THE PHENOMENA OF RUPTURE AND FLOW IN SOLIDS. 
191 
at their melting points, but at lower temperatures there seems to be no definite 
information available. 
This assumption being granted, suppose that a piece of material which contracts on 
decrystallising is being subjected to a stress cycle just sufficient to cause repeated 
slipping in the most favourably disposed crystals. As a result, the material at the 
boundaries of these crystals will become amorphous, and the quantity of amorphous 
material will increase continuously as long as the repeated slipping goes on. But, by 
hypothesis, the unstrained volume of the amorphous phase is less than the space it 
filled when in the crystalline state. Hence all the material in the immediate neigh¬ 
bourhood will be subjected to a tensile stress, and as soon as this exceeds a certain 
critical value a crack will form. It has been observed above that the application of 
a sufficiently large hydrostatic tension may be expected to make a ductile substance 
brittle. Hence the crack may occur either in tension or in shear, according to the 
properties of the material and the nature of the applied stress. Further alternations 
of stress will cause this crack to spread until complete rupture occurs. This theory 
makes the limiting safe range of stress equal to that which just fails to maintain 
repeated sliding in the most favourably disposed crystals. 
It may be asked why such cracking does not take place in a static test where the 
quantity of amorphous material, once yield has fairly started, is presumably much 
greater. The answer to this is two-fold. In the first place, if the material becomes 
amorphous round all, or nearly all, the crystals of a piece of metal, it is evident that it 
will contract as a whole and no great tensile stress will be set up. In the case where 
only a few crystals yield, the tension arises from the rigidity of the unchanged surrounding 
metal. 
In the second place, even if some crystals do crack, the cracks will not, in general, 
tend to spread through the ductile cores of the neighbouring crystals, unless the applied 
load is alternating, on account of the equalisation of stress due to yield. 
The safe limit of alternating stress will usually be less than the apparent stress 
necessary to initiate yield in a static test, on account of initial stresses, including those 
due to unequal contraction of the crystals. 
The theory indicates that the cracking of the first crystal marks a critical point in 
the history of the piece. At any earlier stage the effects of the previous loading may 
be removed by heat treatment, or possibly by a rest interval, but once a crack has 
formed this cannot be done. True, the tension may be relieved and the ruptured 
crystal may even be compressed somewhat, but this cannot, in general, close the crack, 
as cracking is not a “ reversible ” operation. An exception may occur if the top 
temperature of the heat-treatment is sufficient to bring the molecules on either side 
of the crack within mutual range by thermal agitation, but it is unlikely that this 
can happen save in the case of very small cracks. 
If this theory is correct, it appears at first sight that the phenomenon of fatigue 
failure must be confined to substances which contract on decrystallising. This, however 
