COMPLEX STRESS DISTRIBUTION IN ENGINEERING MATERIALS. 343 
apparatus of existing design could not be improved, more particularly as regards the 
satisfaction of this requirement. ‘The problem is an exceedingly intricate one, but 
its essentials clearly consist in a rapid development of stress resulting from propagation 
through, and reflection at the surfaces of, the specimen, striker and apparatus. The 
application of dimensional theory requires that the presumed geometrical similarity 
shall extend to all parts of the system into which the stress is propagated, and we know 
from elastic theory that the two principal velocities with which stress is propagated 
through steel are of the order of 17,000 and 10,500 ft. per second. Now the time of 
fracture, according to the Table given on p. 94 of Dr. Stanton’s and Mr. Batson’s paper, 
ranges from one- to four-thousandths of a second, and in such time the faster wave 
would travel a distance of from 17 to 70 ft., so that many reflections of stress must have 
occurred during the process of fracture. Reflections of stress are, of course, taken into 
account by the dimensional theory, so long as absolute similarity of the specimens 
and apparatus is maintained ; but is it certain that this condition has been realised 
hitherto in every part of the apparatus which lies within 70 ft. of the point of impact ? 
It seems probable that much of the measured “‘ work of fracture”’ will have been propa- 
gated through the swinging arm (which is very stiff) into parts of the apparatus, or 
even into the ground, where it will be lost by dissipation, and that this ‘missing 
quantity ’’ of the experiment will not be a constant fraction of the whole, but will 
depend upon the time of fracture—i.e. upon the striking velocity.’ ® 
To obviate the danger of inaccuracies arising from this cause, I suggested that the 
apparatus ought to be designed with the definite aim of confining the total energy to the 
specimen, striker and anvil—the two latter parts being kept strictly to scale. ‘ All 
that seems necessary, in order to attain this object, is to design the striker and anvil 
as elongated bodies which can be slung like a ballistic pendulum so as to move without 
rotation, and to arrange that, in both, the force of impact acts at the centre of gravity, 
in a direction perpendicular to that of the suspensions. Practically no energy should 
then be transmitted through the suspending chains or cords, owing to their complete 
flexibility, and the total energy lost at impact could be determined by measuring the 
swings of both striker and anvil.’ 
Further consideration has convinced me that the chances of consistent results would 
be greatly improved if the use of a notched bar as a means of concentrating stresses 
were discontinued, and apparatus constructed for applying an impulsive torsional 
couple to a specimen of ‘ hour-glass’ form. Such a specimen could equally be relied 
upon to fracture at the waist, but the distribution of stress at fracture would be im- 
mensely simpler, and in fact should be calculable with fair approximation. Provision 
must be made, as before, for confining the total energy of the test within the specimen 
and apparatus, but this should not be a difficult matter. 
For example, the apparatus might consist of two lathe headstocks, mounted on 
the same lathe bed, and each carrying a heavy chuck. Both spindles must be free 
to turn, and the specimen would be held at one end within the jaws of the first chuck, 
whilst its other end, at the commencement of the test, ran freely within the jaws of 
the second—this second chuck being initially stationary and not tightened up, but 
provided with means for producing a sudden engagement of its jaws with the free 
end of the specimen. The test will then be conducted as follows: The first chuck, 
holding the specimen, is run up to any required speed, and left spinning freely. The 
second (stationary) chuck is then suddenly engaged with the free end of the specimen. 
Its resistance to sudden acceleration brings an impulsive torsional couple to bear on 
the specimen, which breaks at the waist. The energy of fracture can be calculated 
- the difference between the total kinetic energies of the system before and after 
racture. 
The foregoing description is, of course, merely a sketch of the essential features of 
the test proposed ; it introduces several problems of practical design which may 
take considerable time and trouble to solve. I hope that it may be possible in the 
near future to investigate these systematically. 
REFERENCES. 
1¢On the Characteristics of \Notched-bar Impact Tests.—Proc. Inst. C.H., 
vol. cexi. (1921), pp. 67-100. 
2 Loc. cit., p. 71. 3 Loc. cit., p. 71. 4 Loc. cit., p. 79. 
5 Aeronautical Research Committee, R. & M. No. 732 (1921). 
§ Loc. cit., p. 8. 7 Loc. cit., p. 8. 
