Fatigue life analysis and predictions for NR and SBR under variable amplitude and multiaxial loading conditions

This paper investigates the effects of variable amplitude loading conditions on the fatigue lives of multiaxial rubber specimens. Two filled rubber materials were used and compared to investigate the effects of strain-crystallization on crack development NR, which strain crystallizes, and SBR, which does not. The applicability of Miner’s linear damage rule for predicting fatigue lives of variable amplitude tests in rubber and the use of both scalar and plane-specific equivalence parameters to characterize fatigue life results were also investigated. A fatigue life prediction approach that utilizes normal strain to find the critical plane and the cracking energy density on that plane to determine fatigue life is introduced and compared to other approaches. The effects of load sequence and temperature on fatigue life, as well as differences in fatigue lives using both stiffness and critical crack length failure criteria are discussed.     

Stochastic modelling of low-cycle fatigue damage in 316L stainless steel under variable multiaxial loading

In the present study, a stochastic model is developed for the low-cycle fatigue life prediction and reliability assessment of 316L stainless steel under variable multiaxial loading. In the proposed model, fatigue phenomenon is considered as a Markov process, and damage vector and reliability are defined on every plane. Any low-cycle fatigue damage evaluating method can be included in the proposed model. The model enables calculation of statistical reliability and crack initiation direction under variable multiaxial loading, which are generally not available. In the present study, a critical plane method proposed by Kandil et al . ( Metals Soc., London 280, 203–210, 1982) maximum tensile strain range, and von Mises equivalent strain range are used to calculate fatigue damage. When the critical plane method is chosen, the effect of multiple critical planes is also included in the proposed model. Maximum tensile strain and von Mises strain methods are used for the demonstration of the generality of the proposed model. The material properties and the stochastic model parameters are obtained from uniaxial tests only. The stochastic model made of the parameters obtained from the uniaxial tests is applied to the life prediction and reliability assessment of 316L stainless steel under variable multiaxial loading. The predicted results show good aggreement with experimental results.     

不同超弹性本构模型和多维应力下开裂能密度的计算方法

橡胶隔振器的疲劳失效多属于大变形(有限变形)下的多轴疲劳问题。在多轴疲劳载荷下,有效用来驱动裂纹扩展的那部分应变能密度称为开裂能密度。基于开裂能密度和橡胶材料的裂纹扩展特性预测橡胶部件的疲劳寿命时,须计算在外载荷下橡胶部件的开裂能密度。为了由有限元软件ABAQUS默认输出的应变计算在有限变形下的开裂能密度,该文推导了不同超弹性本构模型下开裂能密度在主坐标系下的计算式和所需的积分方法。基于该文开裂能密度的计算方法,采用3次Ogden本构来描述大变形下橡胶材料的本构行为,计算分析了不同应变状态下开裂能密度的分布特点。通过分析计算得到的开裂能密度与应变能密度的关系,说明该文开裂能密度计算方法的准确性。最后将上述计算方法应用到橡胶隔振器的多轴疲劳寿命预测中。     

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

A 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.     

Fatigue life prediction for vibration isolation rubber based on parameter‐optimized support vector machine model

Given the small sample size, nonlinearity, and large dispersion of the measured data of fatigue performance for vibration isolation rubbers, the fatigue life prediction model for vibration isolation rubber materials was established using a support vector machine (SVM). A modified gravity search algorithm (MGSA) is proposed to optimize the parameters of the SVM. Using environmental temperature, the Rockwell hardness of the rubber compound, and the engineering strain peak as the input variables, the model was trained based on the experimental fatigue data of vibration isolation rubber materials. For comparison, the standard genetic algorithm, the standard particle swarm algorithm, and the standard simulated annealing algorithm are also implemented. Moreover, a back propagation neural network regression model is applied to the life prediction, with the conclusion that the prediction accuracy and the efficiency of MGSA are better than those of extant methods. This work can provide reference for further fatigue life prediction and structural improvement of rubber parts.     

Stress‐life prediction of 25°C polypropylene materials based on calibration of Zhurkov fatigue life model

In this study, to evaluate the chemical and mechanical properties of polypropylene (PP), activation‐energy and tensile tests were performed at room temperature (25°C) on pure PP and PP reinforced with glass fibre (GF). To improve the prediction accuracy of the fatigue life, three models based on the calibration of the Zhurkov model were proposed: a regression model, modified strain‐rate model and lethargy coefficient‐based model. Based on the experimental data analysis and statistical assessment results, we proposed a modified strain‐rate model that satisfies the dependency of the physical parameters and is congruent with the predicted fatigue life data. The experimental data and modified strain‐rate model were compared with the direct cyclic analysis results. The tendency of the frequency factor as a correction parameter in the modified strain‐rate model corresponded to the experimental activation energy and the increasing GF content.     

An energy‐based critical fatigue life prediction method for AL6061‐T6

An energy‐based critical fatigue life prediction method is developed and analysed. The original energy‐based fatigue life prediction theory states that the number of cycles to failure is estimated by dividing the total energy accumulated during a monotonic fracture by the strain energy per cycle. Because the accuracy of this concept is heavily dependent on the cyclic behaviour of the material, a precise understanding of the strain energy behaviour throughout each failure process is necessary. Examination of the stress and strain during fatigue tests shows that the cyclic strain energy behaviour is not perfectly stable as initially presumed. It was discovered that fatigue hysteresis energy always accumulates to the same amount of energy by the end of the stable energy region, which has led to a new ‘critical energy’ material property. Characterization of strain energy throughout the fatigue process has thus improved the understanding of an energy‐based fatigue life prediction method.     

An energy‐based damage parameter for the life prediction of AISI 304 stainless steel subjected to mean strain

Abstract

This study extends the plastic strain energy approach to predict the fatigue life of AISI 304 stainless steel. A modified energy parameter based on the stable plastic strain energy density under tension conditions is proposed to account for the mean strain and stress effects in a low cycle fatigue regime. The fatigue life curve based on the proposed energy parameter can be obtained directly by modifying the parameters in the fatigue life curve based on the stable plastic strain energy pertaining to fully reversed cyclic loading. Hence, the proposed damage parameter provides a convenient means of evaluating fatigue life on the mean strain or stress effect. The modified energy parameter can also be used to explain the combined effect of alternating and mean strain/stress on the fatigue life. In this study, the mean strain effects on the fatigue life of AISI 304 stainless steel are examined by performing fatigue tests at different mean strain levels. The experimental results indicate that the combination of an alternating strain and a mean strain strongly influences the fatigue life. Meanwhile, it is found that the change in fatigue life is sensitive to changes in the proposed damage parameter under the condition of a constant strain amplitude at various mean strain levels. A good agreement is observed between the experimental fatigue life and the fatigue life predicted by the proposed damage parameter. The damage parameter proposed by Smith et al. (1970) is also employed to quantify the mean strain effect. The results indicate that this parameter also provides a reasonable estimate of the fatigue life of AISI 304 stainless steel. However, a simple statistical analysis confirms that the proposed damage parameter provides a better prediction of the fatigue life of AISI 304 stainless steel than the SWT parameter.     

Continuous fatigue damage prediction of a rubber fibre composite structure using multiaxial energy‐based approach

This paper details an advanced method of continuous fatigue damage prediction of rubber fibre composite structures. A novel multiaxial energy‐based approach incorporating a mean stress correction is presented and also used to predict the fatigue life of a commercial vehicle air spring. The variations of elastic strain and complementary energies are joined to form the energy damage parameter. Material parameter α is introduced to adapt for any observed mean stress effect as well as being able to reproduce the well‐known Smith‐Watson‐Topper criterion. Since integration to calculate the energies is simplified, the approach can be employed regardless of the complexity of the thermo‐mechanical load history. Several numerical simulations and experimental tests were performed in order to obtain the required stress‐strain tensors and the corresponding fatigue lives, respectively. In simulations, the rubber material of the air spring was simulated as nonlinear elastic. The mean stress parameter α , which controls the influence of the mean stress on fatigue life, was adjusted with respect to those energy life curves obtained experimentally. The predicted fatigue life and the location of failure are in very good agreement with experimental observations.     

Low‐cycle fatigue life prediction of various metallic materials under multiaxial loading

This paper proposed a simple life prediction model for assessing fatigue lives of metallic materials subjected to multiaxial low‐cycle fatigue (LCF) loading. This proposed model consists of the maximum shear strain range, the normal strain range and the maximum normal stress on the maximum shear strain range plane. Additional cyclic hardening developed during non‐proportional loading is included in the normal stress and strain terms. A computer‐based procedure for multiaxial fatigue life prediction incorporating critical plane damage parameters is presented as well. The accuracy and reliability of the proposed model are systematically checked by using about 300 test data through testing nine kinds of material under both zero and non‐zero mean stress multiaxial loading paths.     

Effect of axial ratcheting deformation on torsional low cycle fatigue life of lead-free solder Sn–3.5Ag

Multiaxial fatigue tests were conducted on Sn–3.5Ag solder specimens under axial/torsional loading at room temperature. It was found that the ratcheting strain increased while the fatigue life decreased with the increase of axial stress and shear strain amplitude. A power relationship of ratcheting strain rate versus fatigue life was observed. Equivalent strain approach and critical plane approaches were evaluated with fatigue life data obtained in the tests. Since those approaches excluded the consideration of the ratcheting strain and mean stress, the methods for fatigue life prediction were improper for multiaxial fatigue with ratcheting strain. Coffin model, considered the effect of ratcheting on fatigue life depending on the ratio of ratcheting strain to material ductility, brought the fatigue life predictions on non-conservative side if the ratcheting deformation was large. For this reason, a model with the maximum shear strain range and axial ratcheting strain rate was proposed as a new damage parameter. The new model could not only describe the fatigue life in torsion test, but also predicted torsional fatigue life of the lead-free solder with axial ratcheting.     

A fatigue driving energy approach to high‐cycle fatigue life estimation under variable amplitude loading

In this paper, a concept of fatigue driving energy is formulated to describe the process of fatigue failure. The parameter is taken as a combination of the fatigue driving stress and strain energy density. By assessing the change of this parameter, a new non‐linear damage model is proposed for residual life estimation within high‐cycle fatigue regime under variable amplitude loading. In order to consider the effects of loading histories on damage accumulation under such condition, the load interaction effects are incorporated into the new model, and a modified version is thus developed. Life predictions by these two models and Miner rule are compared using experimental data from literature. The results show that the proposed model gives lower deviations than the Miner rule, while the modified model shows better prediction performances than the others. Moreover, the proposed model and its modifications are ease of implementation with the use of S–N curve.     

Fatigue life prediction of a rubber mount based on test of material properties and finite element analysis

Failure analysis and fatigue life prediction are very important in the design procedure to assure the safety and reliability of rubber components. The fatigue life of a rubber mount was predicted by combining test of material properties and finite element analysis (FEA). The natural rubber material material’s fatigue life equation was acquired based on uniaxial tensile test and fatigue life tests of the natural rubber. The strain distribution contours and the maximum total principal strains of the rubber mount at different loads in the x and y directions were obtained using finite element analysis method. The critical region cracks prone to arise were obtained and analyzed. Then the maximum total principal strain was used as the fatigue parameter, which was substituted into the natural rubber’s fatigue life equation, to predict the fatigue life of the rubber mount. Finally, fatigue lives of the rubber mount at different loads were measured on a fatigue test rig to validate the accuracy of the fatigue life prediction method. The test results imply that the fatigue lives predicted agree well with the test results.     

Fatigue life prediction for metals using an improved strain energy density model

Abstract

An improved strain energy density model is proposed on the basis of critical plane concept to better predict the multiaxial fatigue life of metals, especially during nonproportional loadings. This approach is based on the normal and shear strain energy densities on maximum principal strain range plane. Procedures used to determine the normal and shear strain energy densities are also presented. Experimental data taken from the literature are used to validate the capabilities of the improved model, including 4 different metals and 24 different loading paths. The results show that the proposed model gives good predictions for most of these materials and loading paths.     

The characteristics of fatigue under isothermal and thermo-mechanical load in Cr–Ni–Mo cast hot work die steel

ABSTRACT High temperature isothermal fatigue (IF) and in-phase thermo-mechanical fatigue (TMF) tests in load control were carried out in cast hot work die steel. At the same load amplitude, the fatigue lives obtained in the in-phase TMF tests are lower than those obtained in the isothermal tests. Observations of fracture surface and the response of stress–strain reveal that cyclic creep in the tensile direction occurs and the intergranular cracks dominate in TMF tests, whereas cyclic creep in the compressive direction occurs and the path of the crack growth is mainly transgranular in IF tests. A model of life prediction, based on the Chaboche law, was discussed. Damage coefficients that are functions of the maximum temperature and the variation of temperature are introduced in the model so as to evaluate TMF lives in load control. With this method, the lifetime prediction gives results corresponding well to experimental data.     

Numerical methods of multiaxial fatigue life prediction for elastomers under variable amplitude loadings

In this paper, numerical methods of fatigue life prediction for elastomers subjected to multidirectional, variable amplitude loadings are presented. Because experiments and numerical methods use different stress measures in large deformation, transformation between nominal stress and the second Piola–Kirchhoff stress is performed before fatigue life calculation. In order to incorporate the Mullins effect, the material properties of elastomers are calculated after an initial transition period. An efficient interpolation scheme using load stress/strain curves under unidirectional loading is proposed based on the fatigue characteristic of elastomers. A rainflow counting method with multi‐stress components is developed for variable amplitude loadings, and the critical plane method is applied to find the plane with the maximum damage parameter. Fatigue life predictions using the proposed numerical method are validated against experimental results. As a practical example, the fatigue life of a rubber engine mount is predicted using the proposed numerical method.     

Multiaxial fatigue and failure analysis of helical compression springs

Multiaxial fatigue criteria are applied to the analysis of helical compression springs. The critical plane approaches, Fatemi–Socie and Wang–Brown, and the Coffin–Manson method based on shear deformation, were used to predict fatigue lives of the springs under constant amplitude loading. Experimental fatigue lives are compared with the multiaxial fatigue criteria predictions. The stress analysis was carried out in the finite element code ANSYS, and the multiaxial fatigue study was performed using the fatigue software nCode. A failure analysis was conducted in order to determine the fatigue crack initiation point and a comparison of that location with the most damaged zone predicted by the numerical analysis is made. The Fatemi–Socie critical plane approach gives a good prediction of fatigue life. While the Wang–Brown criterion overestimates spring fatigue life, the Coffin–Mason model gives conservative results.     

Multiaxial fatigue of rubber: Part I: equivalence criteria and theoretical aspects

This paper investigates commonly used approaches for fatigue crack nucleation analysis in rubber, including maximum principal strain (or stretch), strain energy density and octahedral shear strain criteria. The ability of these traditional equivalence criteria, as well as a recent equivalence criterion (the cracking energy density) to predict multiaxial fatigue behaviour is explored. Theoretical considerations are also introduced relating to the applicability of various fatigue life analysis approaches. These include the scalar nature of traditional equivalence criteria, robustness of the criteria investigated for a wide range of multiaxial loadings, effects of crack closure and applications to non‐proportional multiaxial loadings. It is shown that the notion of a stress or strain amplitude tensor used for the analysis of multiaxial loading in metals is not appropriate in the analysis of rubber due to nonlinearity associated with finite strains and near incompressibility. Taken together, these considerations illustrate that traditional criteria are not sufficiently consistent or complete to permit confident analysis of arbitrary multiaxial loading histories, and that an analysis approach specific to the failure plane is needed. Of the three traditional criteria, maximum principal strain is shown to match most closely to the cracking energy density criterion, in terms of a failure locus in principal stretch space.     

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.     

一种新的多轴高周疲劳模型

将疲劳强度以上加载等效为塑性应变,建立了塑性应变与加载应力呈线性关系的表达式,由此得到循环加载的塑性应变能。该塑性应变能使材料微观组织结构发生不可逆变化而引起等效宏观应力。假定该应力符合一种特定的分布函数,导出其最大应力与外加应力叠加达到材料本征断裂应力时的裂纹成核寿命,从而并由微裂纹引起上述两部分应力变化,得到继续加载直至宏观裂纹出现的疲劳寿命。所建立的多轴疲劳寿命公式由3个材料参数表达,并通过单轴疲劳试验数据确定。初步研究表明：该模型对所引用的多轴疲劳试验数据有很好的预测能力。