Multi-scale studies of elastomer materials (in a tire tread) TERATEC 2013 Materials Science Session B. Schnell

Transcription

1 Multi-scale studies of elastomer materials (in a tire tread) TERATEC 13 Materials Science Session B. Schnell TERATEC - 6/6/13 Page : 1 / 7

2 Tire description A tire : a highly functional structure composed of specific successive layers Inner liner Makes the tire almost totally impermeable and maintains the correct inflation pressure Bead area for attachment to the wheel rim Sidewalls Cover and protect the textile casing whose role is to attach the tire tread to the wheel rim Crown plies Reinforced belt with both vertical flexibility and high lateral rigidity providing the steering capacity Tread Thick layer of rubber providing contact with the ground and thus transmitting the efforts (acceleration, braking, ) TERATEC 6/6/13 Page : / 7

3 Tire : a multi-scale approach Prediction of tire performances through FE calculations (given material behaviour law) 3 main performances governed by the tire tread : grip, wear, RR Complex process Complete characterization to get the new material behaviour law is costful Use of descriptors relating materials properties and tire performances Two main goals for multi-scale simulations Improvement of structure-properties relationships at each length scales Design of new structures descriptors Behavior laws by a bottom-up approach Multi-scale materials Tire = multi-component product (~) TERATEC 6/6/13 Page : 3 / 7

4 Multi-scale simulations Bottom-up approach Ab initio All-atom Mesoscopic Macroscopic Explicit electrons Atomistic Force Field Coarse-grained, particle- or molecule-based Materials modeling C C C C C C C C 1- Å 1-1 nm 5-5 nm 1-1 nm >1 nm Molecular simulations (MD (DPD, ) / MC) - Elastomer rigidity wear - Dissipation f / T grip «Mésoscope» Tool for studying nanocomposites - Network structures (chains, fillers) wear, RR FE method most used by Michelin Tire performances TERATEC 6/6/13 Page : 4 / 7

5 Elastomer rigidity (rubbery plateau) Goal : predicting the intrinsic rigidity of an elastomer (microstructure related) Best approach in theory Reproducing the shear modulus evolution G(t) (or G(w)) huge systems (M/Me > ) and long relaxation times (~ ms) not realistic at all-atom scale Mesoscopic scale (works ongoing) Classical experimental curves : cis-pb (M/Me = 6) Wang et al. Polymer 47 (6), p4461 Proposed approach at atomistic scale Using known polymer melt properties 4 k B N A T G N 5 M e Me can be related to Re (analogy to elastomeric network) G N K T) ( R e M 3 Absolute or relative prediction? Universal K(T) proposed by Fetters et al. Macromolecules 1994, vol 7, p4639 Simulation TERATEC 6/6/13 Page : 5 / 7

6 Elastomer rigidity (rubbery plateau) Chosen system size M ch ~ Me (adequate Nch) Compromise between a good description of the packing effect and calculation optimization Ne N Ex: SBR M ch ~ Me (6K) (Equilibration time ns ~ 5 days) Properties <R e /M> =.69 Å.mol.g -1 <R g /M> =.113 Å.mol.g -1 <R e > / <R g > ~ 6,1 Example of investigation "backbone" cycles vs "pending" cycles R 1 R e R n m R R 1 n m Gain in G N TERATEC 6/6/13 Page : / 7

7 Elastomer rigidity (rubbery plateau) N R e N (N 1)C R e N l NC l N G N Simul. Exp. Gain in G N for microstructure A is nicely predicted Semi-quantitative approach (K(T)) but approach seems to be able saying whether or not an important gain can be expected TERATEC 6/6/13 Page : 7 / 7

8 Grip performance G' ; G'' (Pa) tan d 1 1 a Frequency T (z) Traction domain RR In terms of mechanical properties (T > Tg) G' G'' tan Glass transition : very high energy dissipation Glassy plateau Température Grip is highly related to the dynamic glass transition. Improvements can be expected through - a better understanding of polymer melts dynamics (better control of the dissipation: TTS, height, width, ) - calculation of G(t) via simulations and the FT Elastomeric plateau Flowing w (rad.s -1 ) Température ( C) 1.1 tan TERATEC 6/6/13 Page : 8 / 7

9 Grip performance "Reproduction" of a dilatometry experiment Liquid branch very nicely reproduced and good estimation of Tg Validation for studying local dynamics hf - T TERATEC 6/6/13 Page : 9 / 7

10 Grip performance Study of the local dynamics hf - ht Unavailability of Dynamic Mechanical Analysis (DMA) in the frequency domain of use other experiments (dielectric spectroscopy, neutron scattering, NMR, ) and atomistic simulations (specific mechanism?) The method of choice? NMR The orientational order parameter P intervening in the NMR dipole dipole interaction is easily calculated by simulations 1 ( ) c P ( t) dt PDMS c is the segmental time given by NMR PIB 3 P ( t) u u( t). u() 1 TTS (PDMS) < (PIB) Good agreement with exp. moy =,48 TERATEC 6/6/13 Page : 1 / 7

11 Grip performance PDMS Fitted with a WLF law Cis-PB PIB moy =,48 a T Study of local dynamics f T Exp. data well reproduced C (PDMS) ~ < C (cis-pb) ~ 3-35 < C (PIB) ~ 6 New microstructures or mechanisms leading to particular behaviours? Master curve pdms TERATEC 6/6/13 Page : 11 / 7

12 Multi-scale calculation of G(t) Log G(t) (GPa) 1 MD Glassy Zone (Molecular approach, local relaxations) Dissipation Zone Grip 1-3 Rubber Zone (Mesoscopic approach, chain relaxations) DPD Wear T ~ T tire > T g Time (s) (G(t) obtained from the stress tensor fluctuations) - Static properties of the glass-to-rubber transition (G. Maurel s PhD work supervision of P. Malfreyt, ICCF Clermont-Ferrand) - Friction term in DPD (S. Trément s PhD work supervision of B. Rousseau, LCP Orsay) TERATEC 6/6/13 Page : 1 / 7

13 Determination of realistic CG models cis-polybutadiene (CG level l = 5) Bonded Bending Non-bonded w(r) = -k B T ln( g(r) ) r wi 1 wi r k T ln Iterative Boltzmann Inversion NPT Ensemble B g g i MD r r TERATEC 6/6/13 Page : 13 / 7

14 Realistic CG models Static properties and R e /M in good agreement with experiment for the potentials developed in both ensemble (the same g(r) are reproduced during this development) uge pressure needed for "NVT" potentials Cannot model real systems Transferability in temperature : α p (~ K -1 ) TERATEC 6/6/13 Page : 14 / 7

15 Realistic CG models cis-polybutadiene (cis-pb) polydimethylsiloxane (PDMS) polyisobutylene (PIB) G N estimation G N R M ee 3 Possible to distinguish between different microstructures at the mesoscale!!! TERATEC 6/6/13 Page : 15 / 7

16 Realistic CG models Entanglements Primitive Path Analysis Entanglement length M R L e e pp M - M e = 749 g/mol (363 g/mol à partir de G N ) N e = 1 (9) - Poisson-like distribution TERATEC 6/6/13 Page : 16 / 7

17 Realistic CG models Dynamic properties Goal : explicit quantitative determination of the rubbery plateau and more generally to be able studying chains relaxation more quickly Chain relaxation Micro Meso Simulated Time ns ns Calculation Time 1 days 1 day (~1 4 particles, 16 CPUs.67 Gz / GB memory per CPU) Slowing-down of the relaxation but no plateau Plateau observation seems to need N / N e > [1] (N / N e 4-5 in our case) [1] Likhtman, A. E., & Sukumaran, S. K. (1), Macromolecules, 43(8), Slip-link model : a plateau can be distinguished but in a qualitative way TERATEC 6/6/13 Page : 17 / 7

18 Study of polymer networks Why studying polymer networks? Structure obtained by classical vulcanization is not really controlled random network (a priori) NR DQ NMR measurements SBR Develop a method able to give an accurate description of a network (heterogeneity of cross-linking / chain length distribution between cross-links, quantity and nature of defects, trapped entanglements, ) Method coupling NMR double quanta (DQ) and Simulation Able to capture an heterogeneity of cross-linking and to quantify defects (Macromolecules 1, 43, p41) Can identify accurately the structure responsible of NMR signals TERATEC 6/6/13 Page : 18 / 7

19 Study of polymer networks NMR/Simulation coupled method Principle: Kuhn segments of a cross-linked chain fluctuate anisotropically around their mean direction due to topological constraints (cross-linking + entanglements) local nematic order described by the order parameter Sb measurable in NMR calculable by simulation (t) b R Dipolar interactions are q-dependent S b = k D res / D stat S P cos(α( t)) b M c KGD D res stat / k / C n l l p M TERATEC 6/6/13 Page : 19 / 7

20 Study of polymer networks PDMS model network Purpose: check the capability of the coupled method NMR/Simulation PDMS model network (based on Genesky et al., Macromolecules 8) Experimental part C 3 Si Si4 8 O 3 C Structural analysis (M c ~6 g/mol) ~81% (NMR 1 ) Simulation part TERATEC 6/6/13 Page : / 7

21 Study of polymer networks NMR DQ : analysis vs simulation Order parameter distribution P(Dres S b ) (D res / m = 343z PDMS model network Simulation D res / z) TERATEC 6/6/13 Page : 1 / 7

22 Contrainte apparente MPa Study of polymer networks Mechanical properties : analysis vs simulation,4 CFA déplacement traverse Température ambiante PDMS model network Uniaxial traction,35 Simulated "real" traction,3,5,,15,1 Imposed stress + relaxation by simulation Cfa 4 vt5mm/mn Cfa 5 vt 5mm/mn Cfa 6 vt 1mm/mn Simulation traction Contrainte imp. + relaxation, Déformation % Coupling NMR DQ/simulation seems to be a powerful method to predict network behaviours TERATEC 6/6/13 Page : / 7

23 Study of polymer networks Example shown for cross-linked cis-pb (3K) Study of network structures The order parameter distribution and the mechanical response are specific for each network Associating the two analysis leads to an improved characterization of a polymer network (structure-properties relationships) TERATEC 6/6/13 Page : 3 / 7

24 Nanocomposites simulation Approach description : - Only fillers are considered - Polymer is implicitly taken into account through the filler-filler interaction A polymer-mediated POMF for fillers Typical box for Nanocomposites simulation ow to get the POMF? - Analytically (K. Schweizer Urbana Champaign) - From the bottom by simulation Aggregates are reconstructed from TEM TERATEC 6/6/13 Page : 4 / 7

25 Nanocomposites simulation w cc (r) Model composites at atomistic scale to obtain realistic CG polymer-filler potentials of interaction (grafted/non-grafted, density of grafting, ) Simulation of open systems at the mesoscale to get w cc (r) TERATEC 6/6/13 Page : 5 / 7

26 G* Nanocomposites simulation Energie (μn.nm) Example with a colloidal type of POMF,5,4,3,, ,1 DLVO ref LJ ref DLVO 3 LJ 3 -, -,3 X (nm) The well-known phenomena for nanocomposites can be can reproduced G1* - 15% - silice V G1* - 18% - silice V G1* - 1% - silice V G1* - 15% - silice V1 G1* - 18% - silice V1 G1* - 1% - silice V1 G1* - 15% - silice réf G1* - 18% - silice réf G1* - 1% - silice réf G1* - 1% - var pas tps - silice V Payne effect g % Mullins effect TERATEC 6/6/13 Page : 6 / 7

27 Conclusion & Outlook Multi-scale materials constitutive of tire (tread) are particularly well suited for multi-scale simulations possible to improve the structureproperties relationships at each length scale Obtention of a complete quantitative G(t) should be possible through a multi-scale approach (PC could be helpful) Use the method coupling NMR / simulation to design a polymer network with optimized mechanical properties (expansion of the coupling analysis/simulation) Determination of realistic CG filler-polymer interaction in different cases (nature of the grafting, grafting density, ) achieve the establishment of POMF and check whether or not the approach is able to reproduce the behaviour of nanocomposites TERATEC 6/6/13 Page : 7 / 7