM model is used to expand the NR fatigue life data. The analysis of the expanded data demonstrates that the NR fatigue life follows a lognormal distribution. Accordingly, the fatigue reliability evaluation of NR components is carried out.

Fatigue life prediction of natural rubber components using an artificial neural network

AbstractUniaxial tension fatigue tests conducted on dumbbell‐shaped specimens made of vulcanized natural rubber are carried out. Using the fatigue test data, a back‐propagation neural network (BPNN) model for estimating the fatigue life of natural rubber specimens is established. An improved sine‐cosine algorithm (ISCA) is proposed to optimize the parameters of the BPNN model. The peak engineering strain, ambient temperature, and Shore hardness of natural rubber specimens are used as the input variables while the rubber fatigue life as the output variable of the BPNN model. The regression results and predicted life distribution of the established BPNN model are encouraging. For comparison, a genetic algorithm, a particle swarm algorithm, and a standard sine‐cosine algorithm are also used to obtain the BPNN model parameters, respectively. The results showed that the prediction accuracy and efficiency of ISCA are better than other three algorithms. In addition, the sensitivity analysis is introduced to quantify the relative influence of the model inputs on the output.

Fatigue of crystallizable rubber: Generation of a Haigh diagram over a wide range of positive load ratios

A Haigh diagram is built for a carbon black filled rubber blend that exhibits Strain Induced Crystallization (SIC) for a wide range of positive displacement ratios. A strategy for the initiation detection, which becomes difficult for high displacement ratios, is proposed and validated thanks to regular visual follow-up. Some experimental cautions are taken to avoid any temperature and strain rate effects on the results, more specifically on the strain induced crystallization phenomenon. It is found that a reinforcement related to strain induced crystallization is present for load ratios (up to displacement load ratio of 0.35). For higher load ratios, the reinforcement effect reduces leading to a Haigh diagram that looks like a bell, as already shown by Cadwell et al. (S. Cadwell, R. Merrill, C. Sloman, F. Yost, Dynamic fatigue life of rubber, Industrial and Engineering Chemistry 12 (1940) 19–23).

Cracking energy density for rubber materials: Computation and implementation in multiaxial fatigue design

AbstractThis article proposes a heuristic model to predict the fatigue life of rubber parts. The developed model is mainly based on the Cracking Energy Density (CED), originally developed by Mars, for the study of rubber parts fatigue. The main contribution consists in the integration of the theoretical framework of the critical plane analysis proposed by Mars with Saintier's experimental research carried out in tension and torsion modes. The CED parameter, derived from the Strain Energy Density (SED), can predict the occurrence of the first crack and its possible orientation depending on the type of loading path. In this context, an analytical analysis of this parameter is carried out for typical loading cases. Furthermore, the variation of CED by SED ratio (WC/W), as a function of the probable crack angle θ and the principal stretch λ1 is investigated. A finite element (FE) model is, then, developed to measure the performance and efficiency for some basic criteria used to investigate rubber fatigue life in literature. The pertinence of such criteria is evaluated in terms of a determination coefficient. The CED parameter can be considered as the most effective criterion for describing the multiaxial fatigue life of rubbers.

Rubber fatigue life prediction using a random forest method and nonlinear cumulative fatigue damage model

ABSTRACTIn this study, a random forest machine‐learning method is introduced on the basis of the analysis of measured constant amplitude stress fatigue data. This method aims to predict rubber fatigue life under constant amplitude stress. Strain mean value, strain amplitude, and strain ratio are used as independent variables, and the prediction model of rubber fatigue life under constant amplitude stress is established. A nonlinear cumulative fatigue damage model is proposed to calculate rubber fatigue life under the variable amplitude stress. Results show that the random forest method has high precision and generalization capability for rubber fatigue life prediction under constant amplitude stress and the nonlinear cumulative fatigue damage model could be employed to calculate the fatigue life of rubber under variable amplitude stress with enough accuracy according to the constant amplitude stress fatigue life data. This research can provide a reference for rubber fatigue life prediction. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020, 137, 48519.

Strain energy-based rubber fatigue life prediction under the influence of temperature.

Aiming at the problem of the fatigue life prediction of rubber under the influence of temperature, the effects of thermal ageing and fatigue damage on the fatigue life of rubber under the influence of temperature are analysed and a fatigue life prediction model is established by selecting strain energy as a fatigue damage parameter based on the uniaxial tensile data of dumbbell rubber specimens at different temperatures. Firstly, the strain energy of rubber specimens at different temperatures is obtained by the Yeoh model, and the relationship between it and rubber fatigue life at different temperatures is fitted by the least-square method. Secondly, the function formula of temperature and model parameters is obtained by the least-square polynomial fitting. Finally, another group of rubber specimens is tested at different temperatures and the fatigue characteristics are predicted by using the proposed prediction model under the influence of temperature, and the results are compared with the measured results. The results show that the predicted value of the model is consistent with the measured value and the average relative error is less than 22.26%, which indicates that the model can predict the fatigue life of this kind of rubber specimen at different temperatures. What's more, the model proposed in this study has a high practical value in engineering practice of rubber fatigue life prediction at different temperatures.

Recent advances on fatigue of rubber after the literature survey by Mars and Fatemi in 2002 and 2004

Subjected to multiaxial mechanical loading and hostile environment, rubber experiences degradation over a period of time. Therefore, it is of utmost importance to prevent failure of rubber components during the service. As highlighted in Mars and Fatemi [Mars, W.V, Fatemi, A., 2002. A literature survey on fatigue analysis approaches of rubbers. Int. J. Fatigue 24, 949–961; Mars, W.V, Fatemi, A., 2004. Factors that affect the fatigue life of rubber: A literature survey. Rubber Chem. Technol. 77, 391–412], a large number of works focused on the durability of rubber. Furthermore, it has been expanding rapidly until today. For this reason, the present work focuses on collecting and analyzing the vast amount of works on fatigue of rubber conducted in the last 15 years since the review of Mars and Fatemi in 2002 and 2004. To this end, three bibliographic databases are consulted: Google Scholar, Scopus and Web of Science. The collected works are analyzed with the objective to identify the current and future trends and needs in the study of rubber fatigue.

Impact of temperature on the fatigue and crack growth behavior of rubbers

Elasticity and chemical resistance are only two of outstanding properties of elastomers and make them applicable in a broad field of cyclic loaded components. During the cyclic loading, the failure is mainly related to crack growth mechanism. For the description and prediction of the material failure, fracture mechanics concepts represent a valid tool. In the field of elastomer failure under cyclic loading, two main approaches have been developed: (1) the crack nucleation dealing with the lifetime of rubber, due to a specific number of cycles until appearance of a specific crack size and (2) the crack growth approach, devoting the attention to the growth of pre-existing defects. Although both approaches represent effective instruments for fatigue analysis, only little attention has been drawn on the impact of temperature on the failure behavior. Moreover, scientific publications report that temperature influences the fatigue life of rubbers by decreasing the magnitude by four orders. Therefore, a focus on the impact of temperature on the crack growth behavior seems indispensable to rise knowledge in this field. For the evaluation of influence of temperature on the fatigue performance, crack growth tests were implemented. For the characterization of crack growth behavior, pure shear specimens equipped with a camera system to measure the crack growth behavior and the temperature were monitored with contactless thermo-couples to measure the surface temperature during the cyclic loading. Furthermore, the thermal conductivity was measured at different temperatures to allow an accurate evaluation of temperature influence. With the obtained data, a further description of the failure could be provided to extend the fracture mechanics approach through the implementation of the temperature effect within different fatigue models for elastomers.

Cracking energy density calculation of hyperelastic constitutive model and its application in rubber fatigue life estimations

ABSTRACTThe finite deformation of rubber under multiaxial stress will finally result in its fatigue failure. The ability to predict the effects of complex strain histories on fatigue life is a critical need. The cracking energy density (CED) distribution characteristics in the finite deformation and rubber fatigue life estimated by the CED criterion are investigated. Then the influences of the crack orientation angle θ and the principal stretch ratio λ on the relationship between CED and strain energy density (SED) are obtained. Finally, the results are used for predicting the fatigue life of rubber material and are compared to experimental values. The results indicate that the ratios of the predicted lives based on the CED damage parameter and measured lives are within two times scatter factor and that of the predicted lives based on the SED damage parameter and measured lives are greatly influenced by the crack orientation angle θ. The rubber fatigue life has great relationship with the angle of the crack plane normal vector and the first principal stretch direction. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 44195.

Research on the Fatigue Life Prediction Method of Thrust Rod

Purpose of this paper is to investigate the fatigue life prediction method of the thrust rod based on the continuum damage mechanics. The equivalent stress used as damage parameters established rubber fatigue life prediction model. Through the finite element simulation and material test, the model parameters and the fatigue damage dangerous positions were obtained. By equivalent stress life model, uniaxial fatigue life of the V-type thrust rod is analyzed to predict the ratio of life and the life of the test was 1.73, within an acceptable range, and the fatigue damage occurring position and finite element analysis are basically the same. Fatigue life analysis shows that the method is of correct, theoretical, and practical value.

Measurement and modelling of the fatigue life of rubber mounts for an automotive powertrain at high temperatures

A fatigue experiment is carried out on filled natural rubber specimens with two different Shore hardnesses (45 and 50) and three different temperatures (23 °C, 60 °C and 90 °C) under uniaxial tension loads. The measured fatigue life data obtained under different displacement loads are used to formulate fatigue life prediction models corresponding to different operating temperatures for the two hardnesses using the peak engineering strain as the damage parameter. The influences of the temperature, the stress softening at high temperatures and the hardness on the fatigue life of rubbers are measured and discussed. The proposed models are used to predict the fatigue life of a rubber mount for a powertrain mounting system. The validity of the prediction model is demonstrated by comparisons with the measured fatigue life data of the rubber mount at 90 °C. A method for determining the damage parameters required for predicting the fatigue life is presented on the basis of the finite element model of the rubber mount. The Mooney–Rivlin constitutive constants of the hyperelastic rubber material are identified on the basis of the measured data on the specimens. Comparisons of the measured and the estimated fatigue lives of the rubber mount at 90 °C revealed reasonably good agreement. The ratio of the predicted fatigue life to the measured fatigue life was within a factor of 2 under the range of loading conditions considered.

Crack precursor size for natural rubber inferred from relaxing and non-relaxing fatigue experiments

Fatigue life prediction for a dumbbell cylindrical natural rubber component under uniaxial tensile loading conditions was performed based on the Thomas fatigue crack growth model for relaxing (R=0) load cycles and the Mars–Fatemi model for non-relaxing (R>0) load cycles. By using a self-written program, we proposed a new approach to establish the relation between the power law exponent F and the R ratio in the Mars–Fatemi model. The approach is based on rubber fatigue life (S–N) data rather than crack growth rate and tearing energy (da/dN–T) data, avoiding certain difficulties often encountered using the crack growth method. The results indicate that the relation between F and R is a quadratic or cubic function over the range 0<R<0.3. Finally, the quantitative effect of initial crack size on fatigue life was studied. We found that the inferred mean size of crack precursors in the rubber component is around 30–40μm under both relaxing and non-relaxing loading conditions, and the fluctuation of fatigue life is due to the inhomogeneity of crack precursor size except the factors such as unavoidable variations in testing conditions and specimen variations. The good agreement of inferred crack precursor sizes from different R ratio loading conditions is a strong indication that the Mars–Fatemi model provides a proper accounting for the effects of strain crystallization, and it confirms yet again the understanding that nucleated cracks originate from similarly sized precursors in both relaxing and non-relaxing fatigue experiments.

A method for modelling of fatigue life for rubbers and rubber isolators

ABSTRACTA method for modelling fatigue life of rubbers and rubber isolators is presented in this paper. Firstly, a fatigue experiment is carried out for a rubber dumbbell cylindrical specimen and a rubber isolator. Based on the finite element analysis, the damage parameters including the strain energy density, the maximum principal Green–Lagrange strain and the effective stress are calculated and discussed. Secondly, three fatigue life prediction models are established by using the three damage parameters and using the relation between the measured fatigue life of a dumbbell cylindrical specimen and the computed value of the damage parameters. Thirdly, three proposed prediction models are used to investigate which one can be best used to predicting fatigue life of rubber isolators, taking a typical powertrain rubber isolator as studying example. The fatigue lives of the rubber isolator predicted by the three models are compared with the experimental life. The results demonstrate that the predicted fatigue lives of the rubber isolator using the three fatigue models agree well with the experimental fatigue life within a factor of four, and the model using the effective stress as the damage parameter can predict the fatigue life within a factor of two, which has the best accuracy among the three models.