We studied the static, quasi-static, and dynamic compression response of granular materials using phase-contrast x-ray imaging, computed tomography, x-ray diffraction, high-energy diffraction microscopy, photon Doppler velocimetry, and modeling to improve our understanding of these complicated materials and to model their characteristics and capabilities. We implemented significant improvements to current characterization and analytical methods, which enabled improved uncertainty measurements and new diagnostic methods. One achievement was the strain mapping of each grain in an ensemble at quasi-static conditions, which lead to the ability to predict the development of force chains and fractures based on the local ensemble structure. We also mapped shock fronts in dynamically loaded ensembles, revealing structure in the shock regime and indicating clear limitations to the common assumption of many code models that these materials can be approximated as a homogenous bulk material undergoing steady shock. Our research revealed shortcomings in models for fracture, slip, and friction in these materials and led to improved computational models for contact points, force distribution, fracture, and friction, especially for wetted materials. Through further development of these models, we hope to fully link "parent" bulk materials to their discontinuous "daughter" materials.
Compaction of heterogeneous materials due to compression (including granular and porous materials) is a complex, non-linear process with significant applications, from stabilizing a building to sintering a new material to defeating a buried target. A detailed physical understanding of the compaction process in granular media is needed for accurate modeling. The many variables involved in the response to compaction of these materials means that a purely empirical approach is prohibitively expensive; effectively, every variation must be treated as a separate material. This complexity is caused by physical properties such as strength, brittleness, fracture, kinetics, friction, and equation of state, each of which is a major scientific topic in its own right. The widespread use of heterogeneous materials drives a pressing need to build accurate physical models to predict their responses to compression; their complexity makes doing so a world-class scientific challenge.
Most experimental work has focused on bulk materials because they are relatively easy to reproducibly characterize and prepare. A major goal within the granular materials community is to take advantage of this significant body of research by combining it with models for compaction, porosity, density changes, heterogeneity, and so on, to predict the response of under-dense materials. However, these models have poor predictive performance (Knudson et al. 2011) and must be calibrated using expensive dynamic measurement techniques. To move beyond calibration-based models, detailed information about the physics of many internal processes that occur during compaction and shock in these materials are required. Multiple time, pressure, density, temperature, and length scales must be considered, making it difficult to describe these connections. Examples of the variables of a granular assembly include size distribution, composition, particle shape, surface area, strain rate, initial packing, mixing, fillers between grains, point contacts at each grain, friction variation, crystal structure and orientation, grain structure, strength, and chemical reactions. High-quality in situ data about internal compaction processes are sparse, especially in the shock regime. Velocimetry and transit time measurements, the basis for historical experiments, only measure integrated responses. New experimental, statistical, analytical, and theoretical methods are required.
The goal of this project was to improve the ability to relate the static, quasi-static, and dynamic response of bulk materials through modeling. The relevant physical properties are much easier to measure under static or quasi-static conditions. This required significant improvements in the understanding of granular compaction, new data to inform new models, and advances in computational simulations. Specifically, we intended to answer questions about the roles of grain and ensemble size, grain shape, composition, force networks, and point friction upon internal processes during static, quasi-static, and dynamic compaction. To examine changes due to composition, we limited the materials to be studied to quartz (SiO2), glass (SiO2), forsterite (Mg2SiO4), and sapphire (Al2O3). We also included experiments on high-strength ceramics (e.g., yttria-stabilized zirconia) as comparison points. We found that substantial improvements could also be made to specific models of inter-grain friction, slip, and fracture to improve the models. Friction proved to be more complicated to model, so experiments were added to examine the role of lubricants (e.g., water) between grains; these showed that friction and wetting needed new models to capture the response we observed. We also determined that we needed a way to understand the bulk measurements found in the literature, improved image analysis, and x-ray diffraction analysis methods.
During compaction of heterogeneous media, force is transmitted through force chains, which are connected particles in the system, and force networks, which are connected chains. In these networks, some particles are completely shielded, while others are under high strain, creating significant variation. These chains and their variations cannot be observed using integrated measurements, such as velocimetry, which comprise most of the data to date. We showed that the variation in packing alone causes significant errors in velocimetry measurements. Mapping force chains for comparison to predicted behavior is difficult but necessary to test our physical understanding. We used x-ray diagnostics on static and dynamic compression platforms to reveal new data about previously unobservable internal processes of compaction and fracture in grains. For all platform types, we began with the simple, highly idealized case of uniform spheres (Herbold et al. 2018, Hurley et al. 2017). See the figure below.
On the static and quasi-static platforms, these included computed tomography and high-energy diffraction microscopy, which allow the position, crystal structure, and mean stress state of every bead in an ensemble to be determined. (Hurley et al. 2017) On dynamic platforms, we used velocimetry to relate our data to the literature and added phase contrast imaging and x-ray diffraction. These allowed us to determine the mean Hugoniot state (i.e., a one-dimensional deformation in solids), the physical structure and location of compacting regions, and the mean density and phase of the samples. These platforms enabled us to probe and directly compare the in situ experimentally measured static and dynamic response of these materials with our models at different strain rates. Doing so allowed us to replace assumptions with data, thereby improving the models for the granular material and the bulk material (Herbold et al. 2018).
Our research advances the science, technology, and engineering competencies that are the foundation of the NNSA mission. It also supports Lawrence Livermore National Laboratory's core competencies in advanced materials and manufacturing.
This project provided new in situ information about the propagation of force in granular media under compression across multiple strain rates. Our work invalidated some previous models (e.g., for wet materials) and led to the development of new models for fracture, compression, and shock propagation in mesoscale codes used to meet key Laboratory mission goals in energy and climate research, earth sciences, and high-energy-density science. Our research demonstrated the quantitative assessment of compression-induced phase changes in granular media. The scientific knowledge, experimental skills, and analytical methods we developed are directly applicable to future research platforms.
As a result of this project, we developed new fracture models and slip-slide models. Equation-of-state models for quartz were also improved to enable the mesoscale codes to run to completion for comparison with the experimentally determined phase measurements. New image analysis methods were developed to enable assessment of compaction processes, such as finding structure in shock fronts. New x-ray modeling methods were developed to estimate phase fraction in shocked materials, the contribution to diffraction signal, and the distortion of the x-ray pattern due to strain. Detailed analytical methods to determine the stress tensor of each bead in quasi-statically compressed assemblies were refined and improved. New statistical analysis methods were developed to determine the systematic error in Hugoniot experiments, which was previously unaccounted for due to uneven packing in heterogeneous materials.
This project was one of the first users of shock platforms at Argonne National Laboratory's Advanced Photon Source, including the Dynamic Compression Sector. We also were among the early adopters for shock platforms at the European Synchrotron Radiation Facility. This has led to new directions in shock physics research, namely the use of imaging and diffraction on shock platforms to assess fractions of phase changes and shock-front structure. This project also led to new work developing better slip-slide models to account for observed changes in fracture and motion in wetted beads under shock loading and new thermal models for granular media. Planned work to study the diffraction of high-strength ceramic analogues to the geomaterials was not performed due to the high x-ray attenuation of the available materials; therefore, one new direction for future work lies in the development of higher-energy x-ray sources.
From these simple experiments we added complexity, increasing the variation in grain packing, material, ductility/strength, and wetting. Fracture patterns between wet and dry material were observed to differ substantially, which led to the development and implementation of a tensile damage model for the GEODYN hydrocode. Comparing this new model helped confirm the mechanisms of dynamic fracture in these materials (Herbold et al. 2018). By combining experimental and modeling capabilities we estimated the compaction front thickness to be a few grain diameters and observed possible unsteady compaction behavior. We also determined several key limiting factors on the experimental and modeling platforms, including substantial sensitivity to jetting and out-of-plane motion, which requires careful balancing between experimental sample thickness and the ability to resolve the compaction front and also drives the need for careful numerical simulations for accurate interpretation. With refinement, we believe that this method can be used to develop new means to parameterize models of granular materials and tie them to those of their parent materials.
This project generated very large and detailed datasets that can be (re)analyzed in the future by Livermore staff or our collaborators. While advancing expertise in the field, the scope of our work only covered a limited subset of important variables in materials compaction. A larger project or program is needed to increase the depth and breadth of study of these important variables. Any such research in future should include brittle materials of differing strength as well as explosives, which introduce the additional complexity of reactive chemistry.
Herbold, E. B., et al. 2018. "Microscale Investigation of Dynamic Impact of Dry and Saturated Glass Powder." Shock Compression of Condensed Matter 1979(1):070015. doi: 10.1063/1.5044824.
Hurley, R. C., et al. 2017. "Linking Initial Microstructure and Local Response During Quasistatic Granular Compaction." Physical Review E 96(1):012905. doi: 10.1103/PhysRevE.96.012905. LLNL-JRNL-725572.
Knudson, M. D., et al. 2011. "High-Pressure Shock Behavior of WC and Ta2O5 Powders." Sandia National Laboratories Report SAND2011-6770. doi: 10.2172/1030356.
Crum, R. S., et al.2017. "Probing Dynamics in Granular Media of Contrasting Geometries via X-ray Phase Contrast Imaging and PDV." American Physical Society March Meeting 2017, New Orleans, LA, March 2017. LLNL-ABS-708917.
——— . 2017. "Probing Dynamics of 2-D Granular Media via X-Ray Imaging." 20th American Physical Society Topical Conference on Shock Compression of Condensed Matter, St. Louis, MO, July 2017. LLNL-ABS-718864.
——— . 2017. "In Situ Probes of Granular Media via X-Ray Analysis to Advance Predictive Models." EUROMAT 2017, Thessaloniki, Greece, September 2017. LLNL-ABS-720718.
Herbold, E. B., et al. 2017. "Microscale Investigation of Dynamic Impact of Dry and Saturated Glass Powder." SCCM 2017. St. Louis, MO, July 2017. LLNL-PRES-734666.
Homel, M. A., et al. 2017. "Understanding Grain-Scale Mechanisms in Dynamic Compaction of Granular Materials." American Physical Society March Meeting 2017, New Orleans, LA, March 2017. LLNL-ABS-716420.
——— . 2017. "Numerical Simulation of Grain-scale Mechanics in the Dynamic Compaction of Granular Materials." 14th US National Congress on Computational Mechanics, Montreal, Canada, July 2017. LLNL-ABS-725443.
——— . 2017. "Simulations and Experiments of Dynamic Granular Compaction in Non-Ideal Geometries." 20th Biennial Conference of the APS Topical Group on Shock Compression of Condensed Matter, St. Louis, MO, July 2017. LLNL-ABS-725113.
Hurley, R. C., et al. 2017. "Microstructure and Failure Analysis During Granular Compaction Using X-ray CT and 3D X-ray Diffraction." International Conference on Tomography of Materials and Structures, Lund, Sweden, June 2017. LLNL-ABS-719811.
——— . 2017. "Understanding the Mechanics of Granular Solids by Combining 3D X-ray Diffraction and X-ray Computed Tomography." CHESS Users' Meeting, Cornell, June 2017. LLNL-ABS-731720.
——— . 2017. "Investigating In Situ Failure in Granular Materials." SCCM 2017, St. Louis, MO, July 2017. LLNL-PRES-735664.
——— . 2017. "Understanding Mechanics and Stress Transmission in Granular Solids by Combining 3DXRD and XRCT." SCCM 2017, St. Louis, MO, July 2017. LLNL-PRES-732616.
——— . 2017. "Microstructure and Failure Analysis During Granular Compaction Using X-ray Computed Tomography and 3D X-ray Diffraction." LLNL-PRES-733897.
——— . 2017. "Linking Initial Microstructure and Local Response During Quasi-Static Granular Compaction." Physical Review E. 96. LLNL-JRNL-725572.
Pagan, D. 2017. "Combining In-Situ X-ray Imaging with Computational Modeling to Understand Granular Deformation during Dynamic Loading." APS March Meeting, New Orleans, LA. LLNL-PRES-726819 / LLNL-ABS-708077.