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Modelling the viscoplastic properties of carbon black filled rubber: A finite strain material model suitable for Finite Element Analysis
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL. Scania.ORCID iD: 0000-0002-1036-6837
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

An increased environmental awareness, legal demands and the large part of total costs attributable to fuel cost are all incentives for the automotive industry to reduce fuel consumption. The optimal driveline to enable this reduction depends on the operational conditions and the available infrastructure. Moreover, special care is needed when developing the driveline isolators, since the demands on noise, vibration and harshness (NVH) are the same regardless of driveline. To this end, computer aided calculations can be used in order to evaluate a large number of configurations. However, these calculations are only, at best, as good as the material models employed. In the foreseeable future, rubber with reinforcing fillers will be used in vibration isolators in order to obtain the desired properties of these components. However, the stiffness and damping of rubber with reinforcing fillers are highly non-linear functions, and the available material models in commercial software and in the literature are often insufficient. Therefore, a finite strain viscoplastic material model is derived in the time domain and implemented as a user defined material model in Abaqus Explicit. The model captures the strain amplitude and frequency dependency of the storage and loss modulus for a carbon black filled natural rubber. The model is accurate over a wide range of shear strain amplitudes and frequencies, 0.2-50 % and 0.5-20 Hz, respectively, using only 5 material parameters. In addition, the model correctly captures the response from bimodal excitations. The implementation in Abaqus Explicit enables component characteristics to be evaluated early in the development phase, with material parameters derived from simple test specimens. The improved accuracy of simulations of these components can aid engineers develop more optimized solutions faster than with conventional methods.

Abstract [sv]

En ökad miljömedvetenhet, juridiska krav och den stora delen av de totala kostnaderna som kan hänföras till bränslekostnader är alla incitament för fordonsindustrin att minska bränsleförbrukningen. Den optimala drivlinan för att möjliggöra denna minskning beror på driftförhållanden och den tillgängliga infrastrukturen. Dessutom ställs höga krav på utvecklingen av drivlineisolatorer, eftersom kraven på buller och vibrationer (NVH) är desamma oavsett drivlina. För detta ändamål kan datorstödda beräkningar användas för att utvärdera ett stort antal konfigurationer. Dessa beräkningar är, i bästa fall, endast så bra som de använda materialmodellerna. Inom en överskådlig framtid kommer gummi med förstärkande fyllmedel användas i vibrationsisolatorer för att erhålla de önskade egenskaperna hos dessa komponenter. Men styvheten och dämpningen i gummi med förstärkande fyllmedel är kraftigt icke-linjära funktioner, och de tillgängliga materialmodellerna i kommersiella programvaror och i litteraturen är ofta otillräckliga. Därför är en viskoplastisk materialmodell för finita deformationer framtagen i tidsdomänen och implementeras som ett användardefinierat material i Abaqus Explicit. Modellen fångar töjningsamplitud- och frekvensberoendet av lagrings- och förlustmodulen för ett kimröksfyllt naturgummi. Den är korrekt över ett brett intervall av skjuvtöjningsamplituder och frekvenser, 0.2-50% respektive 0.5-20 Hz, och kräver endast 5 materialparametrar. Dessutom fångar modeller responsen från bimodala excitationer. Implementeringen i Abaqus Explicit gör att komponentegenskaper kan utvärderas tidigt i utvecklingsfasen, med materialparametrar som härrör från enkla provkroppar. Den förbättrade noggrannheten i simuleringar av dessa komponenter kan hjälpa ingenjörer att utveckla mer optimerade lösningar snabbare än med konventionella metoder.

Place, publisher, year, edition, pages
Stockholm: US-AB , 2016. , xii, 55 p.
Series
TRITA-AVE, ISSN 1651-7660 ; 2016:12
Keyword [en]
reinforcing fillers, rubber, finite strain, viscoplastic
Keyword [sv]
förstärkande fyllmedel, gummi, finita töjningar, viskoplastisk
National Category
Vehicle Engineering
Research subject
Vehicle and Maritime Engineering
Identifiers
URN: urn:nbn:se:kth:diva-184879ISBN: 978-91-7595-902-3 (print)OAI: oai:DiVA.org:kth-184879DiVA: diva2:917398
Public defence
2016-04-29, D2, Lindstedtsvägen 5, 10044 Stockholm, KTH Campus, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

QC 20160406

Available from: 2016-04-06 Created: 2016-04-06 Last updated: 2016-04-06Bibliographically approved
List of papers
1. Constitutive modelling of the amplitude and frequency dependency of filled elastomers utilizing a modified Boundary Surface Model
Open this publication in new window or tab >>Constitutive modelling of the amplitude and frequency dependency of filled elastomers utilizing a modified Boundary Surface Model
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2014 (English)In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 51, no 19-20, 3431-3438 p.Article in journal (Refereed) Published
Abstract [en]

A phenomenological uniaxial model is derived for implementation in the time domain, which captures the amplitude and frequency dependency of filled elastomers. Motivated by the experimental observation that the frequency dependency is stronger for smaller strain amplitudes than for large ones, a novel material model is presented. It utilizes a split of deformation between a generalized Maxwell chain in series with a bounding surface plasticity model with a vanishing elastic region. Many attempts to capture the behaviour of filled elastomers are found in the literature, which often utilize an additive split between an elastic and a history dependent element, in parallel. Even though some models capture the storage and loss modulus during sinusoidal excitations, they often fail to do so for more complex load histories. Simulations with the derived model are compared to measurements in simple shear on a compound of carbon black filled natural rubber used in driveline isolators in the heavy truck industry. The storage and loss modulus from simulations agree very well with measurements, using only 7 material parameters to capture 2 decades of strain (0.5-50% shear strain) and frequency (0.2-20 Hz). More importantly, with material parameters extracted from the measured storage and loss modulus, measurements of a dual sine excitation are well replicated. This enables realistic operating conditions to be simulated early in the development process, before an actual prototype is available for testing, since the loads in real life operating conditions frequently are a combination of many harmonics.

Keyword
Amplitude dependency, Boundary Surface Model, Carbon black, Filled elastomers, Fletcher-Gent Effect, Natural rubber
National Category
Vehicle Engineering
Identifiers
urn:nbn:se:kth:diva-151310 (URN)10.1016/j.ijsolstr.2014.06.003 (DOI)000341469900012 ()2-s2.0-84906245570 (Scopus ID)
Note

QC 20140917

Available from: 2014-09-17 Created: 2014-09-17 Last updated: 2017-12-05Bibliographically approved
2. An efficient method for obtaining the hyperelastic properties of filled elastomers in finite strain applications
Open this publication in new window or tab >>An efficient method for obtaining the hyperelastic properties of filled elastomers in finite strain applications
2015 (English)In: Polymer testing, ISSN 0142-9418, E-ISSN 1873-2348, Vol. 41, 44-54 p.Article in journal (Refereed) Published
Abstract [en]

An efficient methodology for obtaining hyperelastic material parameters for filled elastomers utilizing unloading curves in uniaxial tension, pure shear and the inflation of a rubber membrane is presented. Experimental results from biaxial extension are crucial when fitting hyperelastic material parameters, and the bubble inflation technique is an excellent method of obtaining this data when specialized test equipment is unavailable. Moreover, filled elastomers have considerable hysteresis, and the hysteresis grows with increasing strain amplitudes. Therefore, the loading curve is in general comprised of both elastic and inelastic contributions, even at very low strain rates. Consequently, it is deemed more accurate to use experimental data from the unloading curve to describe the elastic behavior of the material. The presented methodology enables obtainment of parameters related to both the first and second strain invariant, which is required for a good fit between measurement and simulation results. Finally, it is essential that a chosen material model is accurate in all deformation modes when designing components subjected to a complex, multi-axial load history. An accurate material model enables more concepts and geometries of a component to be studied before a physical prototype is available.

Keyword
Filled elastomers, Hyperelasticity, Material parameters
National Category
Vehicle Engineering
Identifiers
urn:nbn:se:kth:diva-151311 (URN)10.1016/j.polymertesting.2014.10.008 (DOI)000348970100008 ()2-s2.0-84909608138 (Scopus ID)
Note

QC 20140917. QC 20150316. Updated from manuscript to article in journal.

Available from: 2014-09-17 Created: 2014-09-17 Last updated: 2017-12-05Bibliographically approved
3. A finite strain viscoplastic constitutive model for rubberwith reinforcing fillers
Open this publication in new window or tab >>A finite strain viscoplastic constitutive model for rubberwith reinforcing fillers
(English)Manuscript (preprint) (Other academic)
Abstract [en]

A three dimensional viscoplastic constitutive model for finite strains in aco-rotational explicit scheme is developed and implemented using finite elementsthat captures the amplitude dependency, commonly referred to as theFletcher-Gent effect, and frequency dependency of rubber with reinforcingfillers. The multiplicative split of the deformation gradient is utilized andthe plastic flow rule stems from an extension to finite strains of a boundarysurface model with a vanishing elastic region. The storage and loss modulusfor a 50 phr carbon black filled natural rubber are captured over a largerange of strain amplitudes, 0.2 − 50% shear strain, and frequencies, 0.2 − 20Hz. In addition, bimodal excitation is replicated accurately, even though thismeasurement data is not included when obtaining material parameters. Thiscapability is essential when non-sinusoidal loading conditions are to be replicated.By separating the material and geometrical influence on the propertiesof a component, the design engineers have the capability to evaluate more concepts early in the design phase. This also reduces the need of complexprototypes for physical testing, thereby saving both time and money.

Keyword
Finite strains, Viscoplastic material, Polymeric material, Finite elements, Fletcher-Gent effect
National Category
Textile, Rubber and Polymeric Materials
Research subject
Vehicle and Maritime Engineering
Identifiers
urn:nbn:se:kth:diva-184890 (URN)
Note

QS 2016

Available from: 2016-04-06 Created: 2016-04-06 Last updated: 2016-04-06Bibliographically approved
4. Temperature dependency of a viscoplastic materialmodel derived for rubber with reinforcing fillers
Open this publication in new window or tab >>Temperature dependency of a viscoplastic materialmodel derived for rubber with reinforcing fillers
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The temperature dependency of a finite strain time domain viscoplastic materialmodel for filled rubber is studied over the ranges 0.2-50% shear strain,0.8-17.9 Hz and 0 to 85 C. The storage and loss modulus of a 54 phr carbonblack filled natural rubber are accurately captured by the model at eachtemperature, thereby supporting the notion that a viscoelastic network inseries with a plastic element is suitable material model for rubber with reinforcingfillers. The variation of the moduli as a function of temperatureis non-linear, with a stronger dependency at lower temperatures. Therefore,a set of measurements are representative in a broader temperature range athigher compared to lower temperatures. Highly filled rubber are not thermorheologicalsimple materials, and an elevated temperature influences the stiffnessand dissipation differently at low and high strain amplitudes. Therefore,relying merely on low strain amplitude measurements can led to erroneousconclusions, when strain amplitudes in operational conditions are moderate to large. The presented modelling technique enables an accurate evaluationbetween compounds, early in the development phase of new components inindustrial applications.

Keyword
Filled elastomers, temperature dependency, amplitude dependency
National Category
Textile, Rubber and Polymeric Materials
Research subject
Vehicle and Maritime Engineering
Identifiers
urn:nbn:se:kth:diva-184891 (URN)
Note

QS 2016

Available from: 2016-04-06 Created: 2016-04-06 Last updated: 2016-04-06Bibliographically approved

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