Rubber Material Testing and Pre-Conditioning Techniques for Characterization

A proper treatment of the rubber material testing service conditions and material degradation phenomena like strain softening is of prime importance in the testing of rubbers specimens for FEA material characterization. The accuracy and reliability of obtained test data depends on how the mechanical conditioning and representational service conditions of the material have been accounted for in the test data. To simulate a component in unused and unaged conditions, the mechanical conditioning requirements are different than the ones for simulating a component that has gone through extensive field service and aging under different environmental conditions.

To simulate performance of a material or component by Finite Element Analysis (FEA) it should be tested under the same deformation modes to which original assembly will be subjected. The uniaxial tension tests are easy to perform and are fairly well understood but if the component assembly experiences complex multiaxial stress states then it becomes imperative to test in other deformation modes. Planar (pure shear), biaxial and volumetric (hydrostatic) tests need to be performed along with uniaxial tension test to incorporate the effects of multiaxial stress states in the FEA model.

Material stiffness degradation phenomena like Mullin’s effect at high strains and Payne’s effect at low strains significantly affect the stiffness properties of rubbers. After the first cycle of applied strain and recovery the material softens, upon subsequent stretching the stiffness is lower for the same applied strain.

Despite all the history in testing hyperelastic and viscoelastic materials, there is a lack of a methodical and standard testing protocol for pre-conditioning. Comprehensive studies on the influence of pre-conditioning are not available. Readers are referred to Austrell[] and Remache, et al,[]. There are no guidelines for sample pre-conditioning in ASTM D412. However, British Standard BS 903 suggests to perform 5 cycles of pre-conditioning to improve test reproducibility.

There are five (5) different techniques to carry out pre-conditioning and material testing of general elastomer samples.

1. The first technique pertains to a mechanical test where the the testing of the sample is carried out under one single stretch at a speed recommended by the ASTM D412 specification.

2. In the second testing technique the sample is stretched at a constant speed up to the maximum relevant strain brought back to the initial position. Cyclic stretching is then carried out for anywhere for 1 to 7 cycles. The speed of the initial stretch and the number of subsequent cyclic stretches needs to be same. The data curve is then shifted to the origin by zeroing out the stress and strain and used for curve-fitting procedure.

3. In the third testing protocol the sample is stretched to a fraction of the full material stretch capability and brought back to the initial position and cycled back again to this fractional position anywhere from 2 to 7 cycles. The stretch in the sample is then increased to the second level and cycled back to initial position multiple times. The sample is stretched back to an even higher position and cycled back. This progressively continues until the maximum strain capability of the material is reached. This protocol is known as progressive pre-conditioning.

4. In the fourth testing technique the sample is stretched to a fraction of the total stretch capability and relaxed for anywhere from 30 seconds to 120 seconds as per the material. The sample is then again stretched to a higher limit and relaxed again. This is continued until the maximum stretchable capability of the material. This particular technique stretches the material and allows the material to fully creep and relax at each interval so that all the stress softening is accounted for in the test data.

5. In the fifth testing technique the sample is tested under a single stretch but the speed or the rate of stretch is very slow. This ultra-slow speed test is carried out so that the material can creep, relax, and the cross-links in the elastomer are given enough time to expand-contract and come to a balanced position during the stretching. This technique is a combination of the two above testing techniques.

These five (5) testing protocols involve the stretching of the material to different limits under different conditions and suitably cycling the material. The suitability of one testing technique over the other is debatable and one should adopt the technique that most closely resembles the operating conditions of the material and what one expects to back out from the Finite Element Analysis. Figures (1.11) through (1.14) shows the results from using the different testing protocols on a 55 durometer Natural Rubber Compound that finds general application in an automotive engine mount.

Figure 1.11: Uniaxial Tension Test Results

Figure 1.12: Single Stretch Followed by 3 Cycles of Stretching to the Maximum

Figure (1.12) shows the results from comparisons carried out on a uniaxial compression test for an engine mount material characterization. Two protocols were employed to carry out the material characterization. Progressive straining and cycling was carried out first. The material was strained 3 times before reaching the ultimate strain of approximately 75 %. The material was subsequently tested using ultra slow straining protocol. As can be seen the test data output for FEA input is the same using both the techniques. This result confirms the observation by Austrell in his work on conditioning of material samples for characterization i.e., Mullins effect can be negated when enough time is allowed for the material to relax, creep, and flow during the rubber material testing.

Figure 1.13: Progressive Pre-conditioning with Stretching to 3 levels and Cyclic Stretches

Figure 1.14: Progressive Relaxation, Stretching and Relaxation to Maximum Levels

1.2 Guidelines for Rubber Material Testing

Rubber compounds are formulated from recipes of ingredient materials. Depending on the time, location and environment while mixing the compounds, properties are known to vary from batch to batch.

• All testing to characterize a material compound should be performed on the same batch.

• Laboratory validations will help to correlate test specimen slabs against the real components to make sure they have identical cure history.

• Small compression buttons can be extracted from components and compared with slab data.

• The testing should be carried out at the temperature at which the component is expected to perform under field service conditions.

• For seals and o-rings, aging in oils and solutions can be carried out prior to testing.

• Input of more than one test data type in FEA software will increase simulation accuracy by an order of magnitude

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

Testing And Evaluation Methods For Thermoplastics Compounds

A thermoplastic, or thermosoftening plastic, is a plastic polymer material that becomes pliable or moldable at a certain elevated temperature and solidifies upon cooling. Most thermoplastics have a high molecular weight. The polymer chains associate by intermolecular forces, which weaken rapidly with increased temperature, yielding a viscous liquid.

Mechanical Testing of Thermoplastics Materials

Physical testing of Thermoplastics measures the strength, elongation, toughness and other important properties. The most important properties for measurement are;

1) Hardness (ASTM D2240): The resistance of a plastic material to indentation. It is measured on a durometer machine. Normal specificationa is plus or minus 5 and three scales are used: Shore A for flexible, Shore C for semi rigid and Shore D for rigid. Usually a delayed reading of 10 or 15 seconds is used.

2) Tensile Strength (ASTM D638): The maximum nominal stress sustained by a test specimen being pulled from both ends, at a specific temperature and a specific rate of stretching. Specification is a minimum amount in MegaPascals, (N/mm2).

3) Elongation (ASTM D638): The amount of increased length of a material until breakage. Specification is a minimum percentage.

4) Flexural properties (three point bending method): The three point bending flexural test provides values for the modulus of elasticity in bending, flexural stress, flexural strain and the flexural stress-strain response of the material.

5) Creep and Stress Relaxation: Creep is the property of a material to expand or deform continuously over a period of time under the application of a constant force. Creep is one of the most widespread failure mechanism of thermoplastic materials.

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.

Material Pre-Conditioning and Testing Techniques

A proper treatment of the rubber material service conditions and material degradation phenomena like strain softening is of prime importance in the testing of rubbers specimens for FEA material characterization. The accuracy and reliability of obtained test data depends on how the mechanical conditioning and representational service conditions of the material have been accounted for in the test data. To simulate a component in unused and unaged conditions, the mechanical conditioning requirements are different than the ones for simulating a component that has gone through extensive field service and aging under different
environmental conditions. To simulate performance of a material or component by Finite Element Analysis (FEA) it should be tested underthe same deformation modes to which original assembly will be subjected. The uniaxial tension tests are easy to perform and are fairly well understood but if the component assembly experiences complex multiaxial stress states then it becomes imperative to test in other deformation modes. Planar (pure shear), biaxial and volumetric (hydrostatic) tests need to be performed along with uniaxial tension test to incorporate the effects of multiaxial stress states in the FEA model.


Material stiffness degradation phenomena like Mullin’s effect at high strains and Payne’s effect at low strains significantly affect the stiffness properties of rubbers. After the first cycle of applied strain and recovery the material softens, upon subsequent stretching the stiffness is lower for the same applied strain. Despite all the history in testing hyperelastic and viscoelastic materials, there is a lack of a methodical and standard testing protocol for pre-conditioning. Comprehensive studies on the influence of hyperelastic material testing pre-conditioning is not available.

Hyperelastic And Viscoelastic Testing Of Polymers, Composites and Rubber Materials

1) Mechanical Testing of Polymers, Metals and Composite Materials
2) Fatigue and Durability Testing
3) Dynamic Mechanical Analysis (DMA) of Materials and Components
4) Hyperelastic, Viscoelastic Material Characterization Testing
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Hyperelastic and Viscoelastic Characterization of Polymers and Rubber Materials

Deformation Mechanisms in Elastomers – Rubbers

Hysteresis:
The loading and unloading stress–strain graph for rubber in Figure(1.9) shows that the behaviour as a load is removed is not the same as that when the load is being increased. This is called hysteresis and the curves are said to make a hysteresis loop.On a graph of stress against strain: the area between the curve and the strain axis represents the energy per unit
volume. This is the energy absorbed when a material is being stretched and the energy that is released when the force is removed. Rubber absorbs more energy during loading than it releases in unloading. The difference is represented by the area of the hysteresis loop, shown shaded in the stress–strain graph. The effect of hysteresis in rubber is to transfer energy to its molecules, resulting in heating. Goodrich Flexometer Heat Buildup ASTM
D 623 is an empirical method for comparing cured rubber compounds in terms of their hysteretic behavior.


Mullin’s and Payne’s Effect
Similar to the Payne effect under small deformations is the Mullins effect that is observed under large deformations. The Payne effect is a particular feature of the stress-strain behaviour of rubber, especially rubber compounds containing fillers such as carbon black. It is named after the
British rubber scientist A. R. Payne, who made extensive studies of the effect (e.g. Payne 1962). The effect is sometimes also known as the Fletcher-Gent effect, after the authors of the first study of the phenomenon (Fletcher & Gent 1953). The effect is observed under cyclic loading conditions with small strain amplitudes, and is manifest as a dependence of the viscoelastic storage modulus on the amplitude of the applied strain. Above approximately 0.1 % strain amplitude, the storage modulus decreases rapidly with increasing amplitude. At sufficiently large strain amplitudes (roughly 20%), the storage modulus approaches a lower bound. In that region where the storage modulus decreases the loss modulus shows a maximum. The Payne effect depends on the filler content of the material and vanishes for unfilled elastomers. Physically, the Payne effect can be attributed to deformation-induced changes in the material’s microstructure, i.e. to breakage and recovery of weak physical bonds linking adjacent filler clusters. Since the Payne effect is essential for the frequency and amplitude-dependent dynamic stiffness and damping behaviour of rubber bushings, automotive tyres and other products, constitutive models to represent it have been developed in the past (e.g. Lion et al. 2003).
The Mullins effect is a particular aspect of the mechanical response in filled rubbers in which the stress-strain curve depends on the maximum loading previously encountered. The phenomenon, named for rubber scientist Leonard Mullins, working at the Tun Abdul Razak Research Centre in Hertford, U.K., can be idealized for many purposes as an instantaneous
and irreversible softening of the stress-strain curve that occurs whenever the load increases beyond its prior all-time maximum value. At times, when the load is less than a prior maximum, nonlinear elastic behavior prevails. Although the term ”Mullins effect” is commonly applied to stress softening in filled rubbers.

Permanent Set:
Permanent set is the amount of deformation in a rubber after the distorting load has been removed. It can be defined as a permanent deformation that takes place in the material lower than at the yield point of the material. Permanent set is a complex phenomenon. Parameters that affect permanent set can be broadly described into two categories; 1) Service performance related factors 2) Material compound parameters. Service performance parameters include variables like mode of deformation, strain rates, temperature of application etc. While material compound parameters include variables like type of elastomer, its recipe ingredients, degree and amount of cross-linking etc. An O-ring or a Seal under energized conditions must maintain good contact force throughout the functional life of the products. Contact force is generated between the mating surfaces when one of the mating surfaces deflects and compresses the seal surface. In order for the sealing to remain effective the contact surfaces must return to the undeformed original position when the contacting force is removed. Under these conditions the deflection of the sealing element must be fully recoverable and so hyperelastic by nature. If there is any unrecoverable strain in the material the performance of the seal is diminished and leak would occur from between the surfaces. The key to designing a good sealing element is that the good contact force is as high as possible while at the same time ensuring that the deflection remains
hyperelastic in nature. This requires the use of a material with a good combination of force at a desired deformation characteristic. The relationship between strain and stress is described by the material’s stress-strain curve.

Figure 1: Uniaxial Tension Test Results

Figure 1 shows typical stress-strain curves from a polymer thermoplastic material and thermoset rubber material. Both the materials
have plastic strain properties where when the material is stretched beyond the elastic limit there is some permanent deformation and the material does not fully return to its original undeformed condition. The plastic strain, is the area between the loading and unloading line in both the graphs. In automotive application this permanent plastic strain is observed
more easily in under the hood components located near the engine compartments because of the presence of high temperature conditions. If a polymer part such as intake manifold is stressed to a certain and held for a period of time then some of the elastic strain converts to plastic strain resulting in observations of permanent deformation in the component. There are two physical mechanisms by which the amount of plastic strain increases over time, 1) Stress relaxation and 2) Creep. Creep is an increase in plastic strain under constant force, while in the case of Stress relaxation, it is a steady decrease in force under constant applied deformation or strain. Creep is a serious issue in plastic housings or snap fit components.
In Most Finite Element Analysis softwares stress relaxation and creep can both be modeled with the help of experimental test data