Category Archives: material testing

FEA Modeling of Rubber and Elastomer Materials

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The application of computational mechanics analysis techniques to elastomers presents unique challenges in modeling the following characteristics:

– The load-deflection behaviour of an elastomer is markedly non-linear.

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

deflection theory.

– The stress-strain characteristics are highly dependent on temperature and rate effects are pronounced.

– Elastomers are nearly incompressible.

– Viscoelastic effects are significant.

The ability to model the special elastomer characteristics requires the use of sophisticated material models and non-linear Finite element analysis tools that are different in scope and theory than those used for metal analysis. Elastomers also call for superior analysis methodologies as elastomers are generally located in a system comprising of metal-elastomer parts giving rise to contact-impact and complex boundary conditions. The presence of these conditions require a judicious use of the available element technology and solution techniques.

FEA Support Testing

Most commercial FEA software packages use a curve-fitting procedure to generate the material constants for the selected material model. The input to the curve-fitting procedure is the stress-strain or stress-stretch data from the following physical tests:

1  Uniaxial tension test

2  Uniaxial compression test OR Equibiaxial tension test

3  Planar shear test

4  Volumetric compression test

A minimum of one test data is necessary, however greater the amount of test data, better the quality of the material constants and the resulting simulation. Testing should be carried out for the deformation modes the elastomer part may experience during its service life.

Curve-Fitting

The stress-strain data from the FEA support tests is used in generating the material constants using a curve-fitting procedure. The constants are obtained by comparing the stress-strain results obtained from the material model to the stress-strain data from experimental tests. Iterative procedure using least-squares fit method is used to obtain the constants, which reduces the relative error between the predicted and experimental values. The linear least squares fit method is used for material models that are linear in their coefficients e.g Neo-Hookean, Mooney-Rivlin, Yeoh etc. For material models that are nonlinear in the coefficient relations e.g. Ogden etc, a nonlinear least squares method is used.

Verification and Validation

In the FEA of elastomeric components it is necessary to carry out checks and verification steps through out the analysis. The verification of the material model and geometry can be carried out in three steps,

_ Initially a single element test can be carried out to study the suitability of the chosen material model.

_ FE analysis of a tension or compression support test can be carried out to study the material characteristics.

_ Based upon the feedback from the first two steps, a verification of the FEA model

can be carried out by applying the main deformation mode on the actual component

on any suitable testing machine and verifying the results computationally.

Figure 1: Single Element Test

Figure(1) shows the single element test for an elastomeric element, a displacement

boundary condition is applied on a face, while constraining the movement of the opposite face. Plots A and B show the deformed and undeformed plots for the single element. The load vs. displacement values are then compared to the data obtained from the experimental tests to judge the accuracy of the hyperelastic material model used.

Figure 2: Verification using an FEA Support Test

Figure (2) shows the verification procedure carrying out using an FEA support test.

Figure shows an axisymmetric model of the compression button. Similar to the single

element test, the load-displacement values from the Finite element analysis are compared to the experimental results to check for validity and accuracy. It is possible that the results may match up very well for the single element test but may be off for the FEA support test verification by a margin. Plot C shows the specimen in a testing jig. Plot D and E show the undeformed and deformed shape of the specimen.

Figure(3) shows the verification procedure that can be carried out to verify the FEA

Model as well as the used material model. The procedure also validates the boundary conditions if the main deformation mode is simulated on an testing machine and results verified computationally. Plot F shows a bushing on a testing jig, plots G and H show the FEA model and load vs. displacement results compared to the experimental results. It is generally observed that verification procedures work very well for plane strain and axisymmetric cases and the use of 3-D modeling in the present procedure provides a more rigorous verification methodology.

Figure 3: FEA Model Verification using an Actual Part

AdvanSES provides Hyperelastic, Viscoelastic Material Characterization Testing for CAE & FEA softwares.

Unaged and Aged Properties and FEA Material Constants for all types of Polymers and Composites. Mooney-Rivlin, Ogden, Arruda-Boyce, Blatz-ko, Yeoh, Polynomials etc.

Dynamic Properties of Polymer, Rubber and Elastomer Materials

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Non-linear Viscoelastic Dynamic Properties of Polymer, Rubber and Elastomer Materials

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 Using FEA

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.

ASTM D5992 Dynamic Properties of Rubber Vibration Products

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ASTM D 5992 Test Standard applies to Dynamic Properties of Rubber Vibration Products such as springs, dampers, and flexible load-carrying devices, flexible power transmission couplings, vibration isolation components and mechanical rubber goods. The standard applies to to the measurement of stiffness, damping, and measurement of dynamic modulus.

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.

 

Dynamic Characterization Testing as Per ASTM D5992 and ISO 4664

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ASTM D5992 and ISO 4664-1

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

DYNAMIC PROPERTIES OF POLYMER MATERIALS AND THEIR MEASUREMENTS

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.

Dynamic Properties of Polymer Materials and their Measurements

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’

Limitations of Hyperelastic Material Models

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Limitations of Hyperelastic Material Models

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 lm are material constants obtained from the curve-fitting procedure and Jel is the elastic volume ratio.

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

I1 = l12+l22+l32

I2 = l12l22+l22l32+l12l32

I3 = l12l22l32

With the assumption of material incompressibility, I3=1, the strain energy function is dependent on I1 and I2 only. The Mooney-Rivlin form can be derived from Equation 3 above as

W(I1,I2) = C10 (I1-3) + C01 (I23)…………………………………………………………(4)

With C01 = 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 µi and αi are material parameters and for an incompressible material Di=0.

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(C10 + C01 ) …………………………….…(6)

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:

  1. ABAQUS Inc., ABAQUS: Theory and Reference Manuals, ABAQUS Inc., RI, 02
  2. Attard, M.M., Finite Strain: Isotropic Hyperelasticity, International Journal of Solids and Structures, 2003
  1. Bathe, K. J., Finite Element Procedures Prentice-Hall, NJ, 96
  2. Bergstrom, J. S., and Boyce, M. C., Mechanical Behavior of Particle Filled Elastomers,Rubber Chemistry and Technology, Vol. 72, 2000
  3. Beatty, M.F., Topics in Finite Elasticity: Hyperelasticity of Rubber, Elastomers and Biological Tissues with Examples, Applied Mechanics Review, Vol. 40, No. 12, 1987
  4. 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
  5. Blatz, P. J., Application of Finite Elasticity Theory to the Behavior of Rubber like Materials, Transactions of the Society of Rheology, Vol. 6, 196
  6. 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.
  7. Boyce, M. C., and Arruda, E. M., Constitutive Models of Rubber Elasticity: A Review, Rubber Chemistry and Technology, Vol. 73, 2000.
  8. 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.
  9. Srinivas, K., Material Characterization and Finite Element Analysis (FEA) of High Performance Tires, Internation Rubber Conference at the India Rubber Expo, 2005.

Free eBook: Material Characterization Testing and Finite Element Analysis of Elastomers

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The application of computational mechanics analysis techniques to elastomers presents
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.

Download the free eBook here.

 

Here’s what you can expect to learn:

1. Elastomeric materials and their properties

2. Computational Mechanics in the design and development of polymeric components

3. Why there are recommended testing protocols

4. Curve-fitting the Material Constants.

5. Verifications and Validations of FEA Solutions

 

Let’s talk Engineering with Rubber.

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

Abaqus – Tips and Tricks Vol 1

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Abaqus – Tips and Tricks: When to use what Elements?

For a 3D stress analysis, ABAQUS offers different typess of linear and quadratic hexahedral elements, a brief description is as below;

  1. Linear Hexahedral: C3D8 further subdivided as C3D8R, C3D8I, and C3D8H
  2. Quadratic Hexahedral: C3D20 further subdivided as C3D20R, C3D20I, and C3D20H, C3D20RH
  3. Linear Tetrahedral: C3D4 further subdivided as C3D4R, and C3D4H
  4. Quadratic Tetrahedral: C3D10 further subdivided as C3D10M, C3D10I and C3D10MH
  5. Prisms: C3D6 further subdivided as C3D6R, and C3D6H

In three-dimensional (3D) finite element analysis, two types of element shapes are commonly utilized for mesh generation: tetrahedral and hexahedral. While tetrahedral meshing is highly automated, and relatively does a good job at predicting stresses with sufficient mesh refinement, hexahedral meshing commonly requires user intervention and is effort intensive in terms of partitioning. Hexahedral elements are generally preferred over tetrahedral elements because of their superior performance in terms of convergence rate and accuracy of the solution.

The preference for hexahedral elements(linear and uadratic) can be attributed to the fact that linear tetrahedrals originating from triangular elements have stiff formulations and exhibit the phenomena of volumetric and shear locking. Hexahedral elements on the other hand have consistently predicted reasonable foce vs loading (stiffness) conditions, material incompressibility in friction and frictionless contacts. This has led to modeling situations where tetrahedrals and prisms are recommended when there are frictionless contact conditions and when the material incompressibility conditiona can be relaxed to a reasonable degree of assumption.

A general rule of thumb is if the model is relatively simple and you want the most accurate solution in the minimum amount of time then the linear hexahedrals will never disappoint.

Modified second-order tetrahedral elements (C3D10, C3D10M, C3D10MH) all mitigate the problems associated with linear tetrahedral elements. These element offer good convergence rate with a minimum of shear or volumetric locking. Generally, observing the deformed shape will show of shear or volumetric locking and mesh can be modified or refined to remove these effects.

C3D10MH can also be used to model incompressible rubber materials in the hybrid formulation. These variety of elements offer better distribution of surface stresses and the deformed shape and pattern is much better. These elements are robust during finite deformation and uniform contact pressure formulation allows these elements to model contact accurately.

The following are the recommendations from the house of Abaqus(1);

  • Minimize mesh distortion as much as possible.
  • A minimum of four quadratic elements per 90o should be used around a circular hole.
  • A minimum of four elements should be used through the thickness of a structure if first-order, reduced-integration solid elements are used to model bending.

 

 

  1. Abaqus Theory and Reference Manuals, Dassault Systemes, RI, USA

UNIAXIAL TENSION TEST: THE MOTHER OF ALL MECHANICAL TESTS

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UNIAXIAL TENSION TEST: THE MOTHER OF ALL MECHANICAL TESTS

INTRODUCTION:

In engineering design and analysis, stress-strain relationships are needed to establish and verify the load-deflection properties of an engineering component under service loads and boundary conditions. From the tensile testing carried out to evaluate materials, various mechanical properties such as the yield strength, Young’s modulus, Poisson’s ratio etc. are obtained. Strain hardening and true stress-strain etc. values can be calculated by means of conversion using equations from the stress-strain curve. The uniaxial tensile test is the primary method to evaluate the material and obtain the parameters. Uniaxial tension test is also the primary test method used for quality control and certification of virtually all ferrous and non-ferrous type of materials.

Standards for tensile testing were amongst the first published and the development of such standards continues today through the ASTM and ISO organizations. Reliable tensile data, which is now generated largely by computer controlled testing machines, is also crucial in the design of safety critical components automotive, aerospace and biomedical applications.

Tensile testing is also important for polymeric materials as they depend strongly on the strain rate because of their viscoelastic nature. Polymers exhibit time dependent deformation like relaxation and creep under service applications. Polymer properties also show a higher temperature dependency than metals. Multiple temperatures and strain rates are generally used to fully characterize polymer materials.


Figure 1: Uniaxial Tension Test on a Material Sample

Figure 2 shows sample uniaxial stress-strain results from testing a metal specimen. The X axis depicts the strain and Y axis the stress. The stress (σ) is calculated from;

σ = Load / Area of the material sample ……………………………………..(1)

The strain(ε) is calculated from;

ε = δl (change in length) / l1 (Initial length) ……………………………………..(2)

The slope of the initial linear portion of the curve (E) is the Young’s modulus and given by;

E = (σ2- σ1) / (ε2- ε1) ……………………………………..(3)

Point A in the graph shows the proportional limit of the material beyond which the material starts to yield. When this point is not clearly visible or decipherable in a test, the off yield strength at B is taken by offsetting the strain (F-G) by 0.2 % of the gauge length. Similarly, extension by yield under load (EUL) is calculated by offsetting the strain 0.5% of the gauge length. The region between points A and B on the graph is also purely elastic, with full recovery on the unloading of the metal, but it is not essentially linear.

Figure 2: Sample Uniaxial Stress-Strain Results from a Metal Specimen

TRUE STRESS-STRAIN CURVE:
Figure 2 shows the engineering stress-strain curve where the values of stress beyond the proportional limit do not give the true picture of stress in the sample as the cross-sectional area of the sample is assumed to be constant. The engineering stress-strain values can be converted to true stress-strain values by the following relation;

σt = σe (1 + εe) = σeλ , ……………………………………..(4)

εt = ln (1 +εe) = ln λ, where λ = initial length / final length …………………………………..(5)


Figure 3: Sample Uniaxial Stress-Strain Results for a Polymeric Rubber Material

Figure 3 shows typical uniaxial stress-strain results from a test on a 40 durometer rubber material. Unlike the results for the metal specimen the elastomer test results do not have or exhibit a yield limit. The material extends in the classical ‘S’ shape and results in a fracture at the end of the tests. Polymeric rubber materials exhibit the following characteristics;
• The load-deflection behavior of an elastomer is markedly non-linear.
• The recoverable strains can be as high 700 %.
• The stress-strain characteristics are highly dependent on temperature and rate effects are highly pronounced.
• Nearly incompressible behavior.
• Viscoelastic effects are significant.
Typical test results for rubber materials show the values of modulus at 100%, 200% and 300%. Modulus represents stress in such results.

SPECIFIC MECHANICAL ISSUES IN TESTING:

1. Strain Rate
2. Extensometry
3. Alignment and Gripping
4. Testing Machine Frame Compliance
5. Young’s Modulus Measurement
6. Specimen Geometry

Strain rate range of different material characterization test methods

1) Quasi-static tension tests 10-5 to 10-1 S-1
2) Dynamic tension tests 10-1 to 102 S-1
3) Very High Strain Rate or Impact tests 102 to 104 S-1

A fundamental difference between a high strain rate tension test and a quasi-static tension test is that inertia and wave propagation effects are present at high rates. An analysis of results from a high strain rate test thus requires consideration of the effect of stress wave propagation along the length of the test specimen in order to determine how fast a uniaxial test can be run to obtain valid stress-strain data.

IMPORTANCE OF THE UNIAXIAL TENSION TEST:
At the basic level apart from giving us an understanding about the ultimate strain and stress capabilities of the material, tensile tests provide us with information about the factor of safety that needs to be built-in the products using these materials.
1) Fatigue life of engineering materials can be calculated from tensile tests carried out on notched and unnotched specimens.
2) Aging and other environmental effects can be incorporated in the test procedure to characterize the material, as well as predict service life using techniques like Arrhenius equation.
3) Endurance limits in design calculations are calculated from the results obtained from uniaxial tension tests.
4) In manufacturing of rubber materials and products, it is used to determine batch quality and maintain consistency in material and product manufacturing.
5) Electromechanical servo based miniature tensile testing machines can be developed to study material samples of smaller size.

REFERENCES:
1. Dowling, N. E., Mechanical Behavior of Materials, Engineering Methods for Deformation, Fracture and Fatigue Prentice-Hall, NJ, 99
2. Roylance, D., Mechanical Properties of Materials, MIT, 2008.
3. Gedney, R., Tensile Testing Basics, Tips and Trends, Quality Magazine, 2005.
4. Loveday, M. S., Gray, T., Aegerter, J., Testing of Metallic Materials: A Review, NPL, 2004.
5. Srinivas, K., and Pannikottu, A., Material Characterization and FEA of a Novel Compression Stress Relaxation Method to Evaluate Materials for Sealing Applications at the 28th Annual Dayton-Cincinnati Aerospace Science Symposium, March 2003.
6. Ong, J.H., An Improved Technique for the Prediction of Axial Fatigue Life from Tensile Data, International Journal of Fatigue, 15, No. 3, 1993.
7. Manson, S.S. Fatigue: A Complex Subject–Some Simple Approximations, Experimental Mechanics, SESA Annual Meeting, 1965.
8. Yang, S.M., et al. Failure Life Prediction by Simple Tension Test under Dynamic Load, International Conference on Fracture, 1995.

 

SERVICE LIFE PREDICTION OF POLYMER RUBBER COMPONENTS USING ACCELERATED AGING AND ARRHENIUS EQUATION

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Introduction:

Polymeric rubber components are widely used in automotive, aerospace and biomedical systems in the form of seals, o-rings, gaskets, vibration isolators, suspension components etc. The service life of these systems is governed by the useful life of the polymeric materials used in these different applications. Aerospace and biomedical systems are expected to have service life in decades, while automotive components are expected to fully last the 5 years 100,000 warranted miles. Polymeric rubber components can get degraded when exposed to chemical and environmental degradants like ozone, UV rays, oxygen, thermal cycling, engine oils, water etc., and also due to mechanical service stress and strain conditions. It becomes very important to predict life of polymeric and rubber components under these degrading service environments. The most common approach is to accelerate the ageing of a material using elevated temperature tests combined with an extrapolation technique to predict the life time of the material/product at lower temperatures.

Theory and Technique:

One of the most widely used techniques to predict lifetimes of polymeric materials is the use of Arrhenius equation. The technique utilizes accelerated thermal aging of the materials under controlled conditions. Failure times and degradation rate studies are carried out at elevated temperatures and the data is used to extrapolate material performance to ambient conditions. Arrhenius extrapolations assume that a chemical degradation process is controlled by a reaction rate ‘k’,

k = A  e^{-Ea/(RT)}  OR  ln k = ln A +  {-Ea/(RT)}      ———————————(1)

where Ea is the Arrhenius activation energy, R is the universal gas constant (8.314 J/mol °K), T the absolute temperature and A the pre-exponential factor. A log-plot of degradation times (1/k) versus inverse temperature (1/T in °K) is expected to result in a straight line. The linear interpolations along this line can be used to predict properties to lower temperatures.

To be able to successfully use the Arrhenius equation, accelerated testing must be carried out at a minimum of four temperatures above the product application temperature.  To accurately estimate the degradation rate it is important to use a material property which exhibits sufficient range to assure a reliable and accurate determination of the property during the accelerated aging process.  Properties like tensile modulus, tear strength, stress relaxation modulus can be used to study the accelerated aging process and degradation rates.

Figure 1: Tensile Strength of Material at Various Temperatures and Aging Times

 

The identification of ageing mechanisms and the evaluation of dependence of these mechanisms on the mechanical properties of components is important. To successfully apply life prediction technique using the Arrhenius equation, the predominant degradation process has to systematically identified and an appropriate accelerated aging test to replicate the degradation process has to be carried out. The degradation process and failures of aged laboratory samples needs to be correlated to the components in the field. The accelerated aging temperatures need to be suitably chosen to correlate field degradation rates. Generally, a test time of one decade is equivalent to a temperature rise of 10°C

Figure 2: Arrhenius Plot Showing the Degradation Times and Inverse Temperature

 

Key Assumptions:

In most applications involving temperature acceleration replicating a failure mechanism, a degradation process might involve multiple steps with each of the steps having its own rate constants and activation energy. It is assumed that these phenomena can be approximated over the full temperature range by the Arrhenius equation.  It is also assumed that the chemical degradation process plays  major part in the failure mechanism, if the failure is a stress induced one then the Arrhenius equation method cannot be usefully employed. Method assumes that the chemical deterioration induced in the lab is directly correlated to the service life in the field.

Limitations and Benefits:

Arrhenius extrapolation to predict service life using accelerated aging  and degradation exhibits some limitations and many reports showing that temperature effects on degradation kinetics cannot always be described using the Arrhenius equation have been published. However, Arrhenius extrapolation being easy to perform, reproducible, replicable and practically relevant in large amount of field service applications is widely used for lifetime prediction of polymers in different environments.

 

Conclusions:

Various approaches can be applied to determine life of elastomer components used in engineering applications.  It is imperative to define their failure modes and failure mechanisms and establish verification and correlations between field service conditions and laboratory testing samples. The Arrhenius method provides a quantifiable determination of the service life of elastomer components in engineering applications.

 

References:

  1. Celina, M., Gillen, K.T., Assink, R. K., Accelerated Aging and Lifetime Prediction: Review of Non-Arrhenius Behavior due to Two Competing Processes, Polymer Degradation and Stability, Vol. 90, 2005
  2. Leyden, Jerry., Failure Analysis in Elastomer Technology: Special Topics, Rubber Division, 2003
  3. Roland, C.M., Vagaries of Elastomer Service Life Prediction, Institute of Materials, Minerals and Mining, 2009
  4. Bernstein, and Gillen K.T., Predicting the lifetime of Flurorosilicone O-rings, Polymer Degradation and Stability, 2009
  5. Mott, C. M. Roland, Ageing of Natural Rubber in Air and Seawater, Rubber Chemistry and Technology, 2001
  6. Baranwal, Krishna., Elastomer Technology: Special Topics, Rubber Division, 2003
  7. Srinivas, K., and Pannikottu, A., Material Characterization and FEA of a Novel Compression Stress Relaxation Method to Evaluate Materials for Sealing Applications at the 28th Annual Dayton-Cincinnati Aerospace Science Symposium, March 2003.
  8. Srinivas, K., Systematic Experimental and Computational Mechanics Failure Analysis Methodologies for Polymer Components, ARDL Technical Report, March 2008.
  9. Dowling, N. E., Mechanical Behavior of Materials, Engineering Methods for Deformation, Fracture and Fatigue Prentice-Hall, NJ, 99