THE PHENOMENA OF RUPTURE AND FLOW IN SOLIDS. 
187 
sliding from the stable to the unstable state, must be equal to the greatest rate of 
increase in potential energy which occurs during the passage between the two states. 
This rate will depend on the shape of the molecular fields of force, and may in particular 
cases be zero. Liquid crystals are doubtless of this type. The average shear stress, 
during yield, of a random aggregation of a large number of crystals, is doubtless greater 
than that of a single crystal, as the angle between the gliding planes and the maximum 
shear stress must vary from crystal to crystal and can be zero in only a few of them. 
As the mutually gliding portions of a crystal pass from the stable to the unstable 
state, the molecular cohesion between them (normal to the gliding plane) must, in 
general, become less. In particular instances it may diminish to zero before the 
position of unstable equilibrium is reached. In these cases, shearing fracture along 
the gliding planes will occur, unless the material is subjected to a sufficiently high 
“ hydrostatic ” pressure, in addition to the shearing stress. Thus, a crystalline 
substance may be either ductile or brittle, according to nature of the applied stress, 
or it may be ductile at some temperatures and brittle at others, under the same kind 
of stress as has been actually observed by Bengough and Hanson in the case of tensile 
tests of copper. This rupture in shear explains the characteristic fracture of short 
columns of brittle crystalline material under axial compression. The theory indicates 
that such fracture can always be prevented and yield set up by applying sufficient 
lateral pressure in addition to the longitudinal load ; this is in agreement with experi¬ 
ments on rocks such as marble and sandstone.* Conversely, a ductile substance might 
be made brittle if it were possible to apply to it a sufficiently large hydrostatic tension. 
In the case of an alloy of, say, two metals A and B, suppose, as an example, that the 
sequence of molecules on either side of a gliding plane is 
.A.B.B.A.B.B 
B.B.A.B.B.A. 
Let sliding occur (through one molecular space) to an adjoining position of stable 
equilibrium, or, say, to the configuration 
.A.B.B.A.B.B. 
. B . B . A . B . B . A — 
Evidently, the structure in the neighbourhood of the gliding plane is in this case no 
longer the same as in the original crystal formation. It is therefore likely that the 
new state is one of higher potential energy, whence it is reasonable to suppose that 
the maximum rate of increase in potential, in sliding, is greater than it would have 
been had the potential of the two states been the same. Thus an alloy may be expected 
to have a higher yield-point than its most ductile constituent. This is in accordance 
with experience. For example, it is known that quenching from a high temperature 
* T. V. Karman, ' Zeitschr. Ver. Deutsch. lug.,’ 55, 1911. 
VOL. CCXXI.- A. 2 D 
