COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 361 
A large part of the total quantity of heat evolved during ductile strain is produced, 
doubtless, during the gliding movement and therefore after the occurrence of the 
change of physical state which, according to the Beilby theory, must occur before 
gliding is possible within a crystal. This part of the energy is drawn from the strain- 
energy of crystalline layers on either side of the slip-band, which layers are thereby 
relieved of further tendency to glide until restrained by change in the applied forces. 
The period of duration of any one glide is probably limited to the short period of time 
during which energy is transmitted, with the speed of detonation, across short dis- 
tances proportional to the pitches between adjacent slip-bands, pitches which depend 
on the configurations and elasticities of the grains and their boundaries. There is 
little evidence to suggest that fatigue is directly due to repeated to-and-fro slipping on 
one and the same series of slip-bands ; and it seems highly improbable that this is 
the real nature of the action that leads to fracture. The slip-band is stronger than the 
original crystal, and less liable to fail under a second application of the load. 
The complex action of gliding may be likened to the release of a spring resisted by 
a dashpot containing a very viscous liquid that congeals when the exhausted spring 
is no longer able to supply the energy required to keep the liquid warm. The incom- 
pleteness of this analogy is one of its more interesting and valuable features: It is 
apparent that energy would have to be supplied to melt the dashpot initially, before 
the release of the spring could supply further energy to compensate the loss of heat 
by conduction and thereby maintain motion. 
This initial quantity of energy is discussed in the next section. The author con- 
ceives that the energy with which the first few molecules are endowed, as they leave 
the crystalline lattice and enter the vitreous assemblage, is supplied by the strain 
energy between these molecules and their immediate neighbours in the lattice, and 
is intimately related to the limiting value of the strain-energy required to bring the 
metal to its elastic-limit. ; 
Second Law of Thermodynamics in relation to Change of State. 
When one and the same change can be produced in matter at a given temperature, 
by the agency of different forces acting in manners that are thermodynamically 
reversible, the work done by these forces in producing the change is always the same. 
Applications of this principle in the theory of heat engines are well known, and other 
applications are established in physics and chemistry. 
The application of the principle is fraught with difficulty on account of the 
incidence of the phrase ‘thermodynamically reversible.’ If the quantity of work in 
question is measured experimentally, the observed values will be more or less accurate 
according as the experimental processes approach, more or less closely, to the ideal 
of reversibility ; or if the quantity is calculated theoretically, the process of change 
considered must be ideally reversible although not necessarily such as can be carried 
out in any actual experiment. 
In contributions to the reports for 1919 and 1921 the author showed how this 
principle might be applied to deduce an approximate relation between the elastic 
limits of a ductile metal for different simple and complex stresses ; and showed that 
that relation was approximately fulfilled in the wide range of experiments covered 
by published data. The principle will now be applied to deduce the thermal conse- 
quences of the dual process of decrystallisation and recrystallisation which has already 
been described as being conceived to be the cause of mechanical hysteresis and of 
fatigue in metals. 
The change from the crystalline to the vitreous state, in the process of ductile 
strain, is followed by consequences that are far from reversible. In the presence of 
any shear-stress, gliding ensues, and the action of the shearing forces is resisted by 
viscous friction, so that large quantities of strain energy are converted to heat. On 
account of these complications the total quantities of work actually absorbed are 
usually much greater than the invariant quantity required to effect change in a 
reversible manner. In the author’s earlier papers, the resilient strain-energy alone 
was taken as a close first approximation to the invariant quantity. 
In attempting to calculate the ideal invariant quantity in terms of the applied 
stresses and the elastic constants of the metal, we are confronted with two funda- 
mental difficulties as follows: (1) On account of the non-isotropic properties of 
crystalline matter, work done on an ordinary test-piece, containing large numbers 
of grains, is not uniformly distributed among those grains. (2) Itis difficult although 
