Experiment and modeling of uniaxial tension fatigue performances for filled natural rubbers

A tension fatigue model of filled natural rubbers is investigated to study the contributions of two key factors, namely, the damage parameter and the specimen geometry used in the fatigue experiment. The uniaxial tension fatigue experiments were carried out for three filled natural rubber specimens with different geometry: a dumbbell simple tension specimen (STS), a dumbbell cylindrical specimen (DCS), and a hollow cylindrical specimen (HCS). The commonly used damage parameters for fatigue life prediction are discussed. The fatigue life prediction models are formulated using the measured tension fatigue life of the STS together with different damage parameters. The effectiveness of the models is established in terms of a correlation coefficient characterizing the error between the measured and predicted fatigue lives. It is concluded that all the damage parameters considered in the study can effectively estimate the tension fatigue life with correlation coefficients exceeding 0.9. The fatigue life model formulated for the STS was also found to be appropriate for predicting the fatigue life of specimens with different geometry (DCS and HCS) suggesting that the relationship between the tension fatigue life and the damage parameters is independent of the specimen geometry. One may thus conduct tension fatigue tests with STS alone in order to model the tension fatigue life of rubbers with alternate geometry.     

考虑应变均值影响的天然橡胶隔振元件疲劳寿命预测

对橡胶试柱进行单轴疲劳试验,分析了应变幅值一定时,应变均值对疲劳寿命的影响。以哑铃型天然橡胶试柱为研究对象,通过有限元计算分析,得到了加载位移与橡胶试柱危险位置处最大主应变的关系。构建了应变均值函数,以应变比R=0时的 曲线为基准疲劳寿命曲线,建立了不同应变均值和幅值下的天然橡胶隔振元件的疲劳寿命预测模型。使用该模型预测得到的哑铃型天然橡胶试柱疲劳寿命与试验疲劳寿命具有较好相关性。文中提出的天然橡胶元件的疲劳寿命预测模型,可用于建立天然橡胶材料的疲劳寿命数据库。     

A method to develop a unified fatigue life prediction model for filled natural rubbers under uniaxial loads

Rubber components are widely used in many fields because of their superior elastic properties. Fatigue failures, commonly encountered in rubber components, however, remain a critical issue. In this study, the effect of strain ratio R on the fatigue life of filled natural rubbers used in automotive mounts is investigated experimentally and numerically. A uniaxial tension/compression fatigue experiment was conducted on dumb‐bell cylindrical rubber specimens subject to loads representing different R ratios. The experimental fatigue data are used to formulate two preliminary fatigue models based on peak strain and strain amplitude as the damage parameters. The deficiencies of these two models in predicting fatigue life over a wide range of R ratios are discussed, and an alternative life prediction model is proposed. The proposed model incorporates the effect of R ratio using an equivalent strain amplitude. It is shown that the proposed model could effectively predict fatigue life over a wide range of R ratios with an improved accuracy.     

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.     

单轴拉伸状态下橡胶隔振器的疲劳寿命预测研究

针对橡胶隔振器疲劳寿命预测问题,基于哑铃型橡胶材料试片的疲劳寿命试验数据,建立橡胶隔振器的疲劳寿命预测模型,进而提出橡胶隔振器疲劳寿命预测的研究方案。设计了一哑铃型橡胶试片进行拉伸疲劳试验,实测其疲劳寿命数据并以最小二乘法拟合了该试片疲劳寿命的幂函数预测模型。再通过有限元方法计算了橡胶隔振器的三种常见的疲劳寿命评价参数：对数主应变、柯西主应力和应变能密度,最后将橡胶隔振器的疲劳寿命预测值与实测值进行比对。结果发现：当疲劳失效标准静为刚度降级25%时,三种疲劳寿命评价参数均能较好地拟合成幂函数疲劳寿命预测模型,对数主应变的预测值较为接近实测值、应变能密度参数的预测值约为实测值2倍左右、柯西主应力预测寿命的可靠性验证系数均接近5,且三种疲劳损伤评价参数的疲劳寿命拟合曲线形状均较为相似。     

基于橡胶隔振器动静态试验的弹性材料参数反演及预测模型研究

本研究根据WH150橡胶隔振器的动静态实测数据,通过Abaqus与Isight联合仿真,反演弹性材料的超弹本构参数和黏弹本构参数。输入反演的橡胶本构参数,建立橡胶隔振器的预测模型,该模型推导出的三向静刚度、动刚度和动态传递率误差均小于10%。将预测模型应用于隔振器实际使用工况的计算中,可快速评估橡胶隔振器的实际共振频率和疲劳寿命。      

橡胶隔振器加速疲劳试验谱的编制方法研究

通过大量的橡胶动静刚度试验和疲劳试验,分别获取了某填充型天然橡胶材料在各试验条件下的动静比数据表和疲劳寿命数据表。以发动机悬置为例,在充分考虑橡胶材料动态特性的基础上,建立了道路载荷值与应变值的转换关系。对采集的道路载荷谱进行雨流计数,根据Miner线性损伤累积理论与损伤等效原则,编制得到最终的加速疲劳试验谱。用该加速疲劳试验谱对发动机悬置进行疲劳试验,试验结果表明：用该方法编制的加速疲劳试验谱可成功应用于悬置等橡胶隔振器零件的疲劳试验,并且较大程度地缩短了试验与产品开发周期。     

基于开裂能密度及裂纹扩展特性的橡胶隔振器疲劳特性预测

基于开裂能密度的连续介质力学参数及橡胶材料裂纹扩展特性(裂纹扩展速率与撕裂能之关系),获得橡胶部件多轴疲劳特性计算公式,并计算某汽车动力总成橡胶隔振器的疲劳特性。计算与试验对比表明,橡胶隔振器疲劳特性预测(寿命、开裂位置及开裂方向)与实测较一致。预测疲劳寿命分布在实测疲劳寿命的1/2倍分散因子内,满足工程疲劳寿命预测要求。提出的橡胶隔振器多轴疲劳特性预测方法,可用试验效率较高、投入较少的材料裂纹扩展试验代替耗时较多的材料疲劳破坏试验,不仅能为橡胶部件前期疲劳设计提供参考,亦能大幅缩短产品疲劳设计周期。     

Multiaxial creep–fatigue life prediction for cruciform specimen

This paper describes the high temperature multiaxial creep–fatigue life prediction for type 304 stainless steel. Finite element analyses were performed for determining the stress–strain state in the gage part of a cruciform specimen subjected to creep–fatigue loading under four strain waves at three principal strain ratios. Creep–fatigue lives of cruciform specimens were discussed in relation to the principal stress amplitude calculated by finite element analysis. Creep–fatigue damage was evaluated by linear damage rule and the suitability of three low cycle fatigue and three creep damage parameters was discussed.     

Multiaxial fatigue of rubber: Part II: experimental observations and life predictions

Fatigue experiments were conducted with an axial‐torsion specimen covering a wide range of stretch biaxiality and a range of fatigue lives between 10³ and 2 × 10⁶ cycles. These experiments include combined torsion–compression, pure torsion, combined torsion–tension and pure axial tension. Both in‐phase and out‐of‐phase combinations of axial and torsion loading were considered. The multiaxial fatigue experiments described provide empirical evidence from which an understanding of the mechanics of the fatigue process in rubber can be developed. Each of the four equivalence parameters described in Part I has been applied to the axial‐torsion fatigue experiments described in this paper (Part II). These results provide the basis for an analysis of the effects of multiaxial loading on fatigue life, and an assessment of the degree to which the various equivalence parameters are able to rationalize the results in a unified way. For the combined axial and shear strain histories in this study, the maximum principal strain criterion gave the best correlation to fatigue life. Strain energy density gave the worst correlation. The cracking energy density criterion was generally found to give good correlation of fatigue crack nucleation lives from combined axial‐torsion tests. Because it provides a plane‐specific analysis, this criterion appears to be particularly well suited for use in crack nucleation analyses of multiaxial strain histories.     

[±20°]钢丝/橡胶复合材料的疲劳损伤累积

对 钢丝帘线增强的橡胶复合材料在拉伸循环载荷下的疲劳损伤累积进行了研究。结果表明:在载荷控制的疲劳过程中,材料的周期最大应变发展曲线呈现明显的三阶段规律。帘线端头处基体裂纹的出现是宏观疲劳损伤的初始,损伤的累积表现为裂纹数量增加、帘线/基体脱粘和层间裂纹的扩展。以动蠕变为参量建立了线性疲劳损伤累积模型,该模型能够较好地预报两级加载条件下材料的第二级疲劳寿命。     

Fatigue of vulcanized natural rubber under proportional and non‐proportional loading

Two natural rubber (NR) compounds of hardness shore A 60 and 70 with 10 different biaxial displacement/twist paths were investigated using an axisymmetric cylindrical hollow dumbbell specimen. The effects of the proportional and non‐proportional loading modes on the fatigue life are discussed. In total, 52 fatigue test results are reported with fatigue life results of 3,918 to 488,000 cycles. The effect of the channel phase on the fatigue life is discussed.     

A method for assessing critical plane‐based multiaxial fatigue damage models

Fatigue failure is a complex phenomenon. Therefore, development of a fatigue damage model that considers all associated complexities resulting from the application of different cyclic loading types, geometries, materials, and environmental conditions is a challenging task. Nevertheless, fatigue damage models such as critical plane‐based models are popular because of their capability to estimate life mostly within ±2 and ±3 factors of life for smooth specimens. In this study, a method is proposed for assessing the fatigue life estimation capability of different critical plane‐based models. In this method, a subroutine was developed and used to search for best estimated life regardless of critical plane assumption. Therefore, different fatigue damage models were evaluated at all possible planes to search for the best life. Smith‐Watson‐Topper (normal strain‐based), Fatemi‐Socie (shear strain‐based), and Jahed‐Varvani (total strain energy density‐based) models are compared by using the proposed assessment method. The assessment is done on smooth specimen level by using the experimental multiaxial fatigue data of 3 alloys, namely, AZ31B and AZ61A extruded magnesium alloys and S460N structural steel alloy. Using the proposed assessment method, it was found that the examined models may not be able to reproduce the experimental lives even if they were evaluated at all physical planes.     

单向聚酯帘线增强橡胶材料疲劳特性研究

利用自行建立的试验系统, 首次对单向聚酯帘线增强橡胶材料进行了疲劳测试, 研究了应变、频率和温度对疲劳损伤累积的影响, 并给出了疲劳寿命预报方程, 为评价轮胎的疲劳特性、预报轮胎的疲劳寿命提供了有效的手段。      

FRP橡胶隔振器水平剪切特性的初步研究

应用小波变换及自助理论对多自由度系统进行模态参数辨识。通过对结构系统响应信号进行小波变换将其表示在时频域内,在分析了小波变换的时频分辨率特性后,利用最小Shannon熵获取最优小波参数,并运用自助理论估计出模态参数分布的置信区间范围。数值仿真表明了该方法对模态参数估计的有效性。将所提方法应用于一个振动台的模态分析,实验结果表明,提出的小波自助模态参数辨识方法降低了模态参数辨识的难度,提高了模态频率和阻尼比的辨识精度。     

聚酯增强橡胶疲劳破坏实验研究

采用特殊设计的夹具和疲劳测试系统,借助软Ｘ射线技术和ＳＥＭ技术研究了聚酯增强橡胶的疲劳破坏机理,给出了疲劳寿命图。研究表明,定应变控制的聚酯增强橡胶的疲劳过程呈现明显的阶段性,其疲劳破坏机理表现为三种类型：基体裂纹、聚酯／橡胶界面脱粘、帘线断裂。疲劳过程的不同阶段对应不同的基体、界面以及帘线纤维的损伤机理。另外,对材料疲劳过程中的热效应进行了定性分析。     

Material characterization of SS 316 in low-cycle fatigue loading

This study deals with simulation of low-cycle fatigue (LCF), followed by evaluation of fatigue parameters, which would be suitable for estimating fatigue lives under uniaxial loading. The cyclic elastic–plastic stress–strain responses were analyzed using the incremental plasticity procedures. Finite-element (FE) simulation in elastic–plastic regime was carried out in FE package ABAQUS. Emphasis has been laid on calibration of SS 316 stainless steel for LCF behavior. For experimental verifications, a series of low-cycle fatigue tests were conducted using smooth, cylindrical specimens under strain-controlled, fully reversed condition in INSTRON UTM (Universal Testing Machine) with 8,800 controller at room temperature. The comparisons between numerical simulations and experimental observations reveal the matching to be satisfactory in engineering sense. Based on the cyclic elastic–plastic stress–strain response, both from experiments and simulation, loop areas, computed for various strain amplitude, have been identified as fatigue damage parameter. Fatigue strain life curves are generated for fatigue life prediction using Coffin–Manson relation, Smith–Watson–Topper model, and plastic energy dissipated per cycle (loop area). Life prediction for LCF has been found out to be almost identical for all these three criteria and correlations between predicted and experimental results are shown. It is concluded that the improvement of fatigue life prediction depends not only on the fatigue damage models, but also on the accurate evaluations of the cyclic elastic–plastic stress/strain responses.     

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.     

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.     

橡胶复合材料疲劳破坏特性

分别对[00 ]和[ ±200 ]橡胶复合材料在拉伸循环载荷下的疲劳损伤进行了实验研究。两类材料的周期最大应变随循环周次的变化遵循三阶段规律, 三个阶段对应着疲劳损伤从萌生、稳定扩展到加速扩展直至整体破坏的过程。单层和双层材料的疲劳破坏分别为帘线控制和基体控制。实验表明, 用加载最大应力表征的疲劳寿命与循环周次的对数近似成线性关系。疲劳过程中材料的滞后损失基本保持不变。滞后损失和导热系数的差异是造成不同种类试件表面温升差异的主要原因。