THERMODYNAMICS OF PLASTIC DEFORMATION

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000200020018-9
• Release Decision: RIPPUB
• Original Classification: R
• Document Page Count: 10
• Document Creation Date: December 22, 2016
• Document Release Date: May 15, 2012
• Sequence Number: 18
• Publication Date: May 9, 1952
• Content Type: REPORT

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N. S. Fastav
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THERT4OD N 1ICS OF PLASTIC DEFORMATION
STAT'
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'RMODYNAMICS OF pG~S~'1C Dkb1R1'4AT10N
N. S. Fastov
presented by
Academician p. An Rebinder
8 March 191
oration of materials the relation between the
In plastic defor
the deformation tenser ~Lk is net, generally
strews tensor 6and
ueda However, this relation becomes single
speaking, single val
valued in the case of the so-called initial charge, when the
does not diminish with the passing of
~.ntensa.ty
shearing strain
time . As shown in (1, 2) , the free energy of a plastically de
formed body during the infinitely slow isothermic initial charging
~ Yta ~l can be expressed as
. fA _ rYfr1
F- -r L
a 0
(1)
where k c
of volume. (l) can be considered as a general
is the relative change
ization from experimental data.
Starting from (1), which has been established for the in-
fro
finitely slow deformation, we can find an expression for the free
i^rned with a final speed Ec ~, ?
energy of a body plastically defo
For this, considering the entities P and as small, let us
develop (l) into a series ceordi.ng to the powers P and E/~ with
a
a precision up to of the second degree of smallness.
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RDP82-00039 8000200020018-9
STAT
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The ratio S to 1 for the approximation examined here
Figure 1 ? T
is shown in Figure 2.
Figure 1
Figure 2
The segment 01k corresponds to the area of elastic de-
forrna~~~.~on (Hooke's Law), while the segment Acorresponds to the
area of plastic deforrrtation.
the final speed of plastic deformation (for the initial
At
load) the body will not find itself in a statistic equilibriwn and
the cond.tion of the body for the isothermic process will be de-
termfined by the deformation tensor and the relaxation tensor
(3) The relaxation tensor characterizes the degree
0
of removal of the system from the condition of statistic equilibrium .
As the system approaches the condition of statistic equi-
librium the tensor will tend towards its balance value ~?
The free energy per volume unit will be the function of the invari-
E and For a homogeneous
ants formed with the tensors
and isotropic body we can form the following invariants out of the
.
tensors
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Because the plastic deformation begins from the entirely deter-
mined value of intensity of the shearing strain 1 , i.e.,
0
then
In order to transfer (5) into (2) with
where )%. and X. are the constants, must be fulfilled.
The relaxation tensor satisfies the equations
where ? is the time of strain relaxation in the plastic area,
is the time of volume relaxation. In our approximation the time of
volume relaxation in the plastic area is equal to the time of vol-
ume relaxation in the elastic area.
The solution of equations (7) and (8) gives us
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The stress tensor in the unbalance state
in ?the initial
n~ (' E)+~
Thn -?F
.~.~.-
6 _
L - a tip,
where ?)2, is the second duct?lltY.
With the passage from the elastic area to the plastic the
following conditions must be fulfilled;
From these cond'tions we determine the constants Y and
~.
the value of ~ in the transition point according to the speed of
deformation. This value of the intensity of the shearing strain
will be the maximum value of I in the area of elastic deformation.
If we say that the evolution of plastic deformation begins
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w . th ' 0 , then
is the first ductility and
q? is the elongation yield point in infinitely slow deform-
ation.
For the low deformation speed
and (U) assumes the aspect of
Ratios (ii), L2), and (13) determine the relation of the
yield point and of the maximum elastic deformation to the deformation
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speed, the relation of stresses to deformation and to defozmiation
speed in plastic deformation, and also the creep curve, all of
which correspond with the experimental data.
.S crcl r
Institute of Metal "- and
Me i'a is f
Physics of Central Scientific Research
Institute of Ferrous Metallurgy.
Presented
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L. M. Kahanov, Frikl. Matem. i mekh., 5, No. 3 (19b1)?
L. M. KachanOV, DAN, ,E4, 311 (i9116) ?
B. N. Fthnkel s hteY i N. S. Fastov, DAN, 71, 87 (190).
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