Stress transmission in cemented bidisperse granular materials

We analyze stress distributions in a two-dimensional bidisperse cemented granular packing for a broad range of the values of particle-size ratio, the volumes of large and small particles, and the amount of cementing matrix. In such textured porous materials, the stress concentration, which controls the fracture and fragmentation of the material under tensile loading or in grinding processes, reflects not only the porosity but also the contact network of the particle phase and the resulting stress chains. By means of peridynamic simulations under tensile loading, we show how both the texture and stress distribution depend on size ratio, volume ratio, and the amount of the cementing matrix. In particular, the volume fraction of the class of small particles plays a key role in homogenizing stresses across the system by reducing porosity. Interestingly, the texture controls not only the porosity but also the distribution of pores inside the system with its statistical variability, found to be strongly correlated with the homogeneity of stresses inside the large particles. The most homogeneous stress distribution occurs for the largest size ratio and largest volume fraction of small particles, corresponding to the lowest pore size dispersion and the cushioning effect of small particles and its similar role to the binding matrix for stress redistribution across the packing. At higher porosity, the tensile stresses above the mean stress fall off exponentially in all phases with an exponent that strongly depends on the texture. The exponential part broadens with decreasing matrix volume fraction and particle-size ratio. These correlations reveal the strong interplay between size polydispersity and the cohesive action of the binding matrix for stress distribution, which is significant for the behavior of textured materials in grinding operations.

On the effect of local sample slope during modulus measurements by contact-resonance atomic force microscopy

Contact-resonance atomic force microscopy (CR-AFM) is of great interest and very valuable for a deeper understanding of the mechanics of biological materials with moduli of at least a few GPa. However, sample surfaces can present a high topography range with significant slopes, where the local angle can be as large as  ± 50°. The non-trivial correlation between surface slope and CR-frequency hinders a straight-forward interpretation of CR-AFM indentation modulus measurements on such samples. We aim to demonstrate the significant influence of the surface slope on the CR-frequency that is caused by the local angle between sample surface and the AFM cantilever and present a practical method to correct the measurements. Based on existing analytical models of the effect of the AFM set-up's intrinsic cantilever tilt on CR-frequencies, we compute the non-linear variation of the first two (eigen)modes CR-frequency for a large range of surface angles. The computations are confirmed by CR-AFM experiments performed on a curved surface. Finally, the model is applied to directly correct contact modulus measurements on a durum wheat starch granule as an exemplary sample.

Mineral-vegetal co-milling: An effective process to improve lignocellulosic biomass fine milling and to increase interweaving between mixed particles

Fine-milling is a crucial objective for lignocellulosic biomass valorization. Co-milling appears to be a promising technique to improve its efficiency. However, the mechanisms occurring while co-milling remain poorly understood. In this study, an experimental work was performed to produce co-milled powders from both lignocellulosic (wheat, straw or pine sawdust) and mineral materials (limestone, quartzite or tile) with very contrasted physicochemical properties. The main consequences of co-milling were studied for both materials. A two-component mixing law for the prediction of the blend properties was proposed (particle sizes and true densities) to highlight the gain of this single processing step compared to separate milling and mixing. The predicted values were compared with experimental data for co-milled powders at 7 biomass contents from 0% to 100%. In all cases, co-milling leads to a reduction in particle size of lignocellulosic materials and create strong interweaving with mineral particles.

Tensile strength and fracture of cemented granular aggregates

Cemented granular aggregates include a broad class of geomaterials such as sedimentary rocks and some biomaterials such as the wheat endosperm. We present a 3D lattice element method for the simulation of such materials, modeled as a jammed assembly of particles bound together by a matrix partially filling the interstitial space. From extensive simulation data, we analyze the mechanical properties of aggregates subjected to tensile loading as a function of matrix volume fraction and particle-matrix adhesion. We observe a linear elastic behavior followed by a brutal failure along a fracture surface. The effective stiffness before failure increases almost linearly with the matrix volume fraction. We show that the tensile strength of the aggregates increases with both the increasing tensile strength at the particle-matrix interface and decreasing stress concentration as a function of matrix volume fraction. The proportion of broken bonds in the particle phase reveals a range of values of the particle-matrix adhesion and matrix volume fraction for which the cracks bypass the particles and hence no particle damage occurs. This limit is shown to depend on the relative toughness of the particle-matrix interface with respect to the particles.

Rheology of granular materials composed of nonconvex particles

By means of contact dynamics simulations, we investigate the shear strength and internal structure of granular materials composed of two-dimensional nonconvex aggregates. We find that the packing fraction first grows as the nonconvexity is increased but declines at higher nonconvexity. This unmonotonic dependence reflects the competing effects of pore size reduction between convex borders of aggregates and gain in porosity at the nonconvex borders that are captured in a simple model fitting nicely the simulation data both in the isotropic and sheared packings. On the other hand, the internal angle of friction increases linearly with nonconvexity and saturates to a value independent of nonconvexity. We show that fabric anisotropy, force anisotropy, and friction mobilization, all enhanced by multiple contacts between aggregates, govern the observed increase of shear strength and its saturation with increasing nonconvexity. The main effect of interlocking is to dislocate frictional dissipation from the locked double and triple contacts between aggregates to the simple contacts between clusters of aggregates. This self-organization of particle motions allows the packing to keep a constant shear strength at high nonconvexity.

Multiscale force networks in highly polydisperse granular media

We investigate highly polydisperse packings subjected to simple shear by contact dynamics simulations. A major unsolved issue is how granular texture and force chains depend on the size polydispersity and how far they influence the shear strength. The numerical treatment was made possible by ensuring the statistical representation of particle size classes. An unexpected finding is that the internal friction angle is independent of polydispersity. We show that this behavior is related to two mechanisms underlying the stability of force chains: (i) The class of largest particles captures strong force chains, and (ii) these chains are equilibrated by weak forces carried by increasingly smaller particles as the size span broadens. In the presence of adhesion between particles, the Coulomb cohesion increases with size polydispersity as a result of enhanced force anisotropy.

Space-filling properties of polydisperse granular media

We present a systematic investigation of the morphology and space-filling properties of polydisperse densely packed granular media in two dimensions. A numerical procedure is introduced to generate collections of circular particles with size distributions of variable shape and span constrained by explicit criteria of statistical representativity. We characterize the domain of statistically accessible distribution parameters for a bounded number of particles. This particle generation procedure is used with two different deposition protocols in order to build large close-packed samples of prescribed polydispersity. We find that the solid fraction is a strongly nonlinear function of the size span, and the highest levels of solid fraction occur for the uniform distribution by volume fractions. As the span is increased, a transition occurs from a regime of topological disorder where the packing properties are governed by particle connectivity to a regime of metric disorder where pore-filling small particles prevail. The polydispersity manifests itself in the first regime through the variability of local coordination numbers. We observe a continuous decrease of the number of particles with four contacts and the growth of two populations of particles with three and five contacts. In the second regime, radial distribution functions show that the material is homogeneous beyond only a few average particle diameters. We also show that the packing orientational order is linked with fabric anisotropy and it declines with size span.

Strength and failure of cemented granular matter

Cemented granular materials (CGMs) consist of densely packed solid particles and a pore-filling solid matrix sticking to the particles. We use a sub-particle lattice discretization method to investigate the particle-scale origins of strength and failure properties of CGMs. We show that jamming of the particles leads to highly inhomogeneous stress fields. The stress probability density functions are increasingly wider for a decreasing matrix volume fraction, the stresses being more and more concentrated in the interparticle contact zones with an exponential distribution as in cohesionless granular media. Under uniaxial loading, pronounced asymmetry can occur between tension and compression both in strength and in the initial stiffness as a result of the presence of bare contacts (with no matrix interposed) between the particles. Damage growth is analyzed by considering the evolution of stiffness degradation and the number of broken bonds in the particle phase. A brutal degradation appears in tension as a consequence of brittle fracture in contrast to the more progressive nature of damage growth in compression. We also carry out a detailed parametric study in order to assess the combined influence of the matrix volume fraction and particle-matrix adherence. Three regimes of crack propagation can be distinguished corresponding to no particle damage, particle abrasion and particle fragmentation, respectively. We find that particle damage scales well with the relative toughness of the particle-matrix interface with respect to the particle toughness. This relative toughness is a function of both matrix volume fraction and particle-matrix adherence and it appears therefore to be the unique control parameter governing transition from soft to hard behavior.

Self-stresses and crack formation by particle swelling in cohesive granular media

We present a molecular-dynamics study of force patterns, tensile strength, and crack formation in a cohesive granular model where the particles are subjected to swelling or shrinkage gradients. Nonuniform particle size change generates self-equilibrated forces that lead to crack initiation as soon as the strongest tensile contacts begin to fail. We find that the tensile strength is well below the theoretical strength as a result of inhomogeneous force transmission in granular media. The cracks propagate either inward from the edge upon shrinkage or outward from the center upon swelling. We show that the coarse-grained stresses are correctly predicted by an elastic model that incorporates particle size change as metric evolution.