Simulation and numerical implementation of chemo-thermomechanical aging of rubber
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1 OMSOL onfeence 206 Munich Poektteffen / 20 Simulation and numeical implementation of chemo-themomechanical aging of ubbe B.Musil, M.Johlitz, A.Lion Institute of Mechanics Univesität de Bundesweh München Neubibeg, Gemany
2 Outline Intoduction and motivation onstitutive modelling appoach Implementation into OMSOL Simulations Summay and outlook
3 Outline Intoduction and motivation onstitutive modelling appoach Implementation into OMSOL Simulations Summay and outlook
4 Intoduction & motivation Extenal influences on elastomes in technical applications tempeatue O 2 oxygen moistue UV oil adiation souce: F mechanical loads ozone O 3 chemicals
5 Intoduction & motivation Tension/ompession set Aging induced stess elaxation Modell equiements hange of mechanical popeties due to aging Tension/ompession set DLO Effect Mateial behavio: nonlinea themoviscoelasticity DLO Effect
6 Intoduction & motivation Oxidation due to Oxygen and tempeatue Themal induced Netwok scission hemical Aging Themal induced Ehenstein (2007) Netwok efomation hemical Aging Ievesible chemical change as a esult of oxygen diffusion and eaction with the elastome; elevated tempeatues acceleate the aging pocess Degeneation of chemical bonds (Netwok-Degadation) Fomation of new netwok unctions (Netwok-Refomation)
7 Outline Intoduction and motivation onstitutive modelling appoach Implementation into OMSOL Simulations Summay and outlook
8 Modelling Geneal motion of a defomable body Rheological model (Neo-Hooke) F VI F Fi A e...n e R EI Fe d q d q F Haupt (2002) Lion (996) Themo-mechanical consistence (.-D. inequality) ~ q 0 T : E 0 s Gad 0,, J,, q, q c e d, Helmholz fee enegy function
9 Institut fü M Institut fü M Institut fü M Institut fü MEHANIK Set of constitutive eq. and evolution eq. can be evaluated 3 2/3 3 2/3 3 2/3 0 : / ln ~ T T T i i t J J t J q J K J J J J K e d d ISO neq ISO ISO d VOL eq T T T T T ~ ~ ~ ~ ~ Stess (2.PK) Evolution equations T 4 ) : ( ) ( t t q ) ( 2 3 t i i i d d d d q R E c q q R E c q exp exp Evolution eq. fo the stess of the newly efomed netwok Evolution eq. fo inelastic defomation Evolution eq. fo the intenal (aging) vaiables qd and q Johlitz (202) Modelling
10 Modelling Set of constitutive eq. and evolution eq. can be evaluated Heat flux, diffusion flux, eaction tem q c Gad Gadc c k c c c 2 cgadc 0 q gad c gadc c k c (Fouie's law) (Fick's law) (linea eaction) Johlitz (202) Tempeatue and aging dependency of diffusion and eaction coefficient Johlitz (202) c c0 exp Ec exp R q k E R k k q k q exp 0 d 02
11 Outline Intoduction and motivation onstitutive modelling appoach Implementation into OMSOL Simulations Summay and outlook
12 Implementation Weak fomulation of the poblem Balance momentum equation 0 = δe u : T θ, c, q d c, q c dv V V δu b dv + δu t ds S Heat conduction equation 0 = δθ ρ c p θ dv V V Gad δθ λ θ Gadθ + λ c ζδ 2 + ζδθ c Gadc dv S δθ q ds Diffusion-Reaction equation 0 = δc ρc + k c δ + ζc θ dv V V Gad δc λ c δ + ζ θ Gadc dv S δc ds Stongly coupled multifield poblem
13 Implementation eated tenso libay: Weak fom eq. Basic tensos onstitutive laws Auxiliay vaiables Evolution eq.
14 Outline Intoduction and motivation onstitutive modelling appoach Implementation into OMSOL Simulations Summay and outlook
15 Simulations Measued paametes Mateial paametes: Aging paametes: Themal paametes:,,, E 0 e d c p,, E, d,, Estimated paametes hemical paametes: E, k, k, E,,, c, 0 c 0 02 k 3D uniaxial elaxation test in tension Model without aging omsol vs. Expeiment (NBR ubbe)
16 Simulations B:. LS applied displacement u 2. LS applied zeo stess P. Load step u P 68h 00 c 2. Load step 24h t
17 Simulations. Load step esults c concentation ~ T 33 2.PK total stess
18 Simulations 2. Load step esults 3 stech 3 stech ~ T PK Stess of efomated netwok
19 Outline Intoduction and motivation onstitutive modelling appoach Implementation into OMSOL Simulations Summay and outlook
20 Summay & outlook Summay Intoduction to aging pocesses Model oveview phenomenological appoach Modeling of aging, tension set and DLO effect Modeling of mateial behavio: nonlinea themoviscoelasticity Outlook Expeimental identification of chemical paametes Simulation of an industial component Include aging due to dissipative heating
21 OMSOL onfeence 206 Munich Poektteffen / 20 Thank you.
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