164 
MR. A. A. GRIFFITH ON 
grooved surface of a given type, should be capable of estimation with the help of one 
of the two hypotheses of rupture commonly used for solids which are elastic to fracture. 
According to these hypotheses rupture may be expected if (a) the maximum tensile 
stress, (b) the maximum extension, exceeds a certain critical value. Moreover, as the 
behaviour of the materials under consideration, within the safe range of alternating 
stress, shows very little departure from Hooke’s law, it was thought that the necessary 
stress and strain calculations could be performed by means of the mathematical theory 
of elasticity. 
The stresses and strains due to typical scratches were calculated with the help of 
the mathematical work of Prof. C. E. Inglis,* and the soap-film method of stress 
estimation developed by Mr. G. I. Taylor in collaboration with the present author, f 
The general conclusions were that the scratches ordinarily met with could increase 
the maximum stresses and strains from two to six times, according to their shape and 
the nature of the stresses, and that these maximum stresses and strains were to all 
intents and purposes independent of the absolute size of the scratches. Thus, on the 
maximum tension hypothesis, the weakening of, say, a shaft 1 inch in diameter, due 
to a scratch one ten-thousandth of an inch deep, should be almost exactly the same as 
that due to a groove of the same shape one-hundredth of an inch deep. 
These conclusions are, of course, in direct conflict with the results of alternating 
stress tests. So far as the author is aware, the greatest weakening due to surface 
treatment, recorded in published work, is that given by J. B. Kommers,J who found 
that polished specimens showed an increased resistance over turned specimens of 
45 to 50 per cent. The great majority of published results indicate a diminution in 
strength of less than 20 per cent. Moreover, it is certain that reducing the size of the 
scratches increases the strength. 
To explain these discrepancies, but one alternative seemed open. Either the 
ordinary hypotheses of rupture could be at fault to the extent of 200 or 300 per cent., 
or the methods used to compute the stresses in the scratches were defective in a like 
degree. 
The latter possibility was tested by direct experiment. A specimen of soft iron 
wire, about 0-028-inch diameter and 100 inches long, which had a remarkably definite 
elastic limit, was selected. This was scratched spirally (i.e., the scratches made an 
angle of about 45 degrees with the axis) with carborundum cloth and oil. It was 
then normalised to remove initial stresses and subjected to a tensile load. Under 
these conditions the effect of the spiral scratches was to impart a twist to the wire, 
the twisting couple arising entirely from the stress-system due to the scratches. It 
was found that if the load exceeded a certain critical value, a part of the twist, amounting 
* “ Stresses in a Plate due to the Presence of Cracks and Sharp Corners,” ‘ Proc. Inst. Naval Architects,’ 
March M, 1913. 
f 1 Proc. Inst. Mech. Eng.’ December 14, 1917, pp. 755-809. 
X ‘ Intern. Assoc, for Testing Materials,’ 1912, vol. 4a and vol. 4b. 
