Fracture and failure of shear-jammed dense suspensions under impact

TL;DR

This work addresses how dense, initially liquid suspensions fail when driven deep into the shear-jammed state by controlled-speed impact. Using cornstarch, potato starch, and silica in bulk and shallow geometries, the authors measure normal stresses, track the onset of shear jamming $z_{\mathrm{SJ}}$ and fracture $z_{\mathrm{F}}$, and vary particle fraction $\phi$, viscosity $\eta_0$, and surface tension $\gamma$ (with $v_i$ spanning several orders of magnitude). They find a two-stage fracture process with a threshold stress $\sigma_N(z_{\mathrm{F}})$; fracture likelihood increases with $\phi$ and $v_i$, while the material can exhibit either ductile yielding ($E_{\mathrm{eff}} \approx 1$ MPa) or strain stiffening ($E_{\mathrm{eff}} \approx 10$ MPa) near fracture. The results delineate a high-stress fracture regime in the state diagram and reveal confinement-enhanced strength, offering baseline data to predict and control fracture of dynamically jammed suspensions for applications such as impact mitigation and protective materials.

Abstract

Impacted with sufficiently large stress, a dense, initially liquid-like suspension can be forced into a solid-like state through the process of shear jamming. While the onset of shear jamming has been investigated extensively, less is known about the resulting solid-like state in the high stress limit and its failure. We experimentally produce such high-stress failure by impacting dense suspensions at a controlled speed. Using cornstarch suspensions we vary impact speed over several orders of magnitude and change fluid viscosity and surface tension in order to identify the conditions for failure. The results are compared with dense suspensions of potato starch or silica particles. In the case of fracture, we observe two types of cracks: a primary circular crack around the impactor followed by secondary radial cracks. Mapping out the onset of radial fracturing for different volume fractions and impact speeds, we identify the requirements for failure via crack formation to occur with at least 50% likelihood. We find that this likelihood is not sensitive to changes in particle diameter, but increases when the solvent's viscosity or surface tension are reduced. In the state diagram for dense suspensions we delineate the upper limit of shear-jammed rigidity and the crossover into a fracture regime at large volume fraction and normal stress, several orders of magnitude above the onset stress for shear-jamming. We find that the onset of fracturing in many cases is correlated with internal ductile deformation of the shear-jammed material underneath the impactor, observable in normal stress as a function of axial strain. For small suspension volumes and large impact speeds, we find strain-hardening up until fracturing. This more brittle behavior results in a modulus that, just before crack formation, is an order of magnitude larger than in shear-jammed suspensions undergoing ductile deformation.

Figures (11)

• Figure 1: Suspension behavior and typical stress response during impact. a Sketches of initial circular fracture and associated hole formation followed by radial cracking. Black arrows indicate the widening of the hole and the direction of fracture propagation; red arrows indicate the tension around the hole perimeter. b Impact-induced fracturing of a cornstarch suspension in the shallow setup ($v_\text{i} = 10$ mm/s, $\phi = 0.61$). c Still images from a high-speed video tracking a fracture event in the bulk setup for the same suspension and using the same impact speed as in a. Inset in iii: detail of first radial crack shortly after it opened. Circular (C), and radial (R) fracture are labeled in iv. d Corresponding normal stress measurement for the bulk setup, with the labels referring to the images in c. e Corresponding normal stress measurement for the shallow setup. In d,e the depths for shear jamming $z_\text{SJ}$ and fracture $z_\text{F}$ are indicated by blue and red dashed lines.
• Figure 2: Scanning electron microscope images of the particles used. a Cornstarch, b potato starch, and c silica spheres.
• Figure 3: Suspension rheology. Suspension viscosity $\eta$ as a function of shear rate for cornstarch CS1 with $\phi = 0.61$ (red $\textcolor{red}{\bullet}$), CS2 with $\phi = 0.62$ (dark blue $\textcolor{blue}{\bullet}$), CS3 with $\phi = 0.61$ (light blue $\textcolor{Aquamarine}{\bullet}$), CS4 (purple $\textcolor{Mulberry}{\bullet}$) with $\phi = 0.63$, potato starch PS (white o) with $\phi = 0.60$, and silica spheres SS with $\phi = 0.64$ (green, inset $\textcolor{green}{\bullet}$), see Table \ref{['tab:suspension-composition']}.
• Figure 4: a Normal stress $\sigma_\text{N}$ versus axial penetration depth $z$ in the shallow setup at low impact speed ($v_{\mathrm{i}} = 0.1$ mm/s) showing internal yielding at $z=z_\text{Y}$ prior to crack formation at $z=z_\text{F}$. b Correlation between yielding stress and fracture stress. Data are from all trials where yielding was detected in the stress-strain curves for cornstarch CS1 (red $\textcolor{red}{\bullet}$), CS2 (dark blue $\textcolor{blue}{\bullet}$), CS3 (light blue $\textcolor{Aquamarine}{\bullet}$) and CS4 (purple $\textcolor{Mulberry}{\bullet}$), as well as potato starch PS (white o) and silica SS (green $\textcolor{green}{\bullet}$) in the shallow (triangles) and bulk (circles) setups.
• Figure 5: Suspension surface profile during impact. a-d Surface elevation as a function of radial distance $r$ from the axis of the impactor for a CS1 suspension in the bulk setup ($v_\text{i} = 10$ mm/s) at different penetration depths $z$. Insets: images of the suspension surface with the laser sheet used for profile reconstruction. Gray shaded area: position of the impactor. At $z = 0$ the impactor has made first contact with the suspension. Red data: surface elevation, green lines: COMSOL simulation after shear jamming has commenced (panels c,d). e Vertical displacement from the initial, quiescent surface at four radial positions marked by the diamonds in a-d. Triangles: results of COMSOL simulation with bulk modulus 1 GPa and shear modulus 1 MPa. Vertical dashed lines: shear-jamming depth $z_\text{SJ}$ (blue) and fracture depth $z_\text{F}$ (red). Black dotted line: depth of the impactor.