THE PHENOMENA OF RUPTURE AND FLOW IN SOLIDS. 
L 89 
of a large number of crystals there must be many arrangements of this type, in which 
adjacent crystals can execute inelastic oscillations about positions of unstable equilibrium, 
under alternating shear stresses below the ordinary yield stress. The consequent 
observed phenomena would correspond exactly with those known to be manifested 
in metals, under the name “ elastic hysteresis.”* 
Experimentally, elastic hysteresis is distinguished from elastic after-working by the 
circumstance that it is completed very much more quickly. This is just what would 
be expected theoretically, on the view that molecular translation occurs much more 
readily than rotation. 
It has been remarked that when a single crystal of a pure substance is caused to 
yield, its structure is fundamentally unaltered. This cannot hold, however, in the 
case of an aggregate of a large number of crystals arranged at random, or a crystal 
embedded in amorphous material. True, the material in the interior of each crystal 
can retain its original properties, but near the crystalline boundaries the structure 
must be violently distorted. As a result, it may be expected that the number of the 
molecules of inferior stability will be largely increased. Elastic after-working in metals 
should therefore be increased by overstraining or “ cold-working.” This, again, agrees 
with experience. 
The foregoing considerations lend support to the view that each crystal of a severely 
cold-worked piece of metal is surrounded by an amorphous layer of appreciable 
thickness. If such a piece of metal undergoes a shear strain greater than that which 
can initiate yield in the normal crystalline substance, the average stress which is set 
up must be above the normal yield stress, for the part due to the amorphous layers 
must be the elastic stress corresponding with the strain, and this, by hypothesis, is 
greater than the yield stress. This part, moreover, will increase with the strain. It 
follows that yield in cold-worked metal should be less sharply defined, and should occur 
at a higher shear stress than in the normal crystalline variety. That this is actually 
the case is, of course, well known. 
In the case of very large strains an important part of the shear stress must be taken 
by the amorphous boundary layers, and as a result the maximum tensile stress may 
reach a value sufficient to cause rupture of some favourably disposed crystals across 
their planes of least strength. This is, perhaps, the actual mode of rupture in ductile 
materials. On this view, the “ ductility ” of a metal depends simply on the relation 
between the tensile strength of the “ flaws ” and the normal yield stress. A substance 
whose ductility is small may still be “ malleable,” as hammering need not give rise 
to large tensile stresses. 
The formation of non-crystalline material at the intercrystalline boundaries, when a 
piece of metal is over-strained, appears to provide an explanation of the sudden drop 
in stress which occurs immediately after the initiation of yieldf in ductile metals. 
* Guest and Lea, “ Torsional Hysteresis of Mild Steel,” ‘ Roy. Soc. Proc., A, June, 1917. 
f Robertson and Cook, * Roy. Soc. Proc.,’ A, vol. 88, 1913, pp. 462^71. 
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