COMPLEX STRESS DISTRIBUTION IN ENGINEERING MATERIALS. 327 
different points near the opening have been evaluated in terms of the uniform applied 
stress acting across a remote section perpendicular to the direction of loading. In the 
case of a circular hole, the maximum intensity of stress occurs on the margin of the 
opening, on a diameter perpendicular to the direction of the applied load, and is three 
times as great as the uniform stress at a point remote from the hole. If the metal 
behaved elastically, therefore, a plate stressed in this manner might be expected to 
suffer fatigue, and crack when the applied stress was only one-third of that required 
to crack a similar plate without the hole. 
The concentrations of stress induced by discontinuities of any form, in uniform 
plates, have been investigated also by the methods of optical analogy developed by 
Filon,’? Coker,4 and others; and in cases which admit of mathematical analysis, 
the results obtained by optical means agree with those calculated mathematically. 
It is inferred that the materials used in the optical experiments are sufficiently 
elastic for the purpose, and that the optical method may be used with confidence 
when the mathematical analysis proves intractable. The mathematical and optical 
methods are regarded, therefore, as approximately equivalent, and may be adopted 
alternatively, according to the circumstances of the case. Both, however, are based 
on the hypothesis that the metal behaves elastically within the range of stress under 
consideration. 
Since actual metals seldom behave elastically within the ranges of stress that pro- 
mote fatigue, it is to be expected that the conclusions derived from mathematical 
analysis may require to be modified, in different ways for different metals, when the 
object is to deduce the increased liability to fatigue caused by a discontinuity. In a 
British Association Paper (1922) and acontribution to the Report of this Committee,® 
it was shown that in the case of mild steel plates subjected to pulsating stresses— 
such as vary without changing their direction—the load required to cause fatigue 
was nearly as great as that required to cause yield in steady tension. This degree of 
immunity was attributed to the beneficial effect of the slight plastic strain, resulting 
in a redistribution of the concentrated stresses. 
Further experiments have since been carried out with a harder steel; and, in 
order to facilitate the comparison between elastic theory and direct experiment, the 
flat strips used as test-pieces have been pierced with only a single small circular hole 
on the centre-line. 
Experimental Data. 
The metal used in the tests was a cold-rolled strip of high-tensile steel, kindly 
supplied by Mr. J. D. Brunton, of Musselburgh, and was received in a coil that could 
be unwound and straightened without hammering. Surface blemishes were only 
slight, and were removed with fine emery before the pieces were tested. The section 
of the strip measured 1-50 in. by 0-:064in. Ina preliminary tensile test, the elongation 
obtained on fracture measured only 1-4 per cent., although the local reduction of 
area at fracture was 42 per cent. The yield-point and ultimate tensile strength were 
nearly coincident at 36:3 tons/in.2. The extensions under successive loads, being 
plotted, were found to give a curved graph that shows no definite limit of proportion- 
ality. A strip that was loaded repeatedly gave a graph sufficiently straight to indicate 
an approximate value of Young’s Modulus, namely E=12,400 tons/in.”. The metal 
is regarded as typical of high-tensile cold-rolled strip of good quality. 
The fatigue tests were carried out in a Haigh electro-magnetic testing machine 
fitted with clamps similar to those described in the communication to the Report for 
1922 ; but the clamps were fitted with special copper washers that effectively minimised 
the difficulty initially experienced from fracture at the grips. The frequency of 
loading was in all cases 2,000 cycles per minute. 
The applied stress acted as a pulsating tension, being compounded of a steady 
tension §, and a smaller alternating load A. Thus the tension varied from a maximum 
(S + A) to a minimum (S — A). 
In the first series of tests, the immediate object was to find the limiting value of 
the alternating component A, which, in combination with a fixed steady component S 
arbitrarily chosen as 18 tons/in.?, produced a fatigue fracture in an unpierced strip. 
The test-pieces used were 6 in. in length, and gradually reduced in width from 1} in. 
at the ends to 4 in. along the mid-part. The value of A was changed for successive 
strips; but was maintained constant for the testing of each individual strip, except 
in some cases (marked* below) when a second test was made on a strip which remained 
unbroken after an earlier one. The endurances recorded are given in the following 
