THE PHENOMENA OF RUPTURE AND FLOW IN SOLIDS. 
1G5 
in some cases to 15 per cent., remained after the removal of the load. It was inferred 
that at this critical load the maximum stresses in the scratches reached the elastic 
limit of the material. This load was about one-quarter to one-third of that which 
caused the wire to yield as a whole, so that the scratches increased the maximum 
stress three or four times. The readings were quite definite even in the case of scratches 
produced by No. 0 cloth, which were found by micrographic examination to be but 
10 _4 -inch deep. Control experiments with longitudinal and circumferential scratches 
gave twists only 2 or 3 per cent, of those found with spiral scratches, and there was no 
permanent twist. 
This substantial confirmation of the estimated values of the stresses, even in very 
fine scratches, shows that the ordinary hypotheses of rupture, as usually interpreted, 
are inapplicable to the present phenomena. Apart altogether from the numerical 
discrepancy, the observed'difference in fatigue strength as between small and large 
scratches presents a fundamental difficulty. 
2. A Theoretical Criterion of Rupture. 
In view of the inadequacy of the ordinary hypotheses, the problem of the rupture 
of elastic solids has been attacked from a new standpoint. According to the well-known 
“ theorem of minimum energy,” the equilibrium state of an elastic solid body, deformed 
by specified surface forces, is such that the potential energy of the whole system* is 
a minimum. The new criterion of rupture is obtained by adding to this theorem the 
statement that the equilibrium position, if equilibrium is possible, must be one in which 
rupture of the solid has occurred, if the system can pass from the unbroken to the 
broken condition by a process involving a continuous decrease in potential energy. 
In order, however, to apply this extended theorem to the problem of finding the 
breaking loads of real solids, it is necessary to take account of the increase in potential 
energy which occurs in the formation of new surfaces in the interior of such solids. 
It is known that, in the formation of a crack in a body composed of molecules which 
attract one another, work must be done against the cohesive forces of the molecules 
on either side of the crack.f This work appears as potential surface energy, and if 
the width of the crack is greater than the very small distance called the ‘‘ radius of 
molecular action,” the energy per unit area is a constant of the material, namely, its 
surface tension. 
In general, the surfaces of a small newly formed crack cannot be at a distance 
apart greater than the radius of molecular action. It follows that the extended 
theorem of minimum energy cannot be applied unless the law connecting surface 
energy with distance of separation is known. 
* Poynting and Thomson, £ Properties of Matter,’ ch. xv. 
f The potential energy of the applied surface forces is, of course, included in the “ potential energy, 
of the system.” 
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