prof. niguse tebedge msc paper
Post on 06-Feb-2018
216 Views
Preview:
TRANSCRIPT
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
1/115
L HIGH UNIV RSITY
Residual Stresses
in
Thick
Welded
Pla
ME SUREMENT OF
RESIDU L
STRESSE
A
TU Y OF M E T H O
RITZ
ENGINEER
l SOR TORY
LIBRARY
Negussie Tebed
Coran A
lpst
Lambert T
Februa
ry 9
Fritz Engineering Laboratory
Report
No 337
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
2/115
Residual
s t r e s s e s in Thick Welded Pla tes
ME SUREMENT
OF
RESIDUAL STRESSES
A STUDY OF METHODS
by
Negussie
Tebedge
~ r a n
A. Alpsten
Lambert
Tal l
Fr i t z Engineer ing Laboratory
Department
of
iv i l
Engineer ing
Lehigh
Univers i ty
Bethlehem Pennsylvania
February 1971
~ r i t z
Engineering
Laboratory Report
No. 337.8
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
3/115
337.8
TABLE OF CONTENTS
ABSTRACT
1 . INTRODUCTION
2.
THE
METHOD OF
SECTIONING
2.1 In t roduc t ion
2.2
Prepara t ion
o f
Tes t
Specimen
2.3
Measuring Technique
2.4 Evalua t ion
o f
Data
3. THE HOLE DRILLING METHOD
3.1 In t roduc t ion
3.2 Mathar s Method
3.3 S o e t e s
Hole D r i l l i n g
Method
4. OTHER METHODS
A BRIEF
SURVEY
4.1
Grooving-Out
Methods
4.2
Gunner t s
Method
4.3
Schw aighofer s Method
4.4 Def lec t ion Methods
4.5 The Trepanning Method
4.6
The
X-Ray
Method
4.7 The Ult rason ics Method
4.8 The
B r i t t l e
Lacquer Method
4.9
Indenta t ion Methods
5.
SUMMARY AND
CONCLUSIONS
6. ACKNOWLEDGEMENTS
7.
TABLES
AND
FIGURES
8.
REFERENCES
i
5
5
6
10
15
18
18
32
4
4
43
43
44
46
47
49
50
52
53
56
57
104
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
4/115
337.8 i
BSTR CT
ne
of
the major
problems associated
with the use
of
metals a t present i s
tha t created
by the presence
of
residual s t resses .
In general , residual
s t resses
tend to
reduce strength; in some
s i tua t ions
however, the i r
presence
may
improve
the
st rength.
The various phases of the
manufacturing processes
causing
residual s t resses are too
involved
general ly
to permit even
an approximate
prediction
of the magnitude
and
dis t r ibu t ion of them based on theoret ical
considerat ions.
I t
i s
natural therefore , to resor t also to
experimental means
for
the i r determination.
Unfortunately,
residual
s t resses cannot be
measured
di rec t ly
in
the
manner
tha t applied
s t resses
are measured.
Thus, the measurement of res idual s t resses i s ra ther del ica te
requir ing
much time, patience,
and expense.
In
th i s
paper,
some
of
the
di f fe ren t
techniques
of
residual s t ress
measurements
are investigated.
Special
at tent ion i s given to the measurement
of
residual s t resses
in s t ruc tura l
members where
the appl icab i l i ty
simplici ty,
accuracy and
saving
in time each
method
can
offer are
discussed.
For a specif ic comparison of a number of methods,
actua l
comparisons were made under
laboratory
condit ions.
Measurements
of
residual
s t resses
were made using
the method
of sectioning, a destruc t ive method, and two different hole
dr i l l ing
methods both
semi-destruct ive.
For comparison,
the
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
5/115
337.8
ii
methods
w r ~
app l ied to one
specimen
having
uniform
r es idua l
s t r e s s d i s t r i bu t ion along i t s l eng th .
The procedure
of t e s t i ng prepa ra t ion
o f specimen
and requ i red
t o o l s and
measur ing dev ices
working
cond i t ions
and
s imi la r re l evan t in fo rmat ion are descr ibed . The record ing
o f
data as wel l as i t s i n t e rp re t a t i o n
i s
discussed
including
both
manual and
automated procedures using the
computer;
the
necessary t h e o re t i c a l background i s supplemented in br i e f .
The poss ib l e causes of e r ro r s during the record ing and
i n t e rp re t a t i o n of
da ta
and
t he i r minimizat ion are discussed .
othe r
methods
of r es idua l s t r e s s
measurement
which
may
be of genera l i n t e r e s t a re mentioned and
list
of
re fe rences
i s
presen ted .
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
6/115
337.8 -1
1.
INTRODUCTION
One
of
the major
problems
a t presen t assoc ia ted
with the t e chn ica l use
o f
meta l s
i s
t ha t o f
r es idua l s t r e s se s .
Many schemes
and
methods have been dev ised over the p as t
e igh ty years for measuring r es idua l
s t r e s s e s
s ince
Kalakoutsky
performed such measurements in 1888. h i s t o r i c a l survey on
methods
o f
measuring re s idua l
s t r e s s e s
can be found in Refs .
1 2 3 and 4.
Severa l
papers
deal ing
with
the var ious
methods o f r es idua l
s t r e s s
measurement have
appeared during
the
l a s t
few yea rs . The
v a r i e ty
o f proposed
methods shows
t h a t r e s id u a l s t r e s s measurement still arouses cons iderab le
i n t e r e s t in t e chn ica l c i r c l e s .
The var ious
phases of the
manufactur ing processes
caus ing
re s idua l s t r e s se s
in
s t ru c t u ra l m e ~ e r s are
too
i nvo lved g en e ra l l y
to permi t
more
than an approximate
p re d i c t i o n o f
the
magnitude and d i s t r i b u t i o n
o f
r es idua l
s t r e s se s
based
on
t h e o re t i c a l
cons idera t ions .
t
i s
n a tu r a l
the re fo re
to
r e so r t
a l so
to exper imenta l
means fo r t h e i r
determinat ion.
Unfor tunate ly
re s idua l s t r e s se s cannot be
measured
mechanica l ly in
the
manner t h a t
app l ied
s t r e s se s are
measured.
Thus the
measurement
o f
r es idua l s t r e s se s
i s
o f g r ea t
i n t r i n s i c
i n t e r e s t
but r a th e r
d e l i c a t e
requ i r ing
much t ime
and expense.
Laboratory specimens may not reproduce
the
e f f e c t s
o f
r es idua l s t r e s se s
in big
s t r u c tu r e s .
Hence s imple
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
7/115
337.8
-2
sys temat ic , and
p r a c t i c a l methods with s u f f i c i e n t accuracy
and
not excess ive s e n s i t i v i t y ,
app l icab le to
the measurement
o f
re s idua l s t r e s s e s in
f u l l - s c a l e members
o f
var ious c ross
s ec t i o n s are
of
g re a t i n t e r e s t . Ways o f
improving the
s e ns i t i v i t y and
the
p re c i s i o n
of the measuring devices
should
be s tud ied so long as t h i s aim does not c o n f l i c t with the
p ra c t i c a l cond i t ions o f the measurements .
The a v a i l a b l e methods of exp lo ra t ion f a l l i n t o two
ca tegor i e s : mechanical methods and phys ica l
methods. The
former r eq u i r e
d i s tu rbance
o f
the
s t r e s s e s
and
the l a t t e r
do
not .
The
bas i c
concept
adopted
by the mechanical methods
fo r the de termina t ion o f re s idua l s t r e s s s s i s to re l ea se the
r e s i d u a l
s t r e s s
on
the
sur face
by
appropr ia te
removal o f
mate r i a l . Since r e s i d u a l s t r e s se s form an i n t e rn a l l y
balanced sys tem
o f s t r e s s and
are
produced by
mutual i n t e r ac t i o n
o f
var ious elements o f the s t r a ined body, removal of
mate r i a l
such
as
by
cu t t i n g ,
d r i l l i n g , and
grooving,
w i l l
cause
unbalanced
and p a r t i a l r e l a x a t i o n
o f s t r e s s in
each
p a r t .
Thus, the mechanical methods do not measure the
ac tua l
s t r a i n
produced by the ex i s t i n g re s idua l s t r e s s , what they do
measure
i s
the r e l x ~ d
s t r a i n in one p a r t
of the body when
the re s idua l
s t r e s s sys tem i s
di s tu rbed .
The mechanical methods, sometimes known as
r e l a x a t i o n
methods ,
a re
e i t h e r
d e s t ru c t i v e
o r semi
d e s t ru c t i v e
in na tu re .
The d e s t ru c t i v e methods, as the name
impl ies , requ i re t o t a l des t ruc t ion beyond any
hope o f
repa i r ,
before r e s id u a l s t r e s se s can
be
evalua ted . The semi -des t ruc t ive
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
8/115
337.8
-3
methods, on the othe r hand, produce
only
l oca l damage which
gene ra l ly can be
r epa i red
for
example, by
welding.
The
d es t r u c t i v e
charac te r i s t i c s
o f t he
mechanical
methods
have
been
one of the major incent ives
for
using
physica l
methods.
Such
methods
may be
used to .measure
the
ex is t ing r es idua l s t r e s s
d i r e c t l y
without
requi r ing any
des t ruc t ion of the t e s t specimen. Among these methods, the
X-ray
d i f f r a c t i on technique and
t he .u l t ra son ic methods
a re
the
most impor tan t
s ince
they
measure s t r a ins d i r e c t l y
on
the
s t r a in ed metal . Unlike the
mechanical methods,
they
may not deal wi th the average s i t ua t ion but
sample only
a
pa r t i c u l a r
c las s
o f the gra in aggregate . I f the sampling i s
not
r ep r e s en t a t i v e
the
phys ica l methods
and
the mechanical
methods may not measure the same
th ing .
In gene ra l the
mechanical
methods
measure only
macros t resses
the X-ray
methods may superimpose the micros t r e s s to the macros t ress
and
the
u l t rason ic methods provide i ~ f o r m t i o n
only on
the
d i f fe rence between t he pr inc ipa l r es idua l s t r e s s e s and not
on
the abso lu te
magnitude
of these
s t re sses .
This leads
to a s i t ua t ion
seeking
the
answer to the
fami l ia r ques t ion
What i s ac tua l ly
being
measured ?
The
purpose
o f t h i s s tudy
i s to i nves t iga te
d i f f e r e n t
t echn iques
of
r es idua l s t r e s s measurement
taking
in to
cons idera t ion the a pp l i c a b i l i t y
s impl i c i ty economy,
accuracy
and saving in
t ime each
method
can of f e r .
For
the
purpose of
comparison,
the
methods cons idered
a re
app l ied
on one specimen,
with
a uniform r es idua l s t r e s s d i s t r i b u t i o n
along the
l ength .
A l4H202*, STM A36
s t ee l
b u i l t up from
*The des igna t ion H r e f e r s to a
wide f lange
sec t ion bu i l t up
by welding component p la t e s as opposed to the des igna t ion
W for i o l l e d wide-f lange
sec t ions .
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
9/115
337.8
4
flame cu t p la tes
with
fill t welds was the se lec ted
work
piece .
Residual s t r e s s measurements using the method o f
sec t ion ing
and
two
d i f f e r e n t
ho le d r i l l i ng methods were
conducted.
The procedure o f t e s t i ng used as wel l as the
r e s u l t s are discussed
in
de t a i l .
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
10/115
337.8
-5
2. THE
METHO OF SE TIONING
2.1 In t roduc t ion
In
t he
y ea r
1888,
Kalakoutsky(5}
repor ted on a
method o f determining l ong i tud ina l
s t r e s s e s
in
bars
by
s l i t t i n g l ong i tud ina l s t r i p s from the bar and
measur ing
t h e i r
change
in length . his method known
as
the sec t ion ing
method (6 ,7)
i s based on the
p r i n c i p l e t ha t i n t e rna l
s t r e s s e s
in a mater i a l
are r e l i eved
by
sec t ion ing
a
specimen i n t o
many
s t r i p s
o f
,small
cross
sec t ion .
t
i s
bes t
appl ied to
members
when the l ong i tud ina l
s t r e s s e s a lone
are
impor tan t .
The s t r e s s
d i s t r i b u t i o n
over a cross sec t i on can
be determined with reasonab le accuracy from
the
measurement
o f
change in
length o f
each s t r i p t aken befo re and
a f t e r
the
sec t ion ing and by
applying
Hooke's Law. The ana lys i s i s
s i m p l i f i e d
by assuming t ha t the
t r ansver se
s t r e s s e s are
n e g l i g i b l e ,
and t h a t
t he
method
o f cu t t ing produces
no
apprec iable
s t r a i n s .
(2) In pra c t i c e ,
h o w v r ~
t r ansver se
s t r e s s e s
may e x i s t , but
the lower the t r n s v e ~ s e
s t r e s s es ,
the more accura te the
r e s u l t s
w i l l
be. Residual s t re sses
formed
due
to
sawing
alone depend, among
many
other
f ac to r s ,
on the spac ing o f the saw cu t s ,
the th ickness
o f p l a t e , the
speed o f c u t t i ng , and
coo l ing c ha ra c t e r i s t i c s {cool ing
l i qu i ds , e t c . } . In genera l , t he r e s idua l s t r e s s a t the very
edge
o f the
cu t
may
approach
the l oca l y i e l d s t r e n g t h of the
mate r i a l .
The
ac tua l
d i s t r i b u t i o n
o f
r e s idua l
s t r e s s e s
c lose
to the su r f ace wi l l depend on the mechanica l and thermal
e f f ec t s . (8) The s t r e s s decreases very r ap id ly toward the
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
11/115
337.8
6
i n t e r i o r where
the sec t ion ing
measurement
normal ly i s t aken .
This s t r e s s has been obse rved to be of the o rd e r
o f
0.5
to
1 5 k ,
f
d
9)
S l
1n
compress1on o r
o r 1nary
cases .
The s e c t i o n i n g method ~ s been
used
fo r years for
r e s i d u a l
s t r e s s measurements in s t ruc t u r a l s t e e l members. t
has
proved
to be
adequate , accu ra t e
and
economical
if
proper
care
i s
t aken i n the p r epa ra t ion
o f
the specimen
and the
procedure o f
measurement .
2.2
Prepa ra t ion
of
Tes t
Specimen
Se lec t ion
and
Locat ion
o f Specimen
Locat ion of the t e s t p iece a long the l eng th o f the
m ate r i a l
must first be de te rmined . The
t e s t
sec t ion
must
be
comple te ly c l e a r o f co ld -bend
y i e l d
l i n e s if
r es idua l
s t r e s s e s
due
to thermal e f f e c t s a lone are to be
measured.
To avo id
end
e f f e c t s on the
magni tude
and
d i s t r i b u t i o n
of
r e s i d u a l
s t r e s s e s ,
a
d i s t ance
o f
1.5
to
2.0 t imes the maximum l i ne a r dimension
has
been recommended,
though
t h e o r e t i c a l l y a
r a t i o o f 1.0
i s
s u f f i c i e n t . 7,10)
An
edge d i s t ance
o f 2 f t .
was taken
s u f f i c i e n t
to
o f f s e t any
edge
e f f e c t s fo r the 14H202 t e s t specimen. Figure
1
shows
t he
l o c a t io n o f s e c t i o n s fo r sec t ion ing and Fig .
2
the i de n t i f i c a t i o
of var ious e lement s . Two se t s
o f measurements
were t aken fo r
the specimen used, to check
whether t he
v a r i a t i o n o f r es idua l
s t r e s s e s
a long
t he l en g th
o f
a column i s
n e g l i g i b l e .
Since
it i s i n t ended
to
s tudy d i f f e r e n t
methods o f r e s i d u a l
s t r e s s
measurement
on
the same
specimen,
conf i rmat ion o f the
un i fo rmi ty
of the s t r e s s e s a long the l eng th i s
impor tan t .
This
i s
shown
in
a
l a t e r s e c t i o n .
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
12/115
337.8
-7
Prepara t ion
o f Gage Holes
Figure
3
shows
the
d e t a i l o f gage hole l oca t ion fo r
the sec t ioning
of
the 14H202 specimen. Since t r ansve rse
sawing d is tu rbs
the
pa t t e rn o f r es idua l
s t r e s s d i s t r i bu t ion ,
the
gage
hole
l i n e
must be a t some dis tance from the saw cu t
l i ne
to
avoid th is .
e f fec t .
This dis tance
depends
on the
th ickness
o f
the component p la tes of the
shape
and on the
cu t t ing procedure .
(11) A dis tance of 1
inch
from
both ends
i s s u f f i c i e n t fo r t h i s pa r t i c u l a r specimen.
St ra in
measurements
are
taken over
a
10
inch
gage
l eng th by
a
1/10,000
inch Whittemore s t r a i n gage.* The
s t r a i n
readings
are ~ r o m
both top and
bottom
faces
o f the
component
pla te s .
The accuracy in
reading
depends mainly
on the gage
holes . Following the i n s t ruc t ions of the
manufacturer , gage holes were prepared using
a
No.
56
tw i s t
d r i l l (0.0465 inch diameter) to
a
depth o f 0.2
inch. Al l
holes
were reamed
using
an angle
of 60
and depth
o f
0.005
to 0.01
inch. An
i l l u s t r a t i o n i s
shown in Fig.
4
A
drill
b i t q p b l ~ o f
making
such
a
hole
in
a
s ing le
opera t ion
i s
commercia l ly av a i l ab l e .
The gage holes
were cen t ra l ly
loca ted
using
a
s tandard 10 inch punch and the resu l t ing
measured dis tance
between
the gage holes showed
a
var i a t ion
of
0.01
inch.
Prepa ra t ion o f gage holes a t welds and
f l ame-cu t
areas i s
d i f f i c u l t ,
because the mater ia l
has a higher
y ie ld
s t r eng th
a t
such
l o ca l i z ed
areas
due
to meta l lu rg ica l
changes
from
the
high
hea t
inpu t . Unrel iable readings may r e s u l t if
*U.S. Pa ten t No. 1638425-2177605.
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
13/115
337.8
-8
the
gage
holes a re not p rope r ly prepared.
Gage holes
a t
edges o r a t
corne rs ,
though
not
d i f f i c u l t to prepare , may
give unre l i ab l e read ings s ince
the
holes may
have
d i f f e r e n t
al ignments , and the extensometer cannot usua l ly be
made
s t ab l e
while
t ak ing measurements .
Deta i l
fo r
Sect ion ing
The number o f l ong i tud ina l s t r i p s to be cu t depends
on
the an t ic ipa ted r es idua l
s t r e s s
d i s t r i b u t i o n .
This
in
tu rn depends upon many
f ac to r s ,
such as edge prepa ra t ion
(universa l
mi l l ,
welded,
flame
c u t ) ,
grade
o f
s t e e l ,
dimension 6 f the
specimen
and
so
fo r th .
For
the 14H202
sec t ion , a in . spac ing was used a t reg ions o f an t i c ipa t ed
s teep s t r e s s grad ien t , and a t in .
spacing
a t regions o f low
s t r e s s
grad ien t as
shown
in Fig. 3.
To determine the overa l l
p a t t e r n o f
re s idua l s t r e s s
d i s t r i b u t i o n
with
a l e s se r
number
o f
l ong i tud ina l cu t s
a
pa r t i a l sec t ion ing
10,12)
can be made. The re s idua l s t r e s s
d i s t r i b u t i o n through the th ickness of
the
p la t e s
can be
determined
from changes on s t r a i n readings
a f t e r
s l i c ing
o f sawed s t r i p s .
Method o f
P a r t i a l
Sect ion ing
The
number o f l ong i tud ina l s t r i p s to be cu t can
be
reduced s i g n i f i c a n t l y
i
the method o f pa r t i a l sec t ioning
i s
u t i l i z e d . This
method, however,
requ i re s
a p r i o r
knowledge
o f the pa t t e rn o f r es idua l s t r e s s d i s t r i b u t i o n . reasonab le
es t ima te
on
the
pa t t e rn
o f re s idua l s t r e s s d i s t r i b u t i o n r a th e r
than i t s magnitude,
i s
o f more importance for an
e f f ec t i v e
use
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
14/115
337.8
-9
o f t h i s
method. The
approximate
var i a t ion in r es idua l
s t r e s s d i s t r i bu t ion can
be
pred ic t ed from the
geometry
o f the
p l a t e
o r
shape, manufactur ing
process , hea t
t reatment
(such
as
flame
cu t t ing ,
welding ,
e t c . , and the
mechanical
proper t i e s o f the mater ia l .
Locat ions
for
p a r t i a l
sec t ioning
are so
determined
t h a t they l i e near o r a t
l oca t ions of t r a ns i t i ons
of r es idua l
s t r e s s grad ien t s .
Locat ions
B a n d C shown in Fig.
5,
for
example,
would be
the approp r ia te loca t ions for the case o f
the edge welded
p la t e .
t i s
apparent , t ha t
complete
sec t ioning
of the p l a t e from
Locat ion
B to
Locat ion
C i n to smal ler s t r i p s
would
con t r ibu te no s ign i f i c a n t
accuracy
in
r es idua l
s t r e s s
measurement to those obta ined
a f t e r p a r t i a l sec t ion ing i s
made
a t
B a n d
C.
This
i s t rue , provided the r es idua l
s t r e s s
d i s t r i bu t ion
i s l i ne a r in the region. This a l so
holds
t rue
fo r
the
regions
A to B a n d C to D
where
the r es idua l s t r e s s
va r i e s l i ne a r ly , s ince
the e r ro r
caused
by bending
a f t e r
p a r t i a l sec t ion ing i s o f a secondary order . The sequence
o f
p a r t i a l
sec t ioning
has
no
in f luence
on
the
f ina l
r e s u l t s ,
s ince unloading of the
f ibe r s
w i l l
always
be
l i n e a r l y e l a s t i c .
Figure
shows
the
layout o f
cu t t ing
pos i t ions for
p a r t i a l
sec t ioning used
on
the
shape 14H202. The lower
por t ion o f
the f igure
shows the d e t a i l for complete
sec t ioning
to
be performed
on
t ~ p a r t i a l l y sec t ioned
specimen. The
t o t a l
number
of cu t s requ i red
for
p a r t i a l
sec t ion ing i s
only
12
compared to
104 requi red fo r the complete sec t ion ing .
Figure
7 shows one f lange a f t e r
complete
sec t ioning has been
performed. The number o f
cuts
could have been
reduced
to
only four
to obta in a very
s imi la r r e s u l t .
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
15/115
337.8
-10
Figure compares
the r e s u l t s
obta ined
for the
inner and
oute r surfaces of
the f lange
of
the l4H202
sec t ion
a f t e r p a r t i a l
and complete
sec t ioning
i s
performed.
t
i s
observed t ha t the r e s u l t s
obta ined from p a r t i a l
sec t ioning
readings are
not
very much d i f f e r e n t from those
obtained
a f t e r
complete sec t ion ing . The cu t t ing pos i t ions
determined from
a s tudy o f previous t e s t s 13)
compare very
c lose ly to the
es t imated
l oca t ion fo r
changes
in the s t r e s s
gradient .
2.3
Measuring Technique
The
obta in ing of r e l i a b l e r e s u l t s from measured
values
depends
on f ac to r s such as
the type of
s t ra in-measuring
dev ice and
the procedure o f measurement. Mechanical s t r a i n
gages
have been found
to
be p a r t i c u l a r l y su i t a b l e for
s t r a i n
measurement
because
the s t ra in -measur ing device
w i l l
not be
damaged during sec t ion ing
and
the. same device can
be
used
to
measure
repea tedly . The procedure
followed in
the Fr i t z
Engineering Laboratory w i l l be discussed t oge the r with some
add i t iona l suggest ions l a t e r .
The
Whittemore Extensometer
The Whittemore gage i s a se l f - con ta ined
ins t rument
cons i s t ing e s s e n t i a l l y o f two
coaxia l
tubes connected
with
a
p a i r
o f e l a s t i c hinges .
See
Figs .
9
and 10. Since the
gage
i s
in tended
for
repea ted measurement a t a se r i e s o f s t a t ions
r a th e r
than fo r f ixed mounting
a t
one s t a t i on
cons idera t ion
has
been given to con t ro l l ing acc iden ta l l ong i tud ina l
fo rces
which might be
appl ied by the opera tor .
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
16/115
337.8
-11
For s t r a i n measurements, the contac t poin ts are
i n s e r t ed i n to
the d r i l l e d holes
which are 10
0.02
inches
apar t .
Motion
between
the
two frame
members
i s
measured
d i r e c t ly
with
a d i a l i nd ica to r . A
handle,
serv ing
doubly
as
a
sh ie ld aga ins t t empera tu re change and
as
an a id to
uniform sea t ing of the
p o in t s
i s
a t tached to
the gage by
means
o f
two e l a s t i c hinges .
These hinges
preven t app l ica t ion
o f
excess ive. long i tud ina l
forces . A
force
of 5
lb . i s
recommended
for proper ly
sea t ing the points
in
the dr i l l ed
holes .
14)
sea t ing the gage i s
one o f
the ch ie f sources
o f
e r ro r . t
i s
suggested
t ha t a pos i t ion ing
angle
be used
Figs .
10 and 11) to
main ta in
the Whittemore gage in a
perpend icu la r
p o s i t i o n
to the su r face o f
the
specimen being
measured. Other sources of
er ro r
a r i se
from
the
d i a l
ind ica to r measurement of
a
chord r a t h e r
than an
arc l eng th
when
the axis of the dr i l l ed hole and the axis
of
the conical
extensometer po in t do not
co inc ide
and
temperature changes.
However,
the
e f f e c t
o f
temperature
change
on
the
ins t rument
i t s e l f i s pra c t i c a l l y e l imina ted by
the
use o f an invar
tube.
Accuracy
o f Measurements
t i s
ev iden t
t ha t changes in temperature w i l l
a f f e c t s t r a i n
readings
thus leading to wrong da ta for the
eva lua t ion
o f r e s id u a l s t r e s s
d i s t r i bu t ion unless these
e f fec t s are taken
i n to
cons idera t ion . Temperature changes
during readings
may
pra c t i c a l l y
be
e l imina ted
by
using
a
re fe rences
bar o f the same mate r i a l
as
the t e s t specimen.
The
bar should
be
put
on
the
specimen to be t e s t ed
for
a t
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
17/115
337.8 -12
l eas t one hour lS) ahead of t ime. This
i s
to s tab i l ize the
temperature
of the reference bar to
the
environment of the
t e s t
specimen.
I t
has been
reported l6}
tha t
the response
of
the reference
bar
and the specimen are
not
the same for
the same var ia t ion of room temperature. The reference bar
responds fa i r ly closely
to
the
room
temperature variat ions,
while the
specimen
responds with less fluctuat ion and with
considerable
time lag.
The response of
the specimen
therefore , is dependent on i t s
own size.
Measurement should
be
avoided
in direc t
sunl ight
or draf t or any other source which would cause dras t ic
temperature
var ia t ion
and
should
be
made where the
temperature
is
kept
fa i r ly uniform. This wil l
assure
readings with
minimum
effects
of
temperature changes. with such
care
taken
and under
normal
condit ions, temperature
changes may
cause
an error
corresponding
to a
s tress
of approximately 1 ks i
Note tha t a change in temperature of
SO
causes
a difference
of
1 ksi
in
the
s t ress
evaluat ion i f compensation
for
temperature
change i s
not
taken
into
account.
The effects
of
different
invest igators on
the
same readings
~ n
the
personal
effects
on
the readings have
been studied.
16) For both
cases,
no
important difference
was observed to prove these factori .al elements to have a
s ignif icant influence upon the
accuracy.
Further experimental errors may be at t r ibuted to
inaccuracies
in
the
mechanism of
the
extensometer, the dia l
indicator system, and effects
of
los t motion when the motion
i s in the
opposite
direct ion.
Such iriaccuracy
may
not be
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
18/115
337.8
-13
improved s ignif icant ly
by increasing the number
of
measurements on a
gage length. For example
for the
Whittemore
s t ra in
gage
t
was
found
tha t
the
accuracy
would be
imporved
by about 0.2 ksi
by
increasing the
number of measurements from
5
to 15.
16)
For
three
measurements
an accuracy
of
about
1
ksi
with
a
confidence
level of
99
could be obtained.
Procedure of Measurement
Attention should be given to
the importance of
obtaining
a
good
se t
of
i n i t i a l
readings
since
they cannot
be duplicated af ter the
specimen
has been cut . Better
accuracy could
also be obtained
by
estimating
precisely
the l a s t f igure of the reading whenever
the
dia l indicator
l ies between
the smallest
division.
The following i s a recommended
procedure
which has
successfully been followed in the past
in
Fri tz
Laboratory:
1.
Clean a l l
gage
holes using
carbon
te trachloride
or any other cleaning solut ion and
ai r
blas t
2. Take the
reading
on
the reference
bar.
3. Take
readings on the specimen.
I t is suggested
to
take
an intermediate
reference
bar reading
i f the
number
of gage hole readings exceed 15.
4.
Read
the reference
bar again.
5. Repeat
steps
2 3
and
4
unt i l
a l l gage
points
are read.
6. Do step
5
for at leas t three
times
on
the
whole
piece.
7.
I f
three
readings on
the
same
se t
of
holes di f fer
by
0.0001
inch
or more
the
gage holes
should
be
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
19/115
337.8
-14
checked careful ly and
additional
se ts .o f
readings usually two
more) should
be taken
on
the
reference
bar
and
on
the
specimen.
Addit ional
readings up to five more times
may
sometimes
be necessary to get
bet te r
resul ts .
I f
a great variat ion pers is ts t
suggested
to
make a new se t of holes very
near to the discarded ones,
since
badly
dr i l l ed or reamed holes
cause
large deviat ions
in reading.
After the i n i t i a l readings are taken and recorded
on
the data
sheets,
the specimen
i s
par t ia l ly or
completely
sectioned. I t
i s
suggested
to cover
a l l
gage points with
tape
to keep out
d i r t
and to avoid
damage
which
may
occur
in
the process
of
moving, handling,
sawing,
e tc .
The
measuring procedure af te r the par t ia l
or
complete sect ioning
i s proceeded
in
the same manner as
the
i n i t i a l
readings.
An example of
data sheets of
recorded
values for a
por t ion of a
flange i s
shown in Tables
1-5.
Table shows
a
data sheet
for the recording of
in i t i a l
readings,
Table
2
af ter
par t i a l sect ioning,
and
readings af ter complete
sectioning
are
shown in Table 3. Note tha t f ive readings
were taken for gage points 8 and 75
in Table
2 since the
. (
variat ion
in
reading was greater
than
0;0001 in.
Computations
for
res idual
s t resses
af ter
par t ia l and complete sect ioning
are shown in Table 4
and
Table 5,
respectively.
The
formats
used
in
Tables 1-5 have been
found very
convenient for the
recording of data and manual computations
of residual
s t resses .
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
20/115
337.8 -15
2.4 Evaluation of Data
The
computations of the
relaxed
s t ress from ,the
measured s t ra in i s based on the assumption
that
the
dimensional changes caused by the
relaxation
are purely
l inear elas ' t ic .
By
vi r tue of
the
l inear s t ra in dis t r ibu t ion
postulated in
the
beam
theory, the
average axia l
s t ress
cr
in
terms of
top and bottom
strains
e t
and
e
b
read'
from the
cut element
i s :
1)
where
E
i s Young's
ModuluSl
Since s tra ins are read
a t top and
bottom
'surfaces,
evaluat ion
of res idual s t resses a t
the
respective,surfaces
are
made
using the experimental data.
Let
A
be the average valiue of i n i t i a l readings on
one gage length. For each gage . l ~ n g t h
A
i s evaluated
using
1 n
A I:
n
i=l
A.
1
where n =
number
of
readings
on one
gage
l ength usua l ly three.
A = r ~ a d i n g value a t each
~ y ~ l e .
1
The average vlaue
of
i n i t i a l readings on the reference bar
(Ref.
A
i s evaluated for
every
in terval
of
reference bar
reading.
I n a
s imilar
manner, average values
of
f inal
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
21/115
337.8
-16
readings af ter par t i a l or complete
sectioning) for gage
lengths and the
reference bar
wil l be computed as Band
(Ref.
B),
respectively.
Using Hooke's
Law,
the
residual
s t ress a t
the
measured surface i s then,
E
= -E =
L
x
AL
r r
where At i s the recorded
change
in
length.
3
For
manual computation,
use
the data
sheets
(Table 4 or 5), to calculate the
res idual
s t resses as
follows:
1.
Compute
A -
B
(Col.
2.
Compute Ref.
A -
Ref. B
(Col.
3.
Compute
AL
=
(A-B)-(Ref.A-Ref.B)
(Col.
4.
compute
residual
s tress
AL
(Col.
r
=
x E
L
where
L
=
gage
length
(10 in.
for
Whittemore gage) .
5)
6
7
8
Step 3
gives
tens i le
s t resses
as posi t ive and
compressive
s t resses negat ive,
which
i s the usual
convention.
Figure
12 shows
the res idual
s t ress
dis t r ibut ion
measured a t locat ion A.
Comparison
of
residual
s t ress
measurement a t the
two
ends i s
shown in
Fig.
13. Using
the
evaluated
res idual
s t resses , the equilibrium condition for
the
whole
section
was
checked.
Theoretically,
since
no
external
forces exist equil ibr ium
requires tha t
the
sum
of
the s t r esses
over
the
whole
cross sect ion must be zero. For
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
22/115
337.8
-17
th is
par t icu la r
case a
difference of 0.7
ksi was
o m p u t e d ~
This difference may be
at t r ibuted
to the effec t of saw
cutt ing
and
accumulated
experimental
er rors
9)
Use of the computer wil l
great ly reduce the amount
of
numerical
work
involved; i f a large number
of
residual
s tress
measurements
i s
to be
encountered. Computer
programs
for general evaluat ion
of residual
s t resses have been prepared
and
have been found
very
versa t i le 17) These programs
are:
PLOTRS
-
reduces
data
obtained
from
measurements
before
and
af t e r sect ioning
and
s l ic ing to obtain
average readings.
RSN
-
computes
residual s t resses
- plots resul t ing residual s t resses
-
uses reduced data
from
PLOTRS to compute
the
two-dimensional residual s tress dis t r ibut ion
- checks
equilibrium of
residual s t resses
-
provides
input
for
PLOTIS
PLOTIS - plots
i sos t ress
diagram of
residual
s tress
dis tr ibut ion
Using
the computer program
PLOTRS
the residual s tress
dis t r ibut ion for the section 14H202 was
evaluated and
the
resul t ing plo t i s shown in Fig. 14.
The poss ib i l i ty of
automatic
recording of the
original
gage readings
into a tape or cards by means of
l inear
transducers is under
study. 18)
After th i s
s tage
manua
recording computation and plot t ing wil l no longer be required.
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
23/115
337.8
-18
3. THE HOLE-DRILLING METHOD
3.1
Introduction
Principle
The hole-dr i l l ing method,
sometimes referred to as
the
hole-relaxat ion
method,
i s based on
the
fact
that
dr i l l ing
a
hole in
a
s tress f ie ld disturbs the equilibrium
of
the
s tresses thus resul t ing in
measurable
deformations on the
surface
of
the
pa r t
adjacent to
the
hole.
From a
knowledge
of the
magnitude and
direct ion
of
relaxation s t ra ins
size
of
hole,
property
of materia l ,
and
geometry of
the
body being
examined, the
magnitude
of residual s t resses may
be calculated.
Histor ical Review
The hole dr i l l i ng method probably was f i r s t proposed
and
applied
by J . Mathar 19) of the
University
of Aachen
Germany)
in
1932. Mathar
used
mechanical
and
opt ical
extensometers
to
measure the changes
in displacement between
two points across the hole. y
dr i l l ing
a hole,
he observed
a par t i a l e l as t i c recovery in the immediate vic in i ty of
the
hole. From measurement
of th is e las t i c recovery, t
was
possible
to determine
the
residual
s t resses in the specimen.
In
his experiment,
Mathar used a dia l
extensometer,
placed
in
a radia l direct ion
with one
gage point
very near
to the hole.
His experiments were l imited
to
pure
tensi le
and
pure
compressive
s t resses .
The cal ibrat ion of the measuring
gage was accomplished
by
tes t ing a specimen
of
about the same
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
24/115
337.8
-19
s ize as the
work
piece in
a
machine for tension t e s t s
dr i l l ing
the
specimen and a t
the same
time carrying
out
measurements. e then establ ished experimental curves
for the
determination
of the actual
s t resses .
These curves
give the t rue
s t resses
direct ly as
a function of the
dia l
readings. His
apparatus
and resul ts
have been
subject to
cr i t ic ism
because
vibrat ions
during dr i l l ing operations
make
the
reading unsteady
and i r regular .
Replacing the mechanial extensometer with
elec t r ica l
resis tance
wire
s t ra in
gages, Soete
and
vancrombrugge(20)
of the University of
Gent
(Belgium),
eliminated the di f f i cu l t i e s of
measurement
and
improved
the pre,cision. At
the
same time
they were-
able to
determine
the plane
s tress d is tr ibut ion by
measuring
the elas t ic
recovery in three
radia l
directions. On the
basis
of
Airy s
s tress
function, Soete formulated an
equation
for
the
determination
of
s t resses occurring
in
a region
of the
same
size as
the dr i l led hole, and
plotted a
diagram, showing
the
re la t ion between s tresses
and
s ta ins . with the aid
of
empirically
prepared
diagrams,
and by measuring
the s tra ins
produced
during
dr i l l i ng to different depths, Soete
and
Vancombrugge(20)
were able to
determine the
s t resses
occurring
a t different depths
under the surface of
the
work
piece.
Further work on
measuring
non-uniform residual
s t resses
by the hole dr i l l ing method was performed by
Kelsey.
22)
e
developed
a
procedure
to
determine
the
re la t ionship between surface s t ra in and
hole depth for
a
known
uniform s t ress f ie ld ; and
then
to corre la te these
data with those obtained by dr i l l ing a hole
in
a known
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
25/115
337.8 -20
non-uniform s t r e s s f i e ld .
His
approach i s
based
on
the
assumption
t ha t the incremental
su r face r e laxa t ion s t r a in
for
corresponding
hole-dep th
inc rease
i s
propor t iona l
to the
magnitude of the
s t r e s s a t t ha t
depth . The method
i s
empi r i ca l
and
depends on
experimental
ca l ib ra t ion .
Recent
re f inements
in
s t ra in-gage-manufactur ing
techniques have
made t poss ib le to obta in s t r a i n gages
o f very smal l dimensions. Rendler and vigness 23)
repor ted
successful
r e s u l t s o f res idual s t r e s s measurements
using dimensions as smal l as 1/16 in .
diameter holes
and
1/16
i n .
s t r a i n
gages . Cardiano and
sa le rno 24)
repor ted
t ha t
the
exper imenta l data
confirm
with the assumed theory
for measurement o f
r e s id u a l
s t r e s s on p l a t e with
l i n e a r l y varying s t r e s s
f i e ld using the toe
o f t e e -
f i l l e t
welds) .
Recent ly ,
Ber t
e t . a l . 21) repor ted
on the
a p p l i c a b i l i t y
of
the
ho le -d r i l l i ng
technique for experimental
determinat ion of
r e s id u a l
s t resses
in
rec t angu la r o r tho t rop ic
mater ia l s .
Though cons iderab le work has been done i n recen t
years to
e s t a b l i sh
the
method t h e o re t i c a l l y t
would
st ll
seem t ha t
the
so lu t ion o f
the
problem must be
of
an empi r i ca l
na ture .
St ra in
Measurements
The
purpose of
measuring
the
r e l i eved
s t r a i n by
dr i l l i ng i s
to eva lua te
the
r e lease in
s t r e s s .
This
seems
to be the only
manner
o f determining i n t e rn a l s t resses . s ince
the
forces ac t ing w i th in m a te r i a l usua l ly a re unknown,
in
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
26/115
337.8
-21
both magnitude and
d i r ec t i o n .
In
b r i e f
measurement o f
s t r a i n
i s
bas ica l ly the only manner
in
which s t r e s s can
be
determined
s ince
s t r e s s
i s
not
fundamental
phys ica l
quan t i ty
l i k e
s t r a i n
but
only
der ived quan t i ty . These
arguments however
requ i re
two fundamental
assumptions
fo r
the
determinat ion
o f
r es idua l s t r e s se s : the
equ i l ib r ium
o f the
s t r e s se s
i ns ide
body
and the con t inu i ty of the
deformed mate r i a l .
The
s t r a ins
a re
measured
as an
e l a s t i c recovery
a f t e r re l ea se
o f
the p rev ious ly
ex i s t i n g sys tem
o f i n t e rn a l
s t r e s se s . The amount o f recovery i s smal l . For accl i ra te
ev a l u a t i o n
o f
s t r e s s a t
poin t
the gage
l eng th
must be
shor tened .
To
provide care fu l cons idera t ion for these
two f ac to r s
measuring device with
very
s h o r t gage
l eng th
and
high
prec i s ion should be used .
Three types o f measur ing dev ices
are unive rsa l ly
used
namely e l e c t r i c a l op t i ca l and mechanical
gages.
The
bonded e l e c t r i c a l
s t r a i n
gages
o f f e r
the
most
accura te
and
convenien t
means o f measur ing s t r a i n s espec ia l ly
i
re s idua l
s t r e s se s could be
complete ly f reed.
Opt ica l gages can give
accura te read ings because o f the f ac t t h a t beam
o f
l i g h t
can ac t
as an i n f i n i t e l y r i g i d w ei g h t l e s s and i n e r t i a l e s s
p o in t e r
o f
fa r
g re a t e r
l eng th
than would
be p ra c t i c a l
for
mechanical po in te r s . In sp i t e o f the advantages o f
e l e c t r i c a l
and o p t i c a l
methods however pure ly
mechanica l
devices
are
still in widespread
use and
fo r many purposes are much more
convenient .
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
27/115
337.8 -22
Features o f
the
Hole -Dr i l l ing Method
The hole
d r i l l i n g
methodhas the advantage of
removing
a
minimum
amount o f mate r i a l which
makes
it
the
l e a s t des t ruc t ive o f
the
mechanical
methods
for measuring
r es idua l s t r e s s e s . The method can
be termed
as s imi
destr .uct ive
i
holes of very small
d iameters
are
used.
I f des i red , the hole can be f i l l e d
by
welding o r
e l se , a
b o l t
o r plug can
be in se r ted in
the hole .
Unlike o the r
mechanical
methods the hole
d r i l l i n g
method
permi t s
the eva lua t ion
of
r es idua l
s t r e s se s
a t what
i s
e s se n t i a l l y
a
p o in t ,
a
spec ia l app l ica t ion o f
which
i s
the
measurement
of t r ansve rse
r es idua l s t r e s s .
Appl ica t ion
as
a f i e ld
t e s t
i s r e l a t i v e l y
simple and
r e s u l t s
can be
obta ined r ead i ly and economica l ly .
This
method
however
has a l imi t a t ion of depth and i s
used
to measure s t re sses
very near to
the su r face .
3.2
Mathar s
Method
In orde r t o exp la in the
p r in c ip l e
of the method
consider a
specimen
subje6ted to a
un iax ia l s t r e s s which i s
uniform
through
the
th ickness . measuring gage i s
mounted
on
t h i s t e s t piece to measure the
s t r a i n
in the same
d i r ec t i o n
as the
app l i ed s t r e s s .
I f
a c i r c u l a r
hole i s d r i l l e d between
po in t s a
and
b
in Fig .
15
t h i s hole w i l l become e l l i p t i c a l and the
d i s t ance between
a
and
b
wi l l be changed: increased i the
s t r e s s was t ens ion , decreased i the s t r e s s was
compression.
I f the r e l a t i o n s h ip between
the change in
t h i s
dis tance
and
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
28/115
337.8
-23
the s t r e s s i s determined by ca lcu la t ion
o r
ca l ib ra t ion
t e s t ,
then the s t r e s s
in the
t e s t
piece
in
the
d i r ec t i o n
ab
can
be
c lacu la t ed
from
the
change
in
the
dis tance
between
a
and
b .
19
For the case o f b iax ia l s t a t e of s t r e s s , one
measurement w i l l
not
be enough,
and the
deformat ion o f the
hole must be measured in a t l e a s t
three
d i rec t ions in order
to determine the magnitude and d i r e t i o ~ of the
p r in c ip a l
s t r e s se s . In t h i s sec t ion , the case wi th
a uniax ia l
s t a t e
o f
s t r e s s
only
w i l l
be
cons idered .
Cal ib ra t ion Tes t
c a l i b ra t i o n t e s t i s requ i red in order to determine
the r e l a t i o n s h ip between the s t r a i n
of
the t e s t
dis tance
produced due to d r i l l i n g ,
and
the s t r e s s
in
the t e s t piece .
Cal ib ra t ion can
be done
e i the r
by ca lcu la t ion o r by exper iment .
Cal ib ra t ion by ca lcu la t ion
was
f i r s t repor ted by
Kirsch, 25) who ca lcu la ted
the
deformat ion of a
hole in
a
member o f i n f i n i t e width in
terms
of the uniax ia l app l ied
s t r e s s . Willheim
and Leon 26)
extended t h i s
method
approximate l
to
members
o f f i n i t e width . Mesmer 27) genera l i zed the formula
fo r the
case
of plane s t r e s s
d i s t r i b u t i o n ,
under the assumption
t h a t the d i r ec t i o n of the p r in c ip a l s t r e s se s were
known.
fu r the r genera l i za t ion
was
given
by
Campus,
28)
expanding the
formulas
to
the case in which the p r in c ip a l axes d i rec t ions
are
unknown.
Extensive
work
has been done in
recent
years to
e s t a b l i sh c a l i b ra t i o n by
ca lcu la t ion fo r
the
case
of
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
29/115
337.8 -24
uniform 20,29,30,3l,32) and
non_uniform 2l,22,23,33) res idual
s tress dis t r ibut ion over the thickness of
the
pla te
Experimental cal ibrat ion
can
be made
by mounting
a t e s t specimen in a tens i le machine
and
dr i l l ing on the
s tressed
t e s t
piece a hole s imilar to
tha t
to
be used
for
the
residual s tress
determination. The f l a t plate i s loaded
a t various s t ress levels
and
the changes
in distance between
the gage
points
are
determined as dr i l l ing
progresses.
From
th is must be
subtracted the dis tance
increase which
would
have
occurred
i f
the hole
did not
exis t
n
experimental
cal ibrat ion was conducted for a
uniaxial
s t ress s t a t e A known
s t ress
was applied
in the
direct ion of
the
gage lengths on a t e s t specimen,
with
the
hole
and
gage system al igned
as shown
in Fig. 15. The
t e s t specimen
was
designed to sa t i s fy cer ta in design
requirements using available equipment, which are
discussed
in
the
following sections.
The
Calibrat ion Test
Specimen
In
designing
the cal ibrat ion t e s t
specimen
t was
necessary to consider and sa t i s fy
the
following
points :
a)
the
applied t ens i le s tress
must
be uniform
throughout
the
cross-sect ional
area
of
the
specimen.
b a measurable
change
in s t ra in in
the
material
should be
produced.
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
30/115
337.8
-25
c) the hole
must
be
small compared with
the
specimen dimensions
and
must be far
enough
from
a l l
boundaries.
d) the applied
load
must be of a magnitude
not
to produce
plas t ic flow
of
the
mater ia l
near
the hole due to
high
s t ress
concentrat ion.
The specimen, It by 4 in. cross sect ion
and
5 f t .
in
length,
mounted in
an 800,000
lb. mechanical
type
tes t ing
machine may indicate the presence of unwanted f lexural
s t resses .
Requirement
a)
was
sa t i s f ied
by
reducing the
f lexural s t resses in the
t e s t
sect ion
to negl ig ible
values
less than two
percent
of the applied s t ress by proper
alignment.
Alignment was carr ied out
by
mounting s t ra in
gages on a l l four sides of the
specimen
a t a distance of 6
inches from
each grip
end
Fig.
16).
This dis tance i s
suff ic ien t
to make
the
section
of
in teres t
remote from
the
boundary
and
thus
not influenced
by the
St. Venant end effect .
Any change in machine-specimen
alignment
during
t e s t could
be detected from the readings of
the
gages
mounted
on opposite
sides of
the specimen.
I t i s cer ta in tha t
residual
s t resses in
the
s p e i ~ e n
wil l af fect the uniformity
of
the s t ress d i s t r ibu t ion .
To
eliminate the
res idual s tresses ,
the
t e s t specimen was heat
t reated
a t
a
temperature
of l200
0
F
for
one and one-half
hours
1 hour
per
inch of
thickness).
The
specimen
was then l e f t
ins ide
the
furnace
where
t
was
allowed
to
cool
uniformly
a t
a very
slow
ra te . This temperature-time combination wil l
reduce res idual
s t resses
to a negl ig ible value
without
introducing
metal lurgical
changes.
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
31/115
337.8
-26
Requirement
b) was
for
a measurable
s t ra in
output
from
the
gage
lengths. In general ,
the
s t ra in
relaxations
due
to
hole
dr i l l ing
are
very
small
in
value.
This
dif f icu l ty
could be rel ieved by
increasing the magnitude
of the
applied
s t ress
and also
by
increasing the
gage length.
A
Huggenberger
extensometer with 20 and 100 gage
lengths
and nominal
s t ra in
sens i t iv i ty of 0.001 0.0000394
in .
was used for
s t ra in measurement. In
Fig. 17
the extensometer with i t s
accessories i s
shown.
Requirement
c),
tha t
the
boundary must be
a t
such
a distance from
the hole
without affect ing the measurements
may be sa t i s f ied i f a minimum width
of ten
times 20) the
diameter of the
hole i s used. The change
in s tress
dis t r ibu t ion caused
by the unsymmetrical
reduction
of cross
sect ional
area
due to
the
dr i l l ing could be
reduced
s ignif icant ly i f the
cross-sect ional
area of the specimen i s
large compared to tha t of the
hole.
Use of a in.
diameter on
the Ii
by 4
in. specimen
i s
within these
requirements.
This dimension combination
of
hole diameter
ana gage
length
provides suff ic ien t e,dge distance
so
as to
give an
appreciable change
in
s t ra in outside the region
where
plas t ic deformation may be
encountered.
Calculations
based on
equations
given by Timoshenko 34) for a small hole
in a wide plate subjected to a uniaxial tension showed that
the
longitudinal and
the t ransverse s t resses
four diameters
from the
hole axis
in the longitudinal direct ion
deviate
less
than four
and one
percent , respectively
from
the longitudinal
s tress
remote
from the
hole.
Accordingly, the minimum pi tch
i s 2 in.
for
in. diameter holes.
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
32/115
337.8 -27
Requirement (d) was
for
an applied s t ress
of
such
magnitude
tha t
no plas t ic
flow
of
the
mater ia l should occur
in
the
region
of
the
hole.
So
long
as
the
s t resses
are
less
than 4
p e r c e n ~ 1 9 ) of the
proport ional l imi t ,
no plas t ic
deformation due to high.
s t re s s concentrat ion wil l
occur
near
the hole. To improve th is
s i tua t ion ,
a t e s t material
may
be
selected
having
a high yie ld point.
But
for
the
purpose
of
comparison,
the
choice of the
t e s t mater ia l was
res t r ic ted
to A36stee l ,
and
th i s permitted
an
applied
s t ress
of
about
14 ksi .
Preparat ion of Gage Points
Gage lengths
of
20
and
100
rn were
used
simultaneously for the same hole for the purpose of
comparison
(Fig.
15). The gage points
for the
2
gage
length were each located a t 10 rn from
the
center of the
hoie.
The gage
points
for the 100 gage
length were
located a t 10 and 110
rn
from
the
center of the
hole.
The region to be measured was made smooth
and
careful ly prepared. Coating the surface with lay-out dye
was of
help for
smooth scribing. The
gage points
were
marked
f i r s t
with a
l ight
hammer
blow
using a standard
punch
(Fig. 17). The gage
points were.s tee l
bal ls of 1/16
in.
diameter. The gage point fur thest from the hole was
imbedded
using a special punch
(Fig.
17) af ter dr i l l ing a hole smaller
in diameter than
the s tee l
bal l , using
d r i l l
No. 56 (Fig. l8a) .
Since
imbedding
using
a
punch
i t s e l f
may
introduce
undesirable
res idual s t resses ,
those gage points
in
the vicini ty
of the
main hole to be dr i l led were
fixed
using Armstrong A 6 Epoxy
adhesive,
as
shown
in Fig. l8 b) .
In
both cases, care
was
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
33/115
337.8
-28
taken to make sure tha t the holes were imbedded not
too
deeply, to
prevent the measuring gage
from
s i t t i ng properly;
th is
i s done
by
sinking the
ba l l s
equator
s l igh t ly
below
the surface. In
general ,
gage points imbedded using
the
standard
p unch seem to be
more preferable ,
since
they
are
easier to perform, and can be
fixed strongly
in to posi t ion.
Dri l l ing
Technique
The location and alignment of
the
hole was controlled
by means of a hole milling f ixture as shown in Fig.
19. The
hole
was
dr i l led
using
a
i
in .
high
speed
center-cut t ing
end
mill .
The bottom
of the
hole i s to be
f l a t
to permit
meaningful measurements
of
the hole depth.
Hole
depth
increments are read
using
the allowed tolerance of 0.0002
in.
depth gage micrometer. Care was taken to keep the end mil ls
sharp to avoid
blemishes
or tears , and th is was
checked
by
closely
observing
the
condi t ion
of the
cut t ing
edges a t
appropriate operat ion in te rva ls .
At the
ea r l i e r
stage of th is study a boring uni t ,
which included the
end mill., Versamatic
(to reduce speed
of rota t ion) ,
and
e lec t r i c
dr i l l
centered
on
the specimen
by the mill ing f ixture
was
used. Clearance
was provided
beneath
the
milling f ixture for chip removal and for gage
.
point protections. . Both ends of the f ix ture carr ied index
marks for
center ing the uni t
over
the gage assembly
in
the longitudirial direct ion.
With
the uni t held
to
the
specimen
in
the
indexed
posi t ion, a
cross bar
was
placed
against the end of. the f ixture and
clamped
to
the
specimen.
The
cross bar remained
on
the specimen throughout
the t e s t
and provided a posi t ive index stop for the f ix ture . To
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
34/115
337.8
-29
reduce effects tha t may be caused by a high ra te of
dr i l l ing
.
the
1100 rpm speed
of
the
elec t r ic
motor was
reduced
to a
desirable speed of 180 rpm using a speed
reducing
device.
This device ( Versamatic ) also served
s i m u l t n ~ o u s l y
the
purpose
of
acting as
a f lexible coupling.
Figure 2 shows
the equipment
used
in an assembled view. In Fig. 21 a l l
equipment used and the
cal ibrat ion specimen
in
the tes t ing
machine
i s shown.
At a
l a te r
stage of th is
study
a
portable
magnetic
base
press
(Fig.
22 was
available
and
was
used
with
greater
ease
and eff ic iency.
The t ime required
to
complete the
dr i l l i ng
for
one
hole
using th is equipment has reduced to
about f i f teen minutes
compared
to about four hours when
using
the original se t . A speed of 190 rpm was considered suff ic ient
to
minimize
the
residual
s t resses
tha t
may
be
induced
due to
machining.
Test
Results
A i - i n . diameter hole was dr i l led on the cal ibrat ion
specimen to
determine
the re la t ionship
between
the
measured
s t ra in and
the
corresponding hole depth.
The specimen was
st ressed to 13
ksi
in tension
and
the milling was stopped
a t average
increments
of
0.04
inch in depth af te r which
measurements were taken. The
character is t ic curve of
the
measured s t ra in
re laxat ion as
a function
of
non-dimensional
hole-depth is shown in Fig.
23.
The
plot
shown
in Fig. 23
indicates
tha t
the surface
s tra ins increase rapidly up to a depth-diameter
ra t io
of
about
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
35/115
337.8
-30
0.8 and do not change appreciably for
g r ea t e r hole
depths .
Thus, c a l i b ra t i o n
based on a hole depth
o f one diameter
makes
use
of the
maximum re leased
s t r a i n and
was
used as a
s tandard depth to e s t a b l i sh the ca l ib ra t ion
curve.
Cal ib ra t ion
requi red
conduct ing severa l s imi la r
t e s t s on the
same
specimen
while
the
specimen
i s sub jec ted
to d i f f e r e n t
l eve l s
o f loading.
To
obta in
t e s t
points the
r e lease in
s t r a i n
due
to
d r i l l i n g
and
the
corresponding
s t r e s s
o f
the specimen need to be known. o apprec ia te a
be t t e r
unders tanding
o f
the changes in s t r a ins during
the
whole
opera t ion ,
t would
be adv isab le to take
s t r a i n
readings before and a f t e r
changes
in s t r e s se s have occurred .
The following
s t eps
in
s t r a i n
measurements
are recommended:
Take readings:
1)
before the
specimen i s
loaded
2) a f t e r the specimen i s loaded
3) a f t e r d r i l l i n g
i s per formed
4)
a f t e r
the specimen i s
unloaded.
Figure
24
shows
schemat ica l ly the
h is to ry
o f s t r a i n
changes
fo r
an i dea l
case
t ha t
would occur
during
the
whole opera t ion
o f ca l ib ra t ion .
Cal ib ra t ion t e s t s were conducted
for
uniform
s t r e s se s o f
13.3
ks i ,
16.7
ks i
and
20.0 ks i .
The
h is to ry o f
s t r a i n changes i s p lo t t ed for each
t e s t as shown in
Fig.
25.
I n i t i a l
and
f ina l
readings
were
taken while the
specimen
was
under a nominal ly
smal l load 10
kips equiva lent to
1.6
ksi )
in
order
to
maintain the
gr ip
which
was o r i g i n a l l y es tab l i shed
for
the al ignment o f the specimen.
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
36/115
337.8
-31
All
t e s t
resu l ts Fig.
25 show
tha t the unloading
l ines do
not pass through
the origin.
This
discrepancy
may
be due
to the sum
of
the
residual s tress
original ly
exist ing
in the specimen
and
the residual
st resaes induced due
to the
,mil l ing operat ion.
Since
the specimen has been heat- t reated,
the
major
par t of the difference
may
be due
to
the mil l ing
operat ion.
To determine the to ta l change in s t ra in readings
tha t might
have occurred
during the milling operations,
a
t e s t
was
conducted
on
the
unloaded
cal ibra t ion
t e s t
specimen.
Two holes were
dr i l led on
the specimen
using
the same
end
mil l and milling procedure as used previously.
A
to ta l
number of four measurements,
two
longitudinal and
two
t ransverse
readings were taken Fig.
18 before
and
af te r the dr i l l ings .
~ h
resul t ing readings are
given in Table
9. I t
is noted
that
a l l
four
readings are almost ident ical even
for
the
two
different
directions.
Based on
these
four
measurements the
average
residual
s t r a in
due
to the
milling
operations
alone
was
determined as
38 x
10-
4
ro
Table
9). This
value
was
taken in to account,
and separated
from
the
to ta l s tra ins
in
order
to
establ ish the f inal form of the cal ibra t ion
curve.
In
general ,
t
is
necessary to measure such i n i t i a l s tra ins ;
, i t is expected tha t
lower
values
should
yield
be t te r resu l ts .
Figure 6 shows
a
sca t te r band of
t e s t
points
obtained from
f ive
cal ibrat ion tes ts . , The cal ibrat ion curve
shown in
Fig.
7
is
obtained as the
ari thmetic
mean
of
the
t e s t
points .
Using th i s re la t ionship,
the residual
s tress
dis t r ibu t ion
in the
l4H202
section
can
be
determined.
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
37/115
337.8
-32
A t o t a l number
o f
28
holes were
dr i l l ed on the
oute r surfaces of the two f langes of the
14H202
shape using
the
same
procedure
o f
hole
dr i l l i ng
as
appl ied
to
the
ca l ib ra t ion t e s t specimen. Figure 28 shows the layou t of
holes used
on one
f lange o f the shape. A
r a d i a l
d r i l l
press (Fig.
29) was used to
d r i l l
holes
on
the
shape but
a t
a
l a t e r
s tage the por tab le magnetic base d r i l l (Fig.
30)
was
found to
be more
conven ien t .
The s t eps in
s t r a i n
measurements followed were
s imi la r to
those
used
in
the
sec t ioning
method
(Sect ion
3 .3 ) .
Tables 6 to 8
show
the da ta shee ts for recording s t r a ins
and
eva lua t ing
the r e s id u a l
s t r e s se s where hole numbers to 10
are used as an
example.
The d i f fe rence in s t r a i n
readings
obtained from the 28
hole
dri11ings are shown
in
Fig. 31.
Using
the
c a l i b ra t i o n curve
(Fig.
27) and the
d i f fe rence
in
s t r a i n
readings ,
the r es idua l s t r e s se s a t
the
28 loca t ions were determined.
The
average
r es idua l
s t r e s s
d i s t r i bu t ion across
the
surface
of the f lange was
eva1uated
r
and
the
r e su l t
i s shown in Fig. 32.
3.3 Soe te ' s Hole Dri l l ing Method
?r inciple
s oe t e ' s method o f
hole
d r i l l i n g i s based on
the
same
fundamental
p r i n c i p l e
as t ha t of
Mathar s (Sec t ion 3 .2 ) ,
excep t
t ha t in
Soe te ' s
method, measurements are taken using
e l e c t r i c a l r e s i s t an ce wire s t r a i n gages in s tead o f mechanical
extensometers .
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
38/115
337.8 -33
The
s t ra in
gages Soete and
vancrombrugge(20)
used, t h o ~ h
the smallest
available
a t the time,
were
long
compared
to
the
s ize
of
the
hole.
I f
t
is
desired
to
make
residual
s t ress measurements near weldments or flame
cut edges,
t
i s
apparent tha t s t ra in gages having shor t
gage lengths
should
be
used because of the sharp
s t ress
gradients
tha t
exis t in
such
neighborhoods.
Recent
refinements
in strain-gage
manufacturing techniques have
made t possible to obtain
s t ra in gages of
very small
dimensions.
Thus,
a hole of a very
small
diameter and depth
may suff ice
for
a res idual
s t ress
measurement.
Use
of
such
small dimensions cause
only
a to lerable amount of destruction
of
the mater ia l
and
have
a specia l advantage when used in
regions
with
steep s t ress gradients .
In th i s
method too,
the
experimental
approach
requir ing the determination of empirical cal ibrat ion constants ,
was used
to
evaluate
res idual
s t resses .
Calibrat ion
Test
The reasons
for
the cal ibrat ion t e s t and
the
method
of appl icat ion has been
explained
in
Section
3.2. Calibrat ion
was made on the same t e s t
piece
as used for Mathar s method.
The
hole-gage
assembly used
i s
shown
in
Fig. 33. Foil s t ra in
gage rose t te
type EA 09 125RE with a
gage length
of
0.125
inch were
used.
The
main reason
for
using
th is assembly is
because
t was the
only
type
specia l ly
prepared for
residual
s t ress
measurements
avai lable
commercially
a t
the t ime.
With
preassembled
gages,
the necessary
operat ional
sk i l l i s
reduced
to tha t of locating the cut te r in the center
of
the roset te .
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
39/115
337.8
-34
The
radia l
orientat ion
of the gages has
the
advantage
of
obtaining a
sa t i s fac tory
sens i t iv i ty especially a t high
s t ress
levels . 30)
Theoret ical Consideration
The procedure for
obtaining the
cal ibrat ion constants
was simplif ied by
making
the minimum
principal
s t ress
zero
and
by applying a known s t ress in the longitudinal direct ion of the
t e s t
piece.
Under such a uniaxial
condit ion, Rendler and
vigness 23)
have shown tha t cal ibrat ion constants A and B may
be
determined
from
the
formulas:
A
=
5 )
6)
where
~ l
=
radia l
s t ra in
in the direct ion of the
appl ied
load
longitudinal
st.rain) ,
~
=
radia l
s t ra in
in
the
direct ion
perpendicular
t.o
the
appl ied
load
transverse
s t ra in ,
and
a
=
applied
s t ress .
After
the cal ibrat ion
constants
A and B for the
hole-gage
assembly are determined,
the principal
s t resses
can then be
evaluated
using the formulas:
E:I A+B
Sin
.Y)
-
2
A-B Cos ,Y)
max
=
2AB Sin Y
+
Cos
.y)
7
)
E
2
A+B
Cos.y)
-
E
A-B in y)
a
=
8)
mln
2AB Siny
+
Cos
y)
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
40/115
337.8
-35
I
1 -
22
3
where y =
tan
-
I ]
1-3
1 .2
and.
3
=
s t ra ins
measured
by
s t ra in
gages G
l
G
2
and G
3
respect ively
(see
Fig.
33).
The
direct ion of the maximum
principal s t ress
f
measured counterclockwise from the t ransverse direct ion s
given by
3 = iy
9)
To
use the cal ibrat ion constants obtained
from
the
t e s t piece n actual res idual s tress
measurements
on any
specimen, the
following variables
must be considered:
1.
Material -
grade
of s tee l
2. Stress
t ens i le or
compressive (uniform);
bending
(non-uniform)
3.
Geometry
- thickness , width,
length
4.
Hole-gage assembly
5.
Method
of
hole
dr i l l ing
The
cal ibrat ion constants
A and B
contain
the
material constants E and (Young s Modulus and Poisson s
ra t io) , which
are
constant for a l l e las t i c and i sotropic
mater ia ls .
Since
a l l grades
of s t ruc tura l
s tee l have
essen t ia l ly
the same values of E and the. variq.ble caused
by a difference n
mater ia l
may be neglected.
I t
has
been
reported
(22) that cal ibra t ion constants
obtained
under
uniform
tens i le s t ress give resu l t s of less
than
f ive
percent dif ference
than those
obtained under
uniform
-
7/21/2019 Prof. Niguse Tebedge MSC Paper
41/115
337.8
-36
compression
st ress .
This may be at t r ibuted to the exact
s imilar i ty of the s t r ess s t r a in
curves
in tension and
compression.
Assurance must
be provided tha t the
cal ibra t ion
constants
are
independent of
the specimen s ize .
I t
has
been reported 23)
tha t
val id
cal ibra t ion
constants
are
assured for plates whose
boundaries
are
a t a
distance
equal
to
or
greater
than
eight
hole
diameters from the
hole center
l ine and for plates
of
four or more hole diameters in
thickness.
The hole ;gage assembly
is
the predominant variable
tha t changes the
values
of
cal ibrat ion
constants .
The constants
may
be
made
independent of
the assembly
dimensioning
i f a l l
of
the
important dimensions of
the
hole
gage assembly are
made
proportional to
the dimension of the cal ibra t ion model.
s long as th is principle of simili tude is maintained, a l l
the different hole-gage assemblies wil l be represented by a
single
non-dimensionalized specif ica t ion of
the cal ibra t ion
model. This wil l be t rue
provided
the
res t r ic t ions pertaining
to
the
material boundaries
are
observed.
Although the
dr i l l ing technique
affects the
accuracy of the
method,
t should be
pointed out
that
for
a
specified hole diameter
the
method
wil l
be
independent
of
machining s t resses as long as a standardized dr i l l ing
procedure
i s
used
throughout the
whole
operation,
including
the cal ibrat ion t e
top related