Table Of ContentTHE DEVELOPMENT OF PHOTOEIASTIC METHODS
WITH AH APPLICATION TO SCREW THREAD PRCBUSMS.
- . .•'* :* **.. ‘ * . a. , . ^ . • * * V'*-
by
Salah. E.A. BAYCUMI, B.Sc.(Eng.)
A thesis submitted as p art of the requirem ents for
the degree of Doctor of Philosophy in the V ictoria
U niversity of Manehe&ter.
College of Technology,
M anchester. May 1951.
ProQuest Number: 11004840
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ACKNOWLEDGEMENT
The w riter wishes to express hiB thanks to
Professor H. Wright Baker, D.Sc., M .I.M ech.E., for
his in te re st and encouragement, and especially to
Dr. J.H . Lamble, M.&ng., Ph.D., M.I.Mech.E., M.I.N.A
in whose laboratories the experiments were performed
for his able supervision and guidance throughout the
research. Thanks are also due to Mr. J.W.Flowett
for his valuable help in machining p ractice.
C O N T E N T S .
SUMMARY Page /
I. INTRODUCTION Page 2.
I I . THEORETICAL AND EXPERIMENTAL
T^OTiBKTiarrr^rsras^cPTic
g g ^ fT C R " g c ^ 5 im ^ a A T im X s page /*
1. Basic Concepts.
2. A Mechanism for B irefringence.
S. Mechanical Behaviour of Diphase
Structures*
a# F in ite deformations of the e la stic
network skeleton a t the softening
tem perature.
b . Mechanical behaviour a t room*
tem perature.
c. Equilibrium mechanism of stress*
freezing.
4. Stress*B irefrlngence Laws*
a« B irefringence law a t the softening
tem perature.
•4
b. B irefringence law a t room*temperature.
c. B irefringence law a fte r freezing.
5. A pplications and Conclusionss*
a# M aterial fringe*8tress co e fficien t
a t the softening tem perature.
b . C alculation of afte r-creep .
c . E ffect of fu rth er cure on the
m aterial frln g e -stress co efficien t
a t room-temperature for C atalln 800.
d. E ffect of an in itia lly frozen
compressive s tre s s , along the wave
normal, on the m aterial frln g e-
stre ss co e fficien t a t room-temperature.
e. E ffect of an in itia lly frozen
s tre s s , p a ra lle l to the plane of the
wave-front on the m aterial fring e-
stre ss co efficien t a t room-temperature.
f . Hind e ffe c t.
g. S tress-optic analysis beyond the
e la s tic -lim it.
Ill# A R QOM- T£LIPERA TURE 3-DIMENSIONAL TECHNIQUE
. ITH AN APPLIC/TIClT~Tr~SCRE\7'THREAD
PRCBUSMS7 Page
1. General C onsiderations.
2. Coraposite-Model Technique.
3. A pplication to A C ircular Shaft
with A Sem i-circular Notch,
Loaded in Tension.
4. A pplication to Screw Thread
Problems.
5. A nalysis of R esults.
CONCLUSION . page
APPBNDICBS Page
BIBLIOGRAPHY Page
SUMMARY
In th is th esis an attem pt has been made to
inv estigate the fundamental principles underlying
the ap p licatio n of photoelastic methods to stre ss
analysis problems and to show th at the th eo retical
considerations Involved in the present methods may
provide m isleading data. A three-dim ensional
room-temperature technique has been developed which
is su itab le for symmetrical bodies. Results
obtained from the technique are compared with
ex istin g experimental re su lts and mathematical
so lu tio n s. Furthermore, the technique is applied
to the problem of load and stress d istrib u tio n in
screw threads, for which the available existing
knowledge on a q u an titativ e basis is fa r from
adequate.
I . IMTKUXiCTION,
The app licatio n of stress-o p tic an aly sis on a
q u an titativ e basis to a transparent model which is
geom etrically sim ilar to its prototype is based
essen tially on the following three fundamental
*
p rin c ip le si-
1* Existence of a unique stre ss-o p tic
re la tio n for model m aterial9 which perm its the
evaluation of stre ss components from the fringe
pattern*
2* The stress d istrib u tio n governed by the
m aterial s tre s s -s tra in re la tio n is the same for
both model and prototype*
5* S tric t sim ilarity of boundary forces in both
model and prototype*
The lim ited fie ld of application of stress-o p tic
analysis by present day methods and m aterials is due
to the fact th at the present th eo re tica l considerations
underlying stress-o p tic analysis give no clear
conception of the a c tu a l m aterial behaviour when strained*
* These principles w ill apply i f only body forces
are of negligible Influence on the stress distribution*
3
The knowledge of such behaviour is required for the
development of improved m aterials and fo r devising
new techniques•
So fa r, the present theory of stress-b irefrin g en ce
only determines a stress-o p tic co efficien t C which,
w ithin a lim it of proportionality for the m aterial,
expresses the re la tiv e retard atio n r in wave-lengths
as a lin ear function of the difference of the principal
stresses in a plane p a ra lle l to the wave-front* The
8tre ss-o p tic law is expressed in its incriraental form
by
dr * C d t. (p - q ) *
where dt ■ increment of thickness along the wave-
normal p - q are the "plane principal stresses" 0
p a ra lle l to the plane of the wave front*
R otation of the axes of plane p rin cip al stresses
along the wave-normal is generally of n egligib le
* For the actu al m aterials, under constant (p - q ),
birefringence changes with time} a phenomenon th at
works in p a ra lle l with mechanical creep in the
m aterial• The value of C w ill not be constant*
In th is resp ect, the stre ss-o p tic law should lose
its uniqueness*
0 "Plane principal stresses" are defined as the principal
stresses resu ltin g from the stress components which lie
in a plane p a ra lle l to the wave front* At each point
there ex ists only one set of p rin cip al stresses*
However, there ex ists a t the same point an in fin ite
number of "plane principal stresses" depending on the
d irectio n of the wave normal*
