The relevance of stress percolation in polycrystalline solids to the deformation of deep earth materials
Abstract
One of the fundamental challenges in characterizing the plastic properties of deep earth materials at relevant length and time scales is that some form of extrapolation will always be required. With increasing computational power, single crystal mechanical properties will probably be accessible to first principles calculations in the not too distant future. If the relationship between single crystal and polycrystal mechanical properties were straightforward, with some ground truthing in the lab, the bulk behavior could be confidently extrapolated to experimentally inaccessible conditions. However, we currently lack a satisfactory paradigm to describe the relationship between single crystal and polycrystalline deformation. Existing mechanical models, including self-consistent models cannot predict or account for the spatial variations in the local stress and strain states observed in real-world materials. Full field models can be constructed so as to explicitly include the spatial relationships between crystals and their neighbors, but in their explicitness they lose the ability to generalize. Using finite element (FEM) simulations of a polycrystalline material (Figure 1a), I show that local variations in stress and strain participate in large-scale patterns, that are a function of the heterogeneity and statistical distribution of elastic and plastic properties across the population of mechanical components (grains and grain boundaries) in the material. The patterns of modulation in the local stress tensor are similar to the patterns of stress distribution observed in granular materials - often referred to as force chains. Force chains are caused by percolation of stress through strong contacts between particles in a granular aggregate. The patterns in stress modulation observed in the FEM simulations are caused by stress percolation through the elastically heterogeneous mechanical elements. Greater degrees of heterogeneity lead to more intense stress concentrations across a less dense pattern (Figure 1b). Lower degrees of elastic heterogeneity lead to a denser pattern of stress transmission that carries smaller modulations (Figure1e). Paralleling the development of shear bands in granular materials, the stress patterns lead directly to shear localization even in the absence of strain softening. The recognition of stress percolation provides a foundation for devising models that link single crystal mechanics and local interactions to bulk behavior. Such rheological models should provide a more robust platform for extrapolating to deep earth conditions including spatial and time scales. Figure 1: Panel a) FE model mesh, inset shows an enlarged region. Properties are assigned to each of 25 grain sets (coded by color). Panels b)-e) Equivalent von Mises stress patterns for models in compression. For b) Young's modulus E of grain sets ranges from 500 to 0 GPa with v=0.1 to 0.4, for c) E= 500 to 0 GPa with v=0.3 for d) E= 200 to 20 GPa with v=0.3 and for e) E =120 to 100 GPa with v=0.3. The maximum value of the equivalent stress in b) is 10 times that found in e).
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2013
- Bibcode:
- 2013AGUFMMR34A..04B
- Keywords:
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- 3902 MINERAL PHYSICS Creep and deformation;
- 3909 MINERAL PHYSICS Elasticity and anelasticity;
- 3225 MATHEMATICAL GEOPHYSICS Numerical approximations and analysis