360 REPORTS ON THE STATE OF SCIENCE, ETC. 
On the assumption that Hooke’s law is fulfilled, the work done by external forces 
in straining unit volume of an isotropic substance under a combination of three 
principal stresses, x, y, and z, may be expressed in terms of Young’s modulus, HB, and 
Poisson’s ratio, o, thus: 
te + y? + 2)—26 (y.z24+ 2.2 + 2x.y)] 
Under a single tensile stress, f, this reduces to f?/2E ; or under a single shear stress, q, 
the work is g?/2C, where C is the modulus of rigidity. It is conceived that these 
quantities of work are stored in the metal in virtue of changes in the relative positions 
of the molecules or atoms, or in their orbital or oscillatory movements. In a metal 
that is thermodynamically elastic, the resilience and, doubtless, also the internal 
arrangement and motions of the molecules or atoms depend wholly on the state of 
stress and temperature. 
Again, on the assumption that Hooke’s law is fulfilled, the quantity of heat ab- 
sorbed from surrounding bodies by unit volume of an isotropic substance, strained 
without change of temperature, may be expressed : 
Work per unit volume = 
Heat per unit volume = 6.a.f 
where a, is the coefficient of linear thermal expansion and f is the tensile stress applied ; 
@is the absolute temperature. 
The above expressions were used by Lord Kelvin to calculate the slight fall of 
temperature that occurs when a test-piece is extended adiabatically ; and, also, the 
ratio in which the adiabatic modulus slightly exceeds the ordinary isothermal value. 
It appeared to the author, at one time, that hysteresis might be due to conduction 
effects associated with the transferrence of such small quantities of heat into or out 
of the test-piece as a whole ; but simple calculations show that the influence is of too 
small an order, and usually quite negligible. Moreover, the slight conduction effect 
varies, with stress and frequency, in a manner quite different from the action of 
mechanical hysteresis. In metals of highly complex microstructure, comprising 
intermingled constituents with widely different expansibilities, the conduction effect 
may be the cause of a perceptible part of the total observed hysteresis; but in general 
it appears that a more important cause of hysteresis must be sought in another action. 
First Law of Thermodynamics in relation to ‘ Gliding’ Strain: 
Any heat given out by a test-piece, during a cyclic process of strain in which the 
piece is restored to its original dimensions, must be derived from one or other of two 
sources ; viz., work done by the forces applied in straining the test-piece, or change of 
internal energy associated with change of physical state. In the case of ductile 
strain, the heat given out is almost exactly equivalent to the work done on the test- 
piece; the quantity of metal that suffers change of state and energy, in the slip-bands, 
is but a very small fraction of the total mass. 
Since the whole of this large quantity of energy is converted to heat within the 
relatively small masses that suffer the change of state and the subsequent gliding 
movements that result in plastic strain, it follows that the changed metal must attain, 
temporarily at least, a temperature much higher than that reached by the test-piece 
asa whole. Unless the specific heats differ more widely than is currently believed, the 
temperature ratio must be nearly the inverse of the mass ratio; and the changed 
metal must attain a temperature of the order of a bright red heat sufficiently high to 
account for a variety of phenomena which, otherwise, might appear inexplicable. 
So long as the changed metal is maintained at this high temperature, we may 
expect that it will behave as a highly viscous liquid and act as a lubricant between 
adjacent crystalline masses, allowing of gliding movements such as result in plastic 
strain. But films as thin as slip-bands may be expected to cool rapidly, in contact 
with cold unchanged metal, and when the vitreous metal cools it becomes hard and 
rigid, acting as a cement between the crystalline masses. Thus the dual nature of 
the vitreous-liquid, required for the explanation of ductile strain, is completely in 
accord with the idea that the energy available on formation is rapidly dissipated by 
conduction. It is-interesting and significant to note that the more ductile metals 
are commonly good conductors of heat. 
a ae 
