Elasticity and Internal Friction of Beta-Brass

125 Pages·7.697 MB·English

by  Artman, Robert A

ELASTICITY AND XNTERHAL FRICTION OF BETA-BRASS
by
Robert .£* Artman
A thesis submitted in partial fulfillment of the
requirements for the degree of Doctor of
Philosophyf in the Department of Physics
in the Graduate College of the State
University of Iowa
June# 1951
ProQuest Number: 10992028
All rights reserved
INFORMATION TO ALL USERS
The quality of this reproduction is dependent upon the quality of the copy submitted.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if material had to be removed,
a note will indicate the deletion.
uest
ProQuest 10992028
Published by ProQuest LLC(2018). Copyright of the Dissertation is held by the Author.
All rights reserved.
This work is protected against unauthorized copying under Title 17, United States Code
Microform Edition © ProQuest LLC.
ProQuest LLC.
789 East Eisenhower Parkway
P.O. Box 1346
Ann Arbor, Ml 48106- 1346
I t la a pleasure for the author to
eagres# his indebtedness to professor E* F. t* ’
tyndall for hi# supervision of this problem and
fa# enlightening discussions' that arose at' various
timesf. to Hr* Donald 0. Thompson for permission to
Include hi# determinations of the rigidity moduli
of mm crystals and for his assistance in the
laboratory! and. to Hr*. J* 0. Sentlnella and Ms
©hop staff for precision work done in construction
of some of fhe apparatus.
IE! « -f * ;«j W ;#' #,*'*;# « %: * ■* * *
:;$& ^ ^ A^lyoiO.of Ci»3rstnl» ;* «, • »
. i l l ' i ' ,.. /*> * * ¥■■ * #■ * *■: * * # * *■ * * *
| f T \i ,* # -* * * t * ;#: * * * :*
- Y ' INNWI:
A* Elastic 0#cfflel0Bts* » *• « * * » •
B* I&tcrmi Friction At Boom
■ •fAw^Atnr# * * * * * * * ♦ * * « *
-Y I :t femiserate© effects
A* of t&i *
S% fc^crAtec Jtepondojiett of foong1©
MoAttl'ttO
* * * . * # ■ ;*■■.*■ * * 0 '#' ♦ »
' C* ' T©isf>©fAtw I^cMofier of Intoroal
F flO ti^; ■'*'■* >.' .#■, r;»’. r *■.'■ >0 0 * * *
ffl- aomorF of Itoitiit*,
f ill MMU$mm*
1 ,: ' *&#• '9tR^4M^.:<ESaNpn^%^^ , >«► 13:
# Beeifroeal X€rogf s Moaii3.i fs% 0yieotof;io& * • 2?
:; 3 ■ ■ f»* „ n m $ topHtoto fm Crystal
1% lf*$,* % * 3&
«f * * * * * * * * * * * * * *
. of Crystal < xi20)** %1
'■"%ft t o * J
%B of Crystal So* 1# {x 120} • hi
Jfc of crystal so* 8 (x i 2o). • hz
5® . Oofflfoslt®- Ittoropto tog?o$fe of $ry*4N4 So. 6
(X 120) . * * * * - . * * * * * * • • • * • hZ
€& Mieroptotoipraph of Crystal So* 12 (x 120)
Before .i n i freetiae&i * * * * * * * * * * *, * h j
61 Mcr©ptotofrap& of Crystal to* 12 (x 120}
Before tool tyaotaaeiit, * * * ■*. * * * * * * *. h$
fA Micreptoiograpl* of Crystal Ho* 12 <x 120}
Before Meat. &te$Ammk, * * * , * * * • « * • « * w
7B Mieroptotograph of Crystal to* 12 (x **80)
After tost freatmeaat * * * * * * * * * * * hh
8A Composite Mioroptototrapfe of Crystal to* 12
tx 12©} Before toot Treatment * * * * * * * %5
SB Composite Mieropfeotograph of Crystal to* 12
(x 12©} After Heat freatmeot * * * * * * * h$
f Projection Pi&gram for Crystal to* 8 * . • h8
10 Projection Blagram for Crystal to* 12 . . * **9
ir
SI Reciprocal Vtmttg1* MO&Ull tm
Braes Vs# Composition « ..* .* * « * * * * * * ■# 0
If ■ i; Relative. Variation of Observe#. BeelproeaX . ■
fount'*# Moinli Vs* Temperai»e* * #. .* * * * #
•Beletiv* Variation of iecip^eai rotmg*s
IWull in the ftelmtipel Directions Vs*
tampere^re * #■ •# * # * ’# 4 * * * * * * * 4 65'
■' V»* fo&porat^fo # 4 ' 4 * « 4' 4 * * 4
Reciprocal feramg*# t4©iuXus fa-*- temperature1
for Crystal Bo# * * * #■ ■# * . # * * *.#.** * 7^
4
14 Reciprocal f©mng*e Modulus ¥9* temperature for
Crystal 'Be% If# * ■# * * * #.■■♦» * * * * * ■ * * * 73
If ^Contribution of Diserier** fa* temperature* * 77
18 Reciprocal feung*a Ue&nll for PoXyoryetaXXln©
Beta**ltaes fa# temperature * * * * * * * *■ . if
If Decrement of tim fMHtea Crystal Vs* temperature 84
20 f^opertlonaliiy Constant K Vs* Temperature. * B?
21 Values Of R^ for Crystal I©* If Vs. Temperature f|>
if Decrement of ®eta-*Brass at- 21 Kilocycles -gee**
Va.#, 'temperature -* * * * * * * * * * * * * * * 92
23 Decrement of Bet&^Brass at b2 Kilocycles•Sec*2’
f»*. temperature * * * * * * * * * * * * * * * 93
»'Correote4w' Values of the Decrement of Beta*
2&
Brass at 21 Kilocycles See’*1 Vs* temperature 103
25 "Corrected1* Values of the Decrement of Beta-*
Brass at **2 Kilocycles see*! vs* temperature 105
v
-fMMM- w mmM®'
' ^ -i* * .'W; . ;? ‘t ■*-. * # •* ■# f W
ft-. • ■':■ ■ \ of \ ,v
« * # % « # ■ * # * * * ■# # # # ■: 3N&
I lf ®©©p«i*io©n of ' *1^ noted* >
IWNlflW '# f f # ■* •* # * * ■’♦ * % * I®'--'
|f Odjspoollsio** • Pepestaonoa • of Poviood fiopMo
llOOafO&fO * * # * # # 't , •* * •» -4 * * 4 *: * If
f fomo©rattir® f&irlafcion of f®tmg*s MaAAl ■:
in ttot frl&olpal Pftfootitmii * * ♦ * # * « 6©
If Boiotfo# fgqpiation Of Booiprooal M ttt
In' tfe* Firinofpil Dfffegfiono * * * * * * * 6©
v i
1
Chapter t
m o w c n m
Ehe beta-phase of th© eopper-alnc system is the
on© which results from approximately Cqul*atomie mixture#
of the two element#* It# crystal structure l# body-eea-
terei cubic# end at room temperature it possesses a high
degree of order* In cry# tel# In which two type# of atom
site# ere present in equal number#* the long-distance
order Is defined as the difference between the probability
that an atom will occupy its own kind of site and the pro**
bablllty that the other kind of atom will occupy this site*
is the; temperature of the beta-brass is raised* the long-
range ordef disappears gradually first* and then at an ac­
celerated rate* becoming aero at a critical temperature
which depends slightly on Its composition* Du# to simpli­
city of structure and the order-disorder transition,beta-
brass offers interesting possibilities for experimental
and theoretical Investigation*
During the past decade many studies have been
made of the elastic proper tie# of beta-brass*1*2*3***'^
I* Wayne Webb* $&»*• ggy* 55# 29? (1939)%, 4
V3* ww** a* Good * Phya * Bay* t>u, omop 308 (1* u
as to the values of the ©Xattle eeeffie&Mtta*
5
aese, that by X,aaaru»,*. was the &m«
Xu
U»#d to determine all throe of the ‘m
fieieubs* Since his quantitative analyse® of
l&eaiseXvea Indicated that hie crystal® were near the sine*
rich aide of the phase boundary, it was felt worthwhile
to investigate the elastic coefficients on the copper^rloh
side of the phase boundary and ©van a small way into the
with measuring the elastic coeffl-
near and of the beta-
equally wor thwhile to measure
internal friction for
is particularly true the transition from pure beta
crystals to those ning Indus ions of the alpha-phase*
For forced of constant hut small amplitude,
the decrement is m the ratio of the energy dla*
sipated per cycle to twice the vibrational energy and 1®
a measure of the friction* this
3
factions of one another# Iwmm* application
of etrfoftr ik followed by ralawtioms of irations kinds.
As ft stress and stfftta are oft longer in phase.*,
living vtm. fft ft dissipation of energy. .
for the psrpoee of this Investigation a m t of
sii^ift ' osfstftift having suitable, variations in ori®nt®M^
and grown*' Using a dymmieal method*
the Youngfs modulus of ton crystals was determined at room
temperature# and for five of thes© m a funetion of toft*
perature. the Internal friction at room temperature and
the variation of Internal friction of both beta-bras3 end
quarts with tftmperatore were also measured# Precipitation
of the alpha-phase occurred during the heating of $mm of
the crystals through the order^dlsorder transition*' the
effect on Yeung*© modulus ftnd the internal friction of the
resulting inclusion of the aXpha-ph&se within the beta was
investigated* fhe rigidity modulus at room temperature
of some of these same crystals was determined statically
by Thompson.6 His results combined with the Toting’e
64 D* O# ftaapson* thesis, State University of Iowa, C19P>*
modulus results give the value of the elastic coefficients
at room temperature4 ,