Fatigue damage criteria for antivibration systems with filled natural rubber under negative and positive R ratios

Luo R.K.

It is impossible to generate all of the S–N curves for antivibration design and applications under a wide range of rubber compounds in industry. It saves substantial costs if an S–N curve can be calculated from a known stress-based S–N base function. To predict fatigue life of antivibration isolators based on an existing stress-based S–N curve of a known material. The cylinder dumbbell specimens subjected to 30 fatigue cases with different R ratios were used to generate a stress-based S–N base function with the shear modulus using the effective tensile stress criterion. The function was then applied to the ring specimens in 90 fatigue cases, followed by the industrial product MDS (Multidirectional Snubbing) mounts. Correlations were found between the critical locations and the maximum values of the effective tensile stress in all fatigue cases. All predicted points were within a scatter band of 0.9 in the cylinder dumbbell specimens. When the function was used, approximately 87.8% of the points (79 of 90) fell within the scatter band of 2.0 in the ring specimens and the crack initiation would occur at approximately 86 kcycles against observed severe damage at 400 kcycles in the MDS mounts. This approach seems effective, and the application can save significant cost in industry by eliminating substantial fatigue tests. The S–N base function obtained can be useful for engineering design and applications where no fatigue data are available.

Luo R.K.

Rubber fatigue prediction under positive and negative R ratios . • Critical locations were correlated with the maximum value of ε t from both the cylindrical and ring specimens. • The criterion achieved R 2 of 0.85 in an S-N form with a scatter band of 0.5 over 30 fatigue cases under different R ratios. • 96.7% of the predicted data within the measured fatigue band with a scale factor of 2 on the cylindrical samples. • The criterion was validated on 90 fatigue cases with 15 paths and all predicted points were within a scatter band of 1.7. • This potential novel approach without additional fitting variables would save significant time and cost in industry. An effective tensile strain ε t for rubber fatigue under positive and negative ratios was proposed for the design of rubber products in the industry. It was applied to the cylindrical specimens over 30 fatigue cases: achieved the predicted points within a scatter band of 0.5 with R 2 = 0.85. Further application to the ring specimens on 90 fatigue cases including different loading modes and phase angles: achieved the prediction within a scatter band of 1.7. Critical locations were correlated with the maximum values of ε t . The novel approach without additional fitting variables can be used in engineering design and applications.

Warneboldt I., Marco Y., Charrier P., Hervouet W., Champy C., Raoult I., Le Saux V., Szmytka F.

• Extensive multiaxial & uniaxial fatigue test campaign on natural rubber is provided. • Observations confirm connection between lifetime reinforcement and crack features. • Temperature influences relaxing and non-relaxing tests (lifetime & crack features) • Critical plane predictions fail for lifetime reinforcing multiaxial configurations. • Analyses of crack features & lifetimes point to a local microstructure modification. This paper presents an extensive test campaign and analysis to better understand the fatigue behavior and the mechanisms at stake for natural rubber under complex non-relaxing loads. This database includes relaxing uniaxial tests under tension and torsion, relaxing and non-relaxing tension tests for 3 temperatures, relaxing multiaxial tension-torsion proportional tests, and non-relaxing tension-torsion multiaxial sequenced tests for different temperatures. The tests are conducted on hourglass-shaped natural rubber specimens, loaded by coupled and aligned tension and torsion actuators. Various strain ratios, uniaxial and biaxial loading sequences and critical plane orientation histories over a loading cycle are achieved. A total of 240 specimens were tested. Different temperatures are imposed to affect reinforcement and provide a comparison to previous results on crystallization. Furthermore, finite element analyses (FEA) are performed to determine first the respective local mechanical state in the specimens and then to infer the crack orientation predicted from a critical plane approach based on the maximum principal strain. Finally, the results are carefully analyzed based on three indicators: the relative improvement on fatigue lifetime, the cracks features (roughness and branching, from optical and SEM observations) and their comparison to the crack orientation predicted using the critical plane approach.

Luo R.K.

An accurate prediction of the fatigue life of a rubber product is based on a criterion. Since strain can be measured directly in rubber components during a test, it would help design engineers improve product performance effectively if the strain-based damage criteria can achieve high accuracy. Hence, the experimental data on the AE42 and AE2 specimens were utilized to test the suitability of the proposed damage criterion for rubber materials. The criterion includes three principal components determined by both a strain range and a current strain. Data from AE42 specimens, made from styrene-butadiene rubber, contained 40 cases, that is, tension, torsion, and tension-torsion loadings. An S-N curve was obtained, with a scatter band of 0.7 and a coefficient of determination R2 of 0.81. The curve could be useful at the design stage. A sample of AE2, made from natural rubber filled with carbon black, showed the location and orientation of the crack in a nonproportional case. The predicted location of the fatigue crack was consistent with the experimental observation and the crack orientation matched the experimental measurement, that is, the predicted angle of 33.4° versus the measurement of approximately 40°. It would be possible to combine the proposed approach with the critical plane method in nonproportional loadings to save significant CPU time: using the proposed approach to find the critical loading range and then using the critical plane method to find the maximum value of the required damage variables. More engineering cases are needed to further verify this proposed criterion.

Luo R.K.

Luo R.K.

Several researchers have worked on the development of effective criteria for prediction of fatigue failure in rubber. Although many of these criteria have achieved some level of success, they are restrictive in the sense that they apply only to certain loading conditions. A new criterion was proposed to evaluate damage for antivibration design and applications so that different loading modes would not alter the fatigue prediction. It is hypothesized that shear deformation causes fatigue damage in rubber. An effective shear strain criterion was developed by combining three principal strain ranges and verified using the published experimental results from 4 loading sets: 14 tension cases; 31 torsion cases 26 combined tension–torsion cases in phase and 19 combined tension–torsion cases out of phase. In addition, the criterion was validated against a failure of an industrial mount. The predicted cracks were located at the maximum values of the criterion, consistent with where the cracks were observed experimentally. The predicted crack orientations correlated with the experimental measurement. The obtained S–N curve covered over 102 to 2.4 × 106 cycles, achieving high accuracy with a scatter-band of 1.9 based on the 90 fatigue cases. This criterion seems effective and could be used at a stage of fatigue design. In addition, it could be combined with the critical plane method: the proposed approach could be used to find hot spots, whilst the critical plane search method could be utilised locally to find the maximum values of the required damage variables.

Champy C., Le Saux V., Marco Y., Glanowski T., Charrier P., Hervouet W.

• We have generated an extensive Haigh diagram on a rubber-like material over a wide range of load ratio. • A preliminary study is carried out to define an initiation criterion that remains valid for all the testing conditions. • The Haigh diagram presents a bell shape with an improvement of the fatigue properties for positive load ratio up to R_d = 0.35. • This shape is related to strain induced crystallization. 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).

Wang G., Wang W., Liang C., Cao L.

The damage that occurs around the tire bead region is one of the critical failure forms of a tire. Generally, the prediction of tire durability is carried out by the experimental method. However, it takes a lot of money and time to conduct experiments. Therefore, to determine the fatigue life of radial tire bead, a reasonable prediction method is proposed in this paper. Fatigue testing of bead rubber compounds to determine the ΔSED-number of the cycle (Nf) was applied. The maximum strain energy density range (ΔSEDmax) of several bead compounds was obtained by steady-state rolling analysis with a finite element method. This quantity is then inserted into a fatigue life equation to estimate the fatigue life. The experimental results of the 175/75R14 tire were compared with the estimated value, which showed a good correlation. It is concluded that the method can be effectively applied to the fatigue life prediction of the tire bead.

Liang C., Gao Z., Hong S., Wang G., Kwaku Asafo-Duho B.M., Ren J.

Vehicle tires are major components that are subjected to fatigue loading and their durability is of economic interest as it is directly related to the safety of property and the life of producers and consumers. Tire durability is also a major issue of energy conservation and environmental protection. This research aims to establish a reasonable fatigue evaluation and optimization method that effectively improves tire fatigue life. In the study, 11.00R20 and 12.00R20 all-steel radial truck tires were the research objects, and the guiding hypothesis for the research was that “the maximum area of ​​the strain energy density gradient modulus corresponds to the initial failure area, its direction corresponds to the crack propagation direction, and also the maximum strain energy value is inversely proportional to the tire fatigue life.” Through finite element analysis and durability test, the strain energy density gradient was determined as tire fatigue evaluation index, and the hypothesis of tire fatigue life prediction was validated. At the same time, the sensitivities of strain energy gradient to the tire structure parameters were calculated. Besides, the relationship between the structure parameters and the fatigue life was as well established in this paper. This study has formulated a tire fatigue evaluation method and proposed an effective optimization method for enhancing tire fatigue life. The results obtained are of high application value in offering guidance for tire structural design and useful for refining the fatigue failure theory of truck radial tires and improving durability.

Xu X., Zhou X., Liu Y.

Rubber-sleeved studs, which are headed studs wrapped with rubber sleeves, have been found to be prospective to overcome some challenges in the design of steel–concrete composite structures with ordinary stud shear connectors. A finite element-based approach was provided for the fatigue life prediction of rubber-sleeved stud shear connectors. After calculating the stress and strain state of the connector by finite element models, the fatigue crack initiation life was predicted based on the critical surface method, and fracture mechanics was adopted to predict crack propagation life. The prediction method was validated by fatigue push-out test results. The subsequent finite element parametric study revealed the effect of shear stress range, rubber sleeve height, and elastic moduli of rubber and concrete on the fatigue life of shear connectors. Further, fatigue life prediction formulas for ordinary stud and rubber-sleeved stud shear connectors were proposed for facilitating the engineering application. The reliability of these formulas was verified by comparing with S-N curves in the design codes and those obtained from fatigue push-out tests.

Ruellan B., Le Cam J.-., Jeanneau I., Canévet F., Mortier F., Robin E.

Natural rubbers have extraordinary physical properties, typically the ability to crystallize under tension that is assumed to be responsible for their high fatigue resistance. Strain-induced crystallization (SIC) is a high thermo-sensitive phenomenon. Better understanding how SIC reinforces fatigue life and how temperature affects this property is therefore a key point to improve the durability of rubbers. The present study investigates temperature effects on the fatigue life reinforcement due to SIC for non-relaxing loadings. After a brief state of the art that highlights a lack of experimental results in this field, a fatigue test campaign has been defined and was carried out. Results obtained at 23 °C were first described at the macroscopic scale. Both damage modes and number of cycles at crack initiation were mapped in the Haigh diagram. Fatigue damage mechanisms were then investigated at the microscopic scale, where the signature of SIC reinforcement in the crack growth mechanisms has been identified. Typically, fatigue striations, wrenchings and cones peopled the fracture surfaces obtained under non-relaxing loading conditions. At 90 °C, fatigue life reinforcement was still observed. It is lower than at 23 °C. Only one damage mode was observed at the macroscopic scale. At the microscopic scale, fracture surfaces looked like the ones of non-crystallizable rubbers. At 110 °C, the fatigue life reinforcement totally disappeared.

Nyaaba W., Frimpong S., Anani A.

Off-road ultra-large tires experience different modes of heat-related fatigue failure in operation due to inherent material defects that grow into visible cracks under service loads. This study implements the cracking energy density theory to predict nucleation life of selected components of a 56/80R63 tire. The method uses an assumed intrinsic flaw, a fatigue crack growth law, and a rubber constitutive law to compute local crack driving forces from strain history loads obtained via FEA. The results show that the lower sidewall, belt endings, and inner tread lug corners are the critical regions for crack initiation with lives 5.03 × 105, 1.207 × 105, and 2.01 × 104 cycles, respectively.

Zhang J., Xue F., Wang Y., Zhang X., Han S.

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.

Carleo F., Barbieri E., Whear R., Busfield J.

Modelling the viscoelastic behavior of rubber for use in component design remains a challenge. Most of the literature does not consider the typical regimes encountered by anti-vibration devices that are deformed to medium dynamic strains (0.5 to 3.5) at medium strain rates (0.5/s to 10/s). Previous studies have either focused on the behaviour at small strains and small strain rates or in fast loading conditions that result in low cycle fatigue or tearing phenomena. There is a lack of understanding of the dynamic response of natural rubber suspension components when used in real vehicle applications. This paper presents a review of popular viscoelastic nonlinear constitutive models and their ability to model the mechanical behaviour of typical elastomer materials such as Natural Rubber (NR) incorporating different PHR (Parts per Hundred Rubber, XX) of carbon black. The range of strain and strain rate are typical for the materials used in rubber suspensions when operating in severe service operating conditions, such as over rough terrain or over pot-holes. The cyclic strain is applied at different amplitudes and different strain rates in this medium strain range. Despite the availability of many models in the literature, our study reports that none of the existing models can fit the data satisfactorily over a wide range of conditions.

Li W., Xin Z.

Fatigue endurance characteristics investigation of driving belts is of great significance to assure the safety and reliability of the mechanical transmission and evaluate the feasibility of a new product design. R1 type tooth V-belts consisting of fiber reinforced rubber generally operate under cyclic flexural fatigue load caused by a clutch tensioner, resulting in propagation of crack at the compression section rubber and thus losing its efficiency. This paper presents a concise methodology to predict the flexural fatigue life of tooth V-belt through a combination of material property test and finite element analysis method. Hyperelasticity, viscoelasticity and Mullins effect of fiber reinforced rubber were completely considered in the finite element model. De Mattia flexural fatigue specimen was adopted as the simulated sample. Crack formation and crack length extension of the De Mattia specimen tested under various cyclic flexural loads have also been studied. The maximum strain energy density used as the damage parameter was obtained through finite element analysis method. An empirical equation to predict the flexural fatigue life of tooth V-belts was proposed finally. The results demonstrate that the stress soften phenomenon of fiber reinforced compression section rubber is more pronounced after adding short fibers. Moreover, maximum strain energy density decreased drastically with the crack propagating. The predicted fatigue lives were fairly well in agreement with the experiment results, indicating the present method shows a great prospect and effectiveness in practical engineering application.

Kocjan T., Nagode M., Klemenc J., Oman S.

Luo R.K., Thompson M., Xu J., Li X.

In this case study, we introduce a new approach by applying the most recent fatigue criterion, effective tensile stress, to a rail vehicle suspension spring for the first time. Without the need for curve fitting, this criterion can effectively predict fatigue life under positive and negative R ratios. We defined a general S-N function and failure rates based on published results from cylindrical dumbbell samples on 30 fatigue cases. The measured load-displacement curve validated the material model with an elastic constant ratio. Blocks of three different loading sets were applied to a rail vehicle suspension spring for 125k cycles. One crack initiation was observed at 82k cycles and propagated to 97 mm after the test. We successfully predicted crack initiation at 81k cycles (with a failure rate of 7%) and 92k cycles (with a failure rate of 10%) using the Palmgren–Miner law. This prediction agreed with the experiment’s observation, demonstrating the approach’s reliability. The general S-N function could be used for the design and failure analysis of rail vehicle suspensions, providing reassurance in the design process.

Zhang X., Guo A., Li R., Li X., Hou Y., Zhang Y., Han J.

AbstractMetal coordination bonds can be coordinated to specific functional groups in polymers. This special coordination can give the material excellent self‐healing and mechanical properties. Nitrile rubber (XNBR)/CuCl2 composites were prepared by solid‐state blending. By changing the coordination reaction temperature, different coordination bonds were formed between the nitrile rubber and copper ions. The starting temperature of the coordination reaction was determined to be 100°C by observing the changes in the coordination reaction curve. With the increase of temperature from 100°C to 190°C, the copper ions' oxidation state was raised to 3, while part of C ≡ N was transformed to C=N at high temperature. Quantitative analysis revealed that the linear coordination [Cu2+–NL] was predominantly triple‐coordinated, and the curved coordination [Cu3+–NB] was coordinated in the form of ionic clusters. In addition to this, the formation of linear coordination bonds was easier and more reversible based on the calculation of the apparent activation energy of the coordination reaction. Macroscopically, the mechanical properties and self‐repairing ability of XNBR/CuCl2‐10‐100°C were higher than those of XNBR/CuCl2‐10‐190°C. The design of cross‐linked XNBR with good mechanical properties and recycling performance was of great significance in protecting the environment and realizing sustainable development.Highlights XNBR/CuCl2‐10‐100°C composites mainly form linear coordination [Cu2+–3NL]. XNBR/CuCl2‐10‐190°C composites form bending coordination [Cu3+–NB]. [Cu3+–NB] is stronger than [Cu2+–NL] but less reversible.

Luo R.K.

AbstractIn this study, a new concept of the elastic constant ratio was introduced to derive an S‐N base function, which has removed the requirement of the shear modulus to be measured in previous work, allowing much wider applications in fatigue prediction with significant reduction in the costs involved in conducting experiments and acceleration of the design process in industries. In this approach, the damage parameter was the effective tensile stress verified for both positive and negative R ratios (the ratio between the minimum stress and the maximum stress). Existing work only provided a general description of the criterion without detailed explicit equations, which does not provide sufficient clarity to the reader and could lead to variable fatigue life predictions. Here, detailed equations are introduced on the calculation procedure to allow accurate results to be obtained for fatigue assessment. The applicability of the approach was validated using two industrial components, that is, the Metacone spring and the bush spring. The maximum values of the damage parameter corresponded to the same failure locations observed in the experiments. The suggested S‐N base function, correlated with different materials and failure cycles, could be applied in a fatigue design stage and failure analysis for rubber isolators.Highlights For the first time, an elastic constant ratio is introduced on different rubbers. There is no additional test required for the material constants to save cost. The approach is experimentally validated on two industrial isolators. Monitoring stiffness in tests cannot determine the crack initiation accurately.