Evaluation of observed blast loading effects on NIF x-ray diagnostic collimators.

We present the "debris wind" models used to estimate the impulsive load to which x-ray diagnostics and other structures are subject during National Ignition Facility experiments. These models are used as part of the engineering design process. Isotropic models, based on simulations or simplified "expanding shell" models, are augmented by debris wind multipliers to account for directional anisotropy. We present improvements to these multipliers based on measurements of the permanent deflections of diagnostic components: 4× for the polar direction and 2× within the equatorial plane-the latter relaxing the previous heuristic debris wind multiplier.

Direct observation of the alpha-epsilon transition in shock-compressed iron via nanosecond x-ray diffraction.

In situ x-ray diffraction studies of iron under shock conditions confirm unambiguously a phase change from the bcc (alpha) to hcp (epsilon) structure. Previous identification of this transition in shock-loaded iron has been inferred from the correlation between shock-wave-profile analyses and static high-pressure x-ray measurements. This correlation is intrinsically limited because dynamic loading can markedly affect the structural modifications of solids. The in situ measurements are consistent with a uniaxial collapse along the [001] direction and shuffling of alternate (110) planes of atoms, and are in good agreement with large-scale nonequilibrium molecular dynamics simulations.

Fracture in human cortical bone: local fracture criteria and toughening mechanisms.

Micromechanical models for fracture initiation that incorporate local failure criteria have been widely developed for metallic and ceramic materials; however, few such micromechanical models have been developed for the fracture of bone. In fact, although the fracture event in "hard" mineralized tissues such as bone is commonly believed to be locally strain-controlled, only recently has there been experimental evidence (using double-notched four-point bend testing) to support this widely held belief. In the present study, we seek to shed further light on the nature of the local cracking events that precede catastrophic fracture in human cortical bone, and to define their relationship to the microstructure. Specifically, numerical computations are reported that demonstrate that the stress and strain states ahead of such a notch are qualitatively similar irrespective of the deformation mechanism (pressure-insensitive plasticity vs. pressure-sensitive microcracking). Furthermore, we use the double-notched test to examine crack-microstructure interactions from a perspective of determining the salient toughening mechanisms in bone and to characterize how these may affect the anisotropy in fracture properties. Based on preliminary micromechanical models of these processes, the relative contributions of various toughening mechanisms are established. In particular, crack deflection and uncracked-ligament bridging are identified as the major mechanisms of toughening in cortical bone.

On the importance of geometric nonlinearity in finite-element simulations of trabecular bone failure.

The finite element method, which has been successfully applied to studies of the elastic properties of trabecular bone, is now being used to simulate its failure. These simulations have used a geometrically linear (linear kinematic) approximation to the total stiffness matrix; nonlinear terms in the total stiffness matrix have been excluded from the computation in order to achieve efficiency. Because trabecular bone appears to be a slender (i.e., geometrically nonlinear) structure, we studied the validity of the linear kinematic approximation for simulating its failure. Two cases, designed to bracket the extremes of stability behavior, were explored: a single representative spicule of trabecular bone (case 1) and a volume of trabecular bone consisting of relatively low aspect ratio members (case 2). For case 1, geometrically linear (GL) and nonlinear (GNL) analyses were performed with two different materials models: a plastic damage model and a brittle damage model. When GNL terms were included in the total stiffness matrix, we found that load-path bifurcation preceded tissue failure regardless of the form of the damage model. This bifurcation was the result of a complex coupling between material yield and structural instability. The nature of this coupling was highly sensitive to the form of the damage model. None of these behaviors was observed in the linear analyses, where failure was insensitive to the form of the damage model and where structural instabilities were prevented from occurring. For case 2, compressive loading of a volume of trabecular bone, geometric nonlinear effects were pronounced. There was a bifurcation in load response that resulted in large apparent strain to failure. The GL simulations, on the other hand, precluded this bifurcation. We hypothesize that trabecular bone is a geometric nonlinear structure; nonlinear terms must be included in the total stiffness matrix to accurately simulate its failure.