They are required to reduce the transmission of vibrations, providing the desired ride characteristics and protecting the rigid frame. The elastomeric material used in these components tends to naturally degrade over a period of time due to harsh conditions in addition to material degradation. Testing the properties of these mounts under such conditions is critical to make sure that the components meet the expectations. Choosing the correct test parameters required to perform this type of automotive component tests reliably can be challenging. We have more than a decade of experience in the design, analysis and testing of these rubber elastomer mounts.

]]>1) Stress-Strain relationship, Young’s modulus of elasticity

2) Yield strength.

3) Bulk and shear modulus.

4) Poisson’s ratio.

5) Density.

The relationship between applied mechanical force/stress and resulting deformation/strain on a given material is called its stress-strain curve or a constituent relationship equation. Isotropic materials like plastics, metals and elastomers exhibit the same behavior in all their orientations and layouts, while orthotropic and anisotropic materials, such as composites, glass-filled plastics, etc. show mechanical stress-strain properties that vary depending on the directions. Stress-strain equations and behaviors vary greatly by material type, as metals, plastics, elastomers, glass, composites, etc.

AdvanSES is a premier material testing laboratory for mechanical properties testing and component testing. We can test aged and unaged samples. Materials can be tested under static, dynamic and under elevated temperature conditions. In addition to testing and FEA, we have in-house machining facilities to develop test fixtures required to evaluate products and components for stiffness, stress, strain etc.

]]>Static testing of materials as per ASTM D412, ASTM D638, ASTM D624 etc can be cate- gorized as slow speed tests or static tests. The difference between a static test and dynamic test is not only simply based on the speed of the test but also on other test variables em- ployed like forcing functions, displacement amplitudes, and strain cycles. The difference is also in the nature of the information we back out from the tests. When related to poly- mers and elastomers, the information from a conventional test is usually related to quality control aspect of the material or the product, while from dynamic tests we back out data regarding the functional performance of the material and the product.

Tires are subjected to high cyclical deformations when vehicles are running on the road. When exposed to harsh road conditions, the service lifetime of the tires is jeopardized by many factors, such as the wear of the tread, the heat generated by friction, rubber aging, and others. As a result, tires usually have composite layer structures made of carbon-filled rubber, nylon cords, and steel wires, etc. In particular, the composition of rubber at different layers of the tire architecture is optimized to provide different functional properties. The desired functionality of the different tire layers is achieved by the strategical design of specific viscoelastic properties in the different layers. Zones of high loss modulus material will absorb energy differently than zones of low loss modulus. The development of tires utilizing dynamic characterization allows one to develop tires for smoother and safer rides in different weather conditions.

Figure Locations of Different Materials in a Tire Design

The dynamic properties are also related to tire performance like rolling resistance, wet traction, dry traction, winter performance and wear. Evaluation of viscoelastic properties of different layers of the tire by DMA tests is necessary and essential to predict the dynamic performance. The complex modulus and mechanical behavior of the tire are mapped across the cross section of the tire comprising of the different materials. A DMA frequency sweep

test is performed on the tire sample to investigate the effect of the cyclic stress/strain fre- quency on the complex modulus and dynamic modulus of the tire, which represents the viscoelastic properties of the tire rotating at different speeds. Significant work on effects of dynamic properties on tire performance has been carried out by Ed Terrill et al. at Akron Rubber Development Laboratory, Inc.

Non-linear Viscoelastic tire simulation is carried out using Abaqus to predict the hysteresis losses, temperature distribution and rolling resistance of a tire. The simulation includes several steps like (a) FE tire model generation, (b) Material parameter identification, (c) Material modeling and (d) Tire Rolling Simulation. The energy dissipation and rolling re- sistance are evaluated by using dynamic mechanical properties like storage and loss modu- lus, tan delta etc. The heat dissipation energy is calculated by taking the product of elastic strain energy and the loss tangent of materials. Computation of tire rolling is further carried out. The total energy loss per one tire revolution is calculated by;

Ψdiss = ∑ i2πΨiTanδi, (.27)

i=1

where Ψ is the elastic strain energy,

Ψdiss is the dissipated energy in one full rotation of the tire, and

Tanδi, is the damping coefficient.

The temperature prediction in a rolling tire shown in Fig (2) is calculated from the loss modulus and the strain in the element at that location. With the change in the deformation pattern, the strains are also modified in the algorithm to predict change in the temperature distribution in the different tire regions.

]]>In real world applications all materials and products are subjected to a wide variety of vibrating or oscillating forces. Fatigue testing consists of applying a cyclic load to a test specimen or the component to determine in-service performance during situations similar to real world working conditions.

Advanced Scientific and Engineering Services (AdvanSES) specializes in Fatigue Testing of Automotive Components including hoses, engine mounts, vibration isolators, silent bushes etc. Fatigue testing can be carried out in stress & force control, strain control or displacement control. The deformation modes under which fatigue tests are generally carried out are tension – tension, compression – compression, tension – compression and compression – tension.

Dynamic testing is performed on a variety of rubber parts and components like engine mounts, hoses, conveyor belts, vibration isolators, laminated and non-laminated bearing pads, silent bushes etc. to determine their response to dynamic loads and cyclic loading.

Personalized consultation from AdvanSES engineers can streamline testing and provide the necessary tools and techniques to accurately evaluate material performance under field service conditions.

The quantities of interest for measurements are tan delta, loss modulus, storage modulus, phase etc. All of these properties are viscoleastic properties and require instruments, techniques and measurement practices of the highest quality.

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ASTM D5992 covers the methods and process available for determining the dynamic prop- erties of vulcanized natural rubber and synthetic rubber compounds and components. The standard covers the sample shape and size requirements, the test methods, and the pro- cedures to generate the test results data and carry out further subsequent analysis. The methods described are primarily useful over the range of temperatures from cryogenic to 200◦C and for frequencies from 0.01 to 100 Hz, as not all instruments and methods will accommodate the entire ranges possible for material behavior.

Figures(.43and.44) show the results from a frequency sweep test on five (5) different elastomer compounds. Results of Storage modulus and Tan delta are plotted.

Figure .43: Plot of Storage Modulus Vs Frequency from a Frequency Sweep Test

The frequency sweep tests have been carried out by applying a pre-compression of 10 % and subsequently a displacement amplitude of 1 % has been applied in the positive and negative directions. Apart from tests on cylindrical and square block samples ASTM D5992 recommends the dual lap shear test specimen in rectangular, square and cylindri- cal shape specimens. Figure (.45) shows the double lap shear shapes recommended in the standard.

Figure .44: Plot of Tan delta Vs Frequency from a Frequency Sweep Test

Figure .45: Double Lap Shear Shapes

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.

Polymer materials in their basic form exhibit a range of characteristics and behavior from elastic solid to a viscous liquid. These behavior and properties depend on the temperature, frequency and time scale at which the material or the engineering component is analyzed.

The viscous liquid polymer is defined as by having no definite shape and flow deformation under the effect of applied load is irreversible. Elastic materials such as steels and aluminium deform instantaneously under the application of load and return to the original

state upon the removal of load, provided the applied load is within the yield or plastic limits of the material. An elastic solid polymer is characterized by having a definite shape that deforms under external forces, storing this deformation energy and giving it back upon

the removal of applied load. Material behavior which combines both viscous liquid and solid like features is termed as Viscoelasticity. These viscoelastic materials exhibit a time dependent behavior where the applied load does not cause an instantaneous deformation,

but there is a time lag between the application of load and the resulting deformation. We also observe that in polymeric materials the resultant deformation also depends upon the speed of the applied load.

Characterization of dynamic properties play an important part in comparing mechanical properties of different polymers for quality, failure analysis and new material qualification. Figures 1.4 and 1.5 show the responses of purely elastic, purely viscous and of a viscoelastic material. In the case of purely elastic, the stress and the strain (force and resultant deformation) are in perfect sync with each other, resulting in a phase angle of 0. For a purely viscous response the input and resultant deformation are out of phase by 90o. For a

viscoleastic material the phase angle lies between 0 and 90 degree. Generally the measurements of viscoelastic materials are represented as a complex modulus E* to capture both viscous and elastic behavior of the material. The stress is the sum of an in-phase response and out-of-phase responses.

The so x Cosdelta term is in phase with the strain, while the term so x Sindelta is out of phase with the applied strain. The modulus E’ is in phase with strain while, E” is out of phase with the strain. The E’ is termed as storage modulus, and E” is termed as the loss modulus.

E’ = s0 x cosdelta

E” = s0 x sindelta

Tan delta = Loss factor = E”/E’

]]>**Introduction:**

Polymeric rubber components are widely used in automotive, aerospace and biomedical systems in the form of vibration isolators, suspension components, seals, o-rings, gaskets etc. Finite element analysis (FEA) is a common tool used in the design and development of these components and hyperelastic material models are used to describe these polymer materials in the FEA methodology. The quality of the CAE carried out is directly related to the input material property and simulation technology. Nonlinear materials like polymers present a challenge to successfully obtain the required input data and generate the material models for FEA. In this brief article we review the limitations of the hyperleastic material models used in the analysis of polymeric materials.

** Theory:**

A material model describing the polymer as isotropic and hyperelastic is generally used and a strain energy density function (*W*) is used to describe the material behavior. The strain energy density functions are mainly derived using statistical mechanics, and continuum mechanics involving invariant and stretch based approaches.

**Statistical Mechanics Approach**

The statistical mechanics approach is based on the assumption that the elastomeric material is made up of randomly oriented molecular chains. The total end to end length of a chain (*r*) is given by

Where *µ* and *l** _{m}* are material constants obtained from the curve-fitting procedure and

**Invariant Based Continuum Mechanics Approach**

The Invariant based continuum mechanics approach is based on the assumption that for a isotropic, hyperelastic material the strain energy density function can be defined in terms of the Invariants. The three different strain invariants can be defined as

*I*_{1} = l_{1}^{2}+l_{2}^{2}+l_{3}^{2}

*I*_{2} = l_{1}^{2}l_{2}^{2}+l_{2}^{2}l_{3}^{2}+l_{1}^{2}l_{3}^{2}

*I*_{3} = l_{1}^{2}l_{2}^{2}l_{3}^{2}

With the assumption of material incompressibility, *I _{3}=1*, the strain energy function is dependent on

*W(I _{1},I_{2})*

With *C _{01 }= 0* the above equation reduces to the Neo-Hookean form.

**Stretch Based Continuum Mechanics Approach**

The Stretch based continuum mechanics approach is based on the assumption that the strain energy potential can be expressed as a function of the principal stretches rather than the invariants. The Stretch based Ogden form of the strain energy function is defined as

where *µ _{i} *and α

Neo-Hookean and Mooney-Rivlin models described above are hyperelastic material models where, the strain energy density function is calculated from the invariants of the left Cauchy-Green deformation tensor, while in the Ogden material model the strain energy density function is calculated from the principal deformation stretch ratios.

The Neo-Hookean model, one of the earliest material model is based on the statistical thermodynamics approach of cross-linked polymer chains and as can be studied is a first order material model. The first order nature of the material model makes it a lower order predictor of high strain values. It is thus generally accepted that Neo-Hookean material model is not able to accurately predict the deformation characteristics at large strains.

The material constants of Mooney-Rivlin material model are directly related to the shear modulus ‘G’ of a polymer and can be expressed as follows:

*G *= 2(*C _{10} *+

Mooney-Rivlin model defined in equation (4) is a 2nd order material model, that makes it a better deformation predictor that the Neo-Hookean material model. The limitations of the Mooney-Rivlin material model makes it usable upto strain levels of about 100-150%.

Ogden model with N=1,2, and 3 constants is the most widely used model for the analysis of suspension components, engine mounts and even in some tire applications. Being of a different formulation that the Neo-Hookean and Mooney-Rivlin models, the Ogden model is also a higher level material models and makes it suitable for strains of upto 400 %. With the third order constants the use of Ogden model make it highly usable for curve-fitting with the full range of the tensile curve with the typical ‘S’ upturn.

**Discussion and Conclusions:**

The choice of the material model depends heavily on the material and the stretch ratios (strains) to which it will be subjected during its service life. As a rule-of-thumb for small strains of approximately 100 % or *l*=2.0, simple models such as Mooney-Rivlin are sufficient but for higher strains a higher order material model as the Ogden model may be required to successfully simulate the ”upturn” or strengthening that can occur in some materials at higher strains.

**REFERENCES:**

- ABAQUS Inc.,
*ABAQUS: Theory and Reference Manuals, ABAQUS Inc.*, RI, 02 - Attard, M.M.,
*Finite Strain: Isotropic Hyperelasticity*, International Journal of Solids and Structures, 2003

- Bathe, K. J.,
*Finite Element Procedures*Prentice-Hall, NJ, 96 - Bergstrom, J. S., and Boyce, M. C.,
*Mechanical Behavior of Particle Filled Elastomers*,Rubber Chemistry and Technology, Vol. 72, 2000 - Beatty, M.F.,
*Topics in Finite Elasticity: Hyperelasticity of Rubber, Elastomers and Biological Tissues with Examples*, Applied Mechanics Review, Vol. 40, No. 12, 1987 - Bischoff, J. E., Arruda, E. M., and Grosh, K.,
*A New Constitutive Model for the Compressibility of Elastomers at Finite Deformations*, Rubber Chemistry and Technology,Vol. 74, 2001 - Blatz, P. J.,
*Application of Finite Elasticity Theory to the Behavior of Rubber like Materials*, Transactions of the Society of Rheology, Vol. 6, 196 - Kim, B., et al.,
*A Comparison Among Neo-Hookean Model, Mooney-Rivlin Model, and Ogden Model for Chloroprene Rubber,*International Journal of Precision Engineering & Manufacturing, Vol. 13. - Boyce, M. C., and Arruda, E. M.,
*Constitutive Models of Rubber Elasticity: A Review*, Rubber Chemistry and Technology, Vol. 73, 2000. - Srinivas, K.,
*Material Characterization and FEA of a Novel Compression Stress Relaxation Method to Evaluate Materials for Sealing Applications*, 28th Annual Dayton-Cincinnati Aerospace Science Symposium, March 2003. - Srinivas, K.,
*Material Characterization and Finite Element Analysis (FEA) of High Performance Tires*, Internation Rubber Conference at the India Rubber Expo, 2005.

unique challenges in modeling the following characteristics:

1) The load-deflection behavior of an elastomer is markedly non-linear.

2) The recoverable strains can be as high 400 % making it imperative to use the large

deflection theory.

3) The stress-strain characteristics are highly dependent on temperature and rate effects

are pronounced.

4) Elastomers are nearly incompressible.

5) Viscoelastic effects are significant.

The inability to apply a failure theory as applicable to metals increases the complexities regarding the failure and life prediction of an elastomer part. The advanced material models available today define the material as

hyperelastic and fully isotropic. The strain energy density (W) function is used to describe the material behavior.

To help you better understand, we broke down everything you need to know about materials, testing, FEA verifications and validations etc.

Our expert engineers can help you get your next product into the market in the shortest possible team or solve your durability and fatigue problems. To learn more, fill up the contact form and get in touch

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