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COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS, 092 
and in the following year the theorem was verified in experiments carried out 
by Lord Kelvin, then Professor William Thomson. 
: Considering the Carnot cycle of operations in an ice-water heat engine 
_ operating in a small range of temperature near the treezing-point, Thomson 
showed that the work done in a cycle using a difference of pressure dp, acting 
through the small change of volume (V—v) that occurs when ice changes to 
water, could be equated to the work done by an ideal heat engine receiving 
the latent heat, L, of the water produced and working through a range of 
temperature equal to the corresponding depression of the freezing-point. Thus : 
dp (V—v)=L.dT/T 
whence dT /dp =(T/L) (V—») 
where dT/dp is the rate of fall of the freezing-point with rise of pressure. 
In establishing this expression, ‘Thomson considered only the influence of 
fluid-pressure, acting equally in all directions; but in a later paper, of 1861,4 
the application of thermodynamic principles was greatly widened. He then 
states: *. . . I soon positively formed the opinion that any stresses whatever, 
tending to change the form of a piece of ice in ice-cold water (whether these 
stresses be of the nature of pressures or tensions—that is, pulls or pushes—and 
whether they be in one direction alone, or in more directions than one), must 
impart to the ice a tendency to melt away and to give out its cold, which 
will tend to generate, from the surrounding water, an equivalent quantity of 
ice free from the applied stresses.’ The italics are Thomson’s, and appear 
noteworthy in relation to the straining of metals. It would seem that the 
action of gliding may be not unlike the action pictured by Thomson. 
It does not appear that Thomson proceeded to apply to metals the wider 
principle enunciated in 1861; and it has often been pointed out that the regelation 
theorem of 1849 does not in itself suffice as an explanation of the change of 
state that occurs in metals. Unlike water, most metals show a slight expansion 
when they change from the crystalline to the fluid form. 
The Thermodynamic Reversibility of the Stages of Strain. 
In applying the second law of thermodynamics to establish any relation 
between different forces that can effect a specified change, it is essential first 
to define ideal conditions such that the process of change may be reversible 
_ and isothermal. No real process being strictly reversible under working 
_ conditions, it is inevitable that some tax is made on the imagination. 
; The process of permanent strain may be regarded as comprising two distinct 
_ Stages: (a) the initial stage, in which the metal is strained elastically until 
_ the first molecule leaves the ‘ continuous lattice’ of the crystal to enter the 
* discontinuous assembly ’ of the vitreous phase; and (6) the subsequent stage, 
in which, in consequence of the changed physical properties of the metal, 
_ gliding movements are produced by any shear-stress that is applied. 
é It is not suggested that the second stage approximates to a reversible 
_ process. Usually pictured as viscous gliding, but probably more complex in 
action and possibly akin to the process of melting and recrystallisation pictured 
_ by Thomson’s description of the action in the case of ice, the action certainly 
results in large quantities of work being converted to heat, raising the tempera- 
_ ture of the metal. Such an irreversible action affords no basis for an application 
of the second law of thermodynamics. 
It is important to note, however, that this irreversible gliding movement 
is only a consequence of the preceding change of state, and comparable with 
other consequences, such as the recognised changes in thermal and electrical 
conductivity, magnetic permeability. and chemical activity. The motion that 
‘produces permanent strain is possible only when the change of state has been 
‘produced by an earlier cause. 
The initial stage, on the other hand, exhibits the characteristics of a reversible 
process, although, admittedly, experimental reversal may be difficult of 
‘demonstration. Considerations bearing on this point may be summarised as 
follows : (1) Although the work done in straining the metal up to and beyond 
* 
t 4 James Thomson, Proc. Roy. Soc., London, 1861. 
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