Recent experimental measurements using twin-axis load cells in
storage vessels for bulk solids have revealed load-dependent variation of the
wall friction angles measured in the presence of small normal loads on smooth
silo walls. The effect is quite appreciable with smooth particles such as plastic
beads and glass ballotini, but particles with rough surfaces, like some
agricultural seeds, show no such effect.
The inclusion of an intrinsic shear
resistance at zero normal load into the frictional behaviour (after Briscoe and
Tabor) provides a satisfactory prediction of tangential forces required to cause
gross sliding of smooth particles over smooth silo walls. This work applies the
same adhesive friction concepts to the microdisplacements that occur before full
tangential sliding develops.
Mindlin analysed the traction profiles for two spheres
in contact assuming a constant coefficient of friction, independent of normal
stress inside the contact area, with microslip occurring in those portions of the
contact area that had a tangential-to-normal stress ratio exceeding the friction
coefficient. The assumptions of that analysis preclude the existence of the
observed load dependence of wall friction angles. In this paper we re-examine
the micromechanical nature of contacts between elastic spheres incorporating
tangential stress limits that contain two terms: one proportional to the normal
stress at each point in the contact area, the other independent of normal stress.
Two possible physical (and mathematical) interpretations of the
stress-independent term are discussed, one called adhesive slip and the other
stick slip. The resulting traction profiles are examined to determine implications
for both microslip and gross-sliding frictional behaviour. A complete theoretical
analysis requires the solution of the surface displacement integral over the
contact region for a chosen form of the tangential traction profile satisfying
appropriate boundary conditions for elastic displacements. Upper and lower
bounds and an approximate form for the resulting tangential force-displacement
curves are developed and it is shown that such models result in a
load-dependent friction behaviour that is very similar to recent experimental wall
friction and individual particle friction measurements.