~ ---
INVESTIGATION OF THE BAUSCHINGER EFFECT IN COPPER
by
JOSE ROBERTO CANAL
B.M.E.,
Cornell University (1954)
SUBMITED IN PARTIAL FULFILMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May 21, 1960
Signature of Author ........
-,
.---
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--- ----- - - - -
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Departixint of Mechanical Engineering, May 21, 1960
Certified by
...........
Thesis Supervisor
..***.-----**.-...-
***
•••****
_
Accepted by .......
Chairman, Departmental Ccmmitte on Graduate Students
THE BAUSCHINGER EFFECT IN COPPER
by
Jose Roberto Canal
ABSTRACT
r
J. Bauschinger's work in the nineteenth century showed the
existence of anisotropy of the yield point in steel. Since then
several investigators have shown the existence of anisotropy of the
yield point in non-ferrous metals.
Plastic anisotropy, the Bauschinger effect, following plastic
strain in copper has been confirmed. A series of controlled tests
were performed in polycrystalline copper in order to evaluate the
effect of temperature on large and small shear stress reversals.
Thin-walled tubular specimens were loaded in torsion to a predetermined
shear strain and then heated in an inert atmosphere according to a
definite heating pattern, and the results plotted in a series of stressstrain curves.
L
Plastic anisotropy has been divided into two parts:
a) the Bauschinger effect
b) permanent displacement of strain due to reversal.
The Bauschinger effect can be explained in terms of present-day
It has been shown experimentally that there
.
dislocation theor .
is elastic recovery, a definite yield point, after heating the specimen. This recovery is evidenced by the absence of the Bauschinger
effect on strain reversals. The elastic recovery occurs when heating
the material below its re-crystallization temperature and its magnitude (the raising of the yield point on reversal), increases with
increase in temperature during heating.
Permanent softening due to strain reversals has been confirmed.
The mechanical softening has been interpreted in terms of a strain displacement of a magnitude equivalent to the mean free path between major
obstacles.
Additional softening of polycrystalline copper has been observed
when heating the material over 300*-400*C and the effect called thermal
softening.
Thesis Supervisor: Dr. Egon Orowan
Title: George Westinghouse Professor of Mechanical Engineering
ACKNOWLEDGAENTS
The author acknowledges his indebtedness to the following
sources of help and encouragement.
To Professor Egon Orowan, who proposed this interesting project
and who, as my thesis advisor, guided me through this task.
Also for
the many discussions we had together and for his valuable ideas and
suggestions.
To the Wyman - Gordon Company for making this undertaking
possible.
To Bill Henry who so diligently and carefully prepared the test
specimens, which insured the reproducibility presented in this report.
To my wife who assisted me in taking some of the data, in
computing and tabulating the results in addition to preparing the
various graphs presented here.
To all of these, my sincere thanks.
TABLE OF CONTENTS
Page
ABSTRACT
ACKNOWLEDGEMENT
LIST OF FIGURES
INTRODUCTION
1
GENERAL DISCUSSION
4
TEST PROGRAM
6
RESULTS OF TEST PROGRAM
11
Part a
11
Part b
22
Part c
28
CONCLUSIONS ABOUT THE BAUSCHINGER EFFECT
33
BIBLIOGRAPHY
34
APPENDIX "A"
35
APPENDIX "B"
37
APPENDIX "C"
43
APPENDIX "D"
46
------- ----. -
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LIST
i
OF FIGURES
Page
Figure
Definition Illustrate by stress-strain Curves.......
2
Figure
Bauschinger's work illustrated by curve .............
4
Figure
Definition of Displacement by Illustration ..........
5
Figure
Microphotograph of Copper ........................
7
Figure
Microphotograph of Copper ............................
Figure
Stress-strain Curves - Twisted in one direction ......
8
14
Figure
Stress-strain Curve - One stress reversal ............
Figure
Stress-strain Curve - Four cycles stress reversals ....
15
16
Figure
Stress-strain Curve - Seven cycles stress reversal ....
17
Figure
Stress-strain Curve - One stress reversal .............
Figure
Figure
Figure
Figure
Figure
Figure
Figure
18
Stress-strain Curve - One stress reversal 10% strain . 19
Stress-strain Curve - One stress reversal 13% strain . 20
Stress-strain Curve - One stress reversal 21% strain . 21
Stress-strain yurve - Two reversals - heat at 2000C .. 24
Stress-strain Curve - Two reversals - heat at 300C .. 25
Stress-strain Curve - Two reversals - heat at 400°C .. 26
Stress-strain Curve - Two reversals - heat at 500C .. 27
-
Figure
Figure
Load Cell and Strain gage location ................... 39
Figure
Figure
One
One
One
One
reversal - heat at 2000 C ... 29
Stress-strain Curve
Stress-strain Curve
Stress-strain Curve
Stress-strain Curve
Figure
reversal - heat at 3000C ... 30
reversal - heat at 4000C ...
reversal - heat at 5000C ... 32
Figure 22 Wiring Diagram for Load Cell .......................
Figure 23 Calibration Curve for Load Cell ......................
Figure 24
31
Typical Heating Curve - Test Specimens ..............
Figure 25 Sectional View of Heating Furnace ...................
Figure 26
Test Specimen - Drawing of all dimensions ...........
Figure 27
*
Calibration Curve for Test Specimn ................
Figure 28
Skematic representation of demensions ...............
INTRODUCTION
The present work on the Bauschinger effect is a continuation
of a test program initiated by Dr. E. Orowan in 1956, J.
A. Meyer (1)*
and Tung-Ming Wu (2) have investigated the Bauschinger effect using
thin-walled tubular specimens loaded in torsion.
In his investigation,
Meyer noticed that in non-ferrous metals there was a permanent softening
of the material with stress reversals in addition to the Bauschinger
effect.
Wu, at a later date, also found the same occurrence in
aluminum,
copper, brass, and nickel.
Figure la, represents an actual stress-strain curve with one
stress reversal.
Figure lb, shows the same figure plotted in a
conventional way of presenting a reversal curve on a positive quadrant.
The shaded area in Figure lb, represents a measure of the Bauschinger
effect; Polakowski (3)
suggested such an area which he called the
"deformation energy."
Figure lc, shows schematically, the results
presented by Meyer and Wu.
The permanent softening which is referred
by Meyer and Wu is indicated by the downward displacement of the stress
reversal curve as compared with the extrapolated curve, represented by
the dotted line, of a specimen twisted in the forward direction.
Most
investigators had assumed that the curve plotted for a stress reversal
would eventually merge with the extrapolated curve once the Bauschinger
effect had disappeared, this case is shown by Figure lb.
known that this is not the case.
of the present investigation.
It is now
Figure ld shows, essentially, the results
The permanent softening with stress
reversal is still evident, but, in many cases, the reversal curve is
* Numbers in parenthesis refer to bibliography at the end of this report.
b.
C.
Strain
Strain
-
FIGURE
1.
d.
Strain
a) Actual Stress- Strain Curve
b) Conventional Stress - Strain Curve
C) MEYER & WU's RESULTS
d) PRESENT RESULTS
3-
not parallel to the extrapolated curve as expected.
It is surprising to know how little work has been done in
the
investigation of the Bauschinger effect since it was first reported
80 years ago.
The present investigation was initiated in order to
separate and investigate some of the factors that could give an
insight to the Bauschinger effect.
Controlled tests were carried out
on the effect of low temperature heating upon reversal using low strains
and moderate strains.
These tests were performed on commercially pure
polycrystalline copper tubes.
GENERAL DISCUSSION
J. Bauschinger's work (4), (5), (6), in the nineteenth century
gave rise to speculation on the anisotropy of the yield point.
In his
work on mild steel, he found that by loading a bar in tension past its
plastic range, unloading, and loading the bar again in the same direction the elastic limit had increased; whereas loading the bar in the
opposite direction to that of the applied load, there would be little
or no elastic limit.
observations.
Figure 2a, shows the main points of Bauschinger
His main conclusions are summarized as Appendix "A" of
this report.
Forward
Reversal
Strain
Strain
Figure 2a
Many investigators have attributed the Bauschinger effect to
the presence of internal stresses.
Heyn (7),
in 1912, proposed a
mechanism, which still prevails today, based on the anisotropy behavior of the individual grains on loading.
When a tensile load is
applied to a specimen those grains which are most favorably oriented
for slip to occur will yield first.
As the load is further increased
the stress in the grains that had undergone slip increases less
rapidly than the stress in the grains that are resisting slip, (e.g.
grains which remain elastic).
When the applied load is removed the
grains that had undergone slip will find themselves in compression due
to the relaxation of elastic energy from the grains that had resisted
5.
slip.
Incidentally, the grains that had resisted slip will find them-
selves in tension and the net macroscopic stress will be zero.
Upon
reversal, applying a compressive load, the internal stresses present
would aid in the deformation and the material would experience lower
yield point.
Wu in his work concluded that the Bauschinger effect could not
be due solely to the presence of internal stresses since these stresses
did survive strong annealing.
The author would like to divide the problem into two parts,
a) the Bauschinger and
b) permanent softening.
The softening part,
it can be recalled, was represented by a downward displacement of the
stress reversal curve in relation to the extrapolated curve, Figure lc.
As suggested by Professor Orowan, the apparent softening could be
thought as being a strain displacement.
This displacement, as will be
shown later, is constant for a constant strain amplitude and could be
indicative of a mode of microscopic action perhaps the shearing of major
obstacles as proposed by Professor Orowan. Then the stress reversal
curve could be displaced to the left
by a definite strain increment
matching the extrapolated curve, this is
shown in Figure 2b.
This
would leave the Bauschinger effect more or less independent of any
mechanical or thermal softening.
-
mEno
Strain
Strain
Figure 2b
Q)
AS
RECEIVED
X IOO00
b) ANNEALED
AT 700 C- I HR.
X 100
FIGURE 3
MICRO PHOTOGRAPHS OF COMMERCIALLY
COPPER
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MICROPHOTOGRAPH OF ANNEALED
COPPER
AT
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X 1000.
FIGURE
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SPECIMEN
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TEST PROGRAM
The Bauschinger effect was investigated using thin-walled tubular
specimens loaded in torsion.
These specimens were twisted in an Ann
Arbor torsion testing machine, which is the same equipment that has been
used by previous investigators at M.I.T. This equipment has been adequately
described by T. M. Wu (2).
Some improvements, which were suggested by
earlier investigators using the equipment, were incorporated into the
machine.
The load cell was redesigned with a 5-fold increase in
sensitivity.
Details of the change and the corresponding calibration
curves appear as Appendix "B".
The test program reported here was carried out using commercially
The specimens were machined from drawn tubes in the as
pure copper.
received condition and as far as could be determined, all tubes came
from the same extruded lot.
A typical microphotograph of the grain
structure, is shown in Figure 3a.
The test specimens were cut to length, 6 1/81' and machined to
the specifications shown in Figure 26 of Appendix "D."
The specimens
The
were then cleaned and degreased in pure acetone prior to annealing.
specimens were loaded into a Multiple Unit Vacuum Furnace, (see Appendix "C"
for details), and the furnace evacuated by means of a vacuum pump.
furnace
The
was charged with Argon gas to provide the inert atmosphere for
annealing.
The furnace was brought to 7000C and held at this temperature
for one hour.
The furnace was then allowed to cool to room temperature
and the specimens unloaded.
structure.
Figure 3b shows the typical resultant micro-
At first it was thought that the specimens were not fully
9.
annealed, from the appearance of the grain structure,
showed what appeared to be a fine grain aggregate.
tions, it
since some areas
At higher magnifica-
was noted that what appeared to be fine grain structure were
etch - pits that revealed the octahedral plane.
Figure 4 shows a
geometrical array of etch - pits in one grain.
Incidentally, many
annealing twins can be noticed in the microphotographs.
Since twin
boundaries obstruct slip on at least six out of the twelve possible slipsystems they act, essentially, as grain boundaries.
R. L. Woolley (8)
in his work on copper, was able to show that as the number of twins per
unit area increased the initial stress for a given strain also increased.
What effect this may have on the Bauschinger effect was not quite clear
from his discussion.
Nevertheless uniformity of grain size and perhaps
number of twin per grain were kept constant by following a prescribed
heating and cooling cycle, see Appendix "C."
The test program can be thought of being divided into three
areas:
a) Twist a test specimen in one direction, unload, and
twist in the opposite direction.
b) Twist a specimen in one direction, for small strains,
unload, heat to a predetermined temperature, load and
twist in the opposite direction.
c) Twist a specimen in one direction, for large strains
unload, heat to a predetermined temperature, load and
twist in the opposite direction.
The stresses were calculated by means of conventional thin-wall
formulae and the strain was calculated as the tangent of the helical
angle of twist.
An empirical correction factor was applied to the gage
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length and the details of this appear
as Appendix "D."
After a predetermined initial straining, the specimens were
removed from the machine and each successive specimen heated at 1000 C
higher than the preceding one starting at 2000 C, for one hour before
straining in the reverse direction.
At some point were sudden softening
occurred, figure 20, the heating was discontinued.
__
11.
RESULTS OF TEST PROGRAM
Part a)
This group of tests represent one or more strain reversals
without any intermediate heating.
The curves for this group are
presented together as Figure 5 to 12.
Figure 5 shows the results of twisting in one direction only.
Here two specimens were twisted, one to a strain of 25% and the other
to a strain of 35%.
It was noticed that Specimen "A" had slipped in
the jaws of the machine
during twisting at a strain of 18%; the data,
which was questionable, beyond this point was discarded.
A second
Specimen "B" was twisted to a strain of 16.5% and unloaded.
in which the portion that would correspond to that
gage length was fitted with ball-bearings to fit
A mandrel,
'section under the
the inside of the
specimen snugly, was inserted into the specimen to constrain is from
buckling.
The specimen was then reloaded and twisted in the same
direction to 35% strain.
The curve shows some instability beyond 28% strain
which is attributed to creep;consequently the tests were not carried beyond
35% strain.
This curve was used as the bases for the extrapolation of
data for all the curves presented in this investigation.
Figure 6 shows a specimen twisted to 2 1/2% strain and reversed
to 18% strain.
The expected Bauschinger effect is noticed in addition
to the softening effect reported by the previous investigators.
Apparently
at small strains the curve is almost parallel to the original extrapolated
curve.
Figure 7 shows four reversal cycles, each of 2 1/2% strain.
last reversal was continued in the original direction.
The
Usually, dots
-I
12.
represent forward twist and circled dots represent reverse twist.
The
non-parallel feature of the curves can be noticed at early reversals.
Figure 8 shows seven stress reversal cycles each of 2 1/2% strain;
it can be noted, in this figure, the regularity in which the displacement
of the curves occur.
This same regularity also appears in
Figure 7.
Figures 9 and 10 are intended to show strain reversals of 10%
and 14%.
The specimen in this case were twisted to predetermined strain
and reversed exactly by the same amount unloaded and allowed to stand
for one month before applying an
additional stress in the same
reversed direction.
Figure 9, shows essentially no recovery during this rest period
and curve is considered to be a continuation of the same reversal.
Nevertheless, this curve is not parallel to the extrapolated curve as
reported.
Figure 10,
shows the effect of some recovery during this
rest period but this segment of the curve has the same shape as the
original reversal curve.
Both segments of the reversal curve are not
parallel to the extrapolated curve.
Figures ll
again it
is
and 12 show a reversal at 12% and 21% strains.
Here
noticed that curves have the usual Bauschinger effect and
the mechanical softening but are not parallel to the original extrapolated curves.
It appears, from the general trend of the curves, that -the displacement of the curves, upon reversal, is independent of the amount of
plastic strain.
The strain displacements, for a constant 2 1/2% strain reversal,
based on the extrapolated curve are:
13.
For Figure 7
.5, 1.5, 2.7, and 4.2% strain
For Figure 8
.3, 1.5, 3.0, 4.5, 6.0 and 9.2% strain
which seems to suggest a permanent displacement of the curve in one
reversal of 1 1/2% strain.
This is a considerable amount for small
strains but the value seems to remain constant regardless of the amount
of plastic strain, as seen from the other curves of this group.
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I
p
i~~i
fl
-i
i
i
i
-
---I------
II
-
-I--- A-
tw
4
-
~~~1~
-
-
-i---
+-------------
---I- I
-
I.
0-I
I
4
_____________
___________
to
.
I
4
I
-i
L-----~-
-4--
___
-4-
1
_____________
___________
t% 3 H~AR
___________
2t~
~1R411~
-
___________
-
_________
___________
-I
22.
Part b)
All specimens in this group were prestrained in torsion to 2 3/4%
prior to subjecting each to a heating cycle of a predetermined temperature.
These specimens were then twisted in the opposite direction to a strain of
2 3/4%
and reversed again, back to the original direction, for an
This series were carried out in this form
additional strain of 12%.
to evaluate the effect of mild heating on a second reversal and are
grouped together as Figures 13 - 16.
Figure 13 shows that the Bauschinger effect has not changed at all
after heating the specimen to 2000C for one hour.
The second reversal,
likewise, does not seem to be affected by this temperature.
Figure 14, shows that the magnitude of the Bauschinger's effect,
Polakowski's concept, has decreased somewhat,
there is
covery upon heating the specimen at 3000C for one hour.
same elastic reThe second
reversal does not seem to be affected. Plotted on the upper left hand
corner of Figure 14 and to the same scale, is
shown a specimen that was
prestrained to 2%, received the same heat treatment and was reversed to
2% strain.
The same characteristic features appear as in the curve
below; same elastic recovery is noticed.
Figure 15
shows
the effect, mentioned for Figure 14, a little
more pronounced with more recovery on the elastic part of the curve, due
to heating of the specimen at 4000C for one hour.
Likewise, the second
reversal seems not to be affected.
Figure 16 shows almost complete elastic recovery coupled with
some thermal softening additional downward displacement of the curve, when
heating the specimen at 5000C for one hour.
The second reversal is still
23.
unaffected.
Plotted as in Figure 14, is the specimen with a prestrain
of 2% and heated to 500 C, and again the general features are repeated,
namely; elastic recovery and thermal softening.
I
IM
-.
..
j
---------
I
t
-,
I
_- _
. .. ...
.--' - --
1
1 1 ',
I
..
I
l
................ .
_
I" i
-
i- -
i
,
__
-~~
-
*
'
1
---
f-~T
i
I '
%
---
----
I
.
---
- --
-
I
IR-
.
1
Ii EI
I
----
I
102
I
13
14
15
1
I
I
I
STRAI N
S HEPR
--
IRI
-''
L
I:
I
---------
---
t
-
.
I
_
J i
S1
-
.
I
' i
'
I!i
r--
-
-
-
I
" ,
-'
H
-h-1--i----/
--
...
..
-
--
,,,
-
L-I
IST-
-
--
-
--
...
REVERSAL.
--
-i
t
I
_
0 C
HIEAT
QNE
-..
.....
i
F
r-
i
_1_
%
.-
...
'C
2
N
SP
T
.
A
1,
5
I,2
--
. ..
SI
S
i
ST
W $T
i
|E'
%
-
-
-I
SHEAR
-- -
1
-.
. T
VS
- ..
7:
- -
STRAIN .
MEAT;
i
O
STRAIN
I
---
II
t--4
~~~
*
-*
9
.i
U)
-4~
*-
*-
--
w
-4
-5
I
i
I
-
------ i-~--1
0
1
2
.
3
B
4
I
6
i----- i---
------ "---i-------i
1 i r
9
7
%
SHEAR
10
STRAIN
11
12
13
14
15
16
17
Is
_- L
.
..
S
I
-
i
ISPECIMEN,
-..
i
S-
-
..
ONE
.
SI
j
,
t
25
.
-.
.
IST - HEAT 500CC
T
1
'
RVERSAL
,
I
'
.
ci)
.
..
-
.
-
-....
.
.--
,'--------
,--ES-
I.
t----'
J----.
.
-
s
s
w.T- HEAT
At
sooc
I-
%
-
--
;
---
---
---
;-;---
SHEAR
-----
STRAIN
I
-
-
----- n
28.
Part c)
All specimens in this group were prestrained to about 13% prior
to heating and the same heating cycle as applied to as that for part b).
Only one reversal with a strain of 22% was applied in this group.
This
group is presented together as Figures 17 - 20.
Figure 17 shows that there is little change upon the general
shape of the curve after heating the specimen at 2000C for one hour.
Figure 18 shows some elastic recovery after heating the specimen
to 3000C for one hour, same thermal softening is encountered here as
evidenced by the downward displacement of the reversal curve.
Figure 19 shows about the same amount of elastic recovery as in
Figure 18, but thermal softening is more pronounced.
It should also be
noted that these curves do not follow parallel to the extrapolated curve
as mentioned by Meyer and Wu.
Figure 20 shows a drastic recovery* perhaps the recrystallization
temperature has been reached at this amount of prestraining.
Note here
the rapid strain hardening rate that prevails during the reversal, and
the tendency of the curve to level off at a valve which could be interpreted so the
sum of displacement due to thermal softening and to
permanent softening.
These controlled tests were not carried beyond a temperature range
of 5000C.
An additional test was carried out for a specimen prestrained
to 2 3/4% at 6o00C and the general shape that appeared in Figurel6 still
prevailed.
It is planned to carry, at a later date, tests at higher
temperatures until the same effect experienced in Figure 20 is reached
for a prestrain of 2 3/4%.
*I
*
*
-
- -
--
*
1
-.
i
-
-
-
-
---
r
14
U.
w
U,
--I- t2
- -- SIPE
T W4 4
, -tI
t-
,
,
i
i
------
o
10
I
A
20S
;
}I
i i
j
~r.
-4-
I
4
-l
~~HEjR
1-41 1- --
STiES6
si
<V-
7 I
,TT
--
---- I--
'
'7 ti
I
-i
~'..
~ ~~
t
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~,
7-- 1j
.
..
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.
- i
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,
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_
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;
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ttL
~
'-li
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--- --.....
--
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/r
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-
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.. . ...= . .
f
1
T--
-~-~7---r-----r----ip--,
r-----+---- +---- r----:
r - ' ---:-f-- C-----l----~----i
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itj
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.
,VERS
-5
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s eA
T
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0
pcC-
_
:,
ii4i' :
'
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---- --_ - -- ---- t-- -
, __i-
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<1-7;.
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- TRES
.
.
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p
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1-
-'--
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ii
i
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. . ..
,
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_____
o
SAHEARSft
.
Ai-
3v
*
-
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_TAI
3b
--
:--t-.
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+--f
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-~~~~
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t1---
it
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-- --i.-
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tIP-
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---
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i t
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r!
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f
14
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._1
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32.
--------.--
.-
4 pC-lT~-
c'F-Tf:l(l"l.t't~~~n:~lkl1.7
I
e -t i
\I
-
I "L --f''-
11"'
i
-
-i .-.
+
-I-
-tI
-
i t '
1; s64
I
Vt --i
'i I
--
-H- -4q-v-v-Kt-1~I ,
r i
I ' ' I-----c-------tt--t:
.1-i--i-I. I
' ' ' ~' ' I
-f--"-'t-~l1-i ri
-
t;-i
-tIi
til ~-if-t'-l-: -i-
33.
CONCLUSIONS ABOUT THE BAUSCHINGER EFFECT
The most plausible explanation for the observed rounding of
the stress-strain curve on reversal is the accumulation of dislocations
at the end of a slipped zone.
The elastic stresses set-up by these
piled up dislocations against a barrier, Dr. Orowan's concept (a),
make their reverse glide easier than their forward glide.
The permanent softening of the material, a downward displacement
of the reversal curve, could be interpreted as the mean free path
between sheared major obstacles in terms of a strain displacement.
This displacement, as it has been shown experimentally, is proportional
to the number of stress reversal cycles.
This would suggest that the
downward displacement of the reversal curve should be different for
metals having different obstacle forming characteristics, e.g., metals
with low or high stacking fault energies.
Since tests performed on a polycrystalline material can only
represent an average effect, the strain displacement upon reversal
can only reflect, on the average, a mean free slip path which does
appear to be independent of prior plastic strain.
The specimens that were heated at 4000 C or above before a strain
reversal, their curves show an additional downward displacement which can
be thought in terms of thermal softening.
This would be the equivalent
of anihilating, by thermal action, some obstacles which would be the
same as increasing the mean free slip path between obstacles.
It has been shown experimentally that there is elastic recovery
due to heating, prior to reversal, which can be interpreted as the
removal of obstacles with
their corresponding elastic stresses the aid
slip in the reverse direction.
34.
BIBLIOGRAPHY
1. Meyer, J.
A.,
Pre-Sc.D. Thesis - Massachusetts Institute of Technology,
1959.
2. Wu, Tung-Ming, M.Sc. Thesis - Massachusetts Institute of Technology,
1958.
3.
Polakowski, N. H., "Softening of Metals During Cold-working"
and Steel Inst. V. 169 p. 337 (1951).
4.
Bauschinger, J., "Changes of the Elastic Limit and the Modulus of
Elasticity on Various Metals" Zivilingenieur,V. 21
p. 289 (1
J.
Iron
).
5. Bauschinger, J., Mitt. aus dem Mech. Leck. Laboratorium aer K. Lechnischen
Hodischule in M-inchen (1886).
6. Bauschinger, J., Min. Proc. Inst. Civ. Eng., V. 87 p. 463 (1886).
7. Heyn, E.,
"Materialkunde" 2nd ed., p. 280 (1912).
8. Woolley, R. L.,
"Bauschinger Effect in Some Face-centred and Bodycentred Cubic Metals' Phil. Mag., V. 44, p. 597
(1953)
9. Orowan, E., "Stress and Fatigue in Metals" Edited by G. M. Rassweiler
and W. L. Grube Elsenvier Publication Co., (1959).
35.
APPENDIX "A"
In his work published in 1881 and, again in 1886 Bauschinger
intended to show, as a result of his experiments in steel, that:
"The elastic limit (in tension) is lowered as the
result of stretching, often down to zero, so that the specimen, when it is tested immediately after cold-stretching,
has no, or else a very much reduced, elastic limit.
During
the period of rest which follows the cold-stretching, however, the elastic limit increases again.
After several
days it attains the stress with which it was cold-stretched,
and after sufficiently long period, certainly after many
years, it increases to a value even higher than this stress."
"As the result of stressing in tension or compression
beyond the elastic limit, the elastic limit in compression
or tension, respectively, is considerably lowered, so much
the more if the cold-working stresses exceed the respective
elastic limit by larger amounts and even comparatively small
increments of stress beyond the elastic limit, reduce the
elastic limit in opposite direction to zero."
"When an elastic limit, thus lowered in one direction,
is raised again by stressing in that direction, and the exceeded,
then, at once, the elastic limit in the opposite direction is
again reduced to zero, or nearly to zero."
_~4UI~
36.
APPENDIX "A"
(Continued)
"Time in these processes is without any effect,
or at least has very slight influence.
That is to say,
the elastic limit in tension or compression, lowered by
compression or tension, respectively, is not again raised,
at least in the course of three or four days, and in the
course of the next few weeks certainly only a little, if
at all."
37.
APPENDIX "B"
TORSION TEST EQUIPMENT
An Ann Arbor hand wheel torsion machine was used for this
experiment and has been described elsewhere (2) in great detail.
The load cell was redesigned to increase its sensitivity 5-fold,
following the suggestion of previous investigators.
The load cell was machined as shown in Figure 21 from a 1090
cold-rolled steel shaft (1 1/4" diameter drill rod).
Eight SR-4 strain
gages type A-3 were cemented to the shaft as shown in Figure 21.
The
gages were connected in two separate bridge circuits labeled "A" and
"B".
These gages were wrapped in cotton cloth and sealed in wax to
protect them from moisture.
The two gage circuits were connected as
an external Wheatstone bridge to an SR-4 strain indicator.
diagram is shown in Figure 22.
The wiring
The circuits were designed in such a
manner as to give the same slope, as shown by the calibration chart,
in Figure 23, such as to permit the coupling of the two circuits in
one, for an additional two-fold increase in sensitivity.
CELL SHOULD NOT BE USED IN EXCESS OF 1000 IN-LBSw
THIS LOAD
A very close
compromise between sensitivity and linear strain had to be maintained.
The load cell was calibrated by means of a Riehle Torsion Machine
and the data is presented in Table 1 and plotted in the Calibration
Curve of Figure 23.
The angle of twist, which in turn determines the shear strain, was
measured by the use of a goniameter which consisted of a protractor and
an index.
The protractor and the index are mounted concentrically to
fit snugly over the test specimen.
-. . _--~XX*l-I-- ---l~_i- . --~.- ---=-Zq -=Il~
--
38.
APPENDIX "B" (Continued)
TORSION TEST
EQUIENT
Two short plugs, which extended only 1.25" into the specimen
from each end, were inserted into the specimen to prevent local
buckling during clamping.
The specimen was secured to the torsion
machine by means of two split jaws, one at each end, that were
screwed together holding the specimen in place.
The jaws themselves were pinned to the torsion machine by
means of a pin, which was not inserted until the specimen was
clamped and the test ready to commence.
This pin was removed after
the test was completed to prevent accidental twisting of the specimen.
3
5
4
8
.4
3
4
CIRCUIT
CIRCUIT "B"
LOAD
'Jaw
Gr.-W.
r.-W
CELL
FIGURE 21
Br.-W.
Br.-W.
Or.- W.
Or.- W.
BI.- W.
B I.-W.
Location
of
Gages
on
Shaft
End
2
Gr.- W.
Br.-W.
4
Or.- W.
B.I.-
W.
STRAIN
SR-4
W
B
)
0
R
0
GAGE
W
0
0
gr. bl.
or. bl. or br.
WIRING
DIAG
FOR
FIGURE
22
LOAD
CELL
I
II
I
I
I
r Il
II
I
I
O
O
- 12.0
FIGURE
x
Iz
CALIBRATION
GAGE
,,,.5
23
CURVE
READINGS
c)
0
z
VERSUS
o
VAPPLIED
TORQUE
Iw 10.5
9.5
Gage
n
9.0
Slope
Factor
.410D
2.00
in-lb.
/4 in/in
100
200
300
400
500
APPLIED
600
700
800
900
I000 in-lbs.
TORQUE
-H-
---
:I--IXY=-
I
I
---
I=---;---
--
-------
-m
42.
TAPLE I
CALIBRATION DATA FOR LOAD CELL
RIEHLE TORSION MACHINE
Applied
Torque
SR-4 Strain gage readings
Cireul
Circuit
in-lbs
A
in/in.
A
in/in.
000
165
370
448
1000
970
11560
11170
10672
10475
9154
9200
12002
11629
11120
10921
9606
9651
790
600
9630
10093
10070
10538
455
350
248
170
55
336
500
610
10450
10710
10960
11160
11434
10780
10380
10104
10890
11150
11400
11598
11875
11220
10822
10550
750
870
1018
1085
941
800
9764
9475
9110
8945
9275
9618
10205
9922
9560
9400
9729
10060
589
372
235
84
000
10120
10660
10992
11360
11590
10570
11100
11435
11805
12022
Slope for eircuit A and B
in-lbs.
.4096 7r/in.
.
Slope used for calculations .4100 in-lbs
,A in/in.
____ _1_1_ ___~_II~_
___
~________
43.
APPENDIX "C"
ANNEALING EQUIBENT
A Multiple Unit vacuum electric resistance furnace was used to
This furnace was connected to a mechanical
anneal the test specimens.
vacuum pump Cenco-Pressovac which was used to evacuate the furnace.
The specimens were loaded into the furnace after a thorough
cleaning and the furnace was sealed air-tight.
The furnace was
evacuated to about 1 mm of Hg and filled with Argon to provide the
inert atmosphere for annealing.
The Argon was supplied through a
The furnace was pumped down and fill
flow-meter to the furnace.
with
Argon three times in order to insure removal of all extraneous gases.
The temperature inside the furnace was measured by means of a
Chromel-Alumel thermocouple connected to a Leeds and Northrop PotentioA typical heating cycle is shown in Figure 24.
meter.
All the specimens
were annealed at 700C for one hour at a predetermined rate.
For any intermediate heating the specimens were loaded and the
furnace evacuated in the above prescribed manner and the corresponding
temperature recorded.
A record was kept of the position of the
specimens in the furnace in order to assess any variation that could
be attributed to non-uniform annealing.
Figure 25 shows the typical
position of 6 specimens during heating.
The specimens were annealed
in the following group lots:
A
= A,
B
= 1, 3, 4, 5,
C
= 9, 10, and 11
B, 2 and 7
6,
D = 12, 13, and 14
and 8
E = 15, 16, 17, 18, 19, and 20
F = 21, 22, 23, 24, 25,
and 26
,
o
800
w
cr60O
i-
FIGURE
W400
TYPICAL
24
HEATING
TEMR
CURVE
VS TIME
200
0
10
20
30
40
50
TIME
60
IN
70
MINUTES
80
90
100
It:O
----~-----------.-.------ -----.
-;-
,
-
I
c~c~L~-~
n:
TO
0
*1
iII
'LA
__
i
r
Vacuum
*Q
**
~
*
II
..
.
THE R MOCO PLE
Li
u
V
FIGURE 25
SECTIONAL
-POSITION
Argon in.
"%
40-
VIEW
OF
OF
FURNACE
SPECIMEN
DURING
SHOWING
ANNEALING
_~~,
----
___
~.-nn~o*rrz~r~r_~-.
46.
APPENDIX "D"
TEST SPECIMEN
The test specimens were cut to length from a copper draw tube,
.75" I.D. X. 125" wall thickness, and machined to the specifications
shown in Figure 26.
The specimen was polished inside before mounting
on a mandrel for turning in a lathe.
A gage length of 20 mm.
was
provided as the test region and the strain was computed on this bases.
The length chosen proved to be unrealistic and the specimen had to be
calibrated in terms of an equivalent length.
After the specimen was
turned the gage length section was polished.
The specimen was annealed in an inert atmosphere for one hour
at 7000C and allowed to cool in the furnace to room temperature.
The
outside diameter of the gage length was measured with a micrometer in
six places and the average of these readings was used to compute the
mean radius r.
The shoulder of the gage length was measured with
a traveling micrometer microscope.
It was found necessary to calibrate the specimen in order to
determine an equivalent length to be used in the determination of the
strain.
Two specimens were selected and four lines scribed on each
parallel to their axis.
Each line was 900 apart from the other.
After
the specimen was twisted a predetermined amount these lines formed a
helix which could be measured to establish the non-linear portion of
the helix.
Figure 27 shows the corresponding plot of the line position
versus angle of twist for a 30* twist and a 400 twist.
As can be seen
47.
APPENDIX "D" (Continued)
TEST SPECIMEN
from the figure the line was extrapolated in the non-linear region
to find an equivalent length for given angle of twist.
The equiva-
lent length determined by this method was 26.5 mm. and this value
is used to compute the strains, as is suggested in Figure 28.
All specimens were machined to a rll-thickness of 1 rm.
which
was determined by the machinist according to the inside diameter of
each copper tube.
This practice lead to a simple relationship which
enable to compute the mean radius by measuring the outide diameter, the
equations are shown in Figure 28.
in terms of
Meter.
The torque T was measured directly
p inch per inch as Reading R from an SR-4 Strain Gage
The strains were computed using the value of 9
which was
measured directly from the goniometer located on the shoulders of the
test specimen after the other constants were determined from the
measurements of the specimen.
_
__ _I_
~__~ I_
____i
I_
85
25
---
349
3 0.2
34.9
TEST
ALL
-IOmm.R.
SPECIMEN
DIMENSIONS
IN
MILIMETERS
FIGURE
26
~_I_
FI_ _l~
49.
SPECIMEN
1.4
u 1.2
w
z
1.0
W.8
.6
.4
30
20
POSITION
IN
FIGURE
40
DEGREES
27
.~--L~a~-Z--
-- --
~
~_
I
50.
- 7. TTSI psi
T= .4100 R
R=SR-4 GAGE
r=
d-i.o
2
RD'G.
m m/ 2 5.4 (in.)
t = 1.0 mm.= .0394 in,
in
Leq. in
FIGURE
DIMENSIONS
STRESSES
FOR
AND
28
COMPUTING
STRAINS