with phase difference 90°, the maximum of bending moment coincides with zero 
torque, and vice versa; so that friction must have diminished to zero at the 
time when the effect is measured. 
But another circumstance must be considered. Suppose the specimen to be 
simultaneously stressed, and consider the instant when the torque is a maximum 
and the bending moment zero. ‘There still remains the bending due to 
hysteresis; and application of the torque to the bent specimen would give a 
reduced torsional stressing and straining at the parts deflected away from the 
axis of the specimen by this hysteresis bending. But a rough calculation shows 
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: COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS, 335 
% 
» 
Ne 
] 
that the observed effect is too large to admit of this explanation, the hysteresis 
bending (though this was not measured) being evidently too small. The authors 
cannot venture to attempt an explanation of this phenomenon. Since the ranges 
of strains in combined tests agree substantially in magnitude with those under 
: the same ranges of stress applied separately, it might appear that the work 
done in a combined cycle would be equal to the sum of that done in the same 
cycles applied separately. But this cannot be assumed, since the width and 
shape of the corresponding hysteresis curves may not be similar. he authors 
have not as yet attempted to measure the width of the hysteresis diagram; and 
until this is done it seems too early to attempt any explanation. 
. Remarks on Component Strains with Phase Angle Zero. 
Turning now to the two tests with the bending and twisting in phase with 
{ each other—in 117 the range of direct stress due to bending was twice the range 
_ of shear stress due to twisting ; while in A9 the ratio between these respectively 
_ was increased during the test, and during the last stage, at the end of which 
fracture occurred, the ratio was approximately 2°5. Comparison of the ranges 
of shear stress with those of Al, A7, and All, A15, shows that the average 
values of the induced maximum shear stresses producing fracture are almost 
_ exactly the same for both simultaneous and for separate applications of bending 
and twisting. The material in this as in other respects already found, con- 
_ forms .approximately to an extension of Guest’s Law to alternating stresses.® & 
_ These shear stresses are thus about 10 per cent. greater than that of the average 
_ of the shear producing fracture when the phase difference is 90° and p,=2q,. 
The component cyclic strains (elastic + non-elastic) induced towards the end 
of the last stage of the combined tests (phase angle zero) were much below those 
in the final stages of comparable tests in separate bending and twisting. Thus, 
comparing A9 with A7, the reduction in range of total torsional (including 
both elastic and non-elastic) cyclic strain is 50 per cent.; and comparing A9 
with All and A15, the reduction in total cyclic bending strain is 23 per cent. 
omparing A1l7 with A7, the reduction in range of total torsional strain is 
47 per cent. ; and, again, comparing A17 with All and A15, the reduction in range 
_of total cyclic bending strain is 36 per cent. It should be pointed out, however, 
hat the components of the alternating combined stresses at fracture range were 
| individually much less than the stresses at fracture range due to alternating 
ending and twisting applied separately. 
Principal Strains. 
Although the component strains at fracture ranges in the combined tests 
re less than the respective strains in bending or torsion separately applied to 
ifferent specimens, it does not follow that the maximum principal strains will 
be correspondingly smaller. It is therefore of interest to make comparison of 
‘the maximum principal strains. Having calculated the latter, it is easy to 
obtain’ the greatest strain difference. These quantities have an additional 
Titcrest inasmuch as strains may be assumed to follow a linear law of distribution 
from axis to skin of specimen even when the strains are no longer elastic, 
Whereas in the latter condition the stresses have not a linear distribution and 
are not accurately known. 
oe 
_ * See ‘Alternating Stress Experiments,’ Proc. Inst. Mech. Eng., January- 
May, 1917, p. 149. ; 
® B. P. Haigh. Proc. Inst. Mech. Bng., January-May, 1917, p- 190. 
? As suggested by Prof. L. N. G. Filon. 
