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Dynamic Properties of Polymer, Rubber and Elastomer Materials

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.

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ASTM D5992 Dynamic Properties of Rubber Vibration Products

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.

 

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Dynamic Characterization Testing as Per ASTM D5992 and ISO 4664

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

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Limitations of Hyperelastic Material Models

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 (I2–3)…………………………………………………………(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.
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Free eBook: Material Characterization Testing and Finite Element Analysis of Elastomers

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

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Abaqus – Tips and Tricks Vol 1

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
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Fatigue Design Optmization of Torque Arm Bush Mount for Heavy Truck Applications

Design Development and Finite Element Analysis (FEA) of Torque Arm Bush Mount for Heavy Truck Applications

Abstract:

A Torque Arm Bush is a metal-elastomer bonded component that forms an integral part of a heavy truck bogie or suspension system. Many different designs exist in the market today and each one with its own unique geometry, material and load application conditions. This analysis demonstrates the hyperelastic material characterization testing, material constant generation and FEA on the component to predict the service performance.

Methodology:

The physics involved in the simulation are complex and can be summarized as follows:

  1. Elastomer performance is markedly non-linear.
  2. Loading conditions like axial, radial, conical, torsional must be defined in multiple steps as per the service conditions and loading cycles.
  3. Large strain deformation with contacts

Figure 1: Hyperelastic Material Characterization Testing               Figure 2: FEA Model of the Torque Arm Bush Mount Assembly

Approach:

  • Material Study and Characterization to understand static and dynamic material properties.
  • Develop material constants and design concepts based on load-deflection and performance characteristics.
  • Use Finite Element Analysis (FEA) to optimize the design and understand FMEA.
  • Provide assembly modeling & drawings for prototype manufacturing.

Figure 3: Shows the Comparison between FEA and Experimental Testing Results

Figure 4: Deformed Shape and Stress-Strain Distribution in the Torque Arm Bush Mount

Results and Discussion:

The principal deformation modes of a heavy duty suspension component were modeled in Abaqus using hyperelastic analysis. High stresses were noted along the curvature locations in the design under conical deformations and confirmed by fatigue testing. This  locations were identified as ‘hot-spots’ and are fatigue-critical locations. The geometrical and material parameters were optimized to better mitigating the stresses and reduce the fatigue failures.

References:

  1. Dassault Systemes, Abaqus theory and reference manuals
  2. Yunhi, Yu, Nagi G Naganathan, Rao V Dukkipati, A literature review of automotive vehicle engine mounting systems, Mechanism and Machine Theory Volume 36, Issue 1, January 2001.
  3. Srinivas, K., Material Characterization And CAE For Non-Metallic Materials & Manufacturing Processes, SAE Symposium on CAE Applications for Automotive Structures, Detroit, November 2005.

Technicals:

  • Advanced Softwares like Abaqus, Static testing machines are available in-house and design iterations can be carried out on the fly.
  • Full material characterization capabilities of polymeric materials for FEA
  • Capabilities for fatigue durability testing In-house.
  • Advanced material testing facilities like DMA, DSC, TGA and TMA also available.

 

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FAILURE ANALYSIS OF POLYMER AND RUBBER MATERIALS

FAILURE ANALYSIS OF POLYMER AND RUBBER MATERIALS

Polymeric materials  like rubbers cure or harden (set) into a given shape, generally through the application of heat. Curing also known as vulcanizing is an irreversible chemical reaction in which permanent connections known as cross-links are made between the material’s molecular chains. These intra-molecular cross-links give the cured rubber material a solid three-dimensional structure.

Rubber products are designed using engineering principles of loads and deflections applied to a certain volume of material. The use of engineering principles in the development of rubber products provide an application envelope in which the products are expected to perform. Most of the products do provide the required services for satisfactory lifetimes, however  failures do occur. Failures occurring under field services conditions are expensive and it becomes imperative to identify the cause and rectify it as soon as possible. The failure mode of polymers sets limits to the process of engineering design.

Understanding the actual reason for failures is absolutely required to avoid recurrence and prevent failure in similar components, systems, structures or products. The analysis should also help with the understanding and improvement of design, materials selection, and manufacturing techniques.

Failure analysis consists of investigations to find out how and why parts and components failed.

The four major reasons for engineering failures are;

1) Poor and improper design features,

2) Incorrect use of material,

3) Defects introduced during manufacturing and

4) Service conditions.

Traditionally, failure analysis methods have focused on laboratory testing and chemical analysis of components to fully understand why components fail. The evolution of faster computers, as well as the growth of available material information, has made computer-based failure analysis using techniques like Finite Element Analysis (FEA) and Computational Fluid Dynamics (CFD) more feasible and accessible.

Figure 1 shows the flowchart of a systematic approach to a typical failure analysis study. The process of failure study invariably starts with observing the working of the component under service conditions and gathering the facts about the conditions. One can identify patterns in the behavior of the material or component under service conditions and develop a technical hypothesis based on the observations. Once all the observations have been recorded, a failure hypothesis is generated that fits all the observations. This failure hypothesis is now tested to make sure that all the facts and observations fit into the failure narrative. Upon verification and validation of the tested hypothesis the conclusions are formed and finalized.

Figure 1: Systematic Approach to Failure Analysis

 

The failure analysis procedure calls for defining the function and operating condition of the elastomer component and establishing a failure criterion clearly quantifying under what performance and service conditions the component can be declared as having failed. The failure criterion may be an unacceptable change in a property and this change may cause a particular failure. Abnormal changes in the values of properties like stress relaxation, tear resistance, stiffness and modulus change, dynamic properties, etc can be defined. Then next step is to characterize and identify the underlining physics and mechanisms involved in causing this changes. Establish the rate of change by accelerated laboratory testing at different levels of severity and different time intervals. It is important to keep the accelerated test conditions similar to the service conditions and perform the test at atleast four (4) temperatures higher than average service temperature. These four conditions can be suitably used for life predictions using Arrhenius technique.

Figure 2: Failure Analysis

ASTM E860-2013

Any investigation in failure analysis results in large amount of data regarding the sample history, test data, analysis and discussion of results. ASTM E860-2013 specifies a protocol for the examination of forensic evidence pertaining to failure analysis. This well developed method can be taken as a template to follow  and carry out the failure analysis procedure as described. This establishes  a well defined protocol showing the steps followed to collect, document, study and analyze and present the results for failure analysis on material samples and components.

The following shows in brief the information from ASTM E860-2013 specifications;

1) Chain of Custody Documentation

1.1) Copies of receiving and shipping documentation

1.2) Pictures of materials as received

2) Physical Evidence Documentation

2.1) Labelings

2.2) Samples with benchmarks

3) Steps in dissection

4) Steps in Testing

5) Test equipment number, calibration etc.

6) Photo Documentation

6.1) Digital

6.2) SEM, TEM etc.

The approaches discussed in flowcharts 1 and 2 can be applied to determine failure analysis of polymer components used in engineering applications. It is important to define failure modes and failure mechanisms for parts under service conditions. It is also critical to establish validations between field and laboratory samples using different physical and chemical analysis techniques. The primary rate determining mechanism of component failure can be used to predict failures using the accelerated functional tests.

The failure mode analysis effort conducted on polymer materials provides a good materials and process database for design and FEA engineers who can optimize the product without the need for expensive trial and errors thus reducing cost and time to market.

References:

  1. Leyden, Jerry., Failure Analysis in Elastomer Technology: Special Topics, Rubber Division, 2003
  2. Baranwal, Krishna., Elastomer Technology: Special Topics, Rubber Division, 2003
  3. 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.
  4. Srinivas, K., Systematic Experimental and Computational Mechanics Failure Analysis Methodologies for Polymer Components, ARDL Technical Report, March 2008.
  5. Dowling, N. E., Mechanical Behavior of Materials, Engineering Methods for Deformation, Fracture and Fatigue Prentice-Hall, NJ, 99
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Design Analysis of Engine Mounts and Suspension Components

Abstract: A tier 1 OEM supplier was seeking to enhance the durability of the engine mount. Finite Element Analysis (FEA) on its metal-elastomer bonded engine mount designs has been carried out to study the performance of the mounts under service loads. The present work involved studying material properties of the compound and analysis on the part to verify the stiffness and performance characteristics of the mount. The mount design has also been analyzed under six different directional forces.

Methodology:

1) Characterize material properties to adequately represent the rubber material.

2) Mooney-Rivlin, Ogden, Yeoh material models were evaluated to suitably represent the material compound.

3) Multi-step analysis was carried out by first simulating the pre-compression and then simulating the torsion, tension and shear.

4) Large strain deformation analysis along with multi-step analysis procedure had to be carried out.

Results and Discussion:

Results from the co-relation of experimental tests and FEA show the effectiveness of FEA as a tool in the development of suspension components. Analysis results for the directional and moment loads have shown the geometric locations of the excessive deformation taking place in the engine mount. The locations of maximum stress and strain concentration are around the bonding areas of the metal-rubber interface. Results show that for a higher fatigue life of the mount at high loads the deformation in the bonding region needs to be minimized

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