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 D5279are 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.
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.
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;
Frequency Sweep, Strain Sweep, Stress Sweep, Temperature Sweep, Fatigue Test
Stress Relaxation, Fatigue, Crack Growth
Stress 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.
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.
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;
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.
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.
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.
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;
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.
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
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 NuclearIndustry.
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
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.
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
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
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.
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
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
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, Horton and have shown that under radial loads the stiffness of the bushing can be given by,
Figure 1.4: Geometry Dimensions of the
Figure 1.5: Geometry of the Silent Bushing
and G= Shear Modulus = 0.117e0.034xHs, Hs = Hardness of the material. Replacing the geometrical values
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.
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
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
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
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
An attempt was made in the article
to provide information on the verification and validation
processes in computational solid mechanics.
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.
American Nuclear Society, Guidelines for the Verification and Validation of Scientific and Engineering Computer Programs for the Nuclear Industry 1987.
Roache, P.J, American Nuclear Society, Verification and Validation in Computational Science and Engineering, Hermosa Publishing, 1998.
American Institute of Aeronautics and Astronautics, AIAA Guide for the Verification and Validation of Computational Fluid Dynamics Simulations (G-077-1998), 1998.
U.S. Department of Defense, DoD Modeling and Simulation (M-S) Verification, Validation, and Accreditation, Defense Modeling and Simulation Office, Washington DC.
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.
Standard for Models And Simulations, National Aeronautics and Space Administration, NASA-STD-7009, 2008.
Oberkampf, W.L. and Roy, C.J., Verification and Validation in Computational Simulation, Cambridge University Press, 2009.
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.
Austrell, P. E., Modeling of Elasticity and Damping for Filled Elastomers,Lund University.
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.
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 5) Data Cards for Input into FEA, CAE softwares 6) FEA Services 7) Custom Test Setups with NI Labview DAQ
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 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
The main difference between 3 point and 4 point bend tests is the area in which the maximum bend stress occurs. In 3 point bend tests it is under the loading nose while for 4 point bend tests it is distributed in a wider area between the loading points. The 3 point test best applies when the material is homogeneous such as in the case of plastic materials. A 4 point test tends to be the best choice when the material is non-homogeneous such as some types of composites.
The stress concentration of a three point test is small and concentrated under the center of the loading point, whereas the stress concentration of a four point test is over a larger region, avoiding premature failure.
Polymer materials in their basic form exhibit a range of characteristics and behavior from elastic solid to a viscous liquid. These behavior and properties depend on their material constituents, their structure, temperature, frequency and time scale at which the material or the engineering component is analyzed. The viscous liquid polymer is defined as by having no definite shape and flow. Deformation under the effect of applied load is irreversible. Elastic materials such as steels and aluminum deform instantaneously under the application of load and return to the original state upon the removal of load, provided the applied load is within the yield limits of the material. An elastic solid polymer is characterized by having a definite shape that deforms under external forces, storing this deformation energy and giving it back upon the removal of applied load.
polymer resins consist of long polymer molecules which may or may not have side chains attached to them. The
side chains are not linked to other polymer molecules as shown in Figure(1).
Thus there is an absence of cross-links in the thermo- plastic structure.
Thermoplastic resins in a granular form can be repeatedly melted or solidified by heating and cooling. Heat softens or melts the material so that it can be molded.
Cooling in the mold solidifies the material into a given shape. There are two
types of thermoplastic polymers,
Crystalline and Amorphous. Following list enumerates the features and
properties of both the polymer types.
Figure 1: Chains in Thermoplastic Polymers
Crystalline solids break along
particular points and directions.
Crystalline solids have an ordered structural pattern of
Crystalline solids flow well at
a higher temperature.
Reinforcement with fibers in crystalline
polymers increases the load-bearing capabilities.
Crystalline polymers tend to
shrink more than amorphous.
The molecular structure of crystalline polymers
makes them more suitable for opaque
parts and components.
Polypropylene, Nylon, Acetal, Polyethersulfone, etc.
Amorphous solids break into uneven parts with ragged edges.
Amorphous solids have
a random orientation of molecules with no proper
geometrical or pattern formation.
Amorphous solids do not flow as easily
and can give problems
in mold filling.
Examples: ABS, Polystyrene, Polycarbonate, etc.
Figure (2) shows the general types and classification of polymers.
Figure 2: Types of Polymers and Their Classification
The need to improve the mechanical properties of polymers drives the development of various composites. Composites express a mechanical behavior signiﬁcantly different from that of conventional materials. They provide high load carrying capability, high stiffness to weight ratio and tolerance to damage from water, specific industrial oils, greases etc.
Composite materials are
engineered or naturally occurring materials made from two or more constituent
materials. The properties of the constituent materials are mostly significantly
different. The physical, mechanical and chemical properties remain separate and
distinct within the finished material structure. Most composites are made with
stiff and tough fibres in a polymer matrix. The polymer matrix is weaker and acts
more as a binder and parent material. The objective is usually to come up with
a material structure which is strong and stiff able to carry heavy loads. Commercial
grade composite materials mostly have glass or carbon fibres in a matrix of
thermosetting polymers like epoxy, nylons and polyester based resins. Glass
fibres are the most frequently used reinforcing fibres in reinforced polymers.
The mechanical characteristics which are predominantly improved by these fibres
are tensile and compressive strength. In addition, thermal dimensional
stability also increases. Thermoplastic
polymers are preferred as the matrix material where the end goal is to make
moldable parts and components. Glass filled nylon and other polymers offer good
mechanical, chemical at a lower cost. Fibre-Reinforced Polymer (FRP), is a
composite material made of a polymer matrix reinforced with fibres. These
fibres are usually glass or fibres. FRPs are commonly used in the aerospace,
automotive, marine, and construction industries.
materials also employ continuous ﬁber reinforcements in the form of a ply.
Figure 3 shows two types of such plies where unidirectional ﬁbers and woven
fabric bundles are laid out. These plies are impregnated by a polymer resin to
form a ply structure. For most composites, the ply is the basic building block
as a lamina structure. This lamina may be a unidirectional prepreg, a fabric, or
a strand mat.
3: Unidirection and Woven Fabric Composites
Mechanical and Physical
The mechanical and physical testing of polymers and their composites is important to determine the material properties. These properties help us understand the deformation characteristics and failure modes which can further be used in design and analysis of end products. The mechanical and physical testing ensure that material complies with performance requirements in accordance with industrial speciﬁcations, especially to the demanding aerospace, automotive, consumer, medical industries. Mechanical testing of polymeric composites involves the determination of mechanical parameters such as strength, stiffness, elongation, fatigue life etc., to facilitate its use in the design of structures.
most common mechanical properties such as Modulus of Elasticity, Poisson’s
ratio, Tensile strength, and Ultimate tensile strain for composites are
obtained from tensile testing and these properties are affected by the geometry,
size and properties of the reinforcements.
The Modulus of Elasticity and Poisson’s ratio are determined by
measuring the strains during the elastic deformation part of the test,
typically below the strain levels of 0.5%.
Uniaxial Tension Test
4: Uniaxial Tension Test on a Material Sample as per ASTM D638
The stress (σ) in a uniaxial tension test is calculated from;
σ = Load / Area of the material
slope of the initial linear portion of the curve (E) is the Young’s modulus and
E = (σ2- σ1) / (ε2- ε1) ……………………………………..(3)
3 Point Bend Flexure
Test (ASTM D790)
point bending testing is done to understand the bending stress, flexural stress
and strain of composite and thermoplastic materials. The specimen is loaded in
a horizontal position, and in such a way that the compressive stress occurs in
the upper portion and the tensile stress occurs in the lower portion of the
cross section. This is done by having round bars or curved surfaces supporting
the specimen from underneath. Round bars or supports with suitable radius are
provided so as to have a single point or line of contact with the specimen.
Figure 5: 3 Point Bend Test Setup
at AdvanSES as Per ASTM D790
load is applied by the rounded nose on the top surface of the specimen. If the
specimen is symmetrical about its cross section the maximum tensile and
compressive stresses will be equal. This test fixture and geometry provides
loading conditions so that specimen fails in tension or compression. For most
composite materials, the compressive strength is lower than the tensile and the
specimen will fail at the compression surface. This compressive failure is
associated with the local buckling (micro buckling) of individual fibres.
4 Point Bend Flexure
Test (ASTM D6272)
four-point flexural test provides values for the modulus of elasticity in
bending, flexural stress, flexural. This test is very similar to the
three-point bending flexural test. The major difference being that with the
addition of a fourth nose for load application the portion of the beam between
the two loading points is put under maximum stress. In the 3 point bend test
only the portion of beam under the loading nose is under stress.
Figure 6: 4 Point Bend Test Setup
at AdvanSES as per ASTM D6272
arrangement helps when testing high stiffness materials like ceramics, where
the number and severity of flaws under maximum stress is directly related to
the flexural strength and crack initiation in the material. Compared to the
three-point bending flexural test, there are no shear forces in the four-point
bending flexural test in the area between the two loading pins.
Poisson’s Ratio Test as
per ASTM D3039
ratio is one of the most important parameter used for structure design where
all dimensional changes resulting from application of force need to be taken
into account. For this test method, Poisson’s ratio is obtained from strains
resulting from uniaxial stress only. ASTM D3039 is primarily used to evaluate
the Poison’s ratio.
Figure 7: Poisson’s Ratio Test
Setup as per ASTM 3039 at AdvanSES
is performed by applying a tensile force to a specimen and measuring various
properties of the specimen under stress. Two strain gauges are bonded to the
specimen at 0 and 90 degrees to measure the lateral and linear strains. The
ratio of the lateral and linear strain provides us with the Poisson’s ratio.
The compressive properties
of materials are important when the product performs under compressive
Figure 8: Flatwise Compression
Test Setup as per ASTM C365 at AdvanSES
conditions. The testing is carried out in the direction normal to the plane of
facings as the core would be placed in a structural sandwich construction.
test procedures pertain to compression call for test conditions where the
deformation is applied under quasi-static conditions negating the mass and
D6641 is the testing specification that determines compressive strength and
stiffness of polymer matrix composite materials using a combined loading
compression (CLC) test fixture. This test procedure introduces the compressive
force into the specimen through combined shear end loading.
Figure 9: Combined Loading
Compression Setup with Unsupported Gauge Length
ASTM D6641 includes two
procedures; Procedure A: to be used with untabbed specimens such as fabrics,
chopped fiber composites, laminates with a maximum of 50% 0° plies. Procedure
B: is to be used with tabbed specimens having higher orthotropic properties
such as unidirectional composites. The use of tabs is necessary to increase the
load-bearing area at the specimen ends.
ASTM D7791 describes the determination of dynamic
fatigue properties of plastics in uniaxial loading conditions. Rigid or
semi-rigid plastic samples are loaded in tension (Procedure A) and rigid plastic samples are loaded in
compression (Procedure B) to determine the effect of processing, surface
condition, stress, and such, on the fatigue resistance of plastic and
reinforced composite materials subjected to uniaxial stress for a large number
of cycles. The results are suitable for study of high load carrying capability
of candidate materials. ASTM recommends a test frequency of 5 hz or lower.The
tests can be carried out under load or displacement control.
Figure 10: Axial
Fatigue Samples under Test at AdvanSES as per ASTM D7791
The test method allows generation of a stress or
strain as a function of cycles, with the fatigue limit characterized by failure
of the specimen or reaching 107 cycles. The 107 cycle
value is chosen to limit the test time, but depending on the applications this
may or may not be the best choice. The maximum and minimum stress or strain
levels are defined through an R ratio. The R ratio is the ratio
of minimum to maximum stress or displacement that the material is cycled
through during testing. For this standard, samples may be loaded in either
tension or compression.
variety of standardized mechanical tests on composite materials including
tension, compression, flexural, shear, and fatigue have been discussed. These
mechanical properties of polymers, fiber-reinforced polymeric composites immensely
depend on the nature of the polymer, fiber, plies, and the fiber-matrix
interfacial bonding. Advanced engineering design and analysis applications like
Finite Element Analysis use this mechanical test data to characterize the
materials. Second part of the paper will show the use of these mechanical
characterization tests in FEA software like Ansys, Abaqus, LS-Dyna, MSC-Marc
1) Mark J.E.,
Physical properties of polymers handbook. Springer; 2007.
T.H., Mechanical Behaviour of materials, Waveland, 1996.
N.E., Mechanical Behaviour of materials, engineering methods for deformation,
fracture and fatigue, Pearson, 2016.
4) Adams D.O.,
Tensile testing of composites: simple in concept, difficult in practice, High
5) Saba, et al.,
An overview of mechanical and physical testing of composite materials,
Mechanical and Physical Testing of Biocomposites, Fibre-Reinforced Composites
and Hybrid Composites, 2019.
6) Bruno L.,
Mechanical characterization of composite materials by optical techniques: a review,
Optic Laser Eng 2017.
McEnteggart, Composites Testing: Challenges & Solutions, JEC Europe – March