STRENGTH OF MATERIALS 599 flow continues, more slowly than before, until presently the pumps recover their lost ground and the increase of stress is resumed. Again, near the point of rupture, the flow again be- comes specially rapid ; the weight on the lever has again to be run back, and the specimen finally breaks under a diminished load. These features are well shown by fig. 12, which is copied from the auto- graphic diagram of a test > of mild steel. l Harden- 30. But it is not onlyj; iflg effect through what we may call of per- the viscosity of materials that the time rate of load- ing affects their behaviour under test. In iron and steel, and probably in some other metals, time has an- other effect of a very re- Influence markable kind. Let the of time, test be carried to any point a (fig. 13) past the original limit of elasticity. Let the load then be removed ; during the first stages of this removal the material continues to stretch slightly, as has been explained above. Let the load then be at once replaced and loading continued. It will then be found that there is a new yield-point b at or near the value of the load formerly reached ; up to this point there is little other manent set. EXTENSION FIG. 12. Autographic Diagram for a test of mild steel. than elastic strain. The full line be in fig. 13 shows the sub- sequent behaviour of the piece. But now let the experiment be repeated on another sample, with this dif- ference, that an inter- val of time, of a few hours or more, is al- lowed to elapse after the load is removed and before it is re- placed. It will then be found that a process of hardening has been going on during this interval of rest; for, when the loading is continued, the new yield-point appears, not at b as formerly, bu t at a higher load d. Other evidence that a Extension, Per Cent. Fig. 13. 25 ,> /
in '5 Z Q ""-10 U 0: "5
7
5 10 IE
xtenaion. Per Cent
Fig. 14.
change has taken place is afforded by the fact that the ultimate
extension is reduced and the ultimate strength is increased (c,
fig. 13).
31. A similar and even more marked hardening occurs when
a load (exceeding the original elastic limit), instead of being
removed and replaced, is kept on for a sufficient length of time
without change. When loading is resumed a new yield-point
is found only after a considerable addition lias been made to
the load. The result is, as in the former case, to give greater
ultimate strength and less ultimate elongation, Fig. 14 exhibits
two experiments of this kind, made with annealed iron wire. A
load of 23 tons per square inch was reached in both cases; ab
shows the result of continuing to load after an interval of five
minutes, and acd after an interval of 45^ hours, the stress of 23^
tons being maintained during the interval in both cases.
32. It must not be supposed that in a material hardened by
strain the elasticity is perfect up to the yield-points which are
shown in fig. 13 at b and d or in fig. 14 at c. Ill experiments made
for this article, it has been found that, after a piece of very soft
iron wire has been hardened (as in fig. 14) by the continued appli-
cation of a load which had caused stretching, if a small addition
be made to the load (bringing it to a value between a and the
new yield-point), although there is at first no apparent drawing out,
nevertheless if time be given the wire begins again to draw, and
a large amount of stretching at an increased pace may ensue. In
this way wires have been broken with loads considerably short of
1 The increase of strain without increase of stress, which goes on without
limit when a test-piece under tension approaches rupture, is a special case of the
general phenomenon of " flow of solids," which has been exhibited, chiefly for
coinpressive stresses, in a series of beaut if ul experiments by Tresca (Memoires sur
I'L'coulement des Corps Slides, also Proc. Jnsl. Mech. Eng., 1SC7 and 1878).
those which would have been required had the process of loading,
from the point a onward, been continued at a moderately rapid
rate. A slow process of viscous deformation may in fact be occur-
ring at the same time that the metal shows a quasi-elasticity with
respect to rapid alteration of stress. Bauschinger's micrometric
experiments have shown that after a piece has been hardened
by rest the true limit of elasticity, or the point at which Hooke's
law begins to fail, comes far short of the yield-point. He has also
shown that a long interval of rest after the set has taken place
produces a slow rise of the true limit of elasticity, 2 apparently
a slower rise than the lapse of time causes in the yield-point
itself.
83. In the testing of iron and steel the time during which any
state of (pull) stress (exceeding the original elastic limit) exists affects
the result in two somewhat antagonistic ways. It augments exten-
sion, by giving the metal leisure to Mow. This may be called the
viscous effect. But, on the other hand, it reduces the amount of
extension which subsequent greater loads will cause, and it increases
the amount of load required for rupture in the way which has just
been described. This may be called the hardening effect. When
a piece is broken by continuous gradual increment of load, these
two effects are occurring at all stages of the test. If the viscous
effect existed alone, or if the hardening effect were small, the
material would show to greater advantage as regards elongation,
and to less advantage as regards ultimate strength, the more
slowly the load .were applied. Tin and lead may be cited as mate-
rials for which this is the case. But when the hardening effect
is relatively great, as in iron and steel, the material shows less
elongation and a higher breaking strength the more slowly it is
tested. An excellent illustration of this is given by the following
experiment of Mr Bottomley. Pieces of iron wire, annealed and
of exceptionally soft quality, when loaded at the rate of 1 Ib in
5 minutes, broke with 44| R> and stretched 27 per cent, of their
original length. Other pieces of the same wire, loaded at the
rate of 1 Ib in 24 hours, broke with 47 Ib and stretched less than
7 per cent. 3 Again, it has been found that an excessively rapid
application of stress (by the explosion of gun-cotton) makes soft
steel stretch twice as much as in ordinary testing. 4 The case is
very different, however, if the material has been previously hard-
ened by strain. It
does not appear
that such varia-
tions in the rate
of loading as are
liable to occur in
practical tests of
iron or steel have
much influence on
the extension or
the strength, great
as the effects of
time are when the
metal is loaded
either much more
slowly or much
more quickly. In
fig. 15 the results
are shown of tests
of two similar
pieces of soft iron
wire, one loaded
to rupture in 4
minutes and the
other at a rate
about 5000 times
slower.
34. The hard-
ening effect which
intervals of rest
EXTENSION, PER CENT.
Fig. 15.
from load or of constant load produce, once the primitive elastic
limit is passed, has been examined by Beardsley, 5 Thurston,*
Bauschinger, 6 Ewing, 7 and others. The effect of even a few minutes'
pause is perceptible, an hour or two of constant stress has a very
marked influence, and after 24 hours or so there appears to be
little further hardening. The American Board found that iron bars,
previously stressed to about 50,000 ft per square inch, gained in
strength, by intervals of rest from stress, to the extent of about_9
per cent, in oue day, 16 per cent, in three days, and 18 per cent, in
six months. 8
35. It may be concluded that, when a piece of metal has in any
way received a permanent set by stress exceeding its limits of
2 Mitlh. aus dem Mech.-Tech. Lab. in Munchen, Heft 13, ,1886.
3 Proc. Roy. Soc., 1S79, p. 221. See also ELASTICITY, 80
< See remarks by Col. Maitland, Mir,. Proc. lust. C.E., vol. Ixxvi. p. 104.
- See Report of the U.S. Board on Tests of Metals, vol. i. section 4.
7 Proc. Bog. Soc., June 1870. Tlie autographic diagrams given in figs. 13 aud 14 are taken 'from these tests. 8 L OC. cit., p. ill.
