An integrated approach for fatigue design of rail vehicle suspensions under block loading

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.

Luo R.K.

A shape change can initiate fatigue damage in rubber components, which has led to the development of the effective shear strain γt criterion in this investigation. Referring to the previous damage criterion, i.e., effective tensile strain εt, the relation between the two was revealed. To benchmark the effectiveness of different damage criteria, six damage criteria, including the commonly used maximum principal strain, stress, and strain energy density, were compared using cylindrical dumbbell samples in 30 fatigue cases under ± R ratios. A large scatter was generated using either the maximum principal strain or the stress criterion. The strain energy density was in excellent agreement in uniaxial tension loadings but failed in torsional loadings with R = −1. To save significant cost in producing a completed new S–N curve for each rubber material, the derived S–N base functions using both εt and γt have been successfully validated on three independent experiments, i.e., the cylindrical dumbbell specimens, the ring specimens, and the industrial mount MDS. To fully verify the applicability of both εt and γt, the prediction of the crack orientation was performed for the first time using the proposed criteria, to the knowledge of the author, and the results were consistent with the experimental observations. The proposed criteria are useful for antivibration product design.

Yang L., Dai X., Zhao X., Liu F., Xu Y., Wang Y.

Abstract Fatigue failure, commonly encountered in rubber materials, is a critical issue. In this study, the compression fatigue tests of filled styrene-butadiene rubber (SBR) under different loading conditions were performed, applying cylindrical specimens. A stress–strain curve and modulus drop curves were generated by nine fatigue loading cases, covering different R ratios in the range of 0 < R < 1. The temperature variation in the process of compression fatigue was explored. Three different approaches were applied to investigate the fatigue life of the SBR (it is used twice hence abbreviation should be used) vulcanizates. These methods were validated in assessing the fatigue failure of the specimens. According to the experimental fatigue life, a fatigue life prediction model based on strain amplitude as the damage parameter was established. The results demonstrated that both R ratio and strain amplitude could affect the fatigue life. For all the loading cases, the fatigue life generally increases with the increase of R ratio. Under the compression loading condition, the narrower range of strain and the lower mean strain are beneficial to the fatigue resistance of rubbers, which also indicates a larger pre-load provides much higher fatigue resistance. During the fatigue loading, the temperature rises rapidly until it reaches a peak value, then drops slightly, and finally reaches a plateau.

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.

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.

Boulenouar A., Benseddiq N., Merzoug M., Benamara N., Mazari M.

In this paper, a numerical modeling of crack propagation for rubber-like materials is presented. This technique aims at simulating the crack growth under mixed-mode loading based on the strain energy density approach. At each crack increment length, the kinking angle is evaluated as a function of the minimum strain energy density (MSED) around the crack tip, using the Ansys Parametric Design Language (APDL). In this work, numerical examples are illustrated to demonstrate the effectiveness, robustness and accuracy of the computational algorithm to predict the crack propagation path. The results obtained show that the plan of crack propagation is perpendicular to the direction of the maximum principal stretch. Moreover, in the framework of linear elastic fracture mechanics (LEFM), the minimum values of the density are reached at the points corresponding to the crack propagation direction.

Wang X., Shangguan W., Rakheja S., Li W., Yu B.

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.

Zarrin-ghalami T., Fatemi A.

Rubber components have broad applications in industry and they often operate under cyclic loading conditions. Therefore, fatigue analysis is an essential part of the failure analysis and life prediction of such components. In this paper a fatigue life prediction methodology for rubber components is developed, which is then verified by means of the analysis and testing of an automobile cradle mount made of filled natural rubber. The analysis conducted includes constitutive behavior representation of the material, finite element analysis of the component, and a fatigue damage parameter for life predictions. Both the fatigue crack initiation life prediction approach and the crack-growth-based life prediction approach were used. Test results are shown to be in reasonable agreement with the predicted fatigue lives for both the crack initiation approach and the crack growth approach.

ZARRIN-GHALAMI T., FATEMI A.

Elastomeric components are widely used in many applications due to their good damping and energy absorption characteristics. The type of loading normally encountered by these components in service is variable amplitude cyclic loading. Therefore, fatigue failure is a major consideration in their design. In this work capabilities of Rainflow cycle counting procedure, maximum principal strain as a damage criterion, and Miner's linear cumulative damage rule are evaluated with both specimen and component tests. An automotive cradle mount is used as an illustrative component. Comparison of predicted and experimental fatigue lives in both specimen and cradle mount variable amplitude load tests indicate satisfactory predictions in both cases.

Samad M.S., Ali A., Sidhu R.S.

This study was carried out to predict the durability of automotive car jounce bumper using Finite Element Analysis (FEA). Fatigue life correlations were taken from literatures and it was incorporated into FEA codes. The simulated results were validated with experimental work. The FEA results showed good agreement with the experiment conducted on the jounce bumper in term of load–displacement response. In term of the durability of the component, the fatigue life predicted shows agreement at lower fatigue strains. However, the error becomes larger as the fatigue strains become higher. The differences between the predicted fatigue life and the experimental fatigue life were discussed. Finally, the predicted crack initiation side was also validated in the experiment.

SAINTIER N., CAILLETAUD G., PIQUES R.

This study deals with the fatigue crack initiation under multiaxial non-proportional loadings in a natural rubber. Push–pull, torsion and tension-compression with a superimposed static torsion fatigue test results are presented. A short presentation of some important features concerning short fatigue crack growth is given. Two fatigue crack criteria are proposed, the first one based on the first and second invariant of the Cauchy stress tensor, the second, based on the micromechanisms of crack initiation, consist of a critical plane approach under large strain conditions using a micro to macro approach. The second criterion was found to give the best results, by predicting the fatigue lifes, crack orientations and location, even in cases with internal crack initiation.

Wu W., Cook P., Luo R., Mortel W.

A case study is reported on the design of a Metacone mounting used as a primary spring fitted at the wheel axle box on a railway vehicle. In use the rubber layers are loaded in shear and compression and the Metacone mounting provides controlled complicance along three axes. Requirements for increased service life and dimensional limitations (implying high strain levels) have led to an ever closer focus on suspension spring design. (In the current example the general space envelope was 250 mm in diameter by 250 mm high.) Furthermore, as was the case here, end of life is often defined in terms of clearly noticeable cracks or changes in stiffness rather than final failure. The location, formation and early stage development of fatigue cracks are therefore key issues in such cases. Design methods involving finite element (FE) and fatigue life analysis (FLA) were used to redesign the Metacone. As a result the life of the Metacone undergoing customer-specified (single axis) fatigue testing was increased more than ten-fold.

Luo R.K., Wu W.X.

Rubber springs are widely used in industry as anti-vibration components giving many years of service. The metacone type of rubber spring is well established to control vertical and lateral movements. Nowadays, the more demanding operating environment has made the design of such components more challenging than ever before. The purpose of the FE analysis is to obtain an improved fatigue life of the spring from the requirements of our customers. It is shown that a quasi-static simulation for rubber springs using nonlinear software can provide good indication for product design and failure analysis. It is also shown that the virtual fatigue profile of the component can be obtained using both post processor and user subroutines, which provides clear picture of potential failures.