The Roles of Microstructure And Interfaces on Fracture Mechanics of Brittle Materials

The goal of this work is to understand the roles of microstructure and inter-phase interfaces on the fracture mechanics of brittle solids such as concrete, rocks, and granular materials. To achieve this goal, we are employing in-situ X-ray computed tomography (XRCT) and 3D X-ray diffraction (3DXRD) measurements to simultaneously image fracture surfaces and measure 3D stress states in crystalline inclusions within material microstructures. Figure 1 illustrates recent experimental efforts toward achieving the goals of this research effort in concrete, showing an XRCT image of a concrete cube prior to uniaxial compression, XRCT renderings of the single-crystal aggregates and void/fracture networks in isolation, and two of the 52 distinct aggregate stress tensors measured with 3DXRD at each loading step of the experiment.

Fig. 1 – Results from an experiment performed at the Cornell High Energy Synchrotron Source C(HESS) employing XRCT to image microstructure and 3DXRD to measure stress tensors in each of 52 single-crystal quartz aggregate particles (i.e., sand grains) within a concrete specimen.

Currently, we are employing finite element simulations of experimentally imaged concrete microstructures to determine the appropriate failure models for aggregate-mortar interfaces and the appropriate level of microstructure detail needed to reproduce measured stress distributions and fracture patterns.

Figure 2 illustrates recent experimental efforts toward achieving the goals of this research effort in granular materials, showing particle fractures imaged and characterized during uniaxial compaction of a granular material composed of spherical particles, and particle fractures and shear band formation during triaxial compaction of a granular material composed of angular particles.

 (a) XRCT image of spherical grains during uniaxial compaction along with horizontal slices from the raw reconstructed image illustrating the presence of widespread grain fracture1. (b) XRCT image of angular quartz grains experiencing strain localization while subjected to triaxial compression.

Relevant publications:

  • Hurley, R.C., & Pagan, D.C. An in-situ study of stress evolution and fracture growth during compression of concrete. In Review.
  • Hurley, R.C., Lind, J., Pagan, D.C., Akin, M.C., &  Herbold, E.B. (2018). In Situ Grain Fracture Mechanics During Uniaxial Compaction of Granular Solids. Journal of the Mechanics and Physics of Solids, 112, 273-290. Link to Paper.
  • Hurley, R.C., Herbold, E.B., & Pagan, D.C. (2018). Characterization of crystal structure, kinematics, stresses, and rotations in angular granular quartz during compaction. Journal of Applied Crystallography, 51(4), 1021-1034.

Linking Micro- and Macro- Mechanics of Granular Solids

We are exploring relationships between microscopic processes and the macroscopic properties of granular materials using experiments and theory. We have employed in-situ X-ray computed tomography (XRCT) and 3D X-ray diffraction (3DXRD) to resolve grain- and contact-level details of deformation mechanisms in granular materials composed of spherical and angular particles during uniaxial and triaxial compression. We have made highly-resolved calculations of particle kinematics, rotations, inter-particle forces, inter-particle contact kinematics, and inter-particle energy dissipation in-situ during these experiments. Our measurements provide a new understanding of: the statistics of contact kinematics such as slipping, rolling, and twisting, during uniaxial and triaxial compression; the distribution of inter-particle forces and inter-particle energy dissipation in different loading environments; the relationships between particle kinematics (displacements, rotations),  kinetics (inter-particle forces, particle stresses), and particle packing structure (porosity, packing structure); representative volume element (RVE) sizes in different loading environments; relationships between macroscopic elastic or elastoplastic variables and microscopic processes.

Our current research is further exploring the relationships between macroscopic variables and microscopic processes. We are also exploring the implications of particle packing structure and micromechanics on ultrasonic wave propagation through granular materials.

Relevant publications:

  1. Zhai, C., Herbold, E.B., Hall, S.A., Hurley, R.C. Particle rotations and energy dissipation during mechanical compaction of granular materials. In Review.
  2. Hurley, R.C., Lind, J., Pagan, D.C., Akin, M.C., & Herbold, E.B. (2017). Linking initial microstructure and local response during quasistatic granular compaction. Physical Review E, 96(1), 012905. Link to Paper.
  3. Hurley, R.C., Hall, S.A., & Wright, J. (2017). Multi-scale mechanics of granular solids from grain-resolved x-ray measurements. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 473 (2207), 0491. Link to Paper.
  4. Hurley, R.C., Hall, S.A., Andrade, J.E., & Wright, J. (2016). Quantifying interparticle forces and heterogeneity in 3D granular materials. Physical Review Letters, 117, 098005. Highlighted in Physics Synopsis and Caltech News. Link to Paper.
  5. Hurley, R.C., Lim, K.W., Ravichandran, G., & Andrade, J.E. (2016). Dynamic inter-particle force inference in granular materials: Method and application. Experimental Mechanics, 56(2), 217-229. Link to Paper.
  6. Hurley, R., Marteau, E., Ravichandran, G., & Andrade, J.E. (2014). Extracting inter-particle forces in opaque granular materials: beyond photoelasticity. Journal of the Mechanics and Physics of Solids, 63, 154-166. Link to Paper.

Single and Multiphase Flow of Particle Media

We have developed theory explicitly linking the macroscopically observed friction coefficient during simple shear of a granular solid to microscopic dissipation mechanisms1 (see Figure 1(a)). We have also developed a Smoothed Particle Hydrodynamics (SPH) code for modeling continuum-scale granular flows that demonstrates a close agreement with experiments of dry granular flow down inclined planes 2 (see Figure 1(b)). We have extended our SPH code to multiphase flows by coupling a constitutive law for granular materials with one for compressible gas flow 3 (see Figure 1(c)).

Figure 1 – (a) A plot showing the macroscopic friction coefficient in a dry granular flow for two data sets decomposed into contributions from inter-granular friction and intra-granular inelasticity 1 . (b) The top frame shows the initial configuration of a dry granular column collapsing down an inclined plane, simulated using SPH. The bottom frame shows the close agreement of the runout height and length at various times with experimental data 2 . (c) The top frame shows the surface of soil during rapid plume-driven erosion as gas, shown separately in the bottom frame, is driven into the soil by a pressure gradient 3 .
  1. Hurley, R.C., & Andrade, J.E. (2017). Continuum modeling of rate-dependent granular flows in SPH. Computational Particle Mechanics, 4(1), 119-130. Link to Paper.
  2. Hurley, R.C., & Andrade, J.E. (2015). Friction in inertial granular flows: Competition between dilation and grain-scale dissipation rates. Granular Matter, 17(3), 287-295. Link to Paper.
  3. Hurley, R.C., Andrade, J.E. (2015). A Smoothed Particle Hydrodynamics Method for Coupled Gas-Porous Media Flows. Engineering Mechanics Institute Computational Inelasticity Paper Competition, Stanford, CA.