COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS, 329 
by the formation of numerous small cavities along the gliding surfaces, so that 
the action may be not inconsistent with the reduction of density so commonly 
recorded in experiment. ‘l'hat such cavities are formed on the gliding surfaces 
may be inferred also from many phenomena associated with mechanical fatigue. 
It is highly probable that the work done on the small masses that suffer the 
change is drawn in part from the strain-energy of surrounding crystalline 
masses that suffer no change of state. Were this not so, the gliding surfaces 
would doubtless spread more widely than they appear to do. The smaller the 
grain size, the smaller the volume from which a given change can draw strain- 
energy, and the greater the stresses required to attain the elastic limit. 
Few metals being free from internal strain, quantities of work must be 
stored in individual grains before external stresses are applied. These quan- 
tities doubtless contribute to the total constant energy required to effect the 
change; but at present they lie beyond the possibility of estimation. 
The microstructure of most ordinary metals being highly complex, the distri- 
butions of strain-energy between individual grains, or parts of grains, must be 
_ exceedingly irregular, particularly when—as in the case of Ferrite and Cementite 
—the elastic constants differ widely. Even in pure metals and solid solutions, 
the non-isotropic properties of the grains must result in irregular distributions 
of energy, so that some grains suffer permanent strain before others. As a 
general rule, however, we may assume that the ratio between the maximum and 
_ mean intensities of strain-energy will be nearly constant unless the grain size is 
abnormal, so that the mean value may be expected to follow the law governing 
the maximum. The ratio between the elastic limit and the yield-point may be 
closely related to this irregular distribution of energy. 
In view of these considerations, and in spite of the numerous uncertainties 
of detail, it seemed to the author probable that the strain-energy per unit 
volume might attain, at the elastic limit, a nearly constant limiting value inde- 
pendent of the simple or complex nature of the applied stresses; or if the 
strain-energy were found to vary appreciably and definitely, that its changes 
“might afford a serviceable clue to the investigation of the more complex 
phenomena of strain. On plotting the graphs to represent the hypothetical 
values of the elastic limit given by the equation 
(X24 ¥24Z2)—27 (YZ+ZX+XY)=F? 
where F signifies the elastic limit in simple tension, it was found that the 
experimental loci were very close to the hypothetical, not only for compara- 
‘tively pure metals, but also for those of more complex structure, such as 
Pearlitic steels. Judging from the results obtained in a variety of applications, 
the above relation gives, in tho cpinion of the author, a very reliable measure 
of the relation between the elastic limits. 
_ It is not suggested that the non-ductile fracture of a brittle material, or 
even the ultimate strength of a ductile metal, is governed by the thermo- 
dynamic considerations that have been set forth. Even the yield-points are only 
approximately concerned, and the stricter application is limited to the relation 
etween the elastic limits. 
; 
b 
; 
. 
en thom 
VI. 
Alternating Combined Stress Experiments. 
By W. Mason, D.Sc., and W. J. Deuanzy, B.Ena. 
In 1914-15 some tests on the dead mild steel furnished by the British Associa- 
ion Committee on Complex Stress Distribution were published.1 These tests 
included alternating torsion and alternating bending, but these straining actions 
were each applied separately. The experiments now described have been made 
during the past ten months upon the same batch of steel; but in these later 
tests the alternating bending and torsion were simultaneously applied. The 
yes. 
_ 1‘ Alternating Stress Experiments,’ Proc. Inst. Mech. Eng., January-May, 
1917. 
1921 AA 
