Low Velocity Impact Testing

Low Velocity Impact Damage Testing:

Glass and Carbon fiber reinforced thermoplastic composite materials are widely used in automotive, and aerospace applications to make structures light-weight without losing on the stiffness and load carrying capability. Properties like high toughness, high Young’s modulus, low strains, and manufacturability for specific applications make these materials indispensable to modern industry. Most of these applications include high strain, low and high velocity impacts and it becomes imperative to study the behaviour of these materials under such conditions.

AdvanSES offers testing capabilities for testing as per ASTM D7136 (Drop Weight Impact), ASTM D256 (Izod Impact Test), ASTM D6110 (Charpy Impact Test) wherein the damage resistance of these materials and products can be studied. Low Velocity Impact Testing forms one of our core range of services for material and product testing.

Evaluation of Critical Tearing Energy of Rubber Materials

critical tearing energy rubber

Do you know the critical tearing energy of your rubber material?

Critical tearing energy is an important parameter to study crack growth in rubber under fatigue loading and it’s evaluation becomes imperative for the design and evaluation of rubber products. To prevent crack growth and sudden fatigue failures, one of the technique is to improve the tearing energy of rubber. Evaluation and testing of tearing energy properties is of utmost importance.

In automotive, aerospace and biomedical applications, soft elastomers and rubbers often handle cyclic loads and displacement cycles during their entire service duty cycle. When going through long periods of cyclic loading, catastrophic failure frequently happens becuase of crack formation, growth followed by propagation.

Contact us to evaluate the critical energy of your rubber material. More information at https://www.advanses.com

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AdvanSES Materials Testing Services

We at AdvanSES are capable of developing a custom testing protocol for compliance with international standards or for quality assurance. Materials testing services offered by AdvanSES include:

Composition: Whe you need to know with certainty what materials are used in the manufacture of thermoplastics, rubber materials etc.

Shear Test: Materials testing designed to measure shear strength of rubber and composites. These tests show how much stress a specimen can take before failure and is often times used to test and compare the strength of adhesives.

Flexural Test: When a product like an I-beam or girder used in construction must support a predetermined amount of weight without sagging, a flexure materials test is often performed to verify that the specimen can withstand a certain level of stress without flexing.

Environment and High Temperature Exposure Test: When it comes to determining the lifespan of materials, especially elastomer materials intended for outdoor use, exposure to high temperature and oils is carried out to check the degradation of materials.

Tensile/Compression Tests: From plastics and metals to adhesives and rubbers, tensile/compression testing is a form of materials testing that places specimens under precise compressive loads to measure their ability to withstand compression before deformation occurs.

Fatigue Tests: Fatigue tests are important to determine the endurance or breaking load a material can withstand before failing as well as the number of repeated loading cycles it can endure. Fatigue testing looks at a materials limit to withstand stresses and environment degradation. We can conduct stress controlled and strain controlled high cycle fatigue tests from room temperature to 250C on material samples, parts and components.

Applications of Materials Testing:

1) Quality Control
2) Regulatory Compliance
3) Design Development
4) Failure Analysis
5) Performance Prediction
6) Finite Element Analysis Material Constants Data

Advanced Scientific and Engineering Services (AdvanSES) Laboratory Earns Renowned ISO/IEC 17025:2017 Accreditation

AdvanSES announces that its Testing Laboratory has attained ISO/IEC 17025:2017 accreditation vide NABL certificate No. TC-9168. ISO/IEC 17025:2017 is the highest recognized quality standard in the world for calibration and testing laboratories. Accreditation means the lab consistently produces precise and accurate test data and has implemented a rigorous quality management system. The stringent processes in the audits for the accreditation relate to the operations, efficiency and effectiveness of the laboratory. Test data from the laboratory is benchmarked for accuracy, reliability and consistency.

Receiving the accreditation means that test reports and certificates generated from AdvanSES laboratory can now be generally accepted from one country to another without further testing. 

The scope of the accreditation covers tests and properties in the field of rubbers, plastics and composite materials. It is one of the few labs in the world accredited to perform internationally recognized fatigue standards like ASTM D7791.

AdvanSES today is one of the few companies in the world who provide expert problem solving services using Finite element analysis (FEA), provides new product development and material testing and analysis.

National Accreditation Board for Testing & Calibration Laboratories (NABL) provides accreditation to Conformity Assessment Bodies (Laboratories). NABL Schemes include Accreditation (Recognition) of Technical competence of testing, calibration, medical testing laboratories, Proficiency testing providers (PTP) & Reference Material Producers (RMP) for a specific scope following ISO/IEC 17025ISO 15189ISO/IEC 17043 & ISO 17034:2016[3] Standards. It has Mutual Recognition Arrangement (MRA) with Asia Pacific Laboratory Accreditation Cooperation (APLAC), International Laboratory Accreditation Cooperation (ILAC).

NABL is a constituent board of Quality Council of India which is an autonomous body setup under Department for Promotion of Industry and Internal Trade (DPIIT)Ministry of Commerce and IndustryGovernment of India

Static and Dynamic Testing of Engineering Materials and Components

Static and dynamic testing of engineering materials and products involves mechanical loading of a material specimen or product up to a pre-determined deformation level or up to the point where the sample fails. The material properties backed out from these tests are further used to characterize the materials and products. Testing is carried out under essentially two conditions viz; Static and Dynamic.

Physical testing of materials as per ASTM D412, ASTM D638, ASTM D624 etc., can be categorized 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 and parameters employed like forcing functions, displacement amplitudes, and strain cycles. The difference is also in the nature of the information we back out from the tests. Static mechanical testing is carried out at lower frequencies, generally less than one Hertz. The associated loads and applied deformation amplitudes are also smaller and the strain rate is much lower as compared to typical engineering applications. Dynamic loading is generally carried out under forcing functions and with high deformation amplitudes. These forcing functions and amplitudes are applied under a very short time period. When related to polymers, composites and elastomers, the information from a conventional test is usually related to quality control aspects of the materials or products, while from dynamic tests we back out data regarding the functional performance of the materials and products. ASTM D5992, D4092 and D5279 are some of the dynamic mechanical testing standards. High speed tensile, compression, impact, fracture tests using Split Hopkinson Pressure bars (SHPB), Servo-Hydraulic testing machines and cyclic fatigue tests fall under the category of dynamic testing.

Polymer materials are widely used in all kinds of engineering applications because of their superior performance in vibration isolation, impact resistance, rate dependency and time dependent properties. In some traditional applications they have consistently shown better performance combining with other materials like glass fibres etc., and are now replacing metals and ceramics in such applications. The investigations of polymer properties in vibration, shock, impact and other viscoelastic phenomena is now considered critical, and understanding of dynamic mechanical behaviour of polymers becomes necessary. Static and dynamic testing of engineering materials and components becomes imperative for this purpose.

Figure 1: Static and Dynamic Testing Systems at AdvanSES

The absolute values from frequency sweep, strain sweep, temperature sweep dynamic tests are meaningful, but have little utility as isolated data points. They do become valuable data points when compared to each other or some other known variables. A tan delta or damping coefficient value of 0.4 is poor for a natural rubber or EPDM based compound, but very good in FKM materials where the structure of the compound makes it venerable to lower than optimum dynamic properties. Most uncured rubbery compounds start on the viscous side, and as we cure the compound, we shift towards the elastic side.

The importance of dynamic testing comes from the fact that performance of elastomers and elastomeric products such as engine mounts, suspension bumpers, tire materials etc., cannot be fully predicted by using only traditional methods of static testing. Polymer and elastomer tests like hardness, tensile, compression-set, low temperature brittleness, tear resistance tests, ozone resistance etc., are all essentially quality control tests and do not help us understand the performance or the durability of the material under field service conditions. An elastomer is used in all major applications as a dynamic part being able to provide vibration isolation, sealing, shock resistance, and necessary damping because of its viscoelastic nature.

Figure 2: Viscoelastic and Dynamic Studies Correlate Molecular Structure to Manufacturing and Mechanical Properties of Engineering Components

As it stands today, the theory of dynamic properties can be applied judiciously to product development, performance characterization or failure analysis problems. The field of application has evolved over time with availability of highly sophisticated instruments. The problems need to be studied upfront for any time or frequency dependent loading conditions and boundary conditions acting on the components and the theory be suitably applied. Needless to say that dynamic properties have utmost importance when polymeric materials and components show heat generation, and fatigue related field failures. Dynamic characterization relates the molecular structure of the polymeric materials to the manufacturing processes and to the field performance of engineering products. Dynamic properties play an important part in comparing mechanical properties of different polymers for quality, performance prediction, failure analysis and new material qualification. Dynamic testing truly helps us to understand and predict these properties both at the material and component level.

Following are the testing modes that can be implemented in the static and dynamic testing of engineering materials and the results on can back out;

Test Modes:

No.Test ModesTests
1.OscillationFrequency Sweep, Strain Sweep, Stress Sweep, Temperature Sweep, Fatigue Test
2.Stress ControlCreep, Fatigue
3.Strain ControlStress Relaxation, Fatigue, Crack Growth
4.Rate ControlStress ramp and Strain ramp

Test Results Data:

1) Storage or Elastic Modulus (E’) versus temperature, frequency, or % strain

2) Loss or Viscous Modulus (E”) versus temperature, frequency, or % strain

3) Damping Coefficient (Tan Delta) versus temperature, frequency, or % strain

4) Stress vs Strain properties at different strain rates.

5) Strain vs Number of Cycles for a material or component under load control fatigue.

6) Load or Stress vs Number of Cycles for a material or component under strain control fatigue.

7) Fatigue crack growth vs Number of Cycles for a material under strain controlled fatigue.

No single testing technique or methodology provides a complete picture of the material quality or component performance. It is always a combination of testing methods and techniques that have to be applied to obtain a 360 degree view of the material quality and performance.

References:

1) Ferry, Viscoelastic Properties of Polymers, Wiley, 1980.

2) Ward et al., Introduction to Mechanical Properties of Solid Polymers, Wiley, 1993.

3) TA Instruments, Class Notes and Machine Manuals, 2006.

4) Lakes, Roderick., Viscoelastic Materials, Cambridge University Press, 2009.

5) Srinivas, K., and Pannikottu, A., 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.

Polymer Testing for Aerospace Applications

Space research and application demands stringent requirements from materials, making it imperative that they are tested rigorously, by multiple methods and techniques to fully characterize their performance and their ability to handle degradation, mechanical fatigue under extreme conditions.

AdvanSES provides full mechanical characterization of specialty polymers, rubber and in-homogeneous materials, for use in demanding atmospheric and space applications. Mechanical fatigue testing is a core area for us and we can test materials for HCF, LCF as well as elevated temperatures.

We can provide the following testing protocols for your rubbery materials;

1) Uniaxial Tension Test as per ASTM D412
2) Compression Test as per ASTM D575
3) Tear Test as per ASTM D624
4) Crompression Stress Relaxation Test as per ASTM D6147
5) Dynamic Viscoelastic Test ASTM D5992
6) Hyperelastic Material Constants
7) Axial Fatigue as per ASTM D7791

Finite Element Analysis (FEA) Consulting Services

AdvanSES has a history of completing FEA projects for customers from automotive, aerospace, biomedical and consumer durables background. All our projects are delivered using state of the art commercial FEA softwares.

We offer a complete range of Finite Element Analysis FEA consulting services for solving structural, thermal, fatigue, and fluid flow pressure problems. We work with our customers to analyze product behavior, predict service life, and understand failures. Our FEA engineers help our customers make early design choices. Our proactive approach helps our customers expedite products into the market.

Some our strengths in Finite Element Analysis (FEA) are detailed below;

  1. Non-linear Materials: Our regular work includes characterization and implmentation of complex material models for hyperelasticity, elasto-plasticity and viscoelasticity. We can work on any kind of materials to implement them successfully in FEA models.

2) Verifications and Validations: Any kind of simulation without a strong verification and validation basis will mostly fail on expert scrutiny. We have extensive experience in verifications and validations procedures in our laboratory. We can replicate field service conditions, setup custom test rigs and characterize products under static and dynamic loads.

3) Contact-Impact: We offer implementation of full physics in contact, drops and high speed impact analysis.

Contact us for a quick quote.

Verifications and Validations in Finite Element Analysis (FEA)

1.1 Introduction

The finite element method (FEM) is a numerical method used to solve a mathematical model of a given structure or system, which are very complex and for which analytical solution techniques are generally not possible, the solution can be found using the finite element method. The finite element method can thus be said to be a variational formulation method using the principle of minimum potential energy where the unknown quantities of interests are approximated by continuous piecewise polynomial functions. These quantities of interest can be different according to the chosen system, as the finite element method can be and is used in various different fields such as structural mechanics, fluid mechanics, accoustics, electromagnetics, etc. In the field of structural mechanics the primary field of interest is the displacements and stresses in the system.

It is important to understand that FEM only gives an approximate solution of the prob- lem and is a numerical approach to get the real result of the variational formulation of partial differential equations. A finite element based numerical approach gives itself to a number of assumptions and uncertainties related to domain discretizations, mathematical shape functions, solution procedures, etc. The widespread use of FEM as a primary tool has led to a product engineering lifecycle where each step from ideation, design development, to product optimization is done virtually and in some cases to the absence of even prototype testing.

This fully virtual product development and analysis methodology leads to a situation where a misinterpreted approximation or error in applying a load condition may be car- ried out through out the engineering lifecycle leading to a situation where the errors get cumulative at each stage leading to disastrous results. Errors and uncertainties in the ap- plication of finite element method (FEM) can come from the following main sources, 1) Errors that come from the inherent assumptions in the Finite element theory and 2) Errors and uncertainties that get built into the system when the physics we are seeking to model get transferred to the computational model. A common list of these kind of errors and uncertainties are as mentioned below;

  • Errors and uncertainties from the solver.
    • Level of mesh refinement and the choice of element type.
    • Averaging and calculation of stresses and strains from the primary solution variables.
    • Uncertainty in recreating the geometrical domain on a computer.
    • Approximations and uncertainties in the loading and boundary conditions of the model.
    • Errors coming from chosing the right solver types for problems, e.g. Solvers for eigen value problems.

The long list of error sources and uncertainties in the procedure makes it desirable that a framework of rules and criteria are developed by the application of which we can make sure that the finite element method performs within the required parameters of accuracy, reliability and repeatability. These framework of rules serve as verification and validation procedures by which we can consistently gauge the accuracy of our models, and sources of errors and uncertainties be clearly identified and progressively improved to achieve greater accuracy in the solutions. Verifications and Validations are required in each and every development and problem solving FEA project to provide the confidence that the compu- tational model developed performs within the required parameters. The solutions provided by the model are sufficiently accurate and the model solves the intended problem it was developed for.

Verification procedure includes checking the design, the software code and also investigate if the computational model accurately represents the physical system. Validation is more of a dynamic procedure and determines if the computational simulation agrees with the physical phenomenon, it examines the difference between the numerical simulation and the experimental results. Verification provides information whether the computational model is solved correctly and accurately, while validation provides evidence regarding the extent to which the mathematical model accurately correlates to experimental tests.

In addition to complicated discretization functions, partial differential equations repre- senting physical systema, CFD and FEA both use complicated matrices and PDE solution algorithms to solve physical systems. This makes it imperative to carry out verification and validation activities separately and incrementally during the model building to ensure reliable processes. In order to avoid spurious results and data contamination giving out false signals, it is important that the verification process is carried out before the valida- tion assessment. If the verification process fails the the model building process should be discontinued further until the verification is established. If the verification process suc- ceeds, the validation process can be carried further for comparison with field service and experimental tests.

1.2 Brief History of Standards and Guidelines for Verifi- cations and Validations

Finite element analysis found widespread use with the release of NASA Structural Anal- ysis Code in its various versions and flavous. The early adopters for FEA came from the aerospace and nuclear engineering background. The first guidelines for verification and validation were issued by the American Nuclear Society in 1987 as Guidelines for the Ver- ification and Validation of Scientific and Engineering Computer Programs for the Nuclear Industry.

The first book on the subject was written by Dr. Patrick Roache in 1998 titled Verification and Validation in Computational Science and Engineering, an update of the book appeared in 2009.

In 1998 the Computational Fluid Dynamics Committee on Standards at the American Institute of Aeronautics and Astronautics released the first standards document Guide for the Verification and Validation of Computational Fluid Dynamics Simulations. The US Depeartment of Defense through Defense Modeling and Simulation Office releaseed the DoD Modeling and Simulation, Verification, Validation, and Accreditation Document in 2003.

The American Society of Mechanical Engineers (ASME) V and V Standards Commit- tee released the Guide for Verification and Validation in Computational Solid Mechanics (ASME V and V-10-2006).

In 2008 the National Aeronautics and Space Administration Standard for Models and Simulations for the first time developed a set of guidelines that provided a numerical score for verification and validation efforts.

American Society of Mechanical Engineers V and V Standards Committee V and V-20 in 2016 provided an updated Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer .

1.3 Verifications and Validations :- Process and Procedures

Figure(1.1) shows a typical product design cycle in a fast-paced industrial product de- velopment group. The product interacts with the environment in terms of applied loads, boundary conditions and ambient atmosphere. These factors form the inputs into the com- putational model building process. The computational model provides us with predictions and solutions of what would happen to the product under different service conditions.

It is important to note that going from the physical world to generating a computational model involves an iterative process where all the assumptions, approximations and their effects on the the quality of the computational model are iterated upon to generate the most optimum computational model for representing the physical world.

Figure 1.1: Variation on the Sargent Circle Showing the Verification and Validation Procedures in a Typical Fast Paced Design Group

The validation process between the computational model and the physical world also involves an iterative process, where experiments with values of loads and boundary con- ditions are solved and the solution is compared to output from the physical world. The computational model is refined based upon the feedbacks obtained during the procedure.

The circular shapes of the process representation emphasizes that computational mod- eling and in particular verification and validation procedures are iterative in nature and require a continual effort to optimize them.

The blue, red and green colored areas in Figure(1.3) highlight the iterative validation and verification activities in the process. The standards and industrial guidelines clearly mention the distinctive nature of code and solution verifications and validations at different levels. The green highlighted region falls in the domain of the laboratory performing the experiments, it is equally important that the testing laboratory understands both the process and procedure of verification and validation perfectly.

Code verification seeks to ensure that there are no programming mistakes or bugs and that the software provides the accuracy in terms of the implementation of the numerical al- gorithms or construction of the solver. Comparing the issue of code verification and calcu- lation verification of softwares, the main point of difference is that calculation verification

Figure 1.2: Verification and Validation Process

involves quantifying the discretization error in a numerical simulation. Code verification is rather upstream in the process and is done by comparing numerical results with analytical solutions.

Figure 1.3: Guidance for Verification and Validation as per ASME 10.1 Standard

1.4 Guidelines for Verifications and Validations

The first step is the verification of the code or software to confirm that the software is work- ing as it was intended to do. The idea behind code verification is to identify and remove any bugs that might have been generated while implementing the numerical algorithms or because of any programming errors. Code verification is primarily a responsibility of the code developer and softwares like Abaqus, LS-Dyna etc., provide example problems man- uals, benchmark manuals to show the verifications of the procedures and algorithms they have implemented.

Next step of calculation verification is carried out to quantify the error in a computer simulation due to factors like mesh discretization, improper convergence criteria, approxi- mation in material properties and model generations. Calculation verification provides with an estimation of the error in the solution because of the mentioned factors. Experience has shown us that insufficient mesh discretization is the primary culprit and largest contributor to errors in calculation verification.

Validation processes for material models, elements, and numerical algorithms are gen- erally part of FEA and CFD software help manuals. However, when it comes to establishing the validity of the computational model that one is seeking to solve, the validation procedure has to be developed by the analyst or the engineering group.

The following validation guidelines were developed at Sandia National Labs[Oberkampf et al.] by experimentalists working on wind tunnel programs, however these are applicable to all problems from computational mechanics.

Guideline 1: The validation experiment should be jointly designed by the FEA group and the experimental engineers. The experiments should ideally be designed so that the validation domain falls inside the application domain.

Guideline 2: The designed experiment should involve the full physics of the system, including the loading and boundary conditions.

Guideline 3: The solutions of the experiments and from the computational model should be totally independent of each other.

Guideline 4: The experiments and the validation process should start from the system level solution to the component level.

Guideline 5: Care should be taken that operator bias or process bias does not contami- nate the solution or the validation process.

1.5 Verification & Validation in FEA

1.5.1 Verification Process of an FEA Model

In the case of automotive product development problems, verification of components like silent blocks and bushings, torque rod bushes, spherical bearings etc., can be carried. Fig- ure(1.4) shows the rubber-metal bonded component for which calculations have been carried out. Hill[11], Horton[12] and have shown that under radial loads the stiffness of the bushing can be given by,

Figure 1.4: Geometry Dimensions of the Silent Bushing

converted PNM file

Figure 1.5: Geometry of the Silent Bushing

and G= Shear Modulus = 0.117e0.034xHs, Hs = Hardness of the material. Replacing the geometrical values from Figure(1.4),

Krs = 8170.23N/mm,                                                  (1.3)

for a 55 durometer natural rubber compound.  The finite element model for the bushing

is shown in Figure(1.9) and the stiffness from the FEA comes to 8844.45 N/mm. The verification and validation quite often recommends that a difference of less than 10% for a comparison of solutions is a sound basis for a converged value.

For FEA with non-linear materials and non-linear geometrical conditions, there are multiple steps that one has to carry out to ensure that the material models and the boundary conditions provide reliable solutions.

  • Unit Element Test: The unit element test as shown in in Figure(1.7) shows a unit cube element. The material properties are input and output stress-strain plots are compared to the inputs. This provides a first order validation of whether the material
converted PNM file

Figure 1.6: Deformed Shape of the Silent Bushing

properties are good enough to provide sensible outputs. The analyst him/her self can carry out this validation procedure.

  • Experimental Characterization Test: FEA is now carried out on a characterization test such as a tension test or a compression test. This provides a checkpoint of whether the original input material data can be backed out from the FEA. This is a moderately difficult test as shown in Figure(1.8). The reasons for the difficulties are because of unquantified properties like friction and non-exact boundary conditions.
  • Comparison to Full Scale Experiments: In these validation steps, the parts and com- ponent products are loaded up on a testing rig and service loads and boundary con- ditions are applied. The FEA results are compared to these experiments. This step provides the most robust validation results as the procedure validates the finite ele- ment model as well as the loading state and boundary conditions. Figure(1.9) shows torque rod bushing and the validation procedure carried out in a multi-step analysis.

Experience shows that it is best to go linearly in the validation procedure from step 1 through 3, as it progressively refines one’s material model, loading, boundary conditions. Directly jumping to step 3 to complete the validation process faster adds upto more time with errors remaining unresolved, and these errors go on to have a cumulative effect on the quality of the solutions.

Figure 1.7: Unit Cube Single Element Test

Figure 1.8: FEA of Compression Test

1.5.2 Validation Process of an FEA Model

Figure(1.7) shows the experimental test setup for validation of the bushing model. Radial loading is chosen to be the primary deformation mode and load vs. displacement results are compared. The verification process earlier carried out established the veracity of the FEA model and the current validation analysis applies the loading in multiple Kilonewtons. Results show a close match between the experimental and FEA results. Figures(1.10) and

Figure 1.9: Experimental Testing and Validation FEA for the Silent Bushing

(1.11) show the validation setup and solutions for a tire model and engine mount. The complexity of a tire simulation is due to the nature of the tire geometry, and the presence of multiple rubber compounds, fabric and steel belts. This makes it imperative to establish the validity of the simulations.

Figure 1.10: Experimental Testing and Validation FEA for a Tire Model

Figure 1.11: Experimental Testing and Validation FEA for a Passenger Car Engine Mount

1.6 Summary

An attempt was made in the article to provide information on the verification and validation processes in computational solid mechanics.  We  went through the history of adoption   of verification and validation processes and their integration in computational mechanics processes and tools. Starting from 1987 when the first guidelines were issued in a specific field of application, today we are at a stage where the processes have been standardized and all major industries have found their path of adoption.

Verification and validations are now an integral part of computational mechanics processes to increase integrity and reliability of the solutions. Verification is done primarily at the software level and is aimed at evaluating whether the code has the capability to offer the correct solution to the problem, while validation establishes the accuracy of the solution. ASME, Nuclear Society and NAFEMS are trying to make the process more standardized, and purpose driven.

Uncertainty quantification has not included in this current review, the next update of this article will include steps for uncertainty quantification in the analysis.

1.7 References

  1. American Nuclear Society, Guidelines for the Verification and Validation of Scientific and Engineering Computer Programs for the Nuclear Industry 1987.
  2. Roache, P.J, American Nuclear Society, Verification and Validation in Computational Science and Engineering, Hermosa Publishing, 1998.
  3. American Institute of Aeronautics and Astronautics, AIAA Guide for the Verification and Validation of Computational Fluid Dynamics Simulations (G-077-1998), 1998.
  4. U.S. Department of Defense, DoD Modeling and Simulation (M-S) Verification, Validation, and Accreditation, Defense Modeling and Simulation Office, Washington DC.
  5. American Society of Mechanical Engineers, Guide for Verification and Validation in Computational Solid Mechanics, 2006.
  6. Thacker, B. H., Doebling S. W., Anderson M. C., Pepin J. E., Rodrigues E. A., Concepts of Model Verification and Validation, Los Alamos National Laboratory, 2004.
  7. Standard for Models And Simulations, National Aeronautics and Space Administration, NASA-STD-7009, 2008.
  8. Oberkampf, W.L. and Roy, C.J., Verification and Validation in Computational Simulation, Cambridge University Press, 2009.
  9. Austrell, P. E., Olsson, A. K. and Jonsson, M. 2001, A Method to analyse the non- Linear dynamic behaviour of rubber components using standard FE codes, Paper no 44, Conference on Fluid and Solid Mechanics.
  10. Austrell, P. E., Modeling of Elasticity and Damping for Filled Elastomers,Lund University.
  11. ABAQUS Inc., ABAQUS: Theory and Reference Manuals, ABAQUS Inc., RI, 02.
  12. Hill, J. M. Radical deflections of rubber bush mountings of finite lengths. Int. J. Eng. Sci., 1975, 13.
  13. Horton, J. M., Gover, M. J. C. and Tupholme, G. E. Stiffness of rubber bush mountings subjected to radial loading. Rubber Chem. Tech., 2000, 73.
  14. Lindley, P. B. Engineering design with natural rubber , The Malaysian Rubber Producers’ Research Association, Brickendonbury, UK., 1992.

FEA Modeling of Rubber and Elastomer Materials

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

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 categorized 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.