THE PHENOMENA OF RUPTURE AND FLOW IN SOLIDS. 
179 
breaking load is regarded as the sum of the intermolecular attractions. According to 
the theory, large changes in the latter can only occur as a result of large changes in 
the thermal energy of the substance, such as would be immediately evident in alternating 
stress tests, if they took place. 
Lastly, as indicated above, the strain energy at rupture of an elastic solid or liquid 
should on the molecular theory be of the same order as its heat of vaporisation. Hence 
rupture should be accompanied by phenomena, such as a large rise of temperature, 
indicative of the dissipation of an amount of energy of this order. It is well known 
that tensile tests of brittle materials show no such phenomena. 
If, as is usually supposed, the materials concerned are substantially isotropic, there 
is but one hypothesis which is capable of reconciling all these apparently contradictory 
results. The theoretical deduction—that rupture of an isotropic elastic material always 
occurs at a certain maximum tension—is doubtless correct; but in ordinary tensile 
and other tests designed to secure uniform stress, the stress is actually far from uniform 
so that the average stress at rupture is much below the true strength of the material. 
Now it may be shown, 'with the help of elastic theory, that the stress must be 
substantially uniform, in such tests, unless the material of the test-pieces is heterogeneous 
or discontinuous. It is known that all substances are in fact discontinuous, in that 
they are composed of molecules of finite size, and it may be asked whether this type 
of discontinuity is sufficient to account for the observed phenomena. 
With the help of formula (13) above, this question may be answered in the negative. 
Formula (13) shows that a thin plate of glass, having in it the weakest possible crack of 
length 2c inch, will break at a tension, normal to the crack, of not less than 266 J\/ clbs. 
per sq. inch. This result, however, is subject to certain errors, and experiment 
shows that the true breaking stress is about 240/\/c lbs. per sq. inch. But such a 
crack is the most extreme type, either of discontinuity or heterogeneity, which can 
exist in the material. Hence it is impossible to account for the observed strength, 
24,900 lbs. per sq. inch, of the simple tension test specimens, unless they contain 
discontinuities at least 2 X 
/ 240 \ 8 
\24,900/ 
inch, or say, 2 X 10 -4 inch wide. 
This is of 
the order 10 -4 times the molecular spacing. 
The general conclusion may be drawn that the weakness of isotropic solids, as 
ordinarily met with, is due to the presence of discontinuities, or flaws, as they may be 
more correctly called, whose ruling dimensions are large compared with molecular 
distances. The effective strength of technical materials might be increased 10 or 20 
times at least if these flaws could be eliminated. 
It is easy to see why the presence of such small flaws can leave the strength of cracked 
plates, such as those of the foregoing experiments, practically unaffected. The most 
extreme case of weakening is that where there is a flaw very near the end of the crack 
and collinear with it. Here the result is merely to increase the effective length of the 
crack by less than 10 -3 inch. This involves a weakening of less than 0 - l per cent. 
2 c 
VOL. CCXXI.-A. 
