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.

ASTM D5992 Dynamic Properties of Rubber Vibration Products

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.

 

Dynamic Characterization Testing as Per ASTM D5992 and ISO 4664

ASTM D5992 and ISO 4664-1

ASTM D5992 covers the methods and process available for determining the dynamic prop- erties of vulcanized natural rubber and synthetic rubber compounds and components. The standard covers the sample shape and size requirements, the test methods, and the pro- cedures to generate the test results data and carry out further subsequent analysis. The methods described are primarily useful over the range of temperatures from cryogenic to 200◦C and for frequencies from 0.01 to 100 Hz, as not all instruments and methods will accommodate the entire ranges possible for material behavior.

Figures(.43and.44) show the results from a frequency sweep test on five (5) different elastomer compounds. Results of Storage modulus and Tan delta are plotted.

 

Figure .43: Plot of Storage Modulus Vs Frequency from a Frequency Sweep Test

 

The frequency sweep tests have  been carried out by applying a pre-compression of  10 % and subsequently a displacement amplitude of 1 % has been applied in the positive and negative directions. Apart from tests on cylindrical and square block samples ASTM D5992 recommends the dual lap shear test specimen in rectangular, square and cylindri- cal shape specimens. Figure (.45) shows the double lap shear shapes recommended in the standard.

Figure .44: Plot of Tan delta Vs Frequency from a Frequency Sweep Test

 

Figure .45: Double Lap Shear Shapes

Free eBook: Material Characterization Testing and Finite Element Analysis of Elastomers

The application of computational mechanics analysis techniques to elastomers presents
unique challenges in modeling the following characteristics:
1) The load-deflection behavior of an elastomer is markedly non-linear.
2) The recoverable strains can be as high 400 % making it imperative to use the large
deflection theory.
3) The stress-strain characteristics are highly dependent on temperature and rate effects
are pronounced.
4) Elastomers are nearly incompressible.
5) Viscoelastic effects are significant.

The inability to apply a failure theory as applicable to metals increases the complexities regarding the failure and life prediction of an elastomer part. The advanced material models available today define the material as
hyperelastic and fully isotropic. The strain energy density (W) function is used to describe the material behavior.

To help you better understand, we broke down everything you need to know about materials, testing, FEA verifications and validations etc.

Download the free eBook here.

 

Here’s what you can expect to learn:

1. Elastomeric materials and their properties

2. Computational Mechanics in the design and development of polymeric components

3. Why there are recommended testing protocols

4. Curve-fitting the Material Constants.

5. Verifications and Validations of FEA Solutions

 

Let’s talk Engineering with Rubber.

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Abaqus – Tips and Tricks Vol 1

Abaqus – Tips and Tricks: When to use what Elements?

For a 3D stress analysis, ABAQUS offers different typess of linear and quadratic hexahedral elements, a brief description is as below;

  1. Linear Hexahedral: C3D8 further subdivided as C3D8R, C3D8I, and C3D8H
  2. Quadratic Hexahedral: C3D20 further subdivided as C3D20R, C3D20I, and C3D20H, C3D20RH
  3. Linear Tetrahedral: C3D4 further subdivided as C3D4R, and C3D4H
  4. Quadratic Tetrahedral: C3D10 further subdivided as C3D10M, C3D10I and C3D10MH
  5. Prisms: C3D6 further subdivided as C3D6R, and C3D6H

In three-dimensional (3D) finite element analysis, two types of element shapes are commonly utilized for mesh generation: tetrahedral and hexahedral. While tetrahedral meshing is highly automated, and relatively does a good job at predicting stresses with sufficient mesh refinement, hexahedral meshing commonly requires user intervention and is effort intensive in terms of partitioning. Hexahedral elements are generally preferred over tetrahedral elements because of their superior performance in terms of convergence rate and accuracy of the solution.

The preference for hexahedral elements(linear and uadratic) can be attributed to the fact that linear tetrahedrals originating from triangular elements have stiff formulations and exhibit the phenomena of volumetric and shear locking. Hexahedral elements on the other hand have consistently predicted reasonable foce vs loading (stiffness) conditions, material incompressibility in friction and frictionless contacts. This has led to modeling situations where tetrahedrals and prisms are recommended when there are frictionless contact conditions and when the material incompressibility conditiona can be relaxed to a reasonable degree of assumption.

A general rule of thumb is if the model is relatively simple and you want the most accurate solution in the minimum amount of time then the linear hexahedrals will never disappoint.

Modified second-order tetrahedral elements (C3D10, C3D10M, C3D10MH) all mitigate the problems associated with linear tetrahedral elements. These element offer good convergence rate with a minimum of shear or volumetric locking. Generally, observing the deformed shape will show of shear or volumetric locking and mesh can be modified or refined to remove these effects.

C3D10MH can also be used to model incompressible rubber materials in the hybrid formulation. These variety of elements offer better distribution of surface stresses and the deformed shape and pattern is much better. These elements are robust during finite deformation and uniform contact pressure formulation allows these elements to model contact accurately.

The following are the recommendations from the house of Abaqus(1);

  • Minimize mesh distortion as much as possible.
  • A minimum of four quadratic elements per 90o should be used around a circular hole.
  • A minimum of four elements should be used through the thickness of a structure if first-order, reduced-integration solid elements are used to model bending.

 

 

  1. Abaqus Theory and Reference Manuals, Dassault Systemes, RI, USA