Publications

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Sintering is a component fabrication process in which powder is compacted by pressing or some other means and then held at elevated temperature for a period of hours. The powder grains bond with each other, leading to the formation of a solid component with much lower porosity, and therefore higher density and higher strength, than the original powder compact. In this project, we investigated a new way of computationally modeling sintering at the length scale of grains. The model uses a high-fidelity, three-dimensional representation with a few hundred nodes per grain. The numerical model solves the peridynamic equations, in which nonlocal forces allow representation of the attraction, adhesion, and mass diffusion between grains. The deformation of the grains is represented through a viscoelastic material model. The project successfully demonstrated the use of this method to reproduce experimentally observed features of material behavior in sintering, including densification, the evolution of microstructure, and the occurrence of random defects in the sintered solid.

Most previous development of the peridynamic theory has assumed a Lagrangian formulation, in which the material model refers to an undeformed reference configuration. In the present work, an Eulerian form of material modeling is developed, in which bond forces depend only on the positions of material points in the deformed configuration. The formulation is consistent with the thermodynamic form of the peridynamic model and is derivable from a suitable expression for the free energy of a material. It is shown that the resulting formulation of peridynamic material models can be used to simulate strong shock waves and fluid response in which very large deformations make the Lagrangian form unsuitable. The Eulerian capability is demonstrated in numerical simulations of ejecta from a wavy free surface on a metal subjected to strong shock wave loading. The Eulerian and Lagrangian contributions to bond force can be combined in a single material model, allowing strength and fracture under tensile or shear loading to be modeled consistently with high compressive stresses. This capability is demonstrated in numerical simulation of bird strike against an aircraft, in which both tensile fracture and high pressure response are important.

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We have performed a series of ten planar impact experiments on six different materials, including certain reactive powders and two inert materials, using Sandia's 89 - mm powder gun at the STAR facility. Time - resolved particle - velocity histories were determined during each of the experiments from one or more VISAR measurements. We have analyzed the results of these measurements 1) by using jump conditions to determine shock and first reshock states and 2) by comparing measured particle velocity histories to synthetic histories predicted by one - dimensional computational analyses using the CTH shock physics code with various models for inert and reactive materials . These comparisons are consistent with the conclusion for these particular reactive powders, that for the duration of shock loading either 1) there is insignificant reaction or 2) the products of any reaction are indistinguishable from the reactants under the experimental conditions. Shock and reshock states were extracted for shock pressures between 5 and 40 GPa. Densities were at or greater than the theoretical maximum zero - pressure density of the starting mixture. This result would be expected if there were no reaction or negligible reaction for the first two shock states. Two experiments were performed on one reactive powder in a "ring - down " geometry to look for evidence of vapor production on pressure release. In both cases, the measured velocity continued to increase slowly over a period of microseconds for the du ration of the experiment. This observation suggests that vapor is produced along the release path, but information about the mechanism for vapor production cannot be extracted from these data. While it is possible that vapor is produced by a shock - induced reaction involving more than one of the original constituents, a simpler interpretation is that the vapor is made up of products of shock - induced decomposition reactions and/or simple vaporization of the constituents as would be expected to take place under the conditions of these experiments. Other sources of vapor could be water adsorbed on grain surfaces and air originally in the voids. Thus it is not necessary to invoke significant recombination reactions to explain the data. However, in the absence of ring - down control experiments, the possibility remains open. These conclusions are different from those of previous workers, but reassessment of a subset of the earlier data yields results consistent with the present work, i.e., the shock compression data do not provide evidence for strong exothermic reactions.

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Peridynamic correspondence material models provide a way to combine a material model from the local theory with the inherent capabilities of peridynamics to model long-range forces and fracture. However, correspondence models in a typical particle discretization suffer from zero-energy mode instability. These instabilities are shown here to be an aspect of material stability. A stability condition is derived for state-based materials starting from the requirement of potential energy minimization. It is shown that all correspondence materials fail this stability condition due to zero-energy deformation modes of the family. To eliminate these modes, a term is added to the correspondence strain energy density that resists deviations from a uniform deformation. The resulting material model satisfies the stability condition while effectively leaving the stress tensor unchanged. Computational examples demonstrate the effectiveness of the modified material model in avoiding zero-energy mode instability in a peridynamic particle code.

The propagation of large amplitude nonlinear waves in a peridynamic solid is ana- lyzed. With an elastic material model that hardens in compression, sufficiently large wave pulses propagate as solitary waves whose velocity can far exceed the linear wave speed. In spite of their large velocity and amplitude, these waves leave the material they pass through with no net change in velocity and stress. They are nondissipative and nondispersive, and they travel unchanged over large distances. An approximate solution for solitary waves is derived that reproduces the main features of these waves observed in computational simulations. We demonstrate, by numerical studies, that waves interact only weakly with each other when they collide. Finally, we found that wavetrains composed of many non-interacting solitary waves form and propagate under certain boundary and initial conditions.

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