In situ observation of material flow in composite media under shock compression

When a shock wave enters a heterogeneous material, local differences in density and compressibility drive pressure and velocity gradients which can be nearly as sharp as the incident shock. Subsequent momentum equilibration is comparatively slow, relying on shock reverberation, particle collisions, and shear flow. The latter phenomenon depends on constitutive behavior that is often poorly known and so the process can be problematic to simulate. This is compounded by the fact that conventional diagnostics, such as velocimetry, blend the response of both phases and provide only a homogenized comparison for modeling efforts. For these reasons, we have collected spatially resolved and phase-specific measurements on a model particulate composite using in situ synchrotron-based radiography. This revealed the post-shock internal motion, including nanosecond resolution measurement of the metal particles’ trajectories and snapshots of the flow field within the polymer. Comparing this data to analytical and numerical predictions allowed the polymer's shear response to be inferred. The resulting constitutive model was then used in conjunction with direct numerical simulations to demonstrate the physical origins of the observed bulk composite response.

Figure 1

Experimental velocity traces for impact on a pure polymer (solid black) and polymer-5 vol% W composite (solid blue) under the same impact condition. The velocity history for the composite shows orders of magnitude slower acceleration than for the pure polymer. Details of this measurement are reported in Bober et al. [6].

Figure 2

(a) Schematic of the experimental setup showing the impactor arriving from the left, the polymer-W sample and the x-ray imaging direction. Detailed views of the two sample configurations are shown in third-angle orthographic projections in panels (b) and (c). In panel (b) 20-$\mu \mathrm{m}$ W spheres are arranges in a regular lattice, and in panel (c) three W cylinders are encased between layers of polymer and thin Au films. The uppermost projections are of the radiographic imaging direction. The vertical direction is orthogonal to the shock and x-ray directions. To help visualize the particle arrangement, alternating layers of the lattice have been color coded red and blue, which explain the stagger visible in the x-ray projection.

Figure 3

Radiographs of an array of metal spheres (a) and cylinders (b) contained in a polymer matrix undergoing shock compression. Flow in the polymer is tracked by Au films in panel (b). The shock wave is visible as a jump from a light to dark background and the Al buffer plate is shown by the black region at the far left. The black area in the extreme right of the fourth frame in panel (b) is a consequence of shifting the images to follow the buffer motion. This translation brings into the frame an area not captured by the camera, which has been colored black. The images in panel (a) are shown in the laboratory reference frame, while those in panel (b) are shifted to one fixed to the buffer. This change in reference frame make it appear that the buffer is not moving and so highlights the relative motion W wires and Au layers. The labeled times are relative to the first frame, not the events depicted.

Figure 4

An x-t diagram showing the displacement of the Al buffer and metal spheres, plotted as a function of the time elapsed since each was particle struck by the incident shock wave. In panel (a) the displacement is that viewed from the stationary laboratory reference frame, while in panel (b) the reference frame is taken to be moving at the same speed at the Al buffer (1.4 km/s).

Figure 5

An x-t diagram showing the displacement of the metal rods, tracer nanofilms and Al buffer. Like in Figure 2, the reference frame has a constant velocity of 1.4 km/s. The time of the first available camera frame was set to $t=0$. Each observation is marked by a cross.

Figure 6

Trajectory predictions for the metal spheres (a) and cylinders (b)–(d) based on a Newtonian fluid model for the polymer. The best fit viscosities (solid black) are shown along with shaded bands where the best viscosity was scaled by $\times /÷$ 1.25, 1.5, and 2. Predictions bounding the uncertainty due to the measured radii are shown in dashed red. The data is shown as black dots.

Figure 7

Surfaces representing the error of trajectory predictions for the metal spheres (a) and cylinders (b)–(d) based on a pseudoplastic fluid model. The horizontal and vertical axis represent the two input parameters to this model. The white region in panel (d) is where simulation results were not available. The black circles in panel (b) show a sampling of (n, k) values which produced low errors were selected for further examination in Fig. 8.

Figure 8

The observed flow field around the 50.8-$\mu \mathrm{m}$ wire (greyscale) can be compared to simulations using a range of pseudoplastic parameters (yellow). The measured flow field comes from the same Au layers described in Fig. 3.

Figure 9

Experimentally determined shock wave profiles for the polymer filled with 5 vol% (a) and 40 vol% (b) metal spheres (∼16-$\mu \mathrm{m}$-diameter) are shown in black. Predictions from direct numerical simulations using an inviscid polymer model (blue) and a pseudoplastic model (red) are also shown. Cross sections of the simulated velocity fields in the 5 vol% (c) and 40 vol% (d) composites are shown for both the inviscid and pseudoplastic polymers.