Impact-Induced Energy Transfer and Dissipation in Granular Clusters under Microgravity Conditions

The impact-induced energy transfer and dissipation in granular targets without any confining walls are studied by microgravity experiments. A solid projectile impacts into a granular target at low impact speed ($0.045\le v_p\le 1.6\mathrm{m}{\mathrm{s}}^{-1}$) in a laboratory drop tower. Granular clusters consisting of soft or hard particles are used as targets. Porous dust agglomerates and glass beads are used for soft and hard particles, respectively. The expansion of the granular target cluster is recorded by a high-speed camera. Using the experimental data, we find that (i) a simple energy scaling can explain the energy transfer in both soft-particle and hard-particle granular targets, (ii) the kinetic impact energy is isotropically transferred to the target from the impact point, and (iii) the transferred kinetic energy is 2%–7% of the projectile’s initial kinetic energy. The dissipative-diffusion model of energy transfer can quantitatively explain these behaviors.

Figure 1

The top row (a)–(e) shows the impact of a $D_p=4\mathrm{mm}$ glass projectile into a porous-dust-agglomerate cluster at $v_p=0.82\mathrm{m}{\mathrm{s}}^{-1}$ impact speed. The bottom row (f)–(j) shows the impact of a $D_p=6\mathrm{mm}$ glass projectile into a dense-glass-bead cluster at $v_p=0.38\mathrm{m}{\mathrm{s}}^{-1}$ impact speed. In both cases, impact-induced expansion of the target cluster followed by fragmentation can be observed. The dark parts at the top-right corners in panels (a)–(c), (f)–(h) show the target-release system. Movies of these impacts can be found in the Supplemental Material [23].

Figure 2

Kinematic scaling relation between the characteristic acceleration $A_p$, the impact velocity $v_p$, and the projectile diameter $D_p$. The gray line indicates the scaling $A_p{D}_p=C{v}_p^2$ with a fitting parameter $C=0.64$.

Figure 3

The normalized projectile energy after the breakthrough of the target $(v^{\prime }/v_p{)}^2$ as a function of impact velocity $v_p$. The inset shows the same data in a log-log plot. The two lines correspond to the viscoelastic (slope $-2/3$) and plastic (slope $-1/2$) behaviors.

Figure 4

Division of the analyzed target into regions. The black part corresponds to the projected target area. From the center of the longest horizontal axis of the target image (top-left corner of the image), the target is divided into three regions by the azimuthal angle from the vertical direction. While only the right-hand side of the target is shown here, both sides are used in the actual analysis.

Figure 5

Energy-based scaling of the expansion rates at the rim $U_i$ and the center $u_i$, respectively. All impact data are plotted in all the panels. Open and filled symbols correspond to porous-dust-agglomerate and dense-glass-bead targets, respectively. By normalizing $U_i$ and $u_i$ using the mass ratio $(m_i/\mu {)}^{1/2}$, all expansion rates can be collapsed on a unified scaling relation shown by the gray lines, which are linear fittings with slope unity in the log-log plots.