Dynamic Fracture of Nonglassy Suspensions

We study the dynamic fracture of thin layers of suspensions of non-Brownian rigid particles. The impact of a projectile triggers a liquid-to-solid transition and a hole opens in the layer. We show that the occurrence of fracture and the spatial and dynamic features of the cracks depend mostly on the thickness of the layer and the particle volume fraction. In contrast, the properties of the fractured material seem independent of volume fraction. Finally, we measure the velocity of the crack tip, from which we estimate an effective value of the shear modulus of the fractured material.

Figure 1

(a) Schematic of the experimental set-up. (b) Time sequence, extracted from a top view of a layer of corn starch suspension ($[\mathrm{CS}]=0.40$), after the impact of a tungsten carbide rod. $H=(77\pm 1)\times {10}^{-2}\mathrm{m}$, $h=(1\pm 0.1)\times {10}^{-2}\mathrm{m}$. Scale bar: ${10}^{-2}\mathrm{m}$. (c) Timeline of fracture after impact, with definitions of the time at which the hole detached from the surface of the rod $t_d$ and the time at which fracture initiated $t_f$.

Figure 2

(a) Normalized probability density function (PDF) of the number of cracks $N_c$. The plot summarizes 30 experiments. $[\mathrm{CS}]=0.42$, $h=(1\pm 0.1)\times {10}^{-2}\mathrm{m}$, $H=(77\pm 1)\times {10}^{-2}\mathrm{m}$. (b) The average number of cracks ${\overline{N}}_c$ and (c) the average crack length ${\overline{L}}_c$ per impact as a function of the release height $H$. $h=(1\pm 0.1)\times {10}^{-2}\mathrm{m}$, $[\mathrm{CS}]=0.40$ (filled square) and $[\mathrm{CS}]=0.42$ (open circles). (d) Average number of cracks ${\overline{N}}_c$ and (e) average crack length ${\overline{L}}_c$ (bottom) per impact as a function of the thickness $h$ of the layer. $[\mathrm{CS}]=0.40$ (filled square) and 0.42 (open circles); $H=(77\pm 1)\times {10}^{-2}\mathrm{m}$.

Figure 3

(a) Velocity of the hole contour $u_h$ as a function of time $t-t_d$, with $t_d$ the time at which the hole detaches from the rod, for volume fractions $[\mathrm{CS}]=0.39$ black square, $0.40$ red circle, $0.41$ green diamond and $0.42$ blue triangle. Inset: Ultimate strain ${ϵ}_f$ black square and ultimate strain rate ${\dot{ϵ}}_f$ open triangle at which cracks nucleated on the contour as a function of [CS]. $H=(40\pm 1)\times {10}^{-2}\mathrm{m}$, $h=15\times {10}^{-3}\mathrm{m}$.

Figure 4

Velocity of the tip of the crack $u_{\mathrm{tip}}$ as a function of time for $[\mathrm{CS}]=0.4$ (open triangle, $h=10\times {10}^{-3}\mathrm{m}$) and 0.42 (black square $h=5\times {10}^{-3}\mathrm{m}$, red circle $h=10\times {10}^{-3}\mathrm{m}$, green diamond $h=15\times {10}^{-3}\mathrm{m}$). $H=(77\pm 1)\times {10}^{-2}\mathrm{m}$. Inset: Crack tip velocity for two first cracks created by impact from different heights. $[\mathrm{CS}]=0.42$, $h=15\times {10}^{-3}\mathrm{m}$, open square $H=(20\pm 1)\times {10}^{-2}\mathrm{m}$ and green diamond $H=(77\pm 1)\times {10}^{-2}\mathrm{m}$.