Finite Element Analysis (FEA) Consulting Services

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

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

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

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

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

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

Contact us for a quick quote.

Verifications and Validations in Finite Element Analysis (FEA)

1.1 Introduction

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1.3 Verifications and Validations :- Process and Procedures

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

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

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

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

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

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

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

Figure 1.2: Verification and Validation Process

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

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

1.4 Guidelines for Verifications and Validations

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

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

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

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

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

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

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

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

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

1.5 Verification & Validation in FEA

1.5.1 Verification Process of an FEA Model

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

Figure 1.4: Geometry Dimensions of the Silent Bushing

converted PNM file

Figure 1.5: Geometry of the Silent Bushing

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

Krs = 8170.23N/mm,                                                  (1.3)

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

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

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

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

Figure 1.6: Deformed Shape of the Silent Bushing

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

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

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

Figure 1.7: Unit Cube Single Element Test

Figure 1.8: FEA of Compression Test

1.5.2 Validation Process of an FEA Model

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

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

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

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

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

1.6 Summary

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

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

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

1.7 References

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

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.

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

Difference Between 3-point and 4-point Bend Tests

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.

3 Point Bend Test

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.

4-Point Bend Test

MECHANICAL CHARACTERIZATION TESTING OF THERMOPLASTICS AND COMPOSITE MATERIALS

 

Polymers and Composite Materials

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.

Thermoplastic 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 Polymers:

  1. Crystalline solids break along particular points and directions.
  2. Crystalline solids have an ordered structural pattern of molecular chains.
  3. Crystalline solids flow well at a higher temperature.
  4. Reinforcement with fibers in crystalline polymers increases the load-bearing capabilities.
  5. Crystalline polymers tend to shrink more than amorphous.
  6. The molecular structure of crystalline polymers makes them more suitable for opaque parts and components.
  7. Examples: Polyethylene, Polypropylene, Nylon, Acetal, Polyethersulfone, etc.

Amorphous Polymers:

  1. Amorphous solids break into uneven parts with ragged edges.
  2. 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.

Composite 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.


Figure 3: Unidirection and Woven Fabric Composites

Mechanical and Physical Testing:

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.

The mechanical testing of composite materials involves a range of test types and standards like ASTM, ISO, EN etc., along with testing conditions in different environments.

The 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 (ASTM D638)

Figure 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 sample            ……………………………………..(1)

        The strain(ε)  is calculated from;

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

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

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

3 Point Bend Flexure Test (ASTM D790)

Three 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

The 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)

The 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

This 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

Poisson’s 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

Testing 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.

Flatwise Compression Test


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

loading 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.

The test procedures pertain to compression call for test conditions where the deformation is applied under quasi-static conditions negating the mass and inertia effects.

Combined Loading Compression Test

ASTM 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.

Fatigue Test

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.

Summary:

A 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 etc.

References:

1) Mark J.E., Physical properties of polymers handbook. Springer; 2007.

2) Coutney, T.H., Mechanical Behaviour of materials, Waveland, 1996.

3) Dowling, 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

Perform Compos 2015.

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.

7) Ian McEnteggart, Composites Testing: Challenges & Solutions, JEC Europe – March 2015.

Stress Relaxation and Creep

Stress Relaxation and Creep of Polymers and Composite Materials

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.

Figure 1: Stress-Strain Curves from Thermplastic and Thermoset Materials

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, while Stress relaxation is a serious issue in sealing elements. Experimental studies on creep behavior of plastics is carried out using the tensile creep test. The loading is purely under static conditions according to ISO 899-1. The specimens used in the testing are generally as prescribed as 1A and 1B in ISO 527 and ASTM D638. These specimens correspond to the generalized description of specimens according to ISO 3167.

Figure 2: Graphical Representation of Creep and Stress Relaxation

Figure 3 shows the results from Creep testing of an HDPE material. In Most Finite Element Analysis software, stress relaxation and creep both can be simulated with the help of experimental test data.

Figure 3: Sample Creep Test Results for an HDPE Material

Creep modulus Ec(t) is used to describe the time dependent material behavior of plastics. It is defined as the ratio of the applied stress and time-dependent deformation at time (t):

Ec(t) = sigma/epsilom(t)                                                (1)

Creep rate Ec(t)/dt is  used to describe the long-term creep behavior, it is defined from the ratio of deformation or strain increase with respect to time

dot{Ec(t)} = depsilom/dt                                                (2)

Creep Stages

1) Primary Creep: The process starts at a rapid rate and slows with time. Typically it settles down within a few minutes or hours depending upon the nature of material. Strain rate decreases as strain increases.

2) Secondary Creep:

At this state the process has a relatively uniform rate and is known as steady state creep.

Strain rate is minimum and constant. Balance between between recovery and strain hardening.

 Fracture typically does not occur during this stage.

3) Tertiary Creep: This stage shows an accelerated creep rate and terminates with failure or a fracture. It is associated with both necking and formation of voids.

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 or when there are vibratory displacements between the contacting surfaces.  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. Figure 4 shows the family of curves for a stress relaxation experiment carried out at multiple strain levels.

Figure 5 shows the results from a compression stress relaxation test on a rubber material. The results show the test data over a 3 day period.

Figure 4: Stress Relaxation Curves at Multiple Strain Levels

The initial rapid relaxation and decrease in force occurs due to chemical process related degradation of the material, while at longer duration and time frames the drop in force is due to physical relaxation. Numerous studies have shown that the relaxation mechanism in polymers and rubbers is dependent on many factors as the nature and type of polymer, fillers and ingredients used, strain levels, strain rates and also temperature. The rate of relaxation is generally found to decrease at lower levels of filler loading and the rate of stress relaxation increases at higher levels of filler loading. This is attributable to polymer filler interactions

Figure 5: Sample Continuous Compression Test Results for Nitrile Elastomer Material

The molecular causes of stress relaxation can be classified to be based on five different processes.

1). Chain Scission:  The decrease in the measured stress over time is shown in Figures 4 and 5

where, 3 chains initially bear the load but subsequently one of the chains degrade and break down.

2). Bond Interchange:  In this particular type of material degradation process, the chain portions reorient themselves with respect to their partners causing a decrease in stress.

3). Viscous Flow: This occurs basically due to the slipping of linear chains one over the other. It is particularly responsible for viscous flow in pipes and elongation flow under stress.

Figure 6: Chain Scission in an Elastomeric Material

4). Thirion Relaxation: This is a reversible relaxation of the physical crosslinks or the entanglements in elastomeric networks. Generally an elastomeric network will instantaneously relax by about 5% through this mechanism.

5). Molecular Relaxation: Molecular relaxation occurs especially near Tg (Glass Transition Temperature). The molecular chains generally tend to relax near the Tg.

References:

1. Sperling,  Introduction to Physical Polymer Science, Academic Press, 1994.

2. Ward et al., Introduction to Mechanical Properties of Solid Polymers, Wiley, 1993. 3. Seymour et al. Introduction to Polymers, Wiley, 1971.

3. Ferry, Viscoelastic Properties of Polymers, Wiley, 1980.

4. Goldman, Prediction of Deformation Properties of Polymeric and Composite Materials, ACS, 1994.

5. Menczel and Prime, Thermal Analysis of Polymers, Wiley, 2009.

6. Pete Petroff, Rubber Energy Group Class Notes, 2004.

7. ABAQUS Inc., ABAQUS: Theory and Reference Manuals, ABAQUS Inc., RI, 02.

8. Dowling, N. E., Mechanical Behavior of Materials, Engineering Methods for Deformation, Fracture and Fatigue Prentice-Hall, NJ, 1999.

9. Srinivas, K., and Dharaiya, D., Material And Rheological Characterization For Rapid Prototyping Of Elastomers Components, American Chemical Society, Rubber Division, 170th Technical Meeting, Cincinnati, 2006.

High Strain Rate Testing of Materials – Part II

Figure 3 below shows the stress-strain results from a typical tensile test on a polymer material, as can be seen the test plot is made up of four different regimes. The macro-mechanical response of the material comprises of 4 distinct deformation characteristics.

Figure 3: Uniaxial Tension Test Results for a Viscoelastic Rate Dependent Material

The test results show that the slope of the line is not constant throughout the 4 regimes and the material is thus said to exhibit non-linear elasticity. The elastic region is defined in the small initial portion of the results where the slope is constant. On the molecular level the linear elastic phase is caused by the Van der Waal forces acting between the polymer chains. These forces resist the deformation, however once the strain in the material reaches a critical level, the polymer chains begin to slide with respect to one another. The response is non-linear deformation once the Van der Waal forces are overcome.

The yield point shows the local maximum stress value of the material after which the polymer chains show large scale sliding. Subsequently, the response shows a relative softening and later hardening of the material. The strain hardening phase is a result of the randomly oriented polymer chains re-aligning themselves in such a way that requires a higher force application for continued deformation.

Figure 4 shows the test results from testing Polyethylene material as per ASTM D638 at three different speeds under isothermal conditions. At the slowest crosshead speed of 5mm/minute, the yield strength and the modulus of the material are at their lowest value. As the test speed increases, the yield strength and modulus also increase. The material stiffness increases with the increase in strain rate. The material appears to be getting stronger and tougher under high strain rate conditions. The same effect can also be carried out by keeping the strain rate constant but by decreasing the temperature progressively.

Figure 4: Test Results for PE Material under Variable Strain Rate/Speed

At our laboratory we have studied the mechanical behaviour of High Density PolyEthylene (HDPE) polymer under the effect of various temperatures and strain rates. Uniaxial tensile tests were performed to determine the dynamic response of HDPEs at strain rates varying from 0.0001 sec-1 to 10 sec-1. Dynamic tests were performed at seven different strain rates, and the results in terms of true stress-strain curves are shown in Figure5. The results show that yield stress increases with the increase in strain rate.

The experimental results reveal that the stress-strain behaviour of HDPEs is much different at lower and higher strain rates. At higher strain rate, the HDPEs yield at higher stress compared to that at low strain rate. At lower strain rate, yield stress increases with the increase in strain rate while it decreases significantly with the increase in temperature.  Likewise, initial elastic modulus increases with the increase in strain rate. Yield stress increases significantly at higher strain rates in the material. The stress-strain curves show almost similar mechanical response in which initial nonlinear elastic behaviour was observed followed by subsequent yielding, strain softening and hardening. Yield stress changes significantly with the increase in strain rate. An increase of 20.6 % in yield stress was calculated with strain rate increase from 0.0001 sec-1 to 100 sec-1 At all strain rates, ductile behaviour of HDPEs was observed. Strain-rate dependency of the stress-strain behaviour of polymer materials has now been well documented. This feature of mechanical behaviour is important in engineering applications for automotive and aerospace crashworthiness where the design of a polymer component is required to resist shock and impact loading and other strength stiffening effects.

Figure 5: Test Results for HDPE Material under Variable Strain Rate/Speed

Figure 6: AdvanSES Non-contact Measurement and DIC Setup

Some materials have higher strain rate sensitivity as compared to other materials. This is more dependent on the micro structural makeup and deformation physics. It is advisable to test the materials over a range of strain rates and use the data in FEA modelling and simulation.

References:

  1. Dowling, N. E., Mechanical Behavior of Materials, Engineering Methods for Deformation, Fracture and Fatigue Prentice-Hall, NJ,1999.
  2. Srinivas,K.,andDharaiya,D.,Material And Rheological Characterization For Rapid Prototyping Of Elastomers Components, American Chemical Society, Rubber Division, 170th Technical Meeting, Cincinnati,2006.
  3. BelytschkoT.,  Liu  K.W,MoranB.,Nonlinear Finite Elements for Continua and Structures, John Wiley and Sons Ltd,2000.
  4. Kaliske, M., L. Nasdala, and H. Rothert, On Damage Modeling for Elastic and Viscoelastic Materials at Large Strain. Computers and Structures, Vol. 79,2001.
  5. Silberberg, Melvin.,Dynamic Mechanical Properties of Polymers: A Review, PlusTechEquipment Corporation, Natick, Massachusetts,1965.
  6. Lakes, Roderick.,Viscoelastic Materials, Cambridge University Press,2009.
  7. Sperling, Introduction to Physical Polymer Science, Academic Press, 1994.
  8. Ward et al., Introduction to Mechanical Properties of Solid Polymers, Wiley, 1993.
  9. Seymour et al. Introduction to Polymers, Wiley,1971.
  10. Ferry, Viscoelastic Properties of Polymers, Wiley,1980.
  11. Goldman, Prediction of Deformation Properties of Polymeric and CompositeMaterials, ACS, 1994.
  12. Menczel and Prime, Thermal Analysis of Polymers, Wiley, 2009.
  13. Joergen Bergstrom, et al., High Strain Rate Testing and Modeling of Polymers for Impact Simulations, 13th LS-Dyna Users Conference, 2014.
  14. Clive R. S., Jennifer L. J.,High Strain Rate Mechanics of Polymers: A Review, Journal ofDynamic Behavior of Materials,  2:15–32, 3016

High Strain Rate Testing of Materials – Part 1

Polymers, composites and some metallic materials are viscoelastic and strain-rate sensitive. Under high strain rates the micro mechanisms by which these materials deform is different than that experienced at low strain rates. Consequently, use of quasi-static stress-strain data may not produce accurate and reliable predictions of material and product performance at highstrain rates. The use of such data in simulation and FEA leads of improper design of engineering components. An understanding of the mechanical properties of polymers over a range of strain rates, temperatures, and frequencies is thus an imperative requirement. As well as being governed by the composition and microstructure of the materials, these properties are highly dependent on a number of external factors.  Common applications where the high strain rate properties are critical are composite and steel material properties in high speed crash analysis of automotive and aerospace structures, high speed ballistic impacts and drop impacts of consumer durables and electronic items.

Most polymers and composite materials exhibit time and temperature dependent mechanical behaviour. This can be inferred by their rate dependent Young’s modulus, yield strength, and postyielding behaviour. Over a range of strain rates from low to high the mechanical properties of these materials may change from gel-like to rubbery to ductile plastic to brittle like ceramics. Along with these strain rate effects, polymers also exhibit large reversible deformations in addition to incompressibility.

Viscoelastic properties of materials play a very critical part in defining the short and long-term behaviour of metals, polymers and composites. To fully characterize this time, frequency and temperature dependent properties of the materials it is important to characterize them in the defamation modes and the rates at which this materials and their products will perform underfield service conditions.

Quasi static characterization test methods assess the properties of the material under static conditions. This serves as a good starting point in product design but when the goal is of full field 360 degree characterization of properties to serve the full range from implicit to explicit FEA simulations for drops impacts, to high speed deformation cases thenthe use of such data will lead to wrong simulation and interpretation of results. 

Different types of testing techniques are used to generate data under high speed and dynamic conditions.Each test method satisfies a specific range of strain rates and deformation characteristics. Electro-mechanical test systems,Servo-hydraulic test systems and Split Hopkinson bar testing apparatus are typically used to characterize the properties of these materials at progressively high strain rates. Complexities in applying this testing techniques come from multiple factors such as sample gripping, calculation of strain and strain rates, test data acquisition and analysis of the test data to generate the right response curve.

Figure 1: Electromechanical and Servo-hydraulic Test Setup at AdvanSES

AtAdvanSES,We have capabilities to test these materials characteristics using all the three testing apparatus mentioned above.

Figure 2: Split Hopkinson Pressure Test SHPB Test Setup at AdvanSES

Strain rate is the change in strain of a material with respect to time. Longer testing time is related to low strain rate,and shorter testing time iscorrelated to higher strain rates.

When a sample in a tensile test is gradually stretched by pulling the ends apart, the strain can be defined as the ratio {\displaystyle \epsilon }ε between the amount of stretchon the specimen and the original length of the band:

ε(t) = L(t) – L0/L0 

Where, L0 is the original length of the specimen and L(t) is the length at time t. Then the strain rate is defined by,

where v(t)is the speed at which the ends are moving away from each other. The unit is expressed as time-1.