Strain Stiffening in Random Packings of Entangled Granular Chains

Abstract

Random packings of granular chains are presented as a model polymer system to investigate the contribution of entanglements to strain-stiffening in the absence of Brownian motion. The chain packings are sheared in triaxial compression experiments. For short chain lengths, these packings yield when the shear stress exceeds a the scale of the confining pressure, similar to packings of spherical particles. In contrast, packings of chains which are long enough to form loops exhibit strain-stiffening, in which the effective stiffness of the material increases with strain, similar to many polymer materials. The latter packings can sustain stresses orders-of-magnitude greater than the confining pressure, and do not yield until the chain links break. X-ray tomography measurements reveal that the strain-stiffening packings contain system-spanning clusters of entangled chains.PACS numbers: 83.80. Fg, 81.70.Tx, 62.20.mm, 61.41.+e Most materials, ranging from crystalline metals to piles of granular material, become weaker the further they are strained. On the other hand, many polymeric materials are known to strain-stiffen, in which the effective stiffness of the material increases as the material is strained further [1]. Theories suggest strain-stiffening could depend on many factors including chain stiffness, density, temperature, strain rate, and in particular on structures such as entanglements between different chains [2][3][4][5]. However, it has not been possible to directly measure entanglements in experiments because in polymers these structures occur on very small scales. In this letter we present a new experimental approach to investigate the role of entanglements in strain-stiffening using a model system of granular chains consisting of millimeter-scale beads connected by flexible links. Such a macroscopic system has advantages over molecular polymer systems for investigating entanglement. First, the macroscopic size allows for imaging to measure the precise positions of each particle and link in the structure. Second, we can isolate entanglement effects from temperature and strain rate dependent effects because the macroscopic chains have no inherent time scales due to Brownian motion or relaxation.Granular chains have been considered as model polymers in previous studies to characterize the packing structure around the jamming transition for chain packings [6][7][8]. Such chains form tight loops when packed which defines a characteristic loop size and persistence length in analogy to polymers. The free volume in the packing was found to increase with and level off when the chain length exceeded the persistence length, analogous to the behavior of the glass transition temperature for polymers [7]. Similarly, tumbling strings have been considered as a macroscopic model polymer system, in which knotting was found to exhibit statistics analogous to thermodynamic systems [9]. While these works characterized the structures of macroscopic model polymer systems, the stress response of such systems have not previous...

Nonmonotonic dependence of polymer-glass mechanical response on chain bending stiffness

“…It is, so far, difficult to isolate bending stiffness experimentally, since many other factors can influence the mechanical properties. Model systems such as colloidal and granular polymers (CGPs) [30] might be good candidates for verifying our predicted nonmonotonicity, though, as they offer a very high level of control over coarse-grained properties.…”

Structure of hexapod 3D packings: understanding the global stability from the local organization

“…The use of aggregates made from non-convex particles or particles with anisotropic contact laws is an emerging area for both the research in physics [1][2][3][4][5][6][7] and the design of functionalized materials by tuning local properties of the grains [8][9][10][11]. This new field in granular matter science has already shown to be extremely promising for future lightweight and reversible architecture [12].…”

Capillary Breakup of Discontinuously Rate Thickening Suspensions

“…Complex, high aspect ratio structures, such as strings with embedded functionalized elements ("beads") (Figure 1.1), can find applications in optics [16], self-assembly, bioengineering, and custom material design [7]. It was recently shown that such structures can be created by polymerizing a liquid filament undergoing capillary breakup [16].…”