FATIGUE OF METALS

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000200020019-8
• Release Decision: RIPPUB
• Original Classification: R
• Document Page Count: 9
• Document Creation Date: December 22, 2016
• Document Release Date: May 15, 2012
• Sequence Number: 19
• Publication Date: May 9, 1952
• Content Type: REPORT

4
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F~T~GJJ~OJ METALS
Ya I. Feidshtein
authors:
I\1. S. Akulov
I. ?. azin
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STAT,
STAT
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y
? ternating load, has an
portant excep'~a-ona.L
metal under the acta.on of al
. in ractice and in the solution of
s~.gnsf~.c~.nce both p
in the field of mets,llophysics? A
certain theoret~.cal questions
been dedicated to the study of the
large number of works have
Nevertheless, the physical mechanism of
e
to the destruc'bion of a
leading
The phenomenon oI fatigue ,
phenomenon of f ata.gu
' uficaently clarified. It is known
omenon is stall. a.ns
h
en
this p
itutde
le s~ a t a given amp/
that after a definite number of cyc
?on A , the metal is destroyed The de-
. the v ,r
~.bration tens~. . ''
of
a
revoked by the ap;.earance of f atigue cracks
struction is directly p
having reached a certain critical size,
w~rich, once. formed and i?rl and con-
at the expense of the reda.strabut
f tly begin to grow
at the edge of the cracks themselves.
cen'tration of the tens~.or~s reduced
discov?.ry of the nature of fatigue is
Thus the problE;m of
'ormatian and development rr~chanism
to the clarifa,cation of the f
of the cracks (lanainat10n ), the further growth of whjch leads to
destruction.
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' l ratios establishing the connection
The existing emparlca
between A and N! are extremely varied. Thus Lien, Rose and
Awhere C and ~ are the
Cunnl,ngham (2) gave us the forma
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constants depending upon the material and the experimental system.
Stomoyer (2) on the basis of his experiments arrives at the ratio
A .+ C (-7) ) where d is the cycle amplitude in
the presence of an infinite number of cycles. These norms however,
can be applied only to a very narrow variation area o!' H and
nrovan and N. N. Afanastev (5,6), examining fatigue as a special
kind of plastic deformation, arrive at a ratio of the type
Br:: f
L)Vn
(1)
where B is the coeif'icient depending upon the shape of the har-
dening curve, dy and are the tensions corresponding to the
limit of elasticity and the limit of the plastic flow determined
by the hardening curve, ant is the maximum tension in the so
cala.ed 'tplastict' region depending upon external tension, and f is
the number of cycles up to the appearance of lamination in the
plastic region. This formula is qualitatively in agreement with
experimental results. Difficulties arise, however, in the quan-
titative co~rtparison with experimental results, for this theory
does not gave a quantitative connection between 141 and d , on one
side and the dire c tly y de termi ne d value s /\/ and A on the othe r.
We can therefore accept the opinion that the "phenomenon of
metal fatigue is such a complicated question that up to this time
it is far from being developed to a degree corresponding to the
contemporary condition of machine building" (1). In the present
work, on the basis of a simple physical model of the formation of
initial fatigue cracks, we establish a ratio between A and
which is in good agreement with the experimental data of various
It1
14!
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 7~LFI
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?uthors.
As we know, homogeneous, weli-annealed, fine metals with a
well expressed lattice have a very low elasticity limit. Under
the action of very small forces there appear shears, more often
than not along the planes most thickly populated with atoms, and
there appear twinnirtgs which lead to plastic defornta,tion in the
metal. In the course of plastic deformation there takes place a
hardening of the rr~tal with the consequent appearance of a very
pronounced nonhomogeneity in the resistence to shearing on the
part of the various parts of the metal. At the same time there
appears a concentration. of tensions ne~ir to those blocks or
regions of the crystal which most resist the shearing. Let us call
these regions ttrneshingstt. NeLl,r to such rneshings the internal ten-
sions are much stronger than their average intensity.
Let us note that with these esentially "static" fluctuations
1
of the tensions which under the given condition of the metal have
no relation to time there can take place uninterrupted tension fluc-
tuations regulated by the heat motion of atoms (Debyets waves).
These tensions fluctuate and are added to the ttstatictt tensions.
However, these "dynamic" tension fluctuations are generally much
smaller than the static ones and we will not take them into con-
sideration here.
Let now a sign-charging load with an amplitude A act on the
metal in the absence of a constant load (meaning that the average
tension of the cycle is equal to zero). There also is a certain
number of meshings with such a large concentration of tensions near
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t4`~Y
 ^
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them that suxpasses a certain critical value A0,
if .' the amplitude
there occur breaks in the meshings leading to the lamination of th
A
metal in those places. If the arripl~.tude is smoker than. A, then
the meshings do not break, or so few of them break than the rrietal,
under a regular load during a very large number of cyca.es is not
destroyed.
It is easy to see that near each center where a lamination
takes place, there occurs a redistribution of tensions as a result
of which, near to a given destroyed meshing, new localizations of
tensions can be created next to other meshings. We thus obtain a
chain mechanism of destruction of existing centers of localization
and the formation of new ones to replace them after each period
of the sign-changing loading. The vez'y breaks in the meshings which
lead to the formation of laminations, also lead to the formation of
tension concentrations next to new meshings. he following cycles
y the newly formed centers with the subsequent generation of
destro
still new ones. With such a mechanism of destruction the time of
one sign-changing cycle will have no effect on the general larnina-
lion area for one cycle.
With the growth of the amplitude of the sign-changing load
to cLA the lamination area for one cycle will also grow. This is
because the tension near every localization center gradually decre-
ases. Therefore near each such center there exists an area of sub-
critical tensions in which at a given amplitude A there is no
lam With the growth of the amplitude to A the destruct-
~.na~,ion.
ion partially tegins to expand also to this subcritical area. As
a result the lamination for one cycle increases by a certain value
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^
The size of the additionally invaded subcritical area wall be
larger in proportion to the size of the critical area around which
is disposed the area of subcritical tensions. rfhus the value
is proportional to 5 , where S is the total area of lamination
in a unit of volume for one cycles i. e?,
. SScLA (2)
is the coefficient of proportionality. From (2) there
where Q
follows
(3)
A o that is, given A 4a in the sample for one cycle
where A > ,
here appear laminations with an areao in one unit of volume.
t
As a consequence of the nonhomogeneity of the sample the number of
laminations referred to the unit of volume may be different. We
will be interested in the future in those areas of the metal which
correspond to the maximum of emerging laminations. Such a part
x
of the metal we will call the region of fatigue danger.
Figure 1. Fatigue curves for Figure 2. Fatigue curves for
Carbon Steels, (a) -- 0.82 pex-cent steels with additions of Mo, Cr,
of C. (b) _- O. percent of C. W. (a) -- O.~l percent of Mo at
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x destruction x destruction
x destruction x destruction
o no destruction o no destruction
o
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Figure 2 C continued
app degrees Centigrade.
(b).- p,1
percent of No at I~00 degrees Centi-
grade. (c) ~.p,i percent of Mo
at 20 degrees Centigrade. (d)
~. percent Cr, 13.3 percent Ni
and 2.02 percent of W at 20 degrees
Centigrade.
Tf the average lamx 'natior1 area for one cycle remains constant
then for n cycles the whole lamin-
during a large number of cycles,
ation area
sue.
When(~ reaches a certain critical value the change in
~r
? rorlul begins to a:f f'ect the general field
the internal structure st ~ y
of tensions. As a result a:f this a large crack appears. One may
is related. only to the material of the
say that the value ~
he size of the amplitude, in other words is
sample and not Lott
not related to how the critical size of larctirlation is reached.
number c,f cycles I~f ,which is a.ndispensable
(.,orrespondingly, the .
'ng of the critical lamination area, is detern~ned
for the reaching
by the ratio
w
S::s ~ (~)
From here we have
0
Substituting (2) in (6) we gE
0
?111M c (A A d.)
4"or A>A0
+-0e t1 a.
(6)
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PS's"
d theoret~.cail ratios we used the ,ems
To oheck the obta~.ne
riauS authors (2,7). From the\curves we see that
mental data of va
A ~~p is a ~tr~.ig~~
the th,eore
ticrelation of to log/ with ' tion in relation to the absea.ssa for
line tirith a varya.ng . ~.ncl~.na
and 2). the ex~eri.tr,ental paints,
diffez'eflt ma~erials (see figures 1
ence fit well on this straight line.
although giving some c~.verg ,
Submitted on 8 February i9~l
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ULr-
Bibliography
acid the Cyclic strength
towable Stresses in Machine Building
I. A. Going, A~.
of the Metal, 197
Uzh. Oaf, Fatigue of Metals, 1936
G
o
Win, d. Phys?, 20, 113 (1934)
-. 30 N. Akulov U. K. Raewsky,
, N. S. ,Akulov d N. Z. Miasav, ZhTF, 18, Na 3, 389 (19,8)
~, anrY
N. Aj'anas ' yeV, Zh. TF lli., 638 (19th)
Proc. Roy, Soc., 171, 79 (1939)
6, E. Qrowan,
7. M. Hempel G. Tillmann, Mitteil KWI, Eisenf. 1$, 12 (1936)
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