THE PLASTICITY OF SOLIDS

217

for a series of fluids a family of straight lines passing out from
the origin as illustrated in Fig. 76.

*In a plast>ic solid, a certain portion of the shearing force is
**sed irp i** overcoming the internal friction of the material. If
the stress is j "ust equal to the friction or yield value, the material
**iay be said "to be at its elastic limit. If the stress is greater than
the friction f* the excess, F - /, will be used up in producing
Plastic flow according to the formula

dv = M (F - /) dr (73)

where M is a constant which we will call the coefficient of mobility

01*.

Shearing Stress
JJ*XG. 77.—Flow-shear diagram of a plastic solid.
in analogy to the fluidity /of liquids and gases. If we were to
plot the volume of flow against the shearing stress we would
again obtain, a, straight line for a given material but it would
not pass throiagh the origin, ABC Fig. 77.
It is easy now to see why the " viscosity " of plastic substances,
as measured In the usual way for liquids, is not a constant.
Referring to the figure, if we take two determinations of the
flow A and B9 we see that they correspond to entirely different
viscosity curves OD and OE.
When the stress is not equal to the yield value, the material
undergoes elastic deformation and an opposing force arises