358 REPORTS ON THE STATE OF SCIENCE, ETC. 
TIT. 
Thermodynamic Theory of Mechanical Fatigue and Hysteresis 
in Metals. 
By B. Parker Hatan, D.Sc., M.B.EL., M.Inst.C.E£., Royal Naval College, Greenwich. 
Introduction. 
In contributions to the reports of this Committee, in 1919 and 1921, the 
author outlined a thermodynamic theory of ductile strain, and showed how that 
theory could be applied to deduce an approximate relation between the different 
elastic limits exhibited by a given metal when subjected to stresses of different kinds, 
tensile, shear or complex combinations of different principal stresses. The theory 
was summarised in a convenient quadratic equation giving the elastic limit combina- 
tion («, y, z) for a complex stress in terms of the ordinary tensile elastic limit (f) and 
Poisson’s ratio (o = 0-25 to 0-30)— 
(2?-+-y?+-2*) — 20 (y.z+2.24+2%.y) =f? 
It was shown that this theoretical relation is well supported by experimental evidence 
published by many different investigators; thus, for example, fig. 5, reproduced 
from the report for 1919, shows how closely the calculated strength of a thick-walled 
tube agrees with experimental determinations carried out with the greatest care for 
accuracy. 
7 7. 2 851 een 
6ocar) Ratio k-~External/ Internal Diameter of Tube. 
Fig. 5 
It is proposed, in the present paper, to extend the application of thermodynamic 
principles to investigate the problem of mechanical fatigue and the relation between 
the phenomena of fatigue and hysteresis. It will be shown that fractures produced 
by steady tensile stress, or by alternating or pulsating stresses, have certain features 
in common ; and that these indicate an action distinctly different from that ‘ gliding’ 
action which affords a sufficient explanation of ductile or plastic strain. In the view 
of the author, fatigue and hysteresis are associated with, and directly due to, a dual 
process of decrystallisation and recrystallisation, substantially equivalent to the 
dual process of solution and recrystallisation that was shown, in 1861, by the late 
Professor James Thomson, to occur when a crystal immersed in its saturated solution 
is subjected to stresses tending to change its shape. Such a process is associated with 
thermal actions; evolution, absorption and conduction of heat, and with the con- 
version of mechanical work to heat; and is subject to the established thermodynamic 
laws that govern also the actions of working substances in heat engines. 
An introduction to these thermodynamic relations will be found in two papers 
published by Thomson in 1861. In discussing the apparently plastic flow of ice, 
