170 
MR. A. A. GRIFFITH ON 
so that the breaking stress is 
in the case of plane strain, and 
( 12 ) 
(13) 
in the case of plane stress. 
Formula (13) has been verified experimentally. In connection with the experiments, 
interest attaches not only to the magnitude of R, but also to the value of the maximum 
tension in the material, which occurs at the extremities of the crack. This stress may 
be estimated if the radius of curvature of the boundary of the crack, at the points in 
question, can be found. 
Expression (2) gives the maximum tension as 
-•i: \J- .(u) 
P 
in case I. above, p being the radius of curvature at the corners of the elliptic crack. 
Prof. Inglis shows that this expression may also be used, with little error, for cracks 
which are elliptic only near their ends. The foregoing expressions for the stresses 
are obtained, however, on the assumption that the displacements are everywhere so 
small that their squares may be neglected. At the corner of a very sharp crack, it 
cannot be assumed, without proof, that the change in p leaves formula (14) substantially 
unaffected. 
In the case under consideration the displacements at the surface of the crack, due to 
a small tension (?R at distant points, are given by 
Wa 
h 
c 2 dR 
E 
(cosh 2a 0 — cos 2/3) 
u 
0 _ 
h 
= 0 
(15) 
J 
Whence, by resolution, the displacements parallel respectively to the major and minor 
axes are 
2dR 
which may be written 
Ux E 
c sinh a 0 cos (3 
2dR 
( 16 ) 
u y = c cosh a 0 sin /3 
iii 
2dR . , 
u x = —pr x tanh a 0 
2dU 
u„ 
E IJ coth a 0 j 
(17) 
