276 
NATURE 
[JANUARY 21, 1904 
THE ELASTIC LIMIT OF METALS. 
OMMON SENSE, as Lebasteur has remarked, pre- 
vents us from denying the existence of a limit of 
elasticity in metals. It is. true that the smallest load 
on a test-piece will cause a slight permanent set. 
Nevertheless, such structures as iron railway bridges 
retain their shape, and if a piece of metal is subjected 
to a small stress many times in succession, recovery 
after each application becomes almost perfect. What, 
then, is the elastic limit? The Commission des 
Méthodes d’Essai of 1894 announced that it is necessary 
to recognise three such limits :— 
(1) The theoretical limit of elasticity or the maximum 
stress which does not produce a permanent strain (of 
more than a certain small amount), 
(2) The proportional limit of elasticity, within which 
the strain is proportional to the stress. 
(3) The apparent limit of elasticity, corresponding to 
the ‘“‘ breaking-down ”’ point of ductile metals. Above 
this point, perceptible increases in deformation occur 
without a perceptible change of load. 
_ With regard to these limits, M. Frémont points out, 
in a carefully reasoned article contributed to the 
September number of the Bulletin de la Société 
d’Encouragement pour 1’Industrie nationale, that no 
one can say what is the exact difference between the 
first two, and that there are theoretical grounds for 
supposing that they ought to coincide. Moreover, the 
proportionality of deformation has been called in 
question, slight irregularities having been detected 
when the measurements were made with the greatest 
care. 
These matters, however, do not greatly interest the 
practical man. It is not usual for the elastic limit of 
a consignment of steel to be tested, although it is fre- 
quently mentioned in specifications. As a general 
rule the breaking load only is measured, and it is 
assumed that the elastic limit is a definite constant 
fraction of this. In view, however, of the tendency 
of engineers to avail themselves more fully of the 
elastic limit, it is becoming more important to deter- 
mine that limit exactly. In fact, if the elastic limit 
were known with a greater degree of exactness, it 
might be possible to practise economy by using a 
smaller margin of safety than is necessary at present. 
Holding these views, M. Frémont set himself the 
task of discovering whether there is a real limit of 
elasticity, and if the anomalies mentioned above could 
be explained. Calling to mind the dictum of seventy 
or eighty years ago that a metal had passed its elastic 
limit if it had undergone a change of texture under 
stress, he proceeded to examine how far the micro- 
scopic structure of metals was altered by the first 
permanent strain. ; 
In the class of bodies with well-marked breaking- 
gown Points, such as good mild steel, it can be readily 
a served in polished sections at a magnification of 50 
Sehee uE all the grains, without exception, are 
: y deformed at what seems to be the real elastic 
imit. These bodies are nearly homogeneous, and if 
eae of a test-piece is permanently deformed, the line 
be: Ee deforined sete defined on a polished surface 
Fal ed pz coming dull, the change being 
visible even without magnification. In general, how- 
ever, the first deformations are local owing to the 
unequal distribution of stresses. It is almost im- 
possible to adjust the test-piece so that the force may 
act ina straight line in the direction of its axis, and 
so the test-piece is generally deformed obliquely. Local 
action is strikingly illustrated by the fracture of some 
cast-iron or other hard non-ductile test-pieces at a place 
in the head where the section is greater than else- 
where. 
No. 1786, VOL. 69] 
Various devices have been invented to overcome this 
defect, but in none of them is any account taken of 
the effect of stress-hardening. The effect is well 
known, and may be readily demonstrated by a simple 
experiment. Mark a prismatic test-piece with a punch, 
and then file off the mark and polish the metal. If 
the prism is then compressed between two end-pieces 
the mark will reappear as soon as the elastic limit has 
been sufficiently passed. The stress-hardened parts 
resist more than, and do not lose their polish so easily 
as, the unaltered portions of the test-piece. The prin- 
ciple is the same as in the magic mirrors of the East, 
and the effects are observable in actual tests. Traces 
of striz, file-marks, the marks made by the jaws of 
the vice in which the test-piece was held while it was 
being prepared, all reappear in the course of testing. 
Similarly, if the force in testing is not applied equally, 
the part which bears the greatest stress will be de- 
formed first, and ipso facto hardened and strengthened. 
The first giving-way of the metal causes the pressure 
to be more evenly distributed, but the irregularity of 
pressure is succeeded by irregularity of resistance, 
which continues to the end of the test. 
In some experiments on homogeneous boiler-steel 
M. Frémont found that a permanent set could be 
obtained in compression tests under loads varying from 
8-55 to 15-70 kilograms per square millimetre, but 
judging from the dulling of the polished section, the 
deformation was always local, and the elastic limit 
was not passed, except in isolated patches of the metal. 
After painstaking but vain efforts to adjust the force 
accurately, he fell back on the use of test-pieces of 
gradually increasing section. Then the first irregular 
deformations occurred in the weakest section; there 
was a local sinking and adjustment, and the discon- 
tinuous dulled lines tended to lie flat at right angles 
to the force. As the force increased the lines 
approached each other, and coalesced to form a con- 
tinuous sheet the area of which could be measured 
and compared with the stress. 
In Fig. 1 the effects of compression are shown on 
the four polished faces of a test-piece having the shape 
of a truncated pyramid. The first effects are quite 
discontinuous, the dark lines near the upper part of 
the top row of photographs showing the areas which 
have received a permanent set. In the second row 
the effect of a maximum pressure of to15 kilograms 
is shown. In the third row, under a pressure of 1155 
kilograms the discontinuous lines have coalesced, and 
the deformation has been made to advance as a con- 
tinuous sheet, the area of which amounted to 46.8 
square millimetres, so that the real elastic limit was 
found to be 24.60 kilograms per square millimetre. 
The last two rows of photographs show the effects of 
pressures of 1295 kilograms and 1435 kilograms re- 
spectively, corresponding to elastic limits of 24.80 and 
24-65 kilograms per square millimetre. The same 
metal was used as that which underwent local deform- 
ation in an ordinary trial under a pressure of 8.55 kilo- 
grams per square millimetre of the whole section. 
Similar results were obtained by M. Frémont in 
tension tests. The first deformations were apparent 
under a force of 8.5 kilograms, although the real limit 
of elasticity was certainly above 21.5 kilograms. Tests 
on thin flat test-pieces of increasing section gave re- 
sults shown in Fig. 2, where the strained parts, at 
first discontinuous, subsequently form a continuous 
sheet. 
The conditions are different in determining the 
elastic limit of the class of bodies which show no 
definite breaking-down point. The members of this 
class, which includes hard steels and metals of small 
_ elongation, are less homogeneous, and consist of net- 
| works of substances of different elastic limits. 
In the 
