THE PLASTICITY OF SOLIDS

225

For large values of the applied pressure, the last term of Eq.
(86) becomes very small and the curve becomes very nearly
linear and coincident with its asymptote

V r*&,n 4 \ (8?)

t

or

8Z

iruR3

(88)

The curve rises above the asymptote as the applied pressure
becomes very small, but it crosses the pressure (or shearing stress)
axis when P = p (or F = /). On differentiating Eq. (86) in
respect to the pressure one finds that the slope of the curve
vanishes when P = p, hence the curve is tangent to the axis.

The intercept of the asymptote is thus 4/3 of the true friction
which would be obtained by other methods as, for example,
plastic material confined between parallel planes which are being
sheared over each other. If in practice conditions may be
controlled so that all of the observed points lie on a straight line,
it will mean that the flow is taking place practically throughout
the capillary in telescoping layers, the term p/3P3 being negligible.

Were we to assume that the material throughout the capillary
flows in telescoping layers.for all shearing stresses above/, we
will obtain

V CR
4 =?r I r*ch>

* Jo

(P -

21

V
t

(P -

81

(p-n

(89)

which differs from Eq. (88) in having/ in place of 4/3/. It is
highly desirable that some one measure the friction both by the
capillary tube method and other methods using a given material,
to make sure that they give identical values for the friction.
Not being able to reproduce satisfactorily the data of Bingham
and Green, Buckingham has attempted to allow for slippage. If
there is a thin layer of viscous liquid of thickness e separating the
plastic material from the wall, it will increase the velocity of the
plastic material by the amount e<pF, hence the increase in the
volume of flow per unit of time over that given by Eq. (88) is
irR*e<pF approximately. But at present it is not certain that there
is slippage after the flow is established by increasing the shearing