Figure 6. Flow function coefficient and packing density of the binary
blends measured using the SRST.
While comparing FFc and packing density, indeed a correlation can be
found as suggested by Vallejo12. This confirms that
for a mixture of similar materials such as glass beads, packing has a
significant influence on powder flowability. Increased packing is
associated with decreased flowability and lower FFc. The contribution of
adhesion and friction to FFc are further investigated.
4.1.2 Relationship between tensile strength and packing
density
Figure 7 shows the key output from the shear test with its
interrelationships. Figure 7 (a) shows that the FFc relationship mirrors
that of the unconfined yield strength (σu) relationship.
In theory, the total strength of the material should be the summation of
the adhesion component and the frictional component of the system. The
adhesive or tensile component (σt) is shown in Figure 7
(b). It is found that tensile strength (σt), which
represents the stress required to fail the powder in tension, correlates
with the degree of packing of the powder. As the degree of packing of
the powder increases, greater forces are required to separate particles
from their neighbors, increasing the overall tensile strength of the
powder. The results are consistent with Rumpf’s theory of tensile
strength 21.
4.1.3 Relationship between internal angle of friction φ
and packing
density
We further explore the relationship between the internal angle of
friction φ and the packing density (Figure 7 (c)); φ shows the most
deviation with the packing density. While φ shows a linear relationship
with the packing density for 0% to 50% large glass beads, the results
deviate from the packing density as the large glass bead fraction is
increased from 50% to 75%. This seems counterintuitive, as φ still
increases with decreasing packing density. On further increase of large
glass beads beyond 75%, the φ decreases with decreasing packing
density. This behavior is explored in sections 4.2-4.4 by simulating
steady state shearing using DEM.
The steady state shear stress (τpre) correlates well
with φ (see Fig 7(c)). This can be described mathematically using the
Mohr Coulomb failure criterion:
\(\tau=\sigma tan\left(\varphi\right)+\tau_{c}\) (4)
Where τc is the cohesion term which is directly related
to σt by a trigonometric relationship. For glass beads,
the (σpre, τpre) point is colinear to
the yield loci. Based on equation 4, the τ term is dominated by\(\text{σtan}\left(\varphi\right)\); therefore, the
τpre is φ weighted by 2000 Pa.