394 REPORTS ON THE STATE OF SCIENCE, ETC. 
wall, but it also represents the relation between the ranges of strain and stress at any 
point of the tube-wall, provided that constancy of range of strain has been reached. 
The validity of this provisional assumption will be tested with reference to solid 
specimens. 
Alternating Torsion of Solid Specimens, 
Specimen A7 was cut from the same batch of steel as the foregoing hoilow speci- 
mens. It was tested at the various ranges of torque shown in Table II., and at each 
range the strain was allowed to reach a constant value before the next higher range 
was imposed. Since this was also the method of testing the hollow specimens (Table L.), 
the author proceeded as follows. The average value of the shear stress at fracture 
of these hollow specimens was found to be 6-14 tons per sq. in. (see Table IV.). The 
shear stress at fracture of A7 ought presumably to have approximately the same 
value; hence, as a first trial of the foregoing assumption, the real ultimate range of 
stress at the skin was also taken to be 6-14 tons per sq.in. The distribution of stress 
through the body of the specimen was, following the above assumption, taken to be 
represented by lines such as OP, RS, fig. 19 (see also fig. 18). _The’inclination of the 
line OP corresponds to the modulus C = 12-1 x 10% Ib. per sq. in. ; the point S is fixed 
by the ultimate range of strain = 1-935 x 10~*, and by NS, the ultimate (fracture) 
range of stress, which is taken to be 6-14 tons per sq. in. If the strain throughout 
the specimen is represented by a line such as RS, then the inclination of RS will be 
fixed by equating the torque imposed to the resisting torque. That is, 
N 
Torque imposed = [2e. 7, aT = q- 
This calculation (see Appendix I.) makes the inclination of the line RS to correspond 
, 7 
to a ‘ modulus’ C’ of 2-18 x 10° Ib. per sq. in., and 2 =0-18. The ratio a for the 
hollow specimens was, as mentioned previously (p. 392), 0-225. The line RS, 
with this inclination, is plotted in fig. 20. In fig 20 ORDF represents to scale the 
ranges of strain and stresses (as usually calculated) for the skin of specimen A7. 
The ranges of strain had reached constant values at the ranges of stress plotted. 
It will be observed (fig. 20) that the inclination of the line RS makes the point 
of elastic breakdown in the body of the specimen to be at R for the ultimate range 
of constant strain 1-935 x 10~%. Scaling from the figure gives ER = 5-15 tons 
per sq. in., as against 5-30 tons per sq. in. (see Table I., col. 1), which is the average 
of the four hollow specimens before cited. 
It is, of course, more than probable that, if the true distribution of stress through- 
out A7 at the ultimate range of stress and strain is represented by the lines OR, RS, 
the change of modulus at R is not a sharp one as shown on fig. 20. The stress near 
R would be represented by the dotted line, and the calculation of the resisting torque 
will be affected somewhat. ‘The error of assuming a sharp change at R will, however, 
be small, especially for the larger ranges of stress and strain. Ordinates to a straight 
line OD represent the stress throughout the specimen on the basis of linearity of stress, 
at the epoch when the range of strain at the skin had settled down to OB,: the 
strain and stress at a radius 7 = OB, * (radius of specimen) at this epoch appearing 
2 
respectively as OB, and B,D,. This linear distribution of stress throughout the 
specimen is, of course, an absurd supposition, inasmuch as the material near the core 
cannot have suffered a change of modulus. On the basis of the provisional assumption, 
at an epoch when the semi-range of strain at the skin had settled down to OB,, the 
semi-range of stress would be B,S,; and the strain and stress at the same radius 
‘7? (above) would be OB, and B,S, respectively. 
The result of applying to A7 the provisional assumption regarding distribution 
of stress seemed to the author to bring that test so nearly into line with the tests 
of the hollow specimens that he made the torsional tests now to be described. 
Confirmation of the Assumption concerning Distribution of Stress.—In order to 
obtain further evidence concerning the validity of the assumption of p. 392, tests 
were made of four specimens of another steel—the 0-35 per cent. carbon steel provided 
by the Aeronautical Research Committee. Two of these were hollow and two solid, 
and all were tested under alternating torsion. The stress was not applied in steps as 
in the former tests cited. The elastic limits of two of them (see Table III.) were 
Rn, <iy 
