COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 325 
pieces of various forms, the author has reached the conclusion that this object 
may be attained in most cases by making the radius of the fillet at the change 
of section at least five times the working diameter (or corresponding dimension) 
ot the test-piece. 
The only other type of stress concentration which is likely to modify the 
results of mechanical tests is that due to surface scratches. As has been seen, 
advantage may be taken of the scale effect to render this factor unimportant, by 
making the scratches sufficiently fine. Scratches having a depth of the order of 
10-' inch, such as are produced by No. 0 emery cloth, or by grinding with a 
wheel of about No. 80 grit, would appear to be satisfactory in all ordinary cases. 
9. Allowance for Stress Concentrations in Design. 
The author has often been asked by designers what measures can be taken to 
guard against the occurrence of dangerous stress concentrations in practice. It 
is clear from what has already been said that nothing like a complete answer to 
this question is possible at present. All that can be done is to lay down 
approximate rules based not only on calculable cases and such experimental facts 
as have so far been collected, but also very largely on personal judgment. The 
subjoined recommendations, which embody advice which the author has given 
from time to time in the past, may, perhaps, be found useful pending the develop- 
ment of more rational methods. It may be remarked that they have not infre- 
quently been successful in overcoming difficulties encountered in practice. They 
are intended to apply mainly to members possessing some ductility and subjected 
to periodically varying loads. 
in the first place, the radius of the fillet in a re-entrant corner should be at 
least a quarter of a certain dimension which may be called the ruling dimension. 
lor grooves, such as screw-threads and keyways. the ruling dimension is the 
depth of the groove. Alternatively, in a continuously grooved surface, such as 
occurs in a gear wheel, the root thickness of the teeth or ridges may be used if 
this is less than the depth. For sudden bends, as in crankshafts, the ruling 
: dimension may be taken to be the radius of the shaft (or the corresponding 
dimension). At a change of section on a shaft, the smaller radius or the differ- 
ence between the radii, whichever is the less, may be taken. 
The above values of the radius of fillet should be regarded as minima and 
should be exceeded wherever possible. 
In addition, an allowance should be made for the weakening effect of the 
) 
j 
stress concentration. It is impossible at present to give any very definite idea 
of the magnitude of this factor, as it appears to vary so greatly with the nature 
of the material and the kind of load. With the worst materials and pure 
alternating loads it may be necessary to allow the full theoretical concentration 
factor, which with the above values of the radius of fillet will usually be about 
_2to 6. In more favourable cases, e.g., where the load fluctuates but does not 
_ change sign, much lower values may be used. Probably a factor of 2 will be 
found satisfactory in the majority of such cases. 
As has been seen above, plastic flow can be of great value in reducing the 
effect of local stress intensifications. Hence two qualities are desirable in the 
material of a member liable to break at a point of stress concentration. In the 
first place, the fatigue limits should be as wide as possible, and in the second 
the range of stress within which plastic flow is absent should be as small as 
possible. 
10. List of References. 
(1) “Stresses in a Plate due to the Presence of Cracks and Sharp Corners.’ 
é C. E. Inglis, Proc. Inst. Naval Architects, March 14, 1913. 
_ (2) ‘ The Applications of Polarised Light to Mechanical Engineering Problems of 
Stress Distribution.’ E. G. Coker, Inst. Mech. Eng., February 1913. 
‘ “Polarised Light and its Applications to Engineering.’ E. G. Coker, 
4 Royal Institution, February 1916. 
(3) ‘The Use of Soap-films in Solving Torsion Problems.’ A. A. Griffith and 
G. I. Taylor, Inst. Mech. Eng., December 14, 1917. 
Reports and Memoranda of the Advisory Committee for Aeronautics, 
Nos. 333, 334, 392, 399. 
