Mechanical Response of Lattice Structures under High Strain-Rate and Shock Loading

Lattice structures are a class of architected cellular materials composed of similar unit cells with structural components of rods, plates, or sheets. Current additive manufacturing (AM) techniques allow control and tunability of unit cell geometries, which enable lattice structures to demonstrate exceptional mechanical properties such as high stiffness- and strength-to-mass ratios and energy absorption. Lattice structures exist on two length scales corresponding to the unit cell and continuum material, and therefore demonstrate mechanical behavior dependent on structural geometry and base material. These effects extend to the dynamic regime where lattice structures demonstrate distinct deformation modes under varying strain-rate loading. Experimental investigation of the dynamic and shock compression behavior of lattice structures remains largely unstudied and is the central focus of this thesis where the high strain-rate, transient dynamic, and shock compression behaviors of different topologies of lattice materials are explored. The first part of this thesis investigates the high strain-rate behavior of lattice structures via polymeric Kelvin lattices with rod- and plate-based geometries and relative densities of 15-30%. High strain-rate behavior is characterized by deformation modes similar to that of low strain-rate behavior. High strain-rate experiments (1000/s) are performed and validated using a viscoelastic polycarbonate split-Hopkinson (Kolsky) pressure bar system coupled with high-speed imaging. Both low and high strain-rate experiments show the formation of a localized deformation band which initiates in the middle of the specimen. Strain-rate effects of lattice specimens are observed to correlate with effects of the base polymer material and mechanical properties depend strongly on the relative density of the lattice specimen and exhibit distinct scaling with geometry type (rod, plate) and loading rate despite a similar unit cell shape. Explicit finite element simulations with a tensile failure material model are then used to validate deformation modes and scaling/property trends, and match those observed in experiments. The second part of this thesis explores the transient dynamic and transition to shock compression behavior of lattice structures using polymeric lattices with cubic, Kelvin, and octet-truss topologies with relative densities of about 8%. Transient dynamic behavior is characterized by a compaction wave initiating at an impact surface and additional deformation bands with modes similar to low strain-rate modes of deformation. Dynamic testing is conducted through gas gun direct impact experiments (25 - 70 m/s) with high-speed imaging coupled with digital image correlation (DIC) and a polycarbonate Hopkinson pressure bar. Full-field DIC measurements are used to characterize distinct mechanical behaviors induced by topology such as elastic wave speeds, deformation modes, and particle velocities. At lower impact velocities, a transient dynamic response is observed. At higher impact velocities, shock compression behavior occurs and is characterized by a sole compaction wave initiating and propagating from the impact surface of the lattice. One-dimensional continuum shock theory with Eulerian forms of the Rankine-Hugoniot jump conditions is used with full-field measurements to quantify a non-steady shock response and the varied effect of topology on material behaviors. The final part of this thesis examines the steady-state shock compression behavior of lattice structures through stainless steel 316L (SS316L) octet-truss lattices with relative densities of 10-30%. Powder gun plate impact experiments (270 - 390 m/s) with high-speed imaging and DIC are conducted and reveal a two-wave structure consisting of an elastic precursor wave and a planar compaction (shock) wave. Local shock parameters of lattice structures are defined using full-field DIC measurements and a linear shock velocity (us) versus particle velocity (up) relation is found to approximate measurements with a unit slope and linear fit constant equal to the crushing speed. One-dimensional continuum shock analysis is again performed using Eulerian forms of the Rankine-Hugoniot jump conditions to extract relevant mechanical quantities. Explicit finite element simulations of the lattice specimens using the Johnson-Cook constitutive model exhibit similar shock behavior to experiments. The simulations reveal a linear us-up relation and corresponding Hugoniot calculations agree with experimental trends. Notably, 1D shock theory is applied to simulations without resorting to a us-up relation for the base material, which characterizes this deformation regime and compaction wave as a `structural shock.' Major contributions of this thesis include experimental demonstration of ranged strain-rate behaviors for lattice structures of various base materials and topologies including low strain-rate, high strain-rate, transient dynamic, and shock compression regimes; use of full-field quantitative visualization techniques for local mechanical behavior and shock analysis; and finally, characterization of a 'structural' shock compression regime in lattice structures.