Numerical Simulation of Earth Materials

Transcription

1 Numerical Simulation of Earth Materials Summary of part and current research in materials simulation Mark Jessell Université Paul Sabatier, Toulouse

2 How hard can it be? Octachloropropane Grain boundary sliding Plasticity Dynamic recovery Grain boundary migration Grain Boundary Diffusion Sub-grain formation Sub-grain boundary migration

3 Molecular Hierarchy of Numerical Simulations dynamics Dislocation dynamics es erti rop al p ent ns dam itio Fun ond ry C nda Bou Grain-scale simulations Crustal deformation Plate tectonics

4 Figure 1: The left figure shows the simulated stress-strain response of α-quartz to hydrostatic compression at 300oK. The hydrostatic pressure applied (in GPa) is plotted along the y-axis and the mean linear strain (δl / l ) along the x-axis. The atomic structure and the corresponding radial distribution function before (Point A - 19 GPa) and after (Point B - 20 GPa) amorphization are also shown alongside the figure. This reproduces the Pressure Induced Amorphization (PIA) in α-quartz, which has been observed in earlier simulations as well as experiments (Note the change in the RDF plot going from a regular crystal structure to an amorphous structure) Subramanian and Yip unpublished 2001 A B

5 Quartz molecular dynamics Stress-Strain response of SiO2 to unixial compression at 1073K - Plasticity and phase change to planar amorphous structures Subramanian and Yip unpublished 2001 Potential to provide: fundamental constraints on dislocation and grain boundary behaviour Fundamental constants Nye MD Experiment Elastic constants x 10e-11 (m2/newton) s11 s12 s44 s33 s13 s14 Bulk modulus (Pa) Young s modulus e e e e10

6 Molecular dynamics Calculation of the free energy of adsorption of water, as a function of distance away from calcite surfaces. Kerisit et al 2005

7 Lattice Preferred Orientations: TBH Figure 1. Simulation of c-axis texture development in model quartzite. a) Classical Taylor calculation for simple shear up to a shear strain of 3 [Lister et al. 1978]. b) Texture development caused by both intracrystalline slip and dynamic recrystallisation (i.e. nucleation and growth). Steps 30, 32 and 34 are shown, recrystallisation starts after step 30, the texture illustrated in step 34 does not change appreciably with further straining. Equal-area projection. The symbol + indicates old grains, x grains that have nucleated at least once; the size of the symbols is proportional to the grain volume. [Takeshita, Wenk & Lebensohn 1999]

8 Potts + Taylor Model Simulated shear zone fabrics Jessell & Lister mm Quartzite, central Australia Naturally deformed

9 Fibrous growth around rotating object Open crack Mica, SiO2, FeS2 SiO2 1 mm Koehn et al 2000

10 Partial Melt Mechanics using particle codes Granite (Patrice Rey) Park et al. 2004

11 a Dissolution-Precipitation Fueten, Robin and Schweinberger JSG, step finite element calculation of diffusive mass transfer a) Viscosity assumed to be dependent on quartz/mica % δε xx σ xx δε = δ t σ yy 2η yy δε zz σ zz δε xx + δε zz = b δt ( σ xx + σ zz ) = δt p 2η η c b) finite element calculation with volume change allowed c) re-inflation of lost volume (=quartz) uniformly applied across whole model

12 Dissolution-Precipitation Fueten, Robin and Schweinberger JSG,2002 Mica fraction

13 Multi-process simulation Fracture Boudinage V High Strains Ice Dynamics Exchange Reactions Crystallisation Porphyblast growth Regional Localisation Grain scale localisation Knowledge Based Materials Partial Melts

14 Elle: Open Source Multi-Process Modelling Platform Hybrid Data Model and Calculation Schemes Iterative application of processes to achieve processcoupling via microstructure Boundary Nodes

15 Elle: Open Source Multi-Process Modelling Platform Hybrid Data Model and Calculation Schemes Iterative application of processes to achieve processcoupling via microstructure Grain Boundaries

16 Elle: Open Source Multi-Process Modelling Platform Hybrid Data Model and Calculation Schemes Iterative application of processes to achieve processcoupling via microstructure Grains, Phases

17 Elle: Open Source Multi-Process Modelling Platform Hybrid Data Model and Calculation Schemes Iterative application of processes to achieve processcoupling via microstructure Unconnected Nodes

18 Elle: Open Source Multi-Process Modelling Platform Hybrid Data Model and Calculation Schemes Iterative application of processes to achieve processcoupling via microstructure Voronoi Cells

19 Elle: Open Source Multi-Process Modelling Platform Hybrid Data Model and Calculation Schemes Iterative application of processes to achieve processcoupling via microstructure Triangulations

20 Localisation

21 Dynamic Localization: Grain size sensitive flow Simulation system Elle (Jessell et al. 2001) Representation of competing processes as sequential algorithms Initial State Viscosity grain size2 Re-gridding and finite element deformation Control Program Grain boundary migration Vgbm boundary energy Sub-grain formation Psubgrain local finite strain

22 Deformation behaviour: n=1 Without microstructure evolution Strain Rate max min Finite Deformation Mesh

23 Deformation behaviour: n=3 Without microstructure evolution Strain Rate max min Finite Deformation Mesh

24 Deformation behaviour: n=1 With microstructure evolution Strain Rate max min Finite Deformation Mesh

25 Deformation behaviour: n=3 With microstructure evolution Strain Rate max min Finite Deformation Mesh

26 Deformation behaviour n=1 n=3 max Strain Rate min Without microstructure evolution Finite Deformation With microstructure evolution

27 Where and by how much does it localise? Strain Rate max Analogue Experiment min (Rf= intensity of deformation) (Bons & Jessell JSG, 1999) 256 Numerical simulation Power spectrum of strain rate map power n=3, ms n=3, no ms n=1, ms 160 n=1, no ms ocp 128 frequency With microstructure evolution n=3

28 De-localization etc.

29 Other results using this platform Tullis et al 2000

30 Current & Future Challenges Multi-process simulation Multi-scale dislocation sub-grain grain scale to decametric scale Physico-chemical interactions Solid-state Partial melt Water-rock Nucleation of new phases 3D Transport properties

31 Gordon Research Conference Rock Deformation Processes & Patterns Big Sky, Montana, Sept 3-8, 2006 A GRC conference to investigate the processes inherent to rock deformation and how they couple to produce patterns in time and space. Topics Include: History dependent flow laws Non-equilibrium behaviour Scaling of patterns in nature Periodicity of geological processes 4D imaging of rock deformation Single crystal vs aggregate behaviour Rheology from field observations Materials simulation Organisers: Mark Jessell & Greg Hirth

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33 Pyramid Microstructure: e.g. grain size Processes: e.g. diffusion Mechanics: e.g. Flow Laws Boundary Conditions : e.g. temperature

34 Classical Rock Mechanics Natural Samples Techniques Analogue Experiments Numerical Simulations

35 Mechanical Structure Press and Siever, 2001

36 Greywacke schist