296 REPORTS ON THE STATE OF SCIENCE, ETC. 
clamping devices for the test specimen, while the form of the piece also varies 
very much especially as regards the notch cut in it to fix the place of failure. 
These and other circumstances tend to explain why it is so difficult, at present, 
to correlate the results obtained in a complete and satisfactory manner. 
An important element for consideration is the stress distribution produced 
under load in various standard types of discontinuity, and it is proposed to 
examine some simple cases here, and discuss their bearing on the problem. 
It is evident from other cases of discontinuity already described that, within 
the elastic limit, the contour of the notch is of chief importance as regards 
stress concentration, and that whether the notch be subjected to bending or 
tensional stress, the salient facts will be much the same at the contour. There 
is, however, a considerable difference in the experimental difficulties, and very 
little to be gained in a preliminary inquiry by examining a notch under the 
former type of stress. In all these experiments, therefore, notches are cut of 
considerable size in a very wide plate of transparent material, and this plate 
is subjected to uniform tensional stress in a testing machine in order to find 
the stress at the notch contour and across the principal section through the line 
of symmetry. : 
To obtain symmetrical conditions about the line of pull a second notch is cut 
in the plate at the opposite edge. 
In some standard forms used in impact testing the notch is of V form with 
sides inclined at 45°, and with a definite radius of curvature at the apex, 
Fig.4. MAXIMUM STRESSES AT THE APEX 
"OF A 45°VEE SHAPED NOTCH OF 
FIG.3a. FOR VARYING RADII. 
0625 4:25 25 5 75 10 
6976.0.) Radius at Apex of Notch (Uillimeters) 
Such a notch is shown on the accompanying fig. 3a, one centimetre deep 
with a radius of $ cm. at the apex and cut in a plate 13 em. wide. Under load 
there is no great difficulty in measuring the distribution of stress at any point 
of a plate of this size, and when this is carried out along the minimum cross 
section perpendicular to the line of pull, a measure of the general accuracy of 
the observations is obtained, since the value [p.dx along this line should be 
equal to the load registered by the testing machine. 
The values of p and the cross stress y in:this case are shown in the accom- 
panying diagram (fig. 38), from which it appears that the stress rises to a 
maximum of 1,100 lb. per sq. in. accompanied by a cross stress g, which 
is very small except near the ends, where a maximum value of about 
200 pounds per square inch is reached at a distance of between 0.3 to 0.4 of a 
centimetre from the edge of the notch. The mean stress as given by the test- 
ing machine is 230 lb. per sq. in., while the integrated value of the curve 
of distribution corresponds with 240 Ib. per sq. in., or.about 4.8 per cent. 
in exceSs._ Assuming the correctness of the testing mahcine reading, the stress 
cdncenti'ation at the notch is 4.78 times the aVerage stress at the cross section, 
and for an angular distance of about 30° on éach side of this, the stress at the 
contéur does not fall below 4,40 times of this Value, but beyond this the stress 
falls rapidly to zero alang, thé notch contour; If, however, the radius of the. 
Sed 
