362 REPORTS ON THE STATE OF SCIENCE, ETC. 
not impossible to visualise a probable nature for the ideal reversible stages which, 
in any real process of change, must precede the irreversible gliding motion which 
can occur only in the changed metal. The same two difficulties are met with when 
we attempt to study the change in relation to hysteresis and fatigue. 
The reversible process of change is conceived to occur in two distinct stages. 
In the first stage the metal is gradually strained—elastically—to the stress at which 
the change will occur; and in the second stage the first few molecules or atoms are 
projected out of the continuous lattice into the discontinuous assemblage. Even 
without a detailed mental image of this latter stage, it may still be regarded as in- 
herently reversible, for if the first projected molecule struck an imaginary rigid body 
normally, immediately after its projection and before it had suffered loss of energy 
by viscous resistance or conduction, it could only rebound into the lattice and re- 
establish its position ready to make a second sortie. A number of considerations 
lead. the author to the view that the work done in the second stage, per unit volume 
of metal suffering the change, must be nearly independent of the applied stresses, or 
small in comparison with the strain-energy imparted to the metal in the first stage. 
In such circumstances the equation of constant resilience may be used, as described 
in the introduction, as a relation between the elastic limits under simple and complex 
stresses. Thus, for example, the elastic limit in shear should be approximately 
62 per cent. of the tensile elastic limit (instead of only 50 per cent., as is often 
assumed). 
On the assumption or hypothesis that fatigue also is due to consequences that 
follow from the change of physical state in the metal, and no matter exactly what may 
be the processes that connect the change of state with the opening of the crack, 
we may infer that the same quadratic equation will afford an approximate relation 
between the fatigue limits of a ductile metal under different combinations of complex 
stresses. Since the fatigue limits under complex stresses are difficult of determina- 
tion, and are still uncertain, it cannot be said that this relation has yet been verified. 
But a considerable bulk of rough evidence is available to show that the fatigue limits 
in shear and direct stress approximately fulfil the rule; and it is understood that 
recent more accurate experiments support the validity of the 62 per cent. ratio, at 
least as a close approximation. 
Tensile and Fatigue Fractures: Comparison and Cause. 
Although the tensile and fatigue fractures of a ductile metal commonly differ 
widely in appearance, the two have features in common; and the differences are of 
degree rather than fundamental. In both types of fracture, it is considered, rupture 
is associated with and directly due to an action other than that gliding which is 
regarded as a sufficient explanation of plastic shear strain. 
The tensile fracture of a ductile metal exhibits two characteristically different 
zones. The outer annulus, of ‘ cup and cone’ form, is admittedly due to shearing : 
the surfaces coincide with the planes of maximum tangential stress, as in the typical 
plane fractures observed in torsion tests. Within the annulus is observed a second 
zone of characteristically different appearance, nearly flat in many metals, granular 
or even toothed in others. Since this second zone lies on the plane of symmetry of 
elongation, precisely on the cross-section of minimum area, while the surfaces of the 
cup and cone run outwards to edges of greater diameter, it is inferred that the cracking 
of the inner zone is the determining cause of fracture, and interrupts the continuous 
gliding movement of shear which, in other circumstances, might continue further 
without necessarily resulting in fracture. The relative size of the two zones differs 
in different metals that exhibit different local elongations and reductions of area ; 
and varies also with the character of the applied stress, whether steady, pulsating, or 
alternating. The cup-and-cone annulus is to be regarded as characteristic of duc- 
tility, and the inner zone of inherent or induced brittleness. 
In a ductile metal, brittleness may be induced by the action of the complex stresses 
associated with local elongation, which sets in at a particular stage of elongation, 
when the capacity of the metal for hardening—by the cold-work of elongation—falls 
below a certain limit that is unable to compensate the reduction of area. In this 
physical sense, the ultimate strength of a ductile metal is not directly related to its 
resistance to rupture, but is related to its cold-working capacity only. As there 
appears to be much misconception of this point, it may be well to put the matter in 
