Session H5: CM-3: Continuum and Multiscale Modeling

Bringing together computational and experimental capabilities at the crystal scale

Many phenomena of interest occur at the scale of crystals or are controlled be events happening at the crystalline scale. Examples include allotropic phase transformations in metals and pore collapse in energetic crystals. The research community is increasingly able to make detailed experimental observations at the crystalline scale and to inform crystal scale models using lower length scale computational tools. In situ diffraction techniques are pushing toward finer spatial and temporal resolution. Molecular and dislocation dynamics calculations are now able to directly inform mechanisms at the crystalline scale. Taken together, these factors give crystal based continuum models the ability to rationalize experimental observations, investigate competition among physical processes, and, when appropriately formulated and calibrated, predict behaviors. We will present an overview of current efforts, with some emphasis on recent work investigating phase transformations in metals and pore collapse in energetic materials. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 (LLNL-ABS-410456).   

Analytical Modeling of Elastic-Plastic Wave Behavior Near Grain Boundaries in Crystals

It is well known that changes in material properties across an interface will produce differences in the behavior of reflected and transmitted waves. This is seen frequently in planar and oblique impact experiments. In anisotropic elastic materials, wave behavior as a function of direction is usually studied with the aid of velocity (or slowness) surfaces. We have expanded this method to account for inelastic deformation due to crystal plasticity, which led to an implicit problem rooted in the form of the plastic strain rate tensor. To overcome this difficulty an algorithm was developed to search the parameter space defined by a wave normal vector, particle velocity vector, and a wave speed. A solution was said to exist when a set from this parameter space satisfied the governing vector equation. Using this technique we can predict the grain boundary scattering configuration for crystalline materials undergoing deformation by slip. Specifically, we have calculated the configuration of scattered elastic-plastic waves in anisotropic NiAl for an incident compressional wave propagating along a $<$111$>$ direction and contacting a 45 degree inclined grain boundary and found that large amplitude transmitted waves exist owing to the fact that the wave surface geometry forces it to propagate near the zero Schmid factor direction $<$100$>$.   

Numerical Simulations of Lateral Stress Profiles

A series of numerical simulations have been conducted to provide insight into the observed lateral stress profiles in shocked silicon carbide reported in [1]. Utilizing a coupled eulerian-lagrangian simulation approach, the thin epoxy layer has been included in the model. When utilizing the Johnson-Holmquist ceramic model with the constants published in [2], the two-step structure of the lateral stress measurement has been successfully reproduced. The influence of the epoxy layer on the development of the stress profile will be discussed. Additional simulations of specimens having buffer plates will be performed to simulate the lateral stress profile. \\[4pt] [1] Millett, J.C.F., Bourne, N.K. and Dandekar, D.P. 2005. ``Delayed failure in shock-loaded silicon carbide,'' \textit{J. Appl. Phys.} 97, 113513. \\[0pt] [2] Holmquist, T.J. and Johnson, G.R., 2002. ``Response of silicon carbide to high velocity impact,'' \textit{J. Appl. Phys.} 91, 5858-5866..   

Analysis of the annihilation/renucleation mechanism for high velocity dislocations

Properties of plasticity are governed by the motion of dislocations and by their interactions (or dislocation junctions). Among all possible reactions between dislocations, annihilation (ie reaction between dislocations of same circulation but opposite Burgers' vectors) is known as the strongest. However, in shock loadings, dislocation kinetic energy has to be considered in addition to the elastic one, which could notably changes the classical picture for strain hardening. We show in this study that inertial effects could overcome the annihilation reaction and allow for renucleation of a dislocation dipole from a completely annihilated one. To do so, full dynamic simulations using the Peierls-Nabarro Galerkin method are compared to dislocation dynamic simulations. For this latter, a closed-form expression for dislocation equation of motion, including relativistic and retardation effects is considered. It is demonstrated that : i) energy balance using classical expressions for kinetic energy and elastic energy fails to predict the renucleation mechanism, ii) the very high velocity needed to renucleate is due to a complex mechanism of wave emission during the interaction.