Biomedical Engineering Reference
In-Depth Information
The shear stress (t) generated along a defined plane depends on the
normal stress (s) exerted on this plane. If a material is subjected to a
shearing action, a characteristic relation is obtained between normal
and shear stresses for each material. This relationship is graphically
shown in
s
-
t coordinates (Mohr diagrams) and the straight line
obtained finally is the yield locus for a bulk material [11].
All failure stress states for a given consolidation stress are represented
by the Mohr stress circle, which is both tangential to this yield
locus and passes through the origin, representing the unconfined
yield stress state. The major principal stress associated with this
circle is the unconfined yield strength,
f
c
, of the material. There is
one yield locus for each critical consolidation stress and one unique
value of unconfined yield strength for each major principal critical
consolidation stress. Direct shear testers measure the bulk strength
of materials by first generating the yield locus and then constructing
the unconfined Mohr circle stress state from the data. While under a
certain consolidation load, the specimen inside the cell is pre-sheared
to a condition of continual deformation without volume change
(critical state) [11]. The major principal stress in the steady state
flow is called the major consolidation stress (s
1
). It is determined
by drawing the steady-state Mohr circle passing through the point
(s
c
, t
c
) which represents the consolidation conditions in shear tests.
The circle is tangential to the yield locus and the intersection of the
circle with the normal stress axis gives the s
1
value. Unconfined yield
stress (s
c
) is the maximum normal stress value when a solid having a
free and stressless surface flows or deforms. While the yield locus of
a solid is known, is
c
is found by drawing an unconfined yield stress
Mohr circle at a tangent to the yield locus and passing through the
origin (s = t = 0) [12]. There is a corresponding value of s
c
for each
consolidation stress (s
1
). The flow function of the material is obtained
by plotting s
c
against s
1
values. The flow index (
ff
c
) is defined as the
inverse slope of the flow function. Based on the magnitude of the
flow index, the powder materials are classified as: hardened
ff
c
<1;
very cohesive
ff
c
<2; cohesive
ff
c
<4; easy flowing
ff
c
<10; free flowing
ff
c
>10 [12].
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