Variation of the resistance of copper with potential energy of deformation
by Walter T Kerttula
A THESIS Submitted to the Graduate Committee in partial fulfillment of the requirements for the
degree of Master of Science in Engineering Physics
Montana State University
© Copyright by Walter T Kerttula (1946)
Abstract:
The variation of the resistance of copper wire with potential energy of deformation is studied.
Equations for resistivity and resistance in terms of potential energy of deforma-tion are derived oa the
assumption that resistance varies linearly with tension, as found by other observers. The change In
resistance is measured, and the results plotted against the potential energy of deformation. The
experimental data are found to conform to the equations derived, which state that resistance varies
directly with the square root of the potential energy of deformation within the elastic limit.
A determination of the unit change in resistivity for a stress of one kilogram per sgqare centimeter is
made from the data, using Bridgman's equation, which remalts incidentally from the derivation of the
resistance-energy equation. The value is in close agreement with the results of Bridgman and Rolnick*
Data on the behavior beyond the elastic limit are includ-ed, but no definite conclusions are drawn from
them.
An equation for computing the strain sensitivity factor (the ratio of unit change of resistance to unit
strain) used in calibrating commercial strain gages, is included in an appendix, and the strain sensitivity
factor for copper is computed from the experimental data* m a iA T im 0# 352 m s i s m g o g o r o o p p m m m
BBBBGYGF DSFOHmTim
by
vm#BS %, EE8$EGL&
A' s m a i a
B aM ittea to th e Graduate Committee
i&
p a r tia l fu lfillm e n t o f t&e regolremeBta
f o r th e a a g re e o f
Master o f Bolence la Bnglmeerlng Ebyslaa
'at
B b aten a S t a t e G o lleg a
A pproved:
Bozeman* l& B tana
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yh f 7 r
2 -
TABLE OF CONTENTS
ABSTRACT
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HISTORICAL BACKGROUND
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THEORY
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EXPERIMENTAL PROCEDURE
TABLES AND FIGURES
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RESULTS Aim CONCLUSIONS
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APPENDIX
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LITERATURE CITED AND CONSULTED
•A
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19
-3 2
39
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41
ABS3S&#e
The v a ria tio n o f th e
o f eoppar v&ra %lth #ot8@^.
iblGLi aaorgy o f doformatloa la* gta& lel.
S^ aatlw a fo r r e a ls*
t l v l t y and raalsta& ee In teem# o f gotao&lal oaargy o f
t&m are aerivea on th e agaimgtlon that raaletanoa varloa llm*
e a r ly wliUh teBsiom* a s foimdl by other observers ^ The oha&go
la r e a ls ta a o e i s meaiR%rea$ a a l t&s r e s a lta p lo tted a g a la st th e
p o t^ itia l energy o f aoformat Iqa^
The @a$arimeatal 8ata ar#
f&g&& to ooafora t o the egu atloas Gapieea+ Mhiab s t a t e th a t
r e s i s t aaoa v a ries l l e e o t l y with th e sgoare root of tb s potoat l a l eaergy o f Goformatloa w itb la the e la s t l o lim it*
A determ lnatioa o f the w i t ohaage la r e s i s t i v i t y fo r a
s t r e s s o f oao k ilo g ra m p e r s g q a ra o e a tlm o to r Isjaa G o fro m t h e
d a t a , as& ag BrlGgmaa^s e q a a tlo a ^ # b la b r e s u l t s laelG e& t& lly
from th e G erivatloa of the pe&letaaoe^eBergy eggatlaRw
The
v o le e i s la c lo s e egreemeat with th e r e sa lta o f BrlGgmaa ead
Rolaiek*
Data oa th e W baviar beyoaG the e la s t ic lim it are la e la l*
ody but Bo l o f l n l t e eoa ela sloae are Graaa from them.
Aa agoatleo, for oompatlag th e s tr a la s e n s it iv it y fa c to r
{the r a tio o f a a lt obaage o f ra&lataaae to h a lt s tr a W 8S#&
1& c a lib r a tin g oommorolal s tr a in gages, i s IaoludoG l a aa ap*
poadl%y scowl th e stra in s o a s it iv lt y fa c to r fo r ooppor I s ooa*
puted from the experimental data»
a ffe a t o f tea a lo a on th e caalatemoe o f m etals p g r a lla l
t o t&a d irectio n o f the t e n s ile fo rce -ms studied as Icag ago
a s 1888- by TomlInsm^, and a aomsiderahle amount <>2 maat has
Deeas done sin ce th at time* cou slatin g prlncIp a lly o f checlclng
th e o r ig in a l r e s u lts and developing new teehalgues*
P ossib ly
the most e&tensive work was done Dy Bridgman^* who used methods
aomeabat sim ila r to those adopted fo r the praaeut ezperimeata;
th a t i s * th e sample was subjected to & Baoaa t e n s ile stress*
Ojig tli© yssistciBGS s$eaaurBd by mesas o f a pot e a t lcm etcr $. as.ing'
a QMii method*
The ehaage la r e sista n c e due to geom etrical
Gboages gas subtracted from th e t o t a l T esistaaae change* and th e
rem ind er was assumed to be th e change due to s tr e s s e
Later determ inations were made by BolBickc55, using the
method o f vibrations* i , e . » the sample was made to vib rate
lon gitu d in ally* and the change in p o te n tia l between th e two
p oints measured by moans o f a calibrated am plifier*
^ho ampll—
tude o f tW v ib ra tio n s was measured by means o f a IW at beam
r e fle c te d from a mirror vib ratin g w ith the apparatus.
Yoimg?s
m aulus and Poisson^s m t l o were used to compute the s tr e s s and
l a t o r a l c o n tra ctio n * -
V alu es o f th e s e c o n s ta n ts w ere ta k e n xvom
handbooks* or computed from values of the shear modulus*
yor most m etals 5 r e s i s t i v i t y has been found t o vary Iiti^
e a r ly with ten sion w ithin the e l a s t i c lim it*
Ifor most m etals>
th e r e s i s t i v i t y in creases with strain * but in some* notably
sSromtigm aa# bim oah* t&e Wteiom ooeffiolem t o f r o e ie t iv lt y
l a aegatlve*
S t i l l ot&er$» #8a#l<mlaely miokel* Wbmm erne#
more abimnmlly*
a
In t&ia metal* th e r e e io t lv it y aacozeoae# t o
and then b e # a e to iaore&w a@aia w ith irnore&eimg
Oopper has a normal p o e it # o tone ion o o e ffio lo n t o f roa^
le t iv it y * whieh has &wa meamzrei ewe 1.G %
, an! 1^5& z
^
%
ohm-oontimotere per ohm^osntimater
#8]* kilogram par eqaare eaotim etsr hy llf f e r o n t in?oetig a to re *,
Ba&oatly? th is pheaome&ga h&e te#a pat to B raotloal %se
l a the a&alyeie o f str a in by means o f realatanae w ire str a in
gagea^*
39%) str a in seaG ltlT ity fa o to r o f these a&ges* d o flsea
a s th e r a tio of u n it ohtmge o f r e sista a e e to u n it S train 8-.
must* a t present ^ be leteim lneh experim entally & Bega rlln g t h i s s tr a in s e n s it iv it y factor* B* M. B ielsoaP statom
"#er most metals* th e str a in senei t i f I t y .»* vmulh W ezpeotoi
t o Ibat between 1 .6 a n i 1*8 from a consideration o f only te a di­
mensional changes o f the %&re. 2astea&, most m etals and a llo y s
have s e n s itlT ity fa c to r s eoaslderably higher* SEbuKs Jbftet never
Wen eomplately explained^ Bha reason probably l i e s in an
actual change o f volume r e s i s t i v i t y o f th e m e ta l.s
$be fa c t that there i s a change in volume r e s i s t i v i t y I re-f e r r c l to herein a s tSeKssKSxaSii/vdLtLSM*! s&th str a in ltsis Itewast estch lish o d in th e in v e s tig a tio n s mentioned above* hut. a method.of
determining t h is change th eo r etica lly * and thereby elisixBatwng
some o f the tediou s con trol procedures involved in th e man#-.
fa ctn ro o f str a in gages* has s o t been developed*
*8ee appendix
Tim- b asic
'
]&a$W8 o f t&e gheBomaoOB i a a&jULJL
t o sna& l# ag e t o jprOgpwW e##'
■
imaergrb<M3&
th e o ry OQB#@ra#B# # *
I t i s hopea t&at the present worB*. oo&si&eriag. tka aMwAaWM»
O h a B g e f ro m th a 9ts%#&3#& S f p&to&t&sl e&e&gy o f Aeformatima.
may h e lp to throw ll#% t %pom th e prefelem«
Since r e s i s t i v i t y v a ries lin e a r ly with S tr e ss9 we may
w i t e fo r the r e e ls t iv it y a
o f a gpeolmen w i e r a t e n s ile
s tre s s
P * Pod*##)
where *&* i s the ten sio n c o e ffic ie n t o f r e s i s t i v i t y ^ a#& *pgf
the r e s i s t i v i t y o f the an stressea specimen,
%be p o ten tia l energy o f deformation* *W%,ls th e work done
by a ten sion tfT5 a ctin g through a displacement '?a ?,9 and may he
(•e
w ritten W *; i f&e,
A ssm lng Sooke^s law*, t h i s may last %rittWL&
J &
a) # a
\
$:0
.
.
Ise0I e —M=L ==
^
*
ybwa%Lg*s Modulus i s GafIaea by Sdbet equation B * T /A o * #
0 /1 ©
Mbaaee o = W L
'it ™
,
W ^Q :
*
S u b stitu tin g th e se valq es in &) me obtain
o r Sa;) e * V a ^ #
S u b stitu tin g th e
of V
from egnatloa 35) in @ #^ 18#
U p we obtain fo r the r e s i s t i v i t y in. terms o f the p o ten tia l
energy o f deform ation:
I ) p - P^l 1^#
V®" )
Ao&o
A curve of r e e ia t lv it y varaua energy of deformation should,,
th e r e fo r e , f i t equation 4 ) , m i l e r e s i s t i v i t y verm s th e squara
;3?©:0t ©f th e ejae3?s’F o f A e fe rm a tie ii #p%M %.©' a
_________________
m e 9%epe bei&g e g w l to
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easrva against idWbdb Iba gogpaEe
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#arga #e%&& he o f l i t t l e val%@* Geaaaee %&e aomtaal#y*$3*
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sm# ?A * SBaalal haoFe t o # e W kaB 238# t h e #@ 3^ # .& & ? »
.here a mathoA ©f aetetm iniag whether tha eaq&KEla*8c&Rl a # a f #
a OSCTfa o f the focm o f eqsatloB
I f idbe am ve o f r e a le -
tlv lig r Vsrase the#gm8%3R&G& Of # a
€kaRa8@ai$j%B #
a atra&g&t llste* 1#» w i l l mow # a t th e aa&a s a tis fF &#
o f th e form of 4 i ?
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&& a^grozlmate relaM osahl# Mtweea the t o t a l ceeletaaae
aa& the aaecgy o f M formatloh may t o AerWoA fmrn ooaaiAeratioa
of
*%*, a s# Boiasoh^s Batla:* V * . a s f&lle*#*
The reoletaaoe o f a
o f a s t a l Izt glsrse Sagr # » weH -
&#&#& rela tltm
:
B. » #&,
&
-
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Tahaare* fo r a sample ©mler a teh slo h o f
t3*>
f&* i e e^ g el W- Gqfe* snA IbSae ##&*-. W ^qpala
^ AA* ia t lls
t&e cea&g&lvlAy *p* =Kei (^vm TSgr.
,
tio a 11®
#
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e x p e rim a a t o e v e r gzo&e&oa # % 10 , t& e or& er o f m a g a ltg a a o f
n
## I s not more than 1& »
W i s o f the ardor o f magaltads
10"^ * w liile '5T0 0 xms n ew r Wlow th e order o f 10*^«
the seeond term, o f th e espresaioB f<w (-Ad « AA) .ie o f the or*
der o f magBltgae 10*^* %hile th e th ird term i s a t most
130 therefore n eg lect the term AZ^ fo r th e porposes o f t h i s
oxperiiiient and w rite s
A ^AA
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r.
With th ese veln es fo r ^p** *&** sa& W * th e eqa&tloa S)
may be w ritten;
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Ginoe
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aa#
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Performing the iD&laated aiylala&a
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1^rt-CiO@I
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o
gor the vainos o f
r^ntloned above.* th e a a r le s ocmvargem
1
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very rapidly* In f&at* the second team i s more than 1$ tlmea
t b s tb lp c i ts r m f so t h a t I t i # g @ 3 W .$ 8 # # t e
gbo?* t b s zweea&«:
&a& te rm s
3301 t& i# =EczniL* t h e ag^aW xm fear ^e@$6^e«e»
in . t e m a o t 'b e n sto a beossiBsi
5 = %
8i& #& & b tia8 A w
j& a T a3a# ia. t « m g o f * # ' fafom e&j &N
5») ft * &
By oomg&rlsem %&#& sgGK%&&c%i<&yf. 2 t may b s Zaeem IdBat &
Sbree o f *%* Tmeaae *w* wgaia reeem&Ke th e saree o f
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W e a ^ i t i a Im eeage o f _{^<w6iK$gal ^KOges*.
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Trersaa th e s^mer® ro et o f %# %WL# W m str a ig h t
slope' ©r whioh yields- im YSkpressloh f o r %*«
oqg&t&m EKi &e e e ^ o a r e t e a s
pesea o f
^$& #% $^% atea t h e 3 W o # a ^ tf o f
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a n a rmiW >®rls@ t h a t j& =
w ofetafs
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= -AM=* ^
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SyF.
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e o m a ^ may he- o%m&&a& #F0& eg*
Ibgr bot& ag t h a t 't h e ta%m
th e osrrre o f W versas
W
WxthS=S Ism M Bi
Shh 2& s W l e # f o r t h e p ar-'
com pating =GIisr r e s l s t $ ? i t 9 y
q a tf o b
the
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&a i t i e rsfa#& Ba. %& &&.#&
#8*6 iwaat e f ZkriEegpdbadbk 1 » 9W&a* #Wra* 8* 0» S*
&** 4 # &* 3 # &S45SL* iagassrtSF),*
a o ^ i^ ia #
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#@W4 %#& W fa tW l Ia-R R y <# t W fm a lla W a
JBsggB gga& !W & ldaP bea& w #
fWCKw- A w -Ww (BfBTewads
ae. a $ % 3 e e # im
(AmaigpA t& t& e
%#. *Ap*» b a t 2#> ^ r l v a t i O B &&' #&3#& b y «W w w 1% t&e- t i t w t R g e
^oaw aitta**
As # a y b e a e e # %b t t # aW v e
t&$B 1 0 W k
at f i r s t o r g e r e ^ ^ r o x i^ ti o A ^ W i a i a g ^ W y f o r &8# 3% ii#a e f *%*
#&& f a i r l y h i # w lm e a o f
t& e -w & lo #
th e w ii# .
m oasogm
In
t o o b t a i n d a ta r e l a t l a g t&e p o t o a t l a l en erg y Of
deformation to r e s ia t iv lty * &aa o f two v a ria tio n s o f Jwtbod
mlgbt be uaed*
Goa might simply measure the re sle ta o ee and
tanBlaa* and Gompate th e ela&gatioa from %&8ag*8 Modolue and
th e meaeofed len g th o f t&o gpeoiaea*
tlo n oooia he meaaweed d lr a o tly ,
Otherwise, the aloRga*
IElaei la t t e r method m # o&oeea
here* s la e e data on Ibhai m aterial used varioB ooo&iderahly as
given la haadboeka*
Apparatus oaed and methods, fo r preparing
the data Irixe p roseatatloo are o o tlio ed below*
The apparatus oonalated o f a sh eet metal box*, roughly IW
oeatlm eters la len g th , and o f ggimre orosa soetloh* IEksat Genti*metera , reen foread with oa e-h alf Iaeb angle iron* aa& Insolat^
ed on the a id e s, bottom end ends with about two inohes o f as*
W stos * A lo n g itu d in a l s ta tio n and a top view , Shewiag the
apeelaea la plaGe? are givea i a fig u res 1& and IB*
Tho elemp
was a p leas o f Iron rod* d r ille d longltud*
io a lly ,. and f i t t e d with s e t screws fo r clamping th e specimen*
This was brazed secu rely to th e angle iron reenforoemeata a t
one end o f th e box,
The clamp *#** eo&struoted sim ilarly^ was
used to fa ste n the epeolmea to & s t e e l wire lead in g through
th e p u lley s
and *&* to the weight hangar Ti*.
The p u lley
+F* was mounted an a h orizon tal shaft* running th e width o f
tW box.
The mounting o f t h i s p u lley was laauiatad from th e
Tbox w ith s tr ip s o f sh eet aloa* thus one end o f th e specimen
ccmM ire seotuiSed tteongb. tiie hoic to e lim in a te s t a t l o oMjfgos
sit&cmt o therw ise a f f e a t in® th e z%a1stsn.ee rmaearements e.
She re e is ta n o e between th e p o in ts ?A* aa& *B* o f th e 8#$*»
elmen was measured by means of a o e lf^ o o a ta la e l E e lv la Bridge*
t&e e u r re a t olamps o f WBloh were a t
aa& *D** sad th e potaa*
t l a l te rm in a ls were k alfe -ad g a olampa a t
and TB*.
tr a v e lin g mieroeaope&p .*1 * ami *8» , were iasal t o aeag*"
a r e th e oloagatlGm.^
S h e a s w ere m o w te d s e p a r a t e l y from t h e
r e s t o f th e eg ulpoeat on <1 8* TpjLgwa rnoalh® Sikwe le n g th of th e
:
j t
*
tKXKp BwsuLd 1% im r tle a l su p p o rts fa ste n ed to Iblie ta b le w ith wool
aerm m *
#& B old t h e m leroeoopee* IioGLeo w ere W ULlW thareogB
iblie p ip e to f i t th e su p p o rt ro d s o f Idbwa mlorosoopeSp th e ro d s
■ >
.
:
In serted > and. olampod l a p la o e w ith s e t eoreits.
S rs n s p a re a t tran sfo rm er o H was th en poured JLadte th e Bcoc
t o submerge th e speolmoa aa& elam ps.
Boeing th e ezp erlm aatt
th e d l l was a g ita te d manually* i t being B eeessary to a lia # th e
o i l t o same to r e s t b efo re ta k in g re ad in g s on th e m iorosoopes,
T aaperature was measurod w ith o rd in ary meroury therm om eters
d a rin g th e p re lim in a ry experim ents ^ end w ith a Beokmaan vaaenm
thermometer o a lib r a ts d i n hundredths o f a degree G. on th e
f i n a l ezp@rlmec.ts.
BOwever? th e re was l i t t l e aifferen& e l a th e
d a ta o b tain ed l a th e two oases* s is o e th e tem perature f l u o t m tio ii -was n o t v ery g re a t a s a a?uXe»
I t WOs n e e e a ssry to s t a r t w ith th e w ire t a u t so t h a t i t
iBOUld be and rem ain In focus under th e m iarosoopea,
The s t a r t *
I bq tension was taken a s the sene goiht*
ure# %W # o tlo a o f th e po&st
t&o flo e a e&a a t
between th e p o in t
Eieroseope See S aeas-
o f t h e gpooimea* f a r t h e s t from
th e o&8 RGat%o& o f t&a entire, w&re
an& th e alemp* a a wg&l a e any aH pping
in th e eiamp^ ama o th e r rlgi&^bo&y met Iona.
Miereaoope go*. I
moaaiarea ISbwa m otion o f ISbwa p o in t *A** tdtloh eonsl s t e h o f th e
e lo n g a tio n o f Iklie isidre; TbeKSnaetgai ?A* aah *]&?* aa& th e o th e r poaw
Olhlei mot lame megtlOBed above*
Aa each weight was* Sicbigwl to
the hssager* roaaimgo wore taken o% ea@& mlorosoope^
The
fero n ae Wtwean th o ae a&d th e reW lag # for- th e pra#&o%8 tenelom
gave th e motion oau#@& by th e a W e l tension*
% # g iffe re n e e
h e tw e n th e motion moasnreS hy 2fo» S SM th e mot io n Beagtireci
hj
Ho^ I @aw th e e lo n g a tio n an.® to th e ad-ae-s tengio:a o f the-
p o rtio n o f th e speoimen OP-Ser t e s t
%£&■$
fig o m 1 } ? Sinae th e
rigl&-hoSy motlona oni the elmigatlom o f BA (meaeareS Iagr both
mtWrooo^pee) WB t&tts BamwaHoA#
%> g h ta la th e IbcyW
aaJL elc#g&*
t lo n fo r stay teBBloa* i t waa meoeasary -bo mm up the elaaga"*
tio n o for eaeh lnorease in tension from Idfta aero p oin t to the
reqpirea ton al car,
$he r e a lstanae measures -as above ^ was reeordeS fo r each
tension and elangatlon? together w ith the tamperatnre o f the
o i l bath a t the time*
S lroot QRperiaentai data* then? eon*
e ie te a o f the reaSinga o f th e mlerosoopea* th e ten sio n 1&.&110*
grama^ Ehlvln SSrjLcLget roaSInga^ temperature, anS IKbwe o r ig in a l
■
.
•
■
IsBgtfc aM EaBdfes o f the sp ©efeea<,
SSie meWed -of' determ -fefe® tatie e3y^a^tii<m .***' M sr-4ik*a& y
been describ ed 4-. # te tenslom #sws simply eozi#@&te& $9 fSgMowsdSgk
(t>is weight o f th e eoBHeetxng wire l?e.feg segleot©d:| ^ fed .t&ia.
tea@lG& #ae $& o#ea agaiaa# t&e alo^a&fef& <m -0M3#na%y
paper, ^figoros & end 8) * asd th e Sapeai m dar the Ohrvea meea^
nred with e planiim tor fear; each p ofet oor^apohdfeg to #
e lo sg a tlo h .
!ISwa emorgy o f defofeistioii^ *%F** ims obtained from
IibdLer area by m nfeiplyfeg % th e TOSL&ae o f ^igsa* reproooifeed TGgp
each sqoare .Iixoh9.
fe oompotfeg1the r e s i s t i v i t y
the follow in g method.,
TWbladb e3Llm$natee. # e appraallm atfeB # %ae& f e d e r i v i n g t*@WWb)W
Qj and &:} m s adopted®-
fee- equation
ar
--
IRRiBk #se& t o ecmgpWGe th e la&ea%&
Csee p.® f )
* valiae o f 0*33 .
being need for. ^olsson^h R atfe^,
radfea
oorrespond*
fe g t o the p artien la r te n sio n *T ?* where the ehbsoript r e fe r s
...
',• V '.
. ' ' -
' -
'
'
to the number o f the reading, {see fa b le s J 8 XX and .XXX8, and
# . 8&Kt isBist oempq&ed Tbgr eWxtra^tfeg. the A%*.
2 # , &.&*f C&
* r o - 6 35«»
n. ., In th e e a se Wiere th e # a f t l d lim it m s eoWaWL
sa fflo lB B tly lse oanse a meahnr&bXy permmmit # a n g e f e radfea
(fig n re s 8 , it fed XO) * th e average m a W *
meastired a f t e r
th e te n sio n had been removed, was used in plaoe o f
-f^?
dear easing tension®
.iW'
Xhe. length.,
.and th e area
eaoh ten sio n were then eomputed by the agnations i& * id ^ n .
.
.
•
'
a",
as.d,
=S- r^-o
Sxe aeaBtxred resiata& ce was -s-ox^eetecl f w t eape^sAtire. by
th e rala&laa & =
g,, ■ W l
8ta&&ar& te m p e ra tu re
Istaaee a t a temperature
* %h@#& *&* la th e reelata&ee a t a
0* l a t h l # e a se) a&&
I s t h e ire#*
degrees above the a&aadard*
%be
value o f *«*# the temperature o o e ffle le h t o f r e s i s t i v i t y , #ae
taken a s G*0038& per degree 0* a t &0 0*
The i& ltla l^ p o ia t ee8leti#16y$
*
was eomputed. from th e
i n i t i a l point r sa lsta a a s TBg* aa& th e dimensions ?3*o* and tr#*
h y e g u a t l o h S i*
Bow* i f th e r e s i s t i v i t y remalae# eoastaat ua&er tension*
tb s a a tia ip a ted reslsta& oe *B&a* &t & tenalon
would be th a t
oompntad from the r e s i s t i v i t y *#Q,* asd would be equal to the
measured re sla ta a o s
&t the ten sio n
, that isa
zW - P 0 r
a.
BouBver* wo fin d th a t there la a d ifferen ce between the
aa&ioip&tea r e s lsta u o e,
» and IbIaei measured r e sista n c e
d ifferen ce m ist bo due to a ohau^> in r e s i s t i v i t y .
*
Bmce*
a t a tension *%** %%w i l l have a r e s i s t i v i t y *p%* d iffe r e n t
from *Pa*? 8G& the r e sista n c e *8%+ would be given by:
11} Ba - P a g -
D ividing 10} by 11} and so lv in g fo r *&&*& ** bb&aiat
i t TfiJUL &e a e te a tb a* i n oompating
* f o r a%m$ion
»
th e sgaatl<m &* * #{3?n
f erst A_ *
.-H-
■ ..
4 r ) ^ was nae& tm aS e# @f: t&a agq^G&Ws&e
- gfaAfi* (s e e # .
g q n etien #
tisea? h a t t h i n woqia have la#o&#ea ^Ba a # # W # # i< m s .%ae& &&
aer& via# I t *
m i * WBWl'- IxweIvaa acme e f t]#s.B
and t h e egxrog i s Gee o aly t o #g%K%c$0KK8&a3L
"
i n th e assumed v alue o f 9U5» ■ ■ ,
esA t h e
‘
7
;s
I n a c tu a l oom ^taticm y
•
'
_
se m u te d #
eq u atio n M $
ama IKbLlJS w i n e s g # # e & ^ m L t h e #wwx#e&
WA .M&isJW
p o in t r e s i s t i v i t j In sq u a t Ida 1@1 ho ^ e ta p tia e t h e r e s i s t . # '! ^
*p * f o r eatm t 4ms&>a
SSbKesBe v a lu e s .ear t h e ;ci*3d&g^#3&%8l3Egr TmsaeSt
^
'" - . - '. ' " . .
' 'them p l o # e a a ^ & o s t th e eaerg y e f
to
5U loa 4 |» |;f i g w e s S aa41S'>- ••
*i
• \? ‘
‘
. • -•
*"■*
go'(^ea& eqmm&o# #& 'it- m s e a ly %^geem##.W 3B3b8#f.-# »
measured r e s t s Uaahe -against th e eaergy- o f Aefor amtit#:=, ^ •f f i ^ r e s
•;
•- ■*-: !
5 , 9* sad I I )
The sam ples #@ea were'aogp&r
-
■
•
•
'
Sh
.
-
•
,
•
. . . ' » • • •
gauge, m anufactured TBgr th e m a e m d a # e e and Gahle G om pw *&
m shegon^ Mlohisan*
m e p u r i t y o f th e se w ire s ^
ogAWwy # m & a a l maaiygdLe v au ia f a # Ibct
a t m o#* o f
sueh tm%
-t6BR.a.-#e«@L#
w p a se*# list &Wr m re * i&lthr
09& Gmaeeliag, a# Ia tereet
ooBtered. mainly o# th e r e la t iv e
Obmige III realstm m e ?%&&& w angy
deformatioa, mid a e t o&
t&e meamzremeat o f any oonatentev
SBbla made I t po&elblB to
gae hlgbep te&slo&e* a# annealing g r e a tly redueas the Baaalle
strength o f ooppsr.
Tbe wires were somewhat kinked as a r e -
s a lt o f having been wound on spools* bat escsopt fo r @& iaarease
l a the measured elongation for th e f i r s t , and sometimes the
second readings» t h is seemed to have l i t t l e o f f e e t «
The s e l f Oaataised Kelvin Srldga need wag mamifaetnred
by Leeds and I%rthrnp Ooagemy* s e r ia l no^ aiS55d*
In eonjimo-
tlo n with th is* a heeds and ^orthrnp Ayrton Bhont» s e r ia l no.
was u sed t o d eeirease t h e s e n s i t i v i t y o f idle galvanooet*-
e r for I n i t i a l bridge s e t t in g s .
IEhe ^lvanomote r ^ a lso maim-
faotnrad by leeda and gorthrhp» was a w a ll type GKBKfesd; gal­
vanometer baving a a e n s tlv ity o f I t # ml<mmmp@res par m i l l l meter o f dofleotioaa*
IEbak mloroeoopes wore mamifaotnred by Wm*
Oaertner and Ocmyaany* and were eallbr&ted In two-hundrodths
off ii m illim eter, thas reading to .001 m illim eters by In terPQlatlcm9
-
ABB F38QBB8
1E fp in a l g ra p h s o f th e d ata: ta tee a a r e , g l w a on th e fo llo w =
l a g pages,s, to g e th e r v^ith t a b l e s o f d a t a from «kl@h th e y were
- - p lo tte d *
F ig u re I S s a draw ing o f th e arran g em en t u se d f o r
m e a su rin g th e t e n s i o n had.' e lo n g a tio n *
F ig u re s Z and 8 a r e "graphs o f t e n s i o n v e r s u s e l o U g a tlo n 9.
from w hich th e p o t e n t i a l -energy e f d e fo rm a tio n was com puted a
F u l l - s i n e g rap h s^ l i k e f i g u r e 8* w ere u sed f o r t h i s purpose*
F ig u re s % Bi, an d 11 a r e g ra p h s o f r e s i s t an ee v e r s u s en­
e rg y o f defo rm atio n ., w h ile i n f i g u r e -S t h e r e s i s t a n c e SS p l o t ­
t e d a g a in s t th e s q u a re r o o t o f th e e n e r g y o f d e fo rm a tio n to .
cheek e q u a tio n S).s {s e e p* 1 0 ) *
F ig u re s 5 8B& 1 8 a r e p l o t s o f r e s i s t i v i t y , computed a s
d e s c r ib e d p r e v io u s ly ( s e e pp* I S «, I ? ) * a g a i n s t e n e rg y o f
d e fo rm a tio n ? and f i g u r e 6 i s a p l o t o f r e s i s t i v i t y v e r s u s th e
s q u a re r o o t o f th e e n e rg y o f d efo rm atio n , t o check e q u a tio n 4}
( s e e p.» S ) *
.
F ig u re s f an d 10 a r e p l o t s ,o f r e s is ta n c e - v e r s u s te n s io n ? ■
Showing th e l i n e a r v a r ia tio n , w ith in th e e l a s t i c l i m i t ? ,- (##&
p p , 4 and
■A co m p ariso n o f th e value- of
p a r k ilo g ra m per- s q u a re
p
■■■
c e n tim e te r , and & in dynes p e r s q u a re c e n tim e te r* a s d e te rm in e
a d f r o # th e d a ta * w ith v a lu e s fr<m o th e r s o u rc e s i s g iv e n i n
.
IE=
ffei# ta b le i s irnalmW. be anas e lb o f f e r s a Wm-
SBkelaaatiag t h e M o * # o w a t M t # ^bM lM K Lo fpcm #t& a (Was #1&&
tb e
of
3EG& tba@ g3%
0bb&e 8W
*18 tQ33
63 q&@rl*r
JBeadbki aamiraagr*.
fa tb e aisboasiom o f th e ^eabita ^ wbeae%i» i t : i# 3&&q&KM
%
a%
gr
&& ?efe# t o a aipeoifle paMA-w .#
th a t j&gla&t gd&l Txa
ra 2 &Bpe& t o Ibgr ths.htmber glvea Ih IW
bas
:
'.
•
'
*
**Nk>** Ih
I
the eoaceapaa&ihg
t a h le‘ ' i $W
8 * the.
go$B&. 8 - o- f # $ #1 zv e b rege&&
.
_
C
t o t h e ^ o l h t a t ^#*-8# as; W *# #0I&& K W"®} &8 flgpipe. 3&* (a#*
#am.e #
-
21 -
T en sio n (Dynes x 10
-22-
O I n c r e a s i n g T en sio n
D e c re a s in g T en sio n
E lo n g a tio n ( C e n tim e te rs x 10
F ig . 2 .
)
T e n sio n v e r s u s e lo n g a t i o n
-2 3 -
O I n c r e a s i n g T en sio n
A D e c re a sin g T en sio n
3230
D nergy o f D e fo rn a iio n (E rg s x 10 )
F ig . 3 .
R e s i s t a n c e v e r s u s e n e rg y o f d e f o rm a tio n .
O I n c r e a s i n g T en sio n
A D e c re a s in g T e n sio n
E n erg y o f D e fo rm a tio n
F ig . 4 .
R e s i s t a n c e v e r s u s s q u a re r o o t o f e n e rg y o f d e f o r m a tio n .
-2 4 -
O I n c r e a s i n g T en sio n
A D e c re a s in g T en sio n
1 .6 8 7 0
e n e rg y o f D e fo rm a tio n (E rg s x IO4 )
F ig . 5 .
R e s i s t i v i t y v e r s u s e n e rg y o f d e f o rm a tio n .
O I n c r e a s i n g T en sio n
A D e c re a s in g T en sio n
1 .6 8 7 0
E n erg y 1 ^ 2
F ig . 6 .
(E r g s 1/ 2
x IO 2 )
R e s i s t i v i t y v e r s u s s q u a re r o o t o f e n e rg y o f d e f o rm a tio n .
R e s is ta n c e ( Ohms x IO- 6 )
O I n c r e a s i n g T en sio n
(^ D e c r e a s in g T en sio n
8250
T en sio n (Dynes x IO5 )
F ig . 7.
R e s is ta n c e v e r s u s t e n s i o n .
TABLE I
E la s tio ity - R e a is ta n o e - E n e r g y D ata o f a T y p ic a l Copper Sample.
No. 14 B. and S. Grange Bare Copper ,,ir e
No.
T en sio n
(Dynes)
E lo n g a tio n
(Cm.)
0
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
9 . SzlO 5
2 9 .4
3 9 .2
5 8 .8
7 8 .4
9 8 .0
1 1 7 .6
1 3 7 .2
1 5 6 .8
1 7 6 .4
1 9 6 .0
2 1 5 .6
1 9 6 .0
17 6 .4
1 5 6 .8
1 3 7 .2
1 1 7 .6
9 8 .0
7 8 .4
5 8 .8
3 9 .2
1 9 .6
9 .8
0 .0 0
„3
1.20x10
13.3 5
1 8 .4 5
25.10
33.20
4 0 .2 0
4 7 .9 5
55.40
64.80
73.20
81 .5 0
78.80
74.60
67.05
58.10
49.4 5
4 0 .3 0
30.95
22.8 5
12 .7 0
3 .5 5
0 .0 5
L ength:
IQD«56 Cm
R e s is ta n c e
(Ohzas)
—6
8231x10
8232
8234
8236
8238
8240
8242
8245
8247
8249
8250
8251
8250
8248
8247
8246
8244
8242
8239
8237
8236
8234
8233
June 18, 1946.
R e s is tiv ity
( Ohm-Cm.)
Energy
(E rgs)
1 .6 8 7 5 x l0 ” 6
1.6877
1.6879
1.6882
I .6883
1.6886
1 .6887
1 .6892
1 .6894
1 .6895
1.6895
1.6895
1.6893
1.6892
1.6892
I .6892
1.6890
1.6889
1.6885
1.6883
1.6883
1.6881
1.6879
0 .0 0
,
0.12x10*
2 .2 8
4 .6 2
8 .6 4
15.42
22.38
31.20
40.50
56.28
70.32
87.24
81.78
74.16
62.76
50.70
39.84
31.14
24.00
19.02
14.88
13.26
13.14
R a d iu s:
0.0820 Cm
(E n e rg y )V ^
(E rg s) 1 Zti
0 .0 0
0 . SSxlQ2
1 .5 1
2 .1 5
2 .9 4
3 .9 6
4 .7 3
5 .58
6 .3 7
7.50
8 .3 8
9 .33
9 .0 4
8 .6 1
7.92
7.12
6 .3 0
5 .5 8
4 .9 0
4 .3 6
3 .8 6
3 .6 9
3 .6 2
—2 7 —
140
120
1O
I—I
100
T en sio n (Dynes
M
80
60
40
20
-O-
T e n sio n v e r s u s e l o n g a t i o n
R e s is ta n c e (Ohms x IO- 6 )
F ig . 8 .
O I n c r e a s i n g T en sio n
(j) D e c re a s in g T en sio n
13080
E n erg y o f D e fo rm a tio n (E rg s x 10^)
E ig . 9 .
R e s i s t a n c e v e r s u s e n e rg y o f d e f o r m a tio n .
____ A------------ 0
140
„
to
130
y Z
S
R e s i s t a n c e (Ohms x 10'
I
^
/
M
2
I 180
I
3 no
©
O
©
100
O I n c r e a s in g T en sio n
090
13085
^ D e c re a s in g T en sio n
0
20
40
60
F ig . 1 0 .
80
100
T en sio n (Dynes x IO5 )
R e s is ta n c e v e r s u s t e n s i o n .
120
140
160
-29-
O I n c r e a s i n g T en sio n
(J) D e c re a s in g T en sio n
13110
E n erg y o f D e fo rm a tio n (E rg s x 10*)
F ig . 1 1 .
R e s is ta n c e v e r s u s e n e rg y o f d e f o rm a tio n
O I n c r e a s i n g T e n sio n
Q D e c re a s in g T en sio n
E n erg y o f Deformation
F ig . 1 2 .
(E rg s x 10 )
R e s i s t i v i t y v e r s u s e n e rg y o f d e f o r m a tio n .
- 30
TABLE I I
E la s tic ity - H e a la tc in e e - E n e r g y D ata o f a T y p ic a l Copper oam ple.
June 1 9 , 1946.
No. 16 B. and 8 Gauge Bare Copper A r e
No.
T ension
(Dynes)
9 . SxlG5
0
2 9 .4
I
4 9 .0 '
Z
6 8 ,6
3
8 8 .2
4
1 0 7 .8
5
1 2 7 .4
6
1 4 7 .0
7
127.4
8
1 0 7 .8
9
8 8 .2
10
6 8 .6
11
4
9 .0
12
2
9 .4
13
9
.8
14
L ength : 1 00.30 Cm.
R e s is ta n c e
E nergy
E lo n g a tion
(Ohms)
(E r « s )
(Cm.)
0 .0 0
,1 13086x10*°
0 .0 0
I .88x10
16.75x10
13091
6.40
30 .6 0
13095
1 3 .6 8
13097
4 4 .6 5
20.84
13101
55.9 5
32 .7 6
13105
69.55
63.6 4
13118
96.95
8 3 .2 0
13145
108.10
79.36
13145
108.10
71.31
13143
1 01.65
62.00
13139
90.10
51.40
13135
75.85
4 5 .2 4
13128
62.45
4 0 .2 8
13120
4 7 .1 5
3 8 .4 0
13113
3 2 .7 5
Ih id iu s : r = 0.6410
0.6409
TABLE I I I
R e s is ta n c e -E n e rg y D ata o f a T y p ic a l Copper Jam ple.
No. 16 B. and S. Gauge Bare Copper
No.
0
I
2
3
4
5
6
7
8
9
10
11
12
Length:
Energy
(E r^s)
0 .0 0
1.16x10*
4 .2 4
9 .8 4
1 7 .9 6
28.36
4 0 .4 8
3 7 .5 2
23.40
1 4 .0 4
8 .5 2
3 .6 0
2 .4 8
1 0 0 . 3 5 Cm
ire
Ju n e 20
R e s is tiv ity
(Ohm-Cm.)
1 . 6860x10-6
1.0869
1.6871
1.6874
1.6879
1.6882
1.6886
1.6088
1 .6 8 8 4
1 .6 8 7 7
1.6876
1 .6872
1 .6 6 6 8
R e s is ta n c e
( Ohms)
13115x10-*
13120
13124
13129
13135
13140
13146
13144
13140
13132
13128
13122
13117
Radius:
0.06409 C m
m m # ae
;
g a l a e a a f 3R«Bag*$k JBodbdbas* %* &n 4#&ee ;MBPiegsp@a* dew&»
tim e te r , ■eompute-d. from •'a tongatlom -a#a tension.) and 1^ S per Icito**'
gram iwae dK%Q83%& a e n tim e ta f^ oom pated
t h e d a t a hgr agBWB&lsat
CKMagapMaa -%ith maiaa& tr a m o t h e r # o a re a a $
r
Uader in e r e a s in g .t& nstoti^ reeisfcance: anti; r e s i s t i v i t y , r a r y
'
"
i
a s p r e d ic te d Uy e q u a tio n s 8) bm& 41 r e s p e c t i v e l y ^ ' so I obs as.
th e e l a s t i c l i m i t I s net. exceeded:?
aaci 12.)»
( F ig s r e s S7, &s, -§,$ Q3 -9* 11
a s w e ll a s t o -t h e e x a c t e s s .a h im 4) ? I b f a c t s. t h e r e seems- t e
he l e s s s c a t t e r i n g o f th e p o i n t s when resista n ce is- p l o t t e d
a g a in s t e n e rg y o f d e fo rm a tio n than i n t h e ' re sistiv ity -v e rso .,s* » :
e n e rg y curves.,
T h is'i s Sue t o th e f a c t t h a t th e e lo n g a tio n 9e'?
i s need i n t h e c o m p u ta tio n o f r e s i s t i v i t y ( s e e p,. 16* bottom
o f p age) , and hence- the- e x p e rim e n ta l e r r o r -e n t e r s twice- in to
t h e r s s i s t i v i t y - v e r s n s - e m e r g y c a rv e s * s in c e i t i s a l s o w e d in
the. co m p u tatio n o f t h e e n e rg y o f deformation -(see p=- IS* to p
o f p a g e }a
: d•- •r'
I h e d a ta conform t o t h e approximate r e l a t i o n Io q e. 8);
Both e q u a tio n s * th e r e f o r e * r e p r e s e n t t h e d a ta e -
q n a lly w e ll w ith in th e lim its - o f e r r o r .
When th e y i e l d p o i n t i s reached*, the. basic- assum ptionso f equations Bi and 4-,) h r e a t down* and th e d a ta become amUig-
nous. ’
Un d e c re a s in g ' ten sio n * , t h e c u rv e s d i f f e r g r e a t l y from
th o s e p r e d ic te d ,.
Above t h e e l a s t i c l i m i t * the. d a ta a r e am- -
M gnons f o r th e r e a s o n m entioned above..
Below the- e l a s t i c
lim it* t h e m id d le p o r tio n s o f t h e curves a r e s i m i l a r t o th o se,
f o r in c r e a s in g te n s io n (ex cep t, i n t h e ex trem e e a se o f f i g u r e
. r."
...
B.g: where t h e ' elaetie- lim it i s greatly exceeaea)« Im the .Iw-*
e r portIo a s11 iiow rer , th e r e s i s t anee ami r e s i s t i v i t y both See
crease, more rap id ly than preclieted,
I b fig u res 11 ami. 18;9- v&ere"
■the load was kept very Iow5, the owres- almost oolmoMey
H .
appears s th e n , that- i f the yield, point were' not exceeded, th e
omrves fo r increasing and decreasing ten sion wonld he co iset^
d e a t, bnt
- ,
-
a m e ta l a e s o f t a s eopper* t&er@ . i s a a # * *a@t*
-
.
:
-
\
...
-
" ..L
w ith even- V erysm all loads®,
"
fhe shape o f the o w ves fo r d eoreasisg tea slo n i s 4 m t o
the manner o f computing the energy of deformation,
fo r example
the- energy in th e wire a t point IB (figu re 8): was taken to Be
the area under th e top curve minus- the area under th a t portion
o f the lower curve- from point 11 to point IS= ' In a c tu a lity ,
t h i s I s not true,, for* w hile the area! under th e curve from
point 11 to. point- IS rep resen ts th e energy returned i>y th e sye~
tern when the. tension- was. decreased* the energy a t point. 11
the -t o t a l area under the top curve) i s not- the- energy stored in .
the wire* M t represents the energy put- into- th e system* part
o f which was d issip a ted as heat, (.see p»S§) , and part stored in
the wire in an unavailable form,.
A ctu ally, the a v a ila b le poten­
t ia l. energy o f deformation at point IS is, represented by the.
area under th e .lower curve from point 'SB-to point IS 5.'
i s th e energy f in a lly recovered from, th e system.® The energy
it.
-
# # regalitea i s regr&sm&aa By # 0 a#ea WWam t&e tw& m*#-
v es* W t th e e # l a a # %%y #E a@-W3mlaa%@ ±%mi iW&a&»d8Q#8db»
a*##M&ta#wb goBtloa Gf
MWt
SaBMggr T*R& 4 i8 9 ip e ta & 8 sW # a & &
3%BBajj&& s to w # 1& th e BdWr# 88 #&@%gy o f p#Rm#am&
&GfoimatloB,»
i t l a e v l l m t W a t when we jprcKM&gdL a # abepe*. eoib*
traotlB g from t&e eaergy regreaeatea by th e &#&& GBdae th e op*
p e r O trv e t h a t re p re a e m te d b y t h e a r e a w & er t h e 3a#@r e m v e
fro m p o lB t t o # o la t* t h e e r r o r I s ag m u latlv e* r e e u l t l B g &a t h e
clcam w ra IdsbS o f W e BeaistBBQQ- w ersu s e a e rg y e u r r e a t I W Iow^
e e en&»
As -BBQT he SGHBR from figBroo f OBl 10* ro slstsB o e v a ries
l l h a a r l y w ith ta m s lo a @& b o th Ih o re a e lB g Gaal S e e re a a lB $ ta&*
sloB W &&17 th e eimstlG lim it*
g w steep er elope o f th e IlaaB
f o r S e o re a a la g teB S lo h ^ ^ r t l e % * i a r l y a v i d e a t l # f l g o r e 16:* SUP
Sea W the Seoraaga $&
W& jbwwease 1& *%**" 4%%@a&
by th e permsaaBt # r e t m ia & o f tb# War# (s e e aq,m&ie& 93*
8lB.ee t h is l a tame? I f %e p lo tte d resistaB oe a g a la tt e#er@y
o f deformation again* t h is tim e memahrlhg the BBorgy by tb s
area sador the Ieoey eerve* @& woull ohtalh a enzsze o f th s type
reproaeBteS by e g m t lm W* w ith la r g e r valuee o f
and p o ssib ly some oha&ge In W
sa&
and
jSow&rer* t h i s wools
y ie ld ao mors Informatlom than th e method nsed* s la s e im have
&o meaanre o f th e f i n a l energy* l*a*$ th a t Saergy=Stored 1%
t h e w ire by permameBf S eferm afio B li
lienee 5,, t h e W rit ^ ie M s ©b ! ^ one n e ^ in lW -O oselnelens W
w its TesistnneQ - v a r i e s I iT e o t3.J ms tiie sg n a re r o o t o f th e
a v a i l a b l e p o t e n t i a l en e rg y o f " d e fo ra a tio n wiSMn. t h e e l a s t i c
I ia x if s a s p r e a ie f e tl by e q u a fio s 8 } *
f b e S a ta ta k e n above tb© •- e la a f te l i m i t y S eiS l i t t l e in**
fo rm a tio n , b u t th e .fo llo w in g d ls e n s s io n w i l l s e rv o t o b r in g
o u t what e o n e lu s io n s may be- S ram . tkOTsfr©my O l a r l f y some- o f
th e s ta te m e n ts maSo above- r e g a r d in g th e c u r v e s f o r S eeT easin g
t e n s i o n 5; an a w i l l o u t l i n e some o f th e S i f f i o u l t i e s t o b e o v e r­
come i n a f u r t h e f i n v e s t i g a t i o n o f She phenomenon*
i n one e x p e ria e n t.^ {f ig u r e s . S , 4 S and 6) t h e e l a s t io lim ­
i t b e in g exceed ed o n ly s l i g h t l y , a s I n S io a t©S b y th e te n s io n veT -s-us-elongation o n rv e I f l g x r e S l s t h e I n c r e a s e i n T o s is ta n o e
and. r e s i s t i v i t y was l e s s r a p id th e n below th e y ie ld - p o in t,
w h ile i n a n o th e r , C fig u re s 11 an d I S ) 't h e iiio re a.se i s more
rapid than .W lW 'th e y&s&a pointy, the o la e tio I W it a ^ in bo^-
--WTph'
-
-
la g exceed ed o n ly s l i g h t l y *
However., when t h e e l a s t l o Hm-•
.
•'
I t was g r e a t l y ' ex ceed ed ,, the r e sista n c e I n c r e a s e s v e ry Tap-
id. I y 5 a s M f ig u r e S s
T-
1
'
I n t h i s c a se s the- lo a d was so g r e a t
that th e wire continued to str e tc h without in crease o f te n s io n ,
I h i s - i s .ev id en t from an e x a m in a tio n o f f i g u r e 8 S. t h e
te n s io n - v e r s tis - e lo n g a tio n curve*
Between th e r e a d i n g s 7 and B
'"-TW
' ;:wl
( f a b l e 11) , the. w ire e v i d e n tl y c o n tin u e d t o s tr e t c h * s in c e
' ■
th e e lo n g a tio n a t p o i n t S-, -at a lo w er t e n s i o n , was t h e same
• ••.
gas that at 3KX&Q& ^
the
da# mot' ^ e r a & e # be*
tsR&
&
&these readit&B ^j&lgsaa& 8#-* AWtheoe iwieat&Ra that the
%)#& igag* jalsised&
caai&
iigg $e #&&Wk:&3#e 'EN
ax&
aB
bdboai;*#2
&%B&
9 .(flgai* 8}* '#& *&2e gae 4@WW6»g: t& e%wgg*e W k» t&le
tmkslim eacL the point VimaM have Wen moved fartWe <&
3j8*&
gr'
1itk&<6eAg8$lW aadLs bad IK
tB
G
kMtMfgd %W* ta&aa #*»&
&WAwei
rmievhn.g the load,
"The 3B
%
&
G
H
a3&
3w
aaB
$kabtWge- in dimemeiona iogtek* '&
&
tMe ease*, a g&eat faster $& oatsimg the resietaage Shamge.,
Also» as.the wire was ooatIw itg to eicmgate^ the ehange was
33*34%ieothermali and the rise in temperathre of the wire also
Ssrneea the roaistaaoo to lnoreaae rapidly.
!Ebeee factors*
then* tana to dbeeore the effWt of tmmloh in th is ease..
32a additloh to these m e t ^ S T ^ t h a w e r g y pat in&e the Sye*
- tom beyond the elastla limit is not all stored as. potential
SBeegy of a«f6mstioB$ IaB
iedb- j#$. &t eam&et Taet regained f&o# the
FV
sy stem && t h e same way a # i f tW - e O a s tio i± m tt W b e mot m eow a^
e#* & por&iaa of I t !Lss MA &
&oeeeeeaWs the f^lotloasl. " '
■
..
fopose TW
ltailBL the iaeta&# th4 !Las af^lpstaa as Iaaw
scG
, while $
portion le retained in th e .defarmed' metals h&avallabla to do
work :&
&retmhiing the metal tomrd I ts orIginal state..
#e
WWtaa le retiar&ea iESfSgB
i IG
B
uet sy#em #&&&the veWA* @
&
e re­
moved.
ghe energy stored $& the is&ee hy stretohing above the
elaetie limit la* not the aama, then* as that reprohehted by
the area under the dnrw»'
Zn oeder t o iavew tiaote th e w arlatloa o f a e w lo tiv lty be^moaaa t&e e l a s t i c lim it,, a methol o f letam ilM ng th e am&o&t o f
energy stored l a th e germaaemtly aeformed %lre m&at be dmrlaoa^
and* almeo lolascm^s W tlo earn not bo r o lle d agon to gl-ve the
ohamge l a rad las a t th ese te n sio n s, & ^ reelslo a method -fas*
measaring th e radius o f th e sgeoleien ander teaalon at a l l p oints
of I t s len gth mast a ls o be developed^
%& method o f these ex­
periments permits one to measure th e energy not regained from
th e system* but I t osamet Ia d iea ie #L@t p o rtlo & o f t h is energy
is retained In the wire., nor how the addition o f this energy
affects the resistivity:^, except that when a m r © is permanent*=
Iy deformed* the resistivity is inereased.
Baecgy met regained
from the system was tabulated with the correspondIng oba&ge la
resistance, and the resistanca change foe a certain inoremsnt
Of energy computed for each ease* bat the results varied as
mtteh as SOO per-omit , and 'were therefore Aeesed not worthy of
consideration, exeept 1& that they established the sign of
as positive above the ©lastIe limit,
P
Mx ■inolflentai result of the experiment s m s a eonf Irs=
ation o f th e r e s u lts o f Bridgman and Bolniok In th e measaremant o f the u n it change o f r e s i s t i v i t y with ten sio n .
As may
be seen from SDnble IF. th e value o f ^ d e te r m in e d from t h is
' P
data i s in c lo se agreement w ith the r e s u lts o f Bridgman and
B olnick,
The value o f B a lso l i e s w ithin the lim its of the
-rallies fom M i>r et-hers*
BrMgman5S eg aation . I s a ls o oh tain ed S a e M e s t a lly M the
d erivation o f the r e s I s ta a ee^ e a er g y . eqnatlQB$. th e d e r iv a tio n
b e i n g ' Ittelm led Iaerewitli5 e v e s thoagh i t -eoaM a e t he. d e te r s
Blned whether th e same d e r iv a tio n tie s been g iv e s elsew here*
4 p o s s ib le a p p liea ti-o n t o th e problem o i s t r a in g a g es I s drawn
from t h i s e Q p atlos5 and th e stra in , s e n s i t i v i t y f a s t or f o r
t h e m a te r ia ls used I s a ls o computed.
a s ah appendix: to th e t h e s is *
T his m aterial i s In slu S sd
a r m B /g g s a w
e& o&ag
lEhe ,str a in ,s e n s i t iv i t y iactor=^ o r -f7SagO fa o to r ^ o f a r e s latamee wire s tr a in gaga (see #* #) i s 4efineA a s the. r a tio
An eq u a tio n f o r t h i s r a t i o in term s o f vV-t I
a iii
f Ba may be. e a s i l y -S eriy ei from B r M g a a sis B gnatl o n , -,-.
1} - ^ - -
-
iF6' •
AjiL-*v az%
I & $ * ^ ^gp
by remembeW.## IAe
@ab?
s t i t u t lag. .in, ili,. anS _r e a r r a n g in g t h e ' terms*, we o b ta in :
. #&
.;,
W iieli we o aa s o ly e f o r Ifbwe gB&aset f a o to r .:
Siii
= JL * a n 4- #B
'• I f ^P4V 5-.fx? ,. anS *&< r a n b e SotermlmeS t o a ' s u f f i e i e n t
Segree of aoeuraeyf equation il) may %$ uaeS to Setermlne the
str a in s e n s it iv it y f a s t o r fo r the- m a t e r i a l , -as is- done- below
*- - ■,
, -* -
f o r t h e copper w ire used in t h i s experim ent-p. « 0*38
| e f o, p - IS )
-
• •'"••.
I- » 12,0 x 10^^ dynes/om.% * I-SB x IO^ Kg*/om&% ,-(fable i ? |
0 * 1 .3 6 x IO^G em ^/% -
4 ^ A s a,
i fa b le W)
= 1+0.6G+&.66 = 4^32
3B@ri#&&&agB& &y%%*8 @f
Wm&W %#BcB&8
g&dW8&
#& # e 6 -j9tgi%g#»a%ec33&gE ^kas Te^GeRsr.3%ir-i&&wgk agasBdb $W& ig&sst a#i6#& a #
#a%& lpltet $@#8 '## JbKzBBas&i&gs 3#5maa# ^wW &# i&W8e 3BSyg8&ss##8a&&y asG f##8 t& e g*@» -^Be^ea^ ^88&a%08#^b8&3*#W&&J&#8& f@r th $ W W i# & 4g%&9r3%E #WW#& ^8%9&* 3#&W& @8g88&a#*t
m a## A
%U3« W ( w #*$$& »'
'"
-' -
OZBBB ARD 80aS8&#BB
I.
^omLIMBOE, Tremat Boy* Sao*, 1888* 174, I (o ite a l a m #e*
RatifeeiEy-s tilTlie lle t a llie S tateif i »•,
&.
BRTDmMi,. R« %*? R roe,.Amer* AoaQ* Arts S e ! ., 1921» 59*
117,
s.
&.
RomiCR, m m T , m y a , %ev»> ie so * $&* ms*
The M etallle S ta te , R* 85* (Tfee 0%#ar& TB&&*
v a r s ity P ress, Lonaoaj, LBSl)-,,
а.
mimlSOR, Dv Mt* g la o tr o a lo s * &9&S* IG f 1&&*
б.
SOEBmiKOF#* Matfeematloal Theory o f B la s t le lt y * (Bfomk
Rnlyersi t y , ProylQenoe, 1941i$ mlmeogragfeel*
f'
. ■ .
?* SGIEmOS ABSTRACTS, 1939, Abstract No. 8763^
8«
RATE ARB LAST* Tables o f Rfeyslgal anQ Gfeemioal GoastantSf.
&* RB*. (Ici#Bs&*s, Green an! Gom^any, Re# % rk, 1935) *
9.
TTRi.T-T. HARRY Go: 3 Tesetboofe l$i I l e o t r i e i t y and Magnetism*
jgk 129* (aafeB Wiley and Bone, Row York, 19411^
TO* BAmBOOK OF GHmiBTRY ARD MYBTOBt TwOaSyrmam IBaitaLoa*
(Chemical Robber Publlsfeing Compeay, Gleyelaad * 1845>*
MONTANA STATE UNIVERSITY LIBRARIES
3 1762 100 4632 1
#378
- K47v_____ ___________
81292
Kerttula, Walter T.
___ d a T
E
_______________ I S S U E D TO
fa > 66/,
N378
K47v
cop. 2
/, 81292