Good Introduction to Elastomer

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Elastomer Applications In New AgeIndustries And Engineering Support

Akash.A.VandakudriDr.K.S.Krishnamurthy


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Elastomers Application for New Age Industries and Engineering Support

INTRODUCTION TO ELASTOMERS:

Rubber is one of the materials which has benefitted mankind rather immensely and in innumerable ways. It is unimaginable tothink of everyday life without it. Surely, its discovery is one of the greatest of all time. Natural rubber is believed to have beendiscovered initially by a South American Indian woman as the tears of a Crying tree. The natives were using it in a variety ofprimitive ways, viz., for clothing, shoes, and even for making bouncing balls for children to play with. However, rubber in itsoriginal form as derived from latex finds limited use without further processing it to suit a specific need. Actually, natural rubberdoes not have stable properties as it can become plastic even at moderately higher temperatures or become brittle in cold condi-tions. It was left to Charles Goodyear, an inventor, in the year 1839 to accidentally discover the vulcanization process by addingsulfur to natural rubber and heating- that resulted in a harder substance. Synthetic rubbers have come to be known as elasto-mers in the modern polymer era, with names such as Neoprene, Isoprene, Styrene-Butadiene, Butyl, Nitril, Acrylic, Butadiene,Urethane, etc.

The industrial and commercial use of rubber products are immense due to the many outstanding properties of rubber,namely, its elasticity, its mouldability into any desired shape or size, the adaptability for changing it to suit the desiredengineering properties, e.g., strength or toughness, through chemical, pressure and thermal treatments. Vulcanizationprocess changes the structure of the polymer chains of natural rubber permanently, resulting in changed physical andmechanical properties. The present paper briefly discusses a) some aspects of the special elastic properties of rubbercompared to other engineering materials and how these are utilized for industrial applications and b) examples of com-puter simulation of its mechanical behavior by means of the finite element method. Before these are discussed, abrief list of rubber applications are given below:




NEW AGE INDUSTRY APPLICATIONS

Some of the new age industries where elastomers are extensively used are listed below:

Automotive:Tuned mass dampers, rubbers seals, tyre and tube manufacturing, pipes and hoses, boots, sleeves and covers

for various equipments, etc.

Aerospace :Air management ducts, diaphragms, interior foils, hose and hoselines, air spring systems, etc.

Defense:

Coating for radar and other defense equipments, camouflage netting, radar absorbing material, low RCS anten-nas, de-icing of aircraft wings by resistive heating, etc.

Biomechanics and the medical/dental professions :Surgery devices, prostheses, orthopedics, orthodontics, dental implants, artificial limbs, artificial organs, wheel-

chairs and beds, monitoring equipment, etc.

Highway safety and flight safety :

Seat belt design, impact absorbers, seat and padding design, passenger protection etc.

Sports and consumer:Helmet design, shoe design, athletic protection gear, sports equipment safety, etc.

Others:Dental Products, paints and coatings, cement and concrete adhesives, special wood protection coatings,

biocompatible materials, medical and dental adhesives, etc.




MECHANICAL BEHAVIOR OF ELASTOMERS

As stated in the introduction, synthetic rubbers can be manufactured to the needs of the applications they are put to and theproperties vary accordingly. However, certain characteristics of rubbers make them unique, e.g.

Ability to undergo large elongations, as much as 100% to 700%.

High Poisson ratio- resulting in large lateral deformation

Usually in tension, the material softens then stiffens again. On the other hand, in compression, the response becomes

quite stiff.

These special deformational characteristics of rubber are responsible for its wide spread usage in industry e.g.,tyres, sealants, dampers, etc., as it can take shocks, deform locally, stretch and bend, or deform like a liquid underpressure and confinement. The last mentioned property is due to its high Poisson ratio which makes rubber a nearlyincompressible material (See Appendix, # II).

Fig 5: Rubber characteristics under different loading




FAILURE IN ELASTOMER:

Another important and perhaps a difficult to understand characteristic of rubber is its failure. Initiation of failure in rubber canoccur because of several reasons. Some of them are listed below:

Flaws introduced during the manufacturing processes, e.g., compound mixing, extrusion, molding, or vulcanization, etc.

Fatigue caused by service loads.

Material degradation due to environmental/mechanical/thermal conditions.

Environmental reasons.Overrating the product for the specific load rate.

Subjected to high and low temperatures, heavy pressure variation, etc.

Fig 7: Tearing near the bond edges Fig 8: Split open of the Free Edges

Fig 9: Fatigue Failure




DESIGN ENGINEERING SUPPORT:

The engineering support for elastomer design and evaluations is to a great extent assisted by mathematical modeling &computer simulations of elastomer response subjected to real life loading conditions. Computer simulations are an excellentmeans of understanding the complex mechanical behavior using the visualization and graphic capabilities available withmodern FE tools such as Ansys, Abaqus, Nastran, etc. which have advanced material models and computational techniquesbuilt into their code. These programs also provide the user additional capabilities for research and experiment, e.g. provisionto plug in user defined mathematical models, etc. Computer simulations for modeling elastomer behavior, e.g., involve thefollowing:

Mathematical modeling of constitutive behavior

Finite Element Analysis

Rigid body Simulations

Computational Fluid Dynamics




MATHEMATICAL MODELING

The mathematical models used for modeling elastomer mechanical response use the concepts of stretch ratio and the strainenergy potentials( See Appendix II & III). Strain energy potentials are used to relate stresses to strains in hyper-elastic(elastomer) materials. The strain energy potential is nothing but the strain energy function and is also related to the stretchratio.

Based on the strain energy potential and the stretch ratio concepts, there are several mathematical models which arebeing used to describe the stress-strain behavior of elastomers. Some of these are:

Polynomial MethodMooney-RivlinNeo-HookeanYeohArruda- BoyceOgdenBlatz-ko

Hyper foam

Of these, the most commonly used models are those of Mooney-Rivlin* and Ogden .

Mooney-Rivlin Model:

Using this strain energy model with any of the numerical integration techniques the behavior of the material can be calculatedin all the directions, but is restricted to simple models.

2 term strain energy potential

3 term strain energy potential

Fig 7: Elastomer Stress-Strain relation under various loading

*These models are more fully described in text books on large deformation elasticity theory




FE Analysis of Seal

For example of the elastomer modeled used the Ansys FE program has been shown below to study the

self-contacting behavior. Here the compressive load is increased until contact makes the elastomer act like aseal.

RIGID BODY SIMULATIONS

Rigid body simulations give the deformation pattern and load transfer path of the parts made of elastomers when in contactwith rigid parts:

Rigid Simulation of O-Ring:

(Source MSC MARC Technical Paper)

Fi 14: Undeformed Model Fig 15: Deformed Model

Fig 16: Strain is 142.3% Fig 17: Max Strain Region Fig 18: Contact Details

Fig 19: Undeformed

Model

Fig 20: Deformed Model Fig 21: Cauchy Stress Pattern

Ring




Simulation of Rubber Boot :

This summary of rigid simulation on boot in given below:

Large displacements of boot

Large strains and stress in boot

Incompressible material behavior of the material used

Susceptibility to local buckling subjected to loading

Varying boundary conditions caused by the 3-D contact between various parts of the boot

Fig 22: Undeformed

Model

Fig 23: Axial Compression Fig 24: Bending of folds

Fig 25: Deformed boot on shaft (Source MSC MARC Technical Paper)




REFERENCES

Nonlinear FEA of Rubber Components -Engineering ApplicationsMorman, K.N. and T.Y. Pan. Applying FEA to Elastomer Design

Failure of elastomers -Compositional and failure analysis of polymersBy John Scheirs

Numerical MethodsAnsys and Nastran Literature and Technical papers.

Rubber Behavior and CharacterizationTeaching Material of Ansys Corp

Finite Element MethodZienkiewicz, O.C. and R.L. Taylor-The Finite Element Method (4th ed.) Vol.1.

Seal DesignBacker Patent

Halliburton PatentSchlumberger Patent




APPENDIX:

This Appendix explains the principles underlying the behavior, numerical treatment and material mathematical model of nearlyincompressible materials (for more details, see any of the finite element textbooks)-listed in the references for further reading.Incompressibility is one of the most troublesome areas in the finite element analysis of elastomers. Modern computationalmechanics practice in the analysis of incompressible materials is to suppress the volumetric component of the strain field byappropriately selected variational principles

I. Polymeric Structure of Rubber:

In general the elastomers are a class of polymers having the following chemical properties:

They are amorphous in nature and are comprised of long molecular chains.The molecular chains are highly twisted, coiled, and randomly oriented in an undeformed state.These chains become partially straightened and untwisted under tensile loading and upon removal of load thematerial bounce back to original shape and size.Straightening of rubber is achieved by forming crosslink and this is achieved by using vulcanization process.

II. Numerical Treatment:

A simple way to understand why incompressibility results in numerical problems is to examine the familiar elasticity relation-ship:

For nearly incompressible materials, Poissons ratio approaches 0.5, and the bulk modulus becomes large relative to theshear modulus. In the limit, when the material is completely incompressible (= 0.5), all hydrostatic deformation is precluded.In this limiting case, it is, therefore, not possiblare in the range of 0.49 to 0.49999.It is important to note that the usevalues infinite element codes that have not been tailored for incompressibility analysis will lead to very serious numerical errors, cau bythe ill conditioning resulting from the division by a value which is nearly zero.

Fig28: Tangled Molecular

Chains

Before Vulcanization

Fig 29: Untangled

Molecular Chains

Fig 30: Completely Untangled

After Vulcanization


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III. Material Mathematical Model:

The design of elastomer depends on many factors but the one main responsible is the stretch ratio. If we perform a uniaxialtest by pulling a rubber rod in the longitudinal direction, the stretch ratio, , (or stretch) is defined as the ratio of the deformedgauge length L divided by the initial gauge length L0. Based on this the stress invariants and then volume ratio and strainenergy potential are calculated.

Fig 29: Stretch Ratio in different direction

Stretch Ratio

Stress Invariants

Good Introduction to Elastomer

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