Stress Relaxation and Creep

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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. In Most Finite Element Analysis softwares stress relaxation and creep can both be modeled with the help of experimental test data

High Strain Rate Testing of Materials – Part II

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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

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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.

FEA Modeling of Rubber and Elastomer Materials

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The application of computational mechanics analysis techniques to elastomers presents unique challenges in modeling the following characteristics:

– The load-deflection behaviour of an elastomer is markedly non-linear.

– The recoverable strains can be as high 400 % making it imperative to use the large

deflection theory.

– The stress-strain characteristics are highly dependent on temperature and rate effects are pronounced.

– Elastomers are nearly incompressible.

– Viscoelastic effects are significant.

The ability to model the special elastomer characteristics requires the use of sophisticated material models and non-linear Finite element analysis tools that are different in scope and theory than those used for metal analysis. Elastomers also call for superior analysis methodologies as elastomers are generally located in a system comprising of metal-elastomer parts giving rise to contact-impact and complex boundary conditions. The presence of these conditions require a judicious use of the available element technology and solution techniques.

FEA Support Testing

Most commercial FEA software packages use a curve-fitting procedure to generate the material constants for the selected material model. The input to the curve-fitting procedure is the stress-strain or stress-stretch data from the following physical tests:

1  Uniaxial tension test

2  Uniaxial compression test OR Equibiaxial tension test

3  Planar shear test

4  Volumetric compression test

A minimum of one test data is necessary, however greater the amount of test data, better the quality of the material constants and the resulting simulation. Testing should be carried out for the deformation modes the elastomer part may experience during its service life.

Curve-Fitting

The stress-strain data from the FEA support tests is used in generating the material constants using a curve-fitting procedure. The constants are obtained by comparing the stress-strain results obtained from the material model to the stress-strain data from experimental tests. Iterative procedure using least-squares fit method is used to obtain the constants, which reduces the relative error between the predicted and experimental values. The linear least squares fit method is used for material models that are linear in their coefficients e.g Neo-Hookean, Mooney-Rivlin, Yeoh etc. For material models that are nonlinear in the coefficient relations e.g. Ogden etc, a nonlinear least squares method is used.

Verification and Validation

In the FEA of elastomeric components it is necessary to carry out checks and verification steps through out the analysis. The verification of the material model and geometry can be carried out in three steps,

_ Initially a single element test can be carried out to study the suitability of the chosen material model.

_ FE analysis of a tension or compression support test can be carried out to study the material characteristics.

_ Based upon the feedback from the first two steps, a verification of the FEA model

can be carried out by applying the main deformation mode on the actual component

on any suitable testing machine and verifying the results computationally.

Figure 1: Single Element Test

Figure(1) shows the single element test for an elastomeric element, a displacement

boundary condition is applied on a face, while constraining the movement of the opposite face. Plots A and B show the deformed and undeformed plots for the single element. The load vs. displacement values are then compared to the data obtained from the experimental tests to judge the accuracy of the hyperelastic material model used.

Figure 2: Verification using an FEA Support Test

Figure (2) shows the verification procedure carrying out using an FEA support test.

Figure shows an axisymmetric model of the compression button. Similar to the single

element test, the load-displacement values from the Finite element analysis are compared to the experimental results to check for validity and accuracy. It is possible that the results may match up very well for the single element test but may be off for the FEA support test verification by a margin. Plot C shows the specimen in a testing jig. Plot D and E show the undeformed and deformed shape of the specimen.

Figure(3) shows the verification procedure that can be carried out to verify the FEA

Model as well as the used material model. The procedure also validates the boundary conditions if the main deformation mode is simulated on an testing machine and results verified computationally. Plot F shows a bushing on a testing jig, plots G and H show the FEA model and load vs. displacement results compared to the experimental results. It is generally observed that verification procedures work very well for plane strain and axisymmetric cases and the use of 3-D modeling in the present procedure provides a more rigorous verification methodology.

Figure 3: FEA Model Verification using an Actual Part

AdvanSES provides Hyperelastic, Viscoelastic Material Characterization Testing for CAE & FEA softwares.

Unaged and Aged Properties and FEA Material Constants for all types of Polymers and Composites. Mooney-Rivlin, Ogden, Arruda-Boyce, Blatz-ko, Yeoh, Polynomials etc.

Fatigue Testing of Engine, Exhaust Mounts and Vibration Isolators

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OEMs and Tier 1 and tier 2 suppliers are under increased pressure to meet with 5 years and 100 thousand miles warranty on each and every rubber and plastic component in a passenger vehicle. With customer expectations for 100% reliability there is a need to fully test all the design, prototyping stage . Rubber mounts and vibration isolators are used to connect a vehicle’s engine and transmission to its chassis.

They are required to reduce the transmission of vibrations, providing the desired ride characteristics and protecting the rigid frame. The elastomeric material used in these components tends to naturally degrade over a period of time due to harsh conditions in addition to material degradation. Testing the properties of these mounts under such conditions is critical to make sure that the components meet the expectations. Choosing the correct test parameters required to perform this type of automotive component tests reliably can be challenging. We have more than a decade of experience in the design, analysis and testing of these rubber elastomer mounts.

Material Properties for Finite Element Analysis (FEA)

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The basic material properties that need to be known for accurate Finite Element Analysis are:

1) Stress-Strain relationship, Young’s modulus of elasticity
2) Yield strength.
3) Bulk and shear modulus.
4) Poisson’s ratio.
5) Density.

The relationship between applied mechanical force/stress and resulting deformation/strain on a given material is called its stress-strain curve or a constituent relationship equation. Isotropic materials like plastics, metals and elastomers exhibit the same behavior in all their orientations and layouts, while orthotropic and anisotropic materials, such as composites, glass-filled plastics, etc. show mechanical stress-strain properties that vary depending on the directions. Stress-strain equations and behaviors vary greatly by material type, as metals, plastics, elastomers, glass, composites, etc.

AdvanSES is a premier material testing laboratory for mechanical properties testing and component testing. We can test aged and unaged samples. Materials can be tested under static, dynamic and under elevated temperature conditions. In addition to testing and FEA, we have in-house machining facilities to develop test fixtures required to evaluate products and components for stiffness, stress, strain etc.

Dynamic Properties of Polymer, Rubber and Elastomer Materials

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Non-linear Viscoelastic Dynamic Properties of Polymer, Rubber and Elastomer Materials

Static testing of materials as per ASTM D412, ASTM D638, ASTM D624 etc can be cate- gorized as slow speed tests or static tests. The difference between a static test and dynamic test is not only simply based on the speed of the test but also on other test variables em- ployed like forcing functions, displacement amplitudes, and strain cycles. The difference is also in the nature of the information we back out from the tests. When related to poly- mers and elastomers, the information from a conventional test is usually related to quality control aspect of the material or the product, while from dynamic tests we back out data regarding the functional performance of the material and the product.

 

Tires are subjected to high cyclical deformations when vehicles are running on the road. When exposed to harsh road conditions, the service lifetime of the tires is jeopardized by many factors, such as the wear of the tread, the heat generated by friction, rubber aging, and others. As a result, tires usually have composite layer structures made of carbon-filled rubber, nylon cords, and steel wires, etc. In particular, the composition of rubber at different layers of the tire architecture is optimized to provide different functional properties. The desired functionality of the different tire layers is achieved by the strategical design of specific viscoelastic properties in the different layers. Zones of high loss modulus material will absorb energy differently than zones of low loss modulus. The development of tires utilizing dynamic characterization allows one to develop tires for smoother and safer rides in different weather conditions.

Figure  Locations of Different Materials in a Tire Design

The dynamic properties are also related to tire performance like rolling resistance, wet traction, dry traction, winter performance and wear. Evaluation of viscoelastic properties of different layers of the tire by DMA tests is necessary and essential to predict the dynamic performance. The complex modulus and mechanical behavior of the tire are mapped across the cross section of the tire comprising of the different materials. A DMA frequency sweep

test is performed on the tire sample to investigate the effect of the cyclic stress/strain fre- quency on the complex modulus and dynamic modulus of the tire, which represents the viscoelastic properties of the tire rotating at different speeds. Significant work on effects of dynamic properties on tire performance has been carried out by Ed Terrill et al. at Akron Rubber Development Laboratory, Inc.

Non-linear Viscoelastic Tire Simulation Using FEA

Non-linear Viscoelastic tire simulation is carried out using Abaqus to predict the hysteresis losses, temperature distribution and rolling resistance of a tire. The simulation includes several steps like (a) FE tire model generation, (b) Material parameter identification, (c) Material modeling and (d) Tire Rolling Simulation. The energy dissipation and rolling re- sistance are evaluated by using dynamic mechanical properties like storage and loss modu- lus, tan delta etc. The heat dissipation energy is calculated by taking the product of elastic strain energy and the loss tangent of materials. Computation of tire rolling is further carried out. The total energy loss per one tire revolution is calculated by;

Ψdiss = ∑ i2πΨiTanδi, (.27)
i=1
where Ψ is the elastic strain energy,
Ψdiss is the dissipated energy in one full rotation of the tire, and
Tanδi, is the damping coefficient.

The temperature prediction in a rolling tire shown in Fig (2) is calculated from the loss modulus and the strain in the element at that location. With the change in the deformation pattern, the strains are also modified in the algorithm to predict change in the temperature distribution in the different tire regions.

Failure of Rubber Components under Fatigue

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Rubber components under multiaxial cyclic loading conditions are often considered to have failed or degraded when there is a change is the stiffness of the component and it is no longer able to provide the performance it is designed for. Elastomeric polymer components are widely used in many industries like automotive, aerospace and biomedical applications due to their good vibration isolation and energy absorption characteristics. The type of loading normally encountered by these components in service is mutiaxial in nature. Fatigue failure is thus a major consideration in their design and availability of testing techniques to predict fatigue life under these complex conditions is a necessity.

In real world applications all materials and products are subjected to a wide variety of vibrating or oscillating forces. Fatigue testing consists of applying a cyclic load to a test specimen or the component to determine in-service performance during situations similar to real world working conditions.

Advanced Scientific and Engineering Services (AdvanSES) specializes in Fatigue Testing of Automotive Components including hoses, engine mounts, vibration isolators, silent bushes etc. Fatigue testing can be carried out in stress & force control, strain control or displacement control. The deformation modes under which fatigue tests are generally carried out are tension – tension, compression – compression, tension – compression and compression – tension.

ASTM D5992 Dynamic Properties of Rubber Vibration Products

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ASTM D 5992 Test Standard applies to Dynamic Properties of Rubber Vibration Products such as springs, dampers, and flexible load-carrying devices, flexible power transmission couplings, vibration isolation components and mechanical rubber goods. The standard applies to to the measurement of stiffness, damping, and measurement of dynamic modulus.

Dynamic testing is performed on a variety of rubber parts and components like engine mounts, hoses, conveyor belts, vibration isolators, laminated and non-laminated bearing pads, silent bushes etc.   to determine their response to dynamic loads and cyclic loading.

Personalized consultation from AdvanSES engineers can streamline testing and provide the necessary tools and techniques to accurately evaluate material performance under field service conditions.

The quantities of interest for measurements are tan delta, loss modulus, storage modulus, phase etc.  All of these properties are viscoleastic properties and require instruments, techniques and measurement practices of the highest quality.