Adhesion, inelastic contact behavior and simulation of shear dynamics of ultrafine cohesive powder

Studies on the adhesion mechanics of particles give better physical understanding of essential constitutive functions of a cohesive powder “continuum”. The discrete element method (DEM) allows us to consider in detail the contact and adhesion forces within force and momentum balance for each particle in a sheared particle packing. The introduction of irreversible inelastic contact flattening by the model, “stiff particles with soft contacts”, is essential to describe the increase of adhesion force, i.e. of the van der Waals forces during preconsolidation. The history dependent dynamic behaviour of cohesive powder flow can be “microscopically” investigated and understood. Using a model for elastic-plastic contact behaviour between ultrafine particles (about 1 μm), steady-state flow, incipient yielding, dilatancy and consolidation of TiO2 powder will be presented. Dynamic formation of a shear zone is also shown and compared to experiments in a standard Jenike shear cell. contact of two isotropic, stiff, linear elastic, smooth, spherical particles. Thus, the soft or compliant contact displacement is assumed to be small (hK/d << 1) compared to the diameter of the stiff particles. The contact area consists of a representative number of molecules. Hence, continuum approaches are only used here to describe the force-displacement behaviour in terms of nanomechanics. The microscopic particle shape remains invariant during the dynamic stressing and contact deformation at this nanoscale. In powder processing, these particles are manufactured from uniform material in the bulk phase. These prerequisites are assumed to be suitable for the mechanics of dry particle contacts in many cases of industrial practice. Here we introduce the constitutive model of Luding (Luding 2003) to be used in the numerical simulations since realistic and rather complicated contact model presented by Tomas (Tomas 2001), is very machine time spending to be implemented in the simulation software at present, Figure 1. That is why for the simulations we use the simplified contact law developed by Luding (Figure 1). Figure 1. Linearized force displacement contact law At the begin or end of the contact, i.e. when the contact deformation or particle-particle overlap is equal to 0, interaction between the particles starts from a predefined adhesion level (-f0, here attractive forces are negative). The normal force then goes along the linear plastic yield limit with stiffness k1, that takes care of a “perfect” plastic repulsion, considering also a linear dashpot that accounts for dissipation during contact. Inelastic deformation at the contact level is added by a linear spring, with a larger stiffness k2 for unloading and reloading, so that the stiffness increases. The variable adhesion force (or cohesion on a microlevel) between the particles comes into the model by a “cohesive stiffness” kc, which allows for changing the attractive forces up to a maximal attractive force fmin (per absolute value). One should notice also the force equilibrium state at a non-zero contact deformation of 0 k h . Cast into an equation, the normal force is: