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.