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NISTER
A liEW
_MEC15.NISM/OR
INTERNAL
FRICTION*
H. Mitchell Simpson, A. Sosin, and Gary R. Edwardst
University of Utah, Salt Lake City, Utah 84112
Abstract
Simultaneous measurements of damping and elastic modulus
of copper as effected by electron irradiation above room tempera-
ture have been
made.
These data do not follow the standard
analysis, using the Granato-Lucke theory for damping, in which
point
defects,
created
by
irradiation,
are
presumed to act as firm
pinning points on dislocation lines. It is proposed instead
that these defects are dragged along by the dislocation line
moving under oscillating stress.
1
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*Work supported by the Metallurgy and Materials Program of the
Division of Research, U.S. Atomic Energy Commission, Contract
AT(11-1)-1800.
tPart of the work submitted for the M.S. degree. Present Address:
U.S.A.F
Space and Missile Systems Organization
.,
El Segundo, California 90045
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1
.
The analyses of a large number of experiments on internal friction
in metals have been based, with remarkable success, on a theoretical for-
1 2
mulation of Koehler, amplified in detail by Granato and Lucke, the G-L
theory. This theory, a string-model for dislocation bowing under applied
stress, is best known for its predictions, at reasonably low frequencies,
for the strain amplitude-independent decrement and modulus change, 6I and
AE
(-E)I' and for the higher strain amplitude, amplitude-dependent decrement
AE
and modulus
change, OH and (-E)H i
6 = a B (0 -/L L4 (1)
I
AE 2
(-) = b X
L
(2)
EI
and
AE C_/L
611 z (E)H z. i-g-- exp(-i ) · (3)
0 0
B is a
viscous
damping
constant, w is
the
angular
,drive
f.requency,.Lis
the
total
length
of
dislocation line per
unit
volume, L is
the
average
length
of
dislocation
between
pinning
points, and
a,
b,cand.d
are
constants
42
(see Ref. 2). The. L and L dependences in Eqs. (1) and (2)
are
watermarks
of the
G-L
theory.
Irradiation
experiments
are
particularly
well
suited
4 2
for testing this L -L prediction since the accretion of defects on dislo-
cation lines during bombardment or subsequent annealing provides a controlled
method for apparently systematically shortening the loop length, L, while
not affecting any other parameters. If we let
AE/E
Y E (AE/E)0
(4)
.,
-2-
and
Z 6/60 , (5)
the G-L theory predicts a proportionality at low strain amplitudes between
Y2 and Z during irradiation. (The subscript I has been suppressed; the
subscript o designates initial values. Background contributions to the
decrement or modulus are presumed to be subtracted.) On occasion, such
3
fits have been reported; more commonly, the proportionality has not been
45
obeyed. BY invoking the concepts of two dislocation types, ' further
agreement,
particularly with Eqs. (1) and (2),
has
been
achieved at the
expense of introducing more parameters into, the analysis.
A second concern with the G-L theory centers on its prediction of
linear frequency dependence of 6I. The reported values over a relatively
wide range of frequencies have shown little, if any, dependence on fre-
quency,
at
relatively
low
frequency (e.g., near
or
below 1 kHz).
The
observations
reported here show that the G-L theo ry must be
amended or that a new damping mechanism must be considered.
In the experiments reported here, copper foils were irradiated in.a
4
configuration similar to that reported previously by Sosin and co-workers.
(However,
the
method
.of
sample
oscillation
was
electrostatic in
the
present
experiments,
rather
than
magnetic, so that no iron foil
was
needed.) Data
points were taken every three seconds; only a few of the data points are
displayed in Fig. 1. The samples were annealed to 725'C.prior to the ini-
--
tial irradiation.and-to
460'C
between
irradiations,
in
place.
Little or