behavior of materials under conditions of thermal stress2.pdf
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rKERO. ASTRO. LIBRARY
NATIONAL ADVISORY COMMITTEE
FOR
AERONAUTICS
REPORT 117 )
/
7
BEHAVIOR OF MATERIALS UNDER CONDITIONS
OF THERMAL STRESS
By S. S. MANSON
954
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REPORT 117
BEHAVIOR
OF MATERIALS UN ER CONDITIONS
OF THERMAL STRESS
By S. S. M NS ON
Lewis Flight Propul ion Laboratory
Cleve land Ohio
-
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National dvisory Committee for eronautics
H eadquarters
1512
II treet NW Wa shington
26,
D. O.
Cr
e
ated by
act of Congress approved 1 Iarcb 3, 1915, for
the
s
up
ervision and direction of the scientific
study
of
the
problems of fligh t (U. S. Cod
e,
tiLle
50,
sec .
15 1). t member
hip wa increa ed from
12
Lo
15 by acl
approv
ed
March 2, 1929, and
to
17 by
a
ct approv
ed j\ I
ay
25,194 The me
mb
er are
appointed by
th e Pre
ident
,
and
se;rve as such withou , compensation.
JEROME
C. H
UNS
AKE
R,
C. D .,
Massac
hu
etts In st
itute of T
chno]ogy,
Chal:
nnan
D ETLE V
W.
BRO
NK,
PH.
D., Pr
e ident,
Rock
efe
ll er In st
it u
te
for l
l'l
edi
ca
l R
esea
rch , Vice
Chairman
JO Si: PH P .
ADAM
S,
LL.
D ., membcr Civi l Aeronautics Board .
ALLE V. A
TIN
PH. D . D ir
ecto
r National B ureau of tandards.
PRE
STON R.
B
ASSET
T, M .
A.
,
Pr
e
icl
en t,
Spe
rry
Gyroscope
0.,
In
c.
L
EONA
RD
CA RMI
CHAEL, PH.
D.
, Sccretary, mithsonian In
li -
tution.
R
ALPH
S. DAMO N, D. Eng., P rcsidcn t , Tran s World Airlines, In c.
JAM
E
H.
DOOLITTLE
,
C. D.
,
Vi
ce
Pr
es
id
ent,
hell Oil Co.
LLOYD HARRI
SON,
Rear
Admiral,
U
ni ted Stat
.es Nav y, D
ep
uty
and
Assi
stan
t
Chief
of the
Bu
re
au
of
Aeronau
t ics.
RON
ALn
M . HAZEN,
B.
., D ir
ecto
r of Engine rin g, Alii on
Div
ision,
Genera
l
Motor
s
Corp.
H UGH L . DaYDE ,
Pa.
D ., Director
JOH N
W.
CROWLEY, JR ., B. S., Associate Director fo r Research
RA
LPH
A. OFSTIE, Vice
Admiral, United State Navy,
D
cp u
ty
Ch ief of Naval Operations (Air).
Do ALD L. P
UTT.
Lieutenant
General,
United
tate Air Force,
Deputy
Ch
ief of
Staff
(D
C\
cl
opment .
D
ONALD
A. Q
UARLES,
D .
En g
., As
sistant cc
ret a ry of D ef
ense
(R
esea
rch and D e \e
lopment
) .
ARTH
UR E. R AYM
OND, C.
D. , Vice
Pr
e id
en t
- Enginec
rin
g,
D
oug
la
s
Aircraft
Co., I
nc
.
FRANCI "V. R
E C Il
EWE RFE R, Sc. D ., Chief, ni ted ta tes
Weather Bu r
eau.
WALD
RY
AN, LL. D.
,
member, Civ
il
Aeronautics Board.
Nathan F . TWINING, General, Un ited States Air Force, Chief of
Staff.
JOFl F. VICTORY, LL. D., Executive Secretary
EDWARD H. CHA MBER LI N, Executive a.Oicer
H EN RY
J.
E. R m
D, D. En g
., Di rec tor, La ngl
ey Aeronautical
L
abo
r
ato
ry, La ngl
ey Field,
Va .
MI
TH J.
D EFRAN CE, D.
Eng., Di recLo
r , Ames Aer
onautica
l La bora to ry, i\10ffett Field, Ca lif.
EDWARD R. SHARP,
C.
D., Di
rec tor, Lewis
Flight
P
ropul
si
on
La bora
to
r
y, Cleveland Airport,
Cl
eveland
, Ohio
LA GLE
Y
AERONA TICAl.
LABORA
TO RY
La n
gley
Fi
eld, Va.
AM
ES
AERONAUT ICAL L ABORA1ORY
10fIetL Fi eld, Cal if.
L
EW
IS FLIGHT PROPUI.3ION T
,AJlORATO RY
Cleve la
nd Airport,
CIC vC land , Ohio
Conduct under unified contro l for all agencies
of
scientific research on the fundall1ental proble s
of
fl ight
-
7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
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REPORT 117
BE
H VIOR
OF
M TERI L
UNDER ONDIT
ION
OF
THE
R
M L
STRESS
1
y H H : ANSON
MM A
R Y
A r e v i e w 2)1ebented oj awuable information on the behavior
oj br
ittle and ductile mate1 ials
unde1
conditions
oj
thermal
stress and the?malshock. For brittle materials, a simple jormula
1 elating phy ical properties
to
thermal-shock resi tance is
derived and used
to
determine the relative significance
oj
two
indices currently in u e
jor
rating
material
The importance
of
simulating operating conditionb in thermal-
I>hock
testing is
deduced jrom the jormula and is expe1 imentally il lustmted by
showing that BeO could
be
either inferior or superiO?
to
Al
2
0
3
in thermal shock, depending on the testing condition For
ductile material
,
thermal- hock
re
istance deptnds upon the
complex interrelation among several metallurgical varia
bles
which seriously affect stren
gth
and ductility. The e
va? iablel
aTe bTiefly di cus
ed
and illustmted jTom literature sources.
The importance
oj
imulating operating conditions in
te
ts
jor
rating ductile materials is especially to be emphasized becau e
oj
the importance oj testing condition in metallurgy. A num-
b
er
oj practical methods that have been u ed
to
minimize the
delete? ious effects oj thermal stres and thermal shock are
outlined.
I TROD TIO
When a ma terial is ubjected to a temperature gradient
or when a composite material on i
st
ing of two or more
material havjng different coeffici ent of ex
pan
ion i heated
either uniformly or nonuniformly, the variou fiber tend
to
expand different amount
in
accord with their indivjdual
temperature and temperature coefficient of expan ion.
To enabl th body to remain
co
nLinuou ,
rather
t
han
allow
ing each fiber to
expand
individually, a y tem of thermal
strain and a socia ted tre e may be introduced depending
upon the hape of the body and the temperature distribution.
f the material cannot with tand th tre es and
train
rupture
may occur.
Brittle and ductile
ma t
erials react in considerably different
manner to thermal tre . Brittle materials can endure
only a very small amount of train before rup ture; ductile
material can undergo appreciable train withou
rupture.
ince thermal stress behavior depends e sentially on the
ability of the material to ab orb the induced strains necessary
to maintain a continuous body upon the application of a
therm
al gradient,
brittle
material cannot readily with tanel
Lhese sup erimpo
eel
sLrains without inducing enough stress
1,0 cau e rupLure; ductile material on the other hand ,
can usually withstand the e additional strain but may
ultimately fail i subj ected to a number of cycles of imposed
temperature.
Th
e problem of thermal tress is of great importance in
cur
rent
high-power engines.
Th
e present trend toward in-
reasing temperatures has necessitated
Lhe
u e of refractory
maL
erials capable of with tanding much higher tempera
Lure
t
han
normal engineering materials. One sali
ent
prop
erty of the e materials
i
lack of ductility.
For
this reason,
thermal str
ess
i one of the mo t
important
design criteria
in the application of these material. Thermal stress
is
al
0
currently receiving considerable aLtention in connection
with ductile
material
since there is con idel'able evidence
that failure of many ductile engine components can be
at
tributed to thermal cycling.
Th
e problem of high-speed
flight, with attendant increa s of temperature and temper
ature gradient in aircraft bodies, has fUl'ther genera ted
concern over Lhe ignificance of thermal stress in ductile
materials.
Th ermal tre and thermal hock may be di tingui hed
by the fact that in thermal hock the thermal tres e are
produced
by
tran
i
ent
temperature gradients, usually udden
one. For exampl
e,
if a body originally
at
one uniform tem
perature i uddenly imIDer ed
in
a mediunl of different
temperature, a condiLion of thermal hock is introduced.
At
any
instant the stre e are determined by the tempera
ture distribution and are no different from what they would
be if thi temp
rature
distribution could be obtained in the
teady- tate condition. But the temperature gradien t that
can be e tabh hed in the tran ien state are generally much
higher than tbos that occur in the teady tate, and hence
the
rm
al shock is important relative to ordinary hermal
tre becau e of the higher stress thaL can be ind uced.
nother di tinction beLween thermal Lress
and
thermal
hock is that in thermal hock the rate of application of
tre i very rapid,
and
many
materials are affected
by
the
rate
at which load i applied. ome materials are em
brittled by rapid application of tres and Lherefore may not
be able to
with tand
a thermal hock Lre ,vhich if applied
lowly could readily be ab orbed.
I Supersedes A A TN 2933, BehavIor o Materials Under Conditions of Thermal by S. S. Mnnson. 19
53.
Based on I.
ctur
e prese nted at
l 1II).l
osiulII 0
11
Ueat Transfer, Univer
sity
of M c h i ~ a D , June
27-28,
1952 .
1
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2 REPOR
T 1
J 70
-
ATIONAL
ADVISORY COMMITT EE
FOR
AE RO
AUT
I S
.7
10
.6
r
.5
I
I
. I
l
.4
h . 0
I
=
4.J
b
I
.3
I
II
I
2
I
f
/
o
Nondlmensionol
heal transfer,
\
_ ~ h
20 .0
1
0.0
5.0
V
r---
i ----r-..,
3.0
/
r----.
2.0
/
-
-
1.5
/
-
1.0
.5
.1
.1
.2
.4 .5 .6
F IG lIRE
l.
- Kondime nsi
on a
l st l'e s \ er 1I nond im e nRon aJ time for
s
ur f
ace of fia t p lat e.
I t i al 0 nece
ary
to
di
tinguish be tw een a ingle cy
cl
e
of
thermal tres and
th
ermal fatigu
e.
vVb en
failm
e i
caused by the applic
ation
of several similar the
rma
l tress
cy
cle , rather
t
han a
ingle cy
cl e,
tbe pro ce is r efe
rr
ed to
as
th
e
rm
al fatigu
e. Th
e pro ces
es
thaL
ta
ke place in a body
in successive
cycl es
of
st
r
es
applic
ation ar
e extremely com
plex;
th
e
mecha
nism lead
in
g to cyclic failure is a
yet
in
co
mplete
ly
und
erstood . In
mo
st of the
ba
ic work , there
fore,
atten t
ion is d irected
at
the
condition
s
und
er which
failure will occm in one cycl e merely bec
au
se this case le
nd
s
itself to
ana
lysis. Th e
probl
em of t,hermal
fa
t igue is, of
co m se, a most
important on
e in engineerin g appli
ca t
ion .
The obj
ect
iv
es
of thi
pr
e ent a ti
on
are:
Fi r
st, some of
the information
co
nLained
in
recent
publi
c
ation
s on the
math
e
ma
tic
of th
e
rmal
shock will be
ou
tlined,
and
a, imple
formula will be dr
J'i
ved for correla,tion of the
rmal
shock be
havior wit
h
mat
erial proper ties. Second , the va
riab
l
es in
the simplified re
la
tion will be examined
and
from it method s
for minimizing
th
e
rmal
tress will be deduced.
For
brit
tle
mat
erials the single-cycle cri terion of failure will be
co
ns
id
ered; for du
ct
il
e
mat
e
ria
ls
th
e discussion will be
directed at available informat ion
on
the problem of ther
mal
fa t
igue.
THERMAL
SHOCK
OF BRITTLE MATERIALS
AS
DED UCED
FROM STUDY OF FLAT PLATE
General equation for stress.- In order
to ma k
e
th
e dis
cussion specifi
c,
the case considered is tha t of a homogeneous
flat pl
ate
ini t ially at uniform te
mp
erat
ur
e and uddenly im
mersed
in
a me
dium
of lower te
mp
eratm
e.
This
ca e i
treated
because the
temperature prob
lem of the
flat plat
i well known,
and
because
most
of the
recent
p ubli
ca t
ion
on the the
rmal
st
re s problem
0.
1
0
consid er thi ca e (fo
exampl
e,
refs. 1 and 2).
Th
ere i , therefor
e,
a
co
n ide
rab
l
ba
ckground of
in
formation from wbich to dl aw re
ult
a
n
with
which to
ma k
e comparison
s.
FUTthermore, mo t o
Lh
e
on
e-d im en ional problems can be
treated
in
esse
ntia
ll
the s
am
e way a the Oa t
pla
te problem treated herein, an
tborefore any
important
conclusion that pertain to the fla
pl
ate
are
probabl
y al
so va
lid for
ot
her hapes,
provid
e
that the nece ary changes are mad e in the
constant.
r
ot
also that in this case the
temperature
problem
is
one-dimen
sio
nal
; that is,
in
the
fl
at pl
ate
te
mp
erature
var
iation wi
be considered only
in
the thickness dir
ect
ion . The
prob
lem
is treated in this way beca use there are relatively few two
dim ensional
probl
em olved
in
the li terat
ur
e a
nd aL
0 be
cau e the
qualitativ
e conclu ion reached
in
the
fl
at plat
problem are believed to apply to
mor
e comp
li cate
d cas
es
The
first problem in conn ecti
on
with the flat
plate
i t
det
ermine the
temperature
di
st
ribution
at
a time
t aft
er th
urrounding
temperatme ha
been changed.
On
ce thi
t
mp
erature ha been
de t
ermined, the stresse can
read
il
be deter
min
ed in fi.ccordance
wiLh
very
si.mple
fo
r
mula
derived from the
thror
y of elast icity. Assuming that th
prop
er tie of the
mat
erial do not
vary with tem
p
erat
u
re
a
n
that the ma terial is ela tic, the following
equation
c
an
b
wri tten for the
st
ress
at an
y point in the t
hi
ckn p of thp
plat
e
T
a.-
T
To
(1
Ph
ysica
ll
y,
0 *
can be
co
nsidered as
Lb
e
l'I1tio
of the
tr
s
actually developed
Lo
the tress that would
be
developed
thermal expansion were C o m p
C o
n
st
l'oinrcl. rrh r for
mula for
0 *
is
(2
wh
ere
0 actual
st
r ess
1 Pois on ra t io
E c
last
ic modulus
a
coe
ffi
cient of ex
pan
sion
Ta average tempel'atUl e ac ro s
th
ic
kn
ess of plate
T te
mp
erat
ur
e at
point
wbere
st
rr ss i
eo
n idered
o ini tial
uniform
temperature of
pla
te above
amb
ien
te
mp
eratUl e (ambi ent
temperature
assumed to b
zero for simplic
it
y)
Stress at surface .-
In
order to
obtain
the
surface tre
it is therefore nece
ary
fu' t to determine the average tem
peratm
e
and
t he
smface
te
mp
eratUl'
e.
Th
e te
mp
er
atm
problem
ha
s b
ee
n thoroug
hl
y
treated in
the liLeratme
and
th
re ul t is
usuall
y given
in
the form of
an
infinite seri
es
. I
figure 1 are s
hown
the res
ul t
s of orne computation t
ha
t hav
been
mad
e by ubstitu t
in
g the exact seri
es
so
lu tion
fo
temp eratme in
to the stres equations.
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7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
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BEHAVIOR OF MATERIALS UNDER C
ONDI l IO
S OF THERMAL STRESS
3
In
the exact so
lution
there are three
important
variables.
First is the reduced tress, mentioned,
and
second,
the
va
lue
fJ
whicb is
eq
ual to
kh (w
here a
j
the half t
hi
ckn ess
of the plate, h is the heat-transfer coe
ffi
cient, and k is the
conductivity of the ma terial). The heat-transfer coefficient
i d fined a
th
amo un t of h
eat tran
fe
rr
ed from a uni t
area of the surface of the pl
ate
pe
l
unit temperature differ
ence between the
su r
face
an
d the surrounding medium.
Th
e
variables
a
h
and k
alw
ays
occur as a group a a res
ul
t of the
manner
in
which they
appear in
the differential equation;
therefore,
in
the
ge
neralized treatment of the problem it is
not
the individual val ue of
a h,
or
k that
is of
importanc
e
but their va
lu
e as grouped together to form the term fl . The
te
rm {3
is generally known as
Biot
modulu
s,
but
in
the
present discu sian
it wi
ll be called the nondi
men
ional h
eat
transfer parameter. Th e third important variable
i 8
which
will
be called
nondim
en ional time. As shown,
0= ~ ~ 2 wl1el e k i aga
in
the conduct
ivit
y,
t
is the tim
e,
a
is
the
half thickne
p
i the density of the material,
and
c is the
specific heat. In this figure the nondimensional stress at the
su rface
has
been
plotted
as a function of nonclimensional
Lime
for various examined values of nondimen ional h
eat tran
fer.
This pl
ot
contains the essentials of the en tire solution of
surface stress in the flat plate problem; the attainment of
further relations of interest is just a ma t ter of replott
in
g.
Maximum
stress
at surface.
It
is of i
nterest
to
co
nsider
the maximum surface stress a a function of fJ.
In
references
1 and 2 the
maximum
tr e s is analytically determined by
suitable
app
roximation of the serie
so
lu tion. For ex
ample,
Bradshaw
(ref.
1) co
nsiders only mall
va
lues of fJ
for which all but the first two term of the serie
may
be
omitted.
The
maximum tres is then
obtained
by setting
the derivative of stress with time equal to zero. Accurate
results are
thu
obtained,
but
they are valid only for
sma
ll
values of
fJ.
Since figure 1 g
iv
es the complete
variation
of
stre s
with
time, it i not necessary
0
differentiate; the
maximum value of tress
may
be read d irectly from the curve
for each value of
{3,
and the re ul t will be correct over the
complete rang of
f rather than
only
in
certain intervals. A
pIa t of j max ver us fJ is shown
in figUl
2
From this
CUl ve
it is seen that the va
riation
of nondimensional maximum
stre s with {3 i roughly
lin
ear for mall values of
fJ
but
becomes
asymptotic
to a va
lu
e of
unity
at very large values
of {3
In
order
to
obtain
a imple formula for the curve of figure
2, an
approach first used by Bu essem (ref.
3
will be u ed ;
but by somewhat more general a sumptions, a more accur
ate
formula will be obtained.
Th
is derivation is obtained with
the
use of figure 3. In thi figure the
ce
nter line repre en ts
the center of the
plate;
the two olid ver tical lines represe
nt
.
the surfaces of the plate.
Ordinat
e measure temperature .
Th
e temperature di tributions through the thiclmes of the
plate at several different time to t
I
,
i3
after the s
udd
en
application of cold atmosphere are hawn the cu
rv
es
PQ, P Q , etc. These curves mu
st
fit two boundary
co
ndi
tion : 1)
At
the center they
mu st have
a horizontal tangen t
because the
ce
nter of the
plat
e i a line of symmet ry, and
no heat is transferred across
the
center line; (2) at the
surface the slope
must
be
in
accord
with
the urface h
eat
tr
an
fer coefficient , which
is
equivalent to the condition that
the
tangent
to the curves
at
the surface pass through the
fixed
point
0 re
pr
esenting the
ambient
tempe
ratur
e which
has been
ta
k
en
equal to
ze
r
o.
Th
ese tempe
ratur
e distribu
tions
mu
st also satisfy the differential eq
uation
of h
eat
transfer, which is achieved by adju
st
ing ce
rtain
constant so
that the final result will be consistent
with
the c
urv
e of
figure 2, which of
caUl
e does atisfy the differential equation.
t is ass
um
ed that the temperature curve c
an
be
fi tte
d by
an equation of the form
(3)
where
T
c temperature
at
center of
plate at
time when stre s
at
surface i a maximum, as yet
undeterm
ined
M
n
co nstant to be
best
determined to fit theo retical
results
ti
,I:
b
.7
.6
.5
.4
3
/
2 I
/
I
1
a
/
II
V
/
/
V
II
/
4
8 12-
16
20
f3
FIG RE 2.-Analytical solution of nond imensional
maximum
tress
ver us nondimens i
onal
heat transfer.
-
7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
7/37
4
REPORT
1170
- A
no
AL ADVI ORY COMM
ITT
EE F
OR AE
RO
AUT
I CS
,-0
1 - -
Plale
Ihickn
ess
T
=T
2
,c
- M
(- r
3
T
2
c
M = /3+n' (sur face baundary cand,lion)
CT
' =
T2,c
. _n_ . L =
3Ji.
Ta n I /3 n /3 n
l n
1
(F7?+7? /3
CT- =
4
/3
(Buessem, r
ef
. 3)
F I
GI
'
R
:l.- Farll luia far m ax im u
llI
sl rrss al sli rfa e af pl
atc
(fr o
lll
r
d
3)
As long as
n> l ,
Lhis e
qu
at ion
wi
ll automat icall
.\
-
saL
isfy
t.be firs t, houndary eondit ion of horizontal
ta
nge nC)Tat
1
;=
0 .
I f the sur face co nd ilion
-1c = i
to he sa
Li
ned,
Lhr ron
di
tion of equ
ftL
ion (4) mu sL he sftLisf
LC
d
(4)
From rq
uaLions ( I ) ,
(3), and (4),
(5)
or, if R= T +
-
7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
8/37
BEHAVIOR OF
MATERIALS
UNDER COND
ITIO
S OF THERMAL STRE S
5
.9
.8
.
L.----
/
V.---
.7
/
V
V '
1/
V
V
' l '
.6
II
;.--
/
V
/
II
W/
5
l
/
f
W
I
i/ -
t----
f---
1
- - -
3
j
i
/1
,:
2
J
/
- -Exact
__
- .-1 -
=
1.5+ 3.25
-05e-16/.B
1/
(J mOK f
t
Buessem
1
I - - -
i
o
4
8
12
16
f3
20
FIG RE 5.-
Corre
lation of approximate formula i th exact olution
for maximulll s
lrc
s .
can be used
in
this rangc together with equation (7)
in
the
rang 0
-
7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
9/37
--------------
------
------
--
----
---
-
- -
6
REPORT
11
70 -
KATIONAL
A D n
ORY O M M
FOR
AERONAUTIC
to
unit
y .
I t
is intere ting to examine the meaning of
0 *
max= 1 and to determin e under which conditions
0 *
m
Cl
r 1
is achieved. The
co
ndi t ion of 0 * 1I/ux
= 1
means th
at
EaT
o
O maz=
-l
).L
(12)
The produ
ct
aTo is the contraction in tIl e material t h
at
would take place if the
temperature
were reduced
b.\
-
To
and the
mater
ial allowed to contract f con tract ion
i completely
pr
evented application of tress, then
a To
is the cIa tic train t hat
must
be induced in th e material
to prevent this contraction, and this strain multiplied by the
elastic modulu becomes the stress that must be appli ed.
Thc
term
1- L ) results from the fact t
ha
t the problem is for
an infini te plate in which equal
stre
ses are
app
lied in two
mu
tu a
lly perpendicular direction. In this case Ecv.To/l - L )
i
the
tre s
that
must be applied in two perpendicular direc
tion to completely prev
ent
1ny contraction in th e m 1leJ'i al .
Hence, for very large v 11ues of ah lk , equation ( ) sl atrs
th 1 t, the tress dev eloped i ju t enough to prevent any th er
mal exp 1nsion. To obt 1in an ind ex of merit
fo
r rat in g malr
rial under
the
conditions of very large
(3,
e
quation (12)
i.
rewritten as equation
(13),
which ugge t t
hat
th is ind ex
is now
O'b
lEa; 1nd it is ee n th 1 t the conductivit,y fact
0 1'
h
aR
vanished compared
with
th e ind ex lcO b
Ea
.
(13)
The implic 1tion i
that
th e
va
lu e of
the
cond u
ct
ivi
ty
of the
m 1teri 11 does
not
m 1tter ; the tempe1' 1ture
tha
t can be with
stood is in proportion to (1bIEa. Phy ically, thi l'e ult eun
be understood by ex amining the meaning of ver.\- large
(3,
which condition can occur either if
a
is
very
large, if h is
very
large, or
if
e
i
very man.
f
a
is
ve
ry large, it means
that
the
test body is very
la r
ge and that th e urfac.e
can
be brought down to the tempe
ratur
e of t he sUITounding
medium before any temperaturc change OCCll1'S in Lhe bulk
of the body. The urface
la
yer ca
nnot
co ntract becau e
to do so they would
have to
deform the remainder of the body,
and this cam10t be ac
hi
eved for 1 large body. Hence,
in this case, comp lete con tm in t of contract ion i imposed ,
1Dd the stres developed i EaTo/ (l - p. )
il'l'C'
speetivc of the
actual v 11ue of condu
ct
ivity. oim
il 1rl
y, [01' large h eal
transfer coefficient 11 the same res ult can be expected.
The surf 1ce is brough t
down
to the temp emturc of the Ul
rounding
medium before the
remaind
er of the body has h ad
the time to res pond to the impo ed
temperat
ure difference .
Hence,
ag 1in
complete
co
n
st
raint
of
co
ntraction
i imposed ,
and the
st
ress develop ed i ind ependent of
co
nd uct ivity.
Fina
ll
y, if the co nductivity is v e r ~ small, again only the
surf 1ce layers can r eali
ze
the imposed thermal shock cond i
tions, the remainder of the b o d ~ remaining essent ially
at
th e
init
ial temperature. Again, complete co n
tra
in t against
therma
l co
ntraction
i impo ed and t he stress is ind epe nden t
of the preci
se
va lue of
k
provided it, is ver y s
ma
ll .
104 r - - - - - - - - - - - - - - - -
Order of mer it
(exper i
mental)
Cermet
10
'
Cermet
'TiC
~
'
~ O
~
"-
"-
"-
~
- - ,
-
7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
10/37
BEHAVIOR
OF MATERIALS Ur
DER CO
DITIONS
OF THERMAL
STRESS
7
10
10
4
~
1425
0
F'
;=
1
0,QQ
F
9 ~ o F
'
~ F
~
~
t S
te
\\ite 6
0
1
00
c
.2
0
0
-
'
0
Q;
'0
I
-
0
. ::p
u
e
a.
'u
Q.I
n
=
4198 L b
1318
n::
-.
00
0
Cycl
es to fo il
ure
.
n
200
]
IGl :RE
Hl.- Relati
on
of rcc iprocal of cl
ono-atlOJ1
of f ai lu rc
Lo
Lhcrm al
cracki ng res i Lance (from ref. 10) .
ab ili ty to
und
crgo pIa tic strain
und
cr th e c
ond
iLon of
Lh ermal sh ock loading. J us t what property of the m a teri al
iL i Lh
at
impar ts thi sup er
ior ab
ili ty
to
u
nd
ergo pIa t ic
defo
rm at
ion
i no
t
known
. Accord
in
g
to ref
e
re n
ce 10, i t
mi
gh t be imp ac t 1'esi ta nce. ince
an
ea ily m ea ul ed
param
eLer
for co rr ela
tion
pu rpo c wa s
ou
gh t a
nd
ince data
were av ailab le only on the room-tem peratme im pacL r esis t
an
ce
, th ese
da
la wer e u
se
d
for
c
om p
arati
ve
purpo
e
for a
rough
co rrelation
, whi ch is sh
own in
t
ab
le I V. Of c
our
e,
the
i
mp ac t ]
e i tance th
at
is of r eal
impo
r tance is t he im
pa
ct
rcsi
stance
a
ft
cr the ma ter ial h a been
ub
j
ecte
d t o the c
om
})li
ca
ted the
rm
al
and
m ech
an
ical
hi
Lory associ
ate
d with Lhis
pa
rt i
cular tes tin g procedUl'e, \\7
hi
ch
ha
s all'eady be
en eli
.
Cll
e lL
i nece a
)
y to follow up t
hi
s le
ad
on t he s igni f
t
ca nce of im pact resis tance to verify the ten ta
tive
concl usi
on
reached in reference 10. I t is no t, however , an
Utl.l'
ea ona ble
co nclusion in ce, a pr ev iou ly point ed ou t, the speed of
load ing in the lhel ma.l sho ck Lest m a.\- bo an imporLant fac lor,
and this speed of l
oad
ing i a t lea t simul
ate
d
in
an imp
act
Lesl.
Th
e m
ost
s ign ifi
ca
nLfindi.n g of reference 10
wa
Lhe incli
cat
ion of
th
e rad ically
cl
i
O'
ere
nt
beh av
ior
of s i.x m a ter ials
hav ing, in th e ma in , V O
l .
- im ilar m echanical
and
therm al
pl'opel'tie . Thus, alth
ou
gh it is no t r eas
on
a
bl
e Lo con
clud
e
t hat ne iLher the convent iona lly m eas ured m echan ical proper
ti es nor the th e
rm al
proper t ies a1'e ign.ifican t in d
ctcrm
ining
Lher
ma
l sI
wck
r esi
st a
nce, iL m igh L be a id t h
at
these
prop
e
r
ties combinc with a th ird a
nd
ver y importan t ty pe of prop rLy
to produ cc
an
ovcr -all therm al shock ) esista nce. Thi
third type of
pr
oper ty i probab ly the m eLallur
gy
of Lh e Lest
ma
lerial, as a lready discu scd.
T RBl NE DI SK S
Another componcn t of the gas-l ul'biue engin e wlticll i
ub ject to thermal shock ,
0 1
aL leas L the
rm
al
L
l
C
s, i th e
di
sk
\\-h iC h cani e the rota t ing blad es. The rim of th e disk
is hea ted by contact \\-illl hot gas, a well as b y c
onduc t
ion
from
th
e rolaLing blad es. The cen ter ,
on
the oth
er
hanel, is
n
ea
l bearing and cooling is generally e
mploycd in
or
de
r to
p r
oL
ect t hese bea
rin
g .
A
high
temp
era tm e gradi e
nt
theref
or
e uS
Ll
ally exis ls he
tw
een
Lh
e cen ter of Lh e
eli
k a
nd
th e rim. Th is high temp crat m e gm lien t pr
odu
ccs very
large the
rm
al s
tr
es
e .
eve
r al
in
vest
i
ga t
i
on
(r ef .
11
a
nd
12) were m ade to d etcrmine t h e significan ce of Lhese the
rm
a
s tr c
c .
T
emperatures
.- In o
rd
er to d
etc
rm ine th stress,
ty
pica
LemperaLm es were fU st determined. A t urbine di k of
early
d esign wa
inst
nlllcll
Le
d wiLh Lh e
rmo coupl
e
as
h
own in
fi
gu
re 20,
and
Lh e engme was then oper
at e
d in accordance
o 0
o o l i vones
T
he
rmocou ples-; ,
o
o
0
o
F IGURE 20 .- T hc rm oco up le locat ion for st ud . - of d i k t emperatu
re
dis[ ribu t ion (from rpf. 11 ).
-
7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
20/37
BEHAn OR OF MATER IAL UNDER CONDIT
IO
S OF THERMAL S
l'RESS
17
with a cycle shown
in fi
g
Ul
e 2l.
IL
was brough t up to idle
peed of 4000 rpm in 1 minu te , operated at idle speed for
4 minute , t hen brought up in 15 second to a speed of 75 00
rpm to simulate taxiing on the
run
way
fo
llowed by a 2-min uie
idling
at
40
00
rpm to
imu
lat e oper
at
ion while awaitino-
cleara nce for t
ak
e-o
ff
. Finally, t he engine was accelerated
a rapidly as po sible to rated sp
ee
d of 11 ,500 rpm to
s
imulat
e
tak
e-off cond ition , and Lhis engine p
ee
d
\Va
maintained for 15 minu te .
Th
e measUl ed te
mp
e
ratm
e di
st
ributions are hown in
fi
g
UT
e 2
2.
Along the ab cis a is the disk radius in
in
che and
alono the ordinate, the temperatUl e in
of .
E ach et
of
cm ve re
pr
esen ts
th
e tempe
ratm
e condit ion
at
ome Lm e
after the ta r t of engine operat ion. Tluee cm ves are shown
in
each set. The lower CUTve
in
each case is the tempera tm e
di Lribu tion along the face of the disk ubj ected to au: dr
aw
n
in by c
oo
ling vane .
Th
e main p
UTp
ose of this ail
flo
w is to
maintain c
oo
l bearing . The upper cm ve how the rad ial
temp era tm e di tribution on the un cooled face of the di k ;
th
e middle c
mv
es how the radial tcmp eratme di tr ibution
in a plane tlu:ough the center of the disk normal to
th
e axis of
100
-0
Ta
ke-o
ff
a
nd
cli
mb
Q)
75
C
Q)
8.
-0
50
Q)
Q)
S -
Q)
25
:
'c;,
c:
W
I Ta
xi
\
I
W
Id
le
0
4
8
12
16
20
24 28
Time, min
F IG URE 21.-
Ta k
e-off sequ en ce for t urbojet engi
ne
(from re
f.
11).
rota
t ion. At the end of 10 minutes , dUl ing which time the
engine was idling, the temp e
ratm
e at
th
e hub of
th
e di k wa
90 F on th cooled side, 200 F in the center pl
an
e, and 400
F on the uncooled id . A the engine was brought up to
fu
ll
peed , the
tem
pe
ra
tm e rose rapidly, as sho
\\
-n on these
CUl ve. The ~ x i m u m temp era tm e difference betw
ee
n the
,wo faces of th e disk reached 5 0 F at the end of 16
minut
e .
Stresses.- Stre s calcula tion were made wi th all thre
t empera tm e distribut ion ; for the presen t, those calculaLion
will bo di cu sod whie
hw
er e ma 10
with
the to
mp
eratu l e dis
t
ribution
on th e coo led face of tho disk becauso it repre ents
tho mo t evere ca e. In fLUTO 23 is hown a en trifugal
tre dist
ribution in
tho eli k at ra tod peed. The e aro tho
r adial
and
ta
ngential s
tr
es e
du
e only to
rotat
ion.
At
tho
c nLer of the di k , the tre s i approximately 31,000 pounds
pel
qu
aro inch . In figm e
24
are hown tho radial and tan
gential tre es with both tho centrifugal
and
the the
rma
l
efl ect
tak
en
in
to account. Each curve hows the
tr
ess dis
tribution a t a different tinle after the s
tart
of tbo te t; and for
clarity oparate plots hav o been made of rad ial and Lan
ge
ntia
l s
Lres
ses. I t is seen that at the center of the di k the
1200
800
400
l; -
I
I
1
10 mm
12 min
-1
..-/
0
ncoo
d side
f - -
J
- -Cente r
. /
/ /
- - - Cooled side
--
V
--
: /
-
-
/
f - -
f - -
- '
I - -
f- - -
0
Q
a.
1200
E
8
00
400
14
min
1;1
16 min
/I
22min
rJ
/,
_
v
V
/
/
/ /
-
-- /
/
.....
/
--
I - -
--
/
--
/
-------
-
~
o
50 100 0 50 100 0
50 100
Disk
rad ius, , o
rce
nt
F IG RE
22.- T
em
perat
ur
e dist ribu ti
on
in
tu
rbi
ne
disk (
fr
on, re
f.
11)
stresses
hav
e been
rou
g
hl
y doubled by inclusion of the
the
rma
l e
ff
ect.
Th
ey
ar
e now a
ppro
ximately 70 ,000 pounds
PO l' square inch . At the
rim
the st resses are very highly com
pressive. Aft er 16 minutes, t he elastic compressive tress at
the rim is 120,000 pound per
squar
e
in
ch , ,\Thich is much
higher than the yie
ld
stress. H ence , plastic flow mu t O
CC
UT
in compression
at th
rim , calcul
ation
s
fo
r which arc shown in
figUTe 25. After 16 minute , owing to pIa tic flow, t he s tress
i reduced to the neig
hb
orhood of 0,000 pounds per quare
inch compre ive a t the
rim
but at the cen ter
it
i sLll of the
order of
60
,000 pound per quare inch tensile
Lr
e s.
40,000
30,000
iii
-
~ Q O O O
Vi
10,000
o
-
= :: :
p--
\
\\
Rad
ial
- - -
Tan ge
ntial
\
25
50
75 1
00
F I GUR E 23.-
Cent
rif
uga
l st rc e at ra
ted
s
peed
(from re
f.
l l
).
-
7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
21/37
18
REPORT
1
L
70
-
NATIONAL
ADVISORY
CO
MMITTEE FOR AE
RO NA U
TI
CS
\Yhile the pIa tic flow ha reduced t he operating tre
s it
ha in1ro lu ced a new pl'oblem- re idual tres when the
engine is stopped. The free length oC the r im has been eA'ec
lively shor tencd b.' the plastic How , and upon r
et
urn to
room-temperature condition , tbe tendency of th e remaindeT
of the disk to for ce the rim to iL initial length induces Len ile
s lre s. '1'11(
'
computed res i lua.l Lr e es, again
ba
ed on l
oo
r
mation tbe01 )
of pIa ticity, are shown
in
figUl e 26. I n Lhese
calcul
at
ions
th
e
rim
is a s
um
ed to be
co
ntinuou
s; or,
in
e
ff
ecL
a ,,-heel 'itll welded blael e i considered .
Th
e doLted curve
shows
th
e residual stre ba ed on the computation of Lhe
tempera ture di tr ibution in the eent er plane of the disk, and
th
e
da
shed curve shows t
he
re
idua
l str e dist
ribution ba
eel
011
th
e temperatme di tribution in the cooled side of the cl isk.
In either ca e, very high ten iIe stres es remai.n in the rim
after engine s toppage. These high re id ual stres es coupled
wiLh
the pos ibility of tre con entrations associated wi h
blade fastenings ma y exceed the elastic limit of the material
and cause further plasLi flow in tension. pon sub eq uent
engine operation, plastic flow is in compression , and so on .
EYer) time an engine i operated , alLernate compre sive and
tens
il
e pIa tic flow
may
take place. T his plastic flow, to
get her witb
meta
llurg ical c
ha
nges oc curring as a
1e
ult of
80,000
60,000
40,000
~
~
~
--
~
---
-
J -
- 1 -
~
I
1 - - -
- - I
R a d i a l
I
\ .
20,000
~
~
80 ,000
60,000
;;;::::-- --
-
--
9
VI
40 ,000
a.
.n
VI
20,000
f)
0
20,000
-4 0 ,0 00
-6 0
,
000
-80,000
-
100,000
- . .
-
- - -
- -
--
-
~
\
Tangenl,al
-
r--
l\\
-----
~
~
~
\
T ime , min
1
-
10
~
\\
12
-
14
I
16
\ \
22
~
120,0000
2
3 4 5 6
7
8
Disk radius, in.
FJ Gl RE 24.- Elast ic
tr e
sses for tempe
ra
tu re distribu t ion on cool d side
of turb ine di k (from ref. l l ) .
80,000
60,000
~
40,000
20,000
0
60,000
= = ~
n
000
a.
v
VI
20,0
00
f)
0
20,000
-40,000f
-60,000
-80,000
-
100,0000
.-.:-
~
--
-=-
';;;;.:;-
< ~
f
--=-
f..=...---
~
--.
: :
- ,
..;;.;:
-
' '=-.
~ ~
' \, -
r
r--
~
\
~
Time, min
\
.. -
2
10
12
14
16
22
345
Disk rad iu
s,
i n.
6
~
Rad ial
;\
~
,
Tan
ge
ntial
~
l \ ~
. /
~
. -
f\ /
\
\ \
r---- ......
7
8 9
F I
G l-RE
25.-
PJa
st ic s t resses for
tempe
rature d i
st ri
b
ulion
on cooled
side of t urbine disk (
from
ref. 11 ) .
engine operat ing temperatures, may ultima tely result in rim
fiLiIure.
Effects on rims with
inserted
blades .-
Th
e e
ff
ect of the
thermal stre dep e
nd
primarily
on
the de ign of the wheel
T wo
t.
\-pes of designs have been us ed in th is c
ountr
y, the mos
popular of which has the fir-t ree-type blade fastening. Figm
27
show a close-
up
of uch a bl
ad
e
attac
hm e
nt
, as well a
cra cks that occurred at the base of the atLachment a a r e
ult of alternate tens ilc and compressive plast ic flow. uch
crack are not c
ommon
in wheels wiLh fir-tree attachment
in f
act
, there has been no evidence of such faiJures in fix-tre
wheel until very recenLly. The e partic
ul
ar crack occulTed
in conn ection with a program that required cycling b
et
ween
idling and full power lh ree time per hour.
Th
e wheel had
,,ithstood J1('a r ,- 1000 hour or 3000 c.\cles before Lhe
cra cks occurred. NoLe tha t th e e cracks occ ulTed on th
cooled side where lhe Lemperature
gra
dient ancl t res es wer
a t a max imu m . \
iVh
en detected , the crack had no t ye
progr
es eclt
hrollgh the thickne of
Lhe
wh cel to the
un
coole
side. Even in wheel with fir- tree attachment, therma
tres cracks can
ocelll .
Other effect of thermal tre s
in
fir-tree wheel
relate
t
blade loosenino- and tightening. Wh
en
lh e blade is made of
mat
erial
havin
g approximately th e same , or a high er, co
efficien t of thermal expansion as the whee l, and when th
initial fit b
et
ween hlade
and
wheel is moderaLely t ight, th
-
7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
22/37
BEHA
YIOR OF MATERIALS
UNDER CON
DI T
IO
S OF THERMAL STRESS
9
40 000
2QO
00
0 t-
-20,0
00
0
40,00
120,000
iiiIOO,O
a.
VI
VI
00
80,0
/)
60,000
40 000
20,000
f - - - - - - -
-20,0
00
00
40 0
0
I
Rad ial
r- - -
- - -
r - - -
_
l
-? '
r-- -
r - -
- -
r
-
- - --
- - -
...---
1- - - _
r - - -
-
I
-
--
Temperaturedistribution
Tangential
/
- -
Central pla
ne
of disk
/
Cooled side of disk
/
I
i
I
/
Ii
I
I
/
/
j
- - -
_:/
--- -
-
---
1--- -
25 50
75
100
Disk radius, percent
1"1 ,l -RE 26 Re idual s tr el'scs aft er
ope
rat ion (from re f. 11 ) .
blades ar c generall)-
found
to
be
100 e
in
th eir mount
after
th ey lu\,V e once been run. Thi 100 ening
i dl
to the faeL
thaL compressive
pla
s ti c
rI
ow in th e rim ha
hortened the lengtb of
e["raLed
segm ent of
bo t
h blade
and
whee
l.
Upon
r
eturn
to rooIn-tempeJ'atme c
ond
i
Lion
, t he
i fo[' the b lades to pull a w a ~ from th e wh eel land .
In
the
case of the ,,-e
lded
blades, thi is not pos ihle
he
cau
th e blades
ar
c an integral
part
of the ,,-heel
and th
erefore
tcn il e s tl'C ses 1'e lilt.
In
\I-heel \I-ith th e fIr-tree typc of
blade,
hO\l
-e \"('r , it is po s ible for the hlades to pull aw
a.,
- from
the wheel. Hence , in doing 0 hecome
\"er.
,- loosc uncleI'
t t i o n r ~ cond itions. The.,- migh
t
Ligh ten up , howe\,e
[
,
upon returning to operating condi tion.
In ot
her insLance fir-t le e
blade
have
he
come cven tighte r
in thei r mounts than \\'h en in serted . Tbi
faeL
wa
at fir L considered strange in the lighL of the prior experience
of 100 enlllg al read.,- eli cu ed.
Fpon
in\ (' tigation it wa
found , ho\\-e\'er, tbat
tightening
occurred wh
en
lIle co
efficient of e
span
ion of t he b lade
material
was
mu
ch
10
-
e1
tban the coeffi cient of e:q)ansion of the \\-heel
material.
Thu , when t he wheel is aL operatin g
temperatur
e th e hlade
ba e , which do noL expand 0
mu
ch as Lle \\-heelland , e sen
t i a l l ~ shrink from the ( \\-heel Jand . The compre iye
st
resses du e to thermal temperature gradient in the disk
ha v
e
to
be
absorbed, therefore , in the \\'h eel regi
on be
low the blade
fa tening
rath
er than in Lhe bl
ade fa ste
ning
area as
when th e
blades h
ad
approxima tel.\' the sam e coe fflcienL of expansion as
the wheel. Upon retu. rn to staL ic condition tl le pIa tic Ho w
ca
u es Lh e region immediately below
Lhe
rim region to bec
om
e
ma
ll eI'
th en it s
in
itial
iz
e ; the disk
land
s
arc thu
s pu lled
omewhaL
in
toward the
ce
nt er of th e disk. Th e blades arc
t.herefor e tigh teneel.
Effect on rims with
welded
blades.- In t he case of wheels
with
we
ld
ed blade , not onl.'- is
the
full
re
iclu al
tre
s de
veloped because th e blaeles canno t pull away from Lhe rim ,
bu t Lhere usuall y are
pre
sent s tress con ce n trations produced
di
scont
inuiLies
beLw
een adjacent blades. Th
erma
l
crac
k
ing has thu s b een a severe
prob
lem wi th such whee ls. Th e
small rim cra cks in fi gure
28
resul ted from
eno-
ine operati
on
wi th a
ty
pi
ca
l earlv welded wheel. To prove that
th
ese
crack were the resul
t.
of thermal st re a
nd not
t he effect of
rotation, the wh
ee
l wa al Lernately indu ction-h
eate
d and
cooled to
imulate
engine
tempe
rature gradient without
rotation. ome of the cr
ack
progressed e c i
as
shown in
the figure.
evera
l
potential
r em edies for
rim
cracking of eli ks with welded blacles will be ci iscu ed
in
a
la ter ection. AL Lhe pre enL time , the
te
nd en c.\-
ha
been to
abandon the welded blade
co
nst
ru
ction
in
favor of the i.1 -
tree-type of attachm en t. This Lrend
i
parLl)- du e to prob-
1 m of blad e replacement. in Lhc fielel ,
bu
t primarily
it
is
becau e of the problem of Lhermal cracking.
Effect on
bursting
.- Thu far th e efl'ecL of Lhel'lnal st ress
h a been considered on1.'- in Lhe
rim
reo-ion of the disk. Th e
question ari e as to it importan cc
aL
th e cent er of Lhe disk.
In the
di
k pre\'ioll ly described , the tres es at the center
W re rough l.\- douhled til pre ence of the temperature
graciient.
I t
i conceinble that Lhese therm al Lre s may
IN H
14
F I GL'RE 27
Th rmal
crack s in
turbin
e wheel with fir-tree blade
attac
hm
e
nt
s.
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7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
23/37
20
REPORT 1170
-
NA'I'lO
AL DVlSORY COMMIT
TEE
FOR
AERO
AUTI CS
('Huse the disk to bursL 0011
-
7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
24/37
-
7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
25/37
22
REPORT
1170-
NATIO
AL
ADV
ISORY COMMI'rTEE FOR AERONA TICS
failure ah ,-ays 0 CU
lT
d first
at
the ba e of the harp e t
notch. These te t were followed by attemp t to improve
the
resistance of the di
ks
to
therma
l
crack
i
ng
by
dri
lling
small hole beneath the base of the no tch. I n general ,
it
\\
a found that th ese hole h
ad
a beneficial e
ff
ect
in
at least
r
etardin
g the ini t iation
and prop
agation of
the
cr
ael,-s.
Combustion -ch
amber
liners .-
Another
inve LigaLion Lhat
pointed
out
the importance of tress
co
ncent ra,tion in thermal
60
0
notch
:
k
n.
deep
,
0 .
005
to
0.010 in
.
rod
.
at
bottom -
- -
- I
I . d
32
In.
ro ,
I . d
64
In .
ro .
,
ikin. rOd -
. /4-- - _ . -
- I . d
is, , ro .
,
,
I
'
64' '
. /
"-.
. .
:
I
d
32
lrt ro
.
'-6 0
0
. d
note : 16
In
. eep,
0.005 to 0.0
10
rod.
at bottom
: r---.- - - r t . . . ; - - - - i
[l
n
,
F I G l llE ~ o t c h e d r i m d isk u ed in th erm a l s t re s inves tigation
(from ref. 14) .
fatigu e
wa
s described in reference I S, whi ch conce
rn
s the
determillation of the mechani ms of failure of tur
bojet
com
bu stion liners. uch liners, hown in figure 33 , erve thr
purpose or properly distributing the a ir into the combust
ion
chamber.
The
circu lar hol es feed the a ir
into
the co mbu -
tion chamber, an d the louver hown
in
the center of each of
Lhe L,o C ombu t ion liner cool the liner in the areas between
Lhe hole. These louvers are fabricated
by fi
r t punching
Lhe line
'
ancl then bend ing the Hap out of the plane of the
liner. The geometry of the louver can better be een in
fL
g
lire 34 , which i a
photograph
of the louver a well a of the
sLre s-n' licving holes at the
ha
e of
the
louver. Al 0 shown
arc variou types of crack t
ha
t o(;eur in operation. Although
th e circular holes are in tended for relieving the str
es
at the
effective
notch pre ent
at the
ba
e of each louver,
it \V
a
found thaL the fabr ication of the e holes by punching in tro
du ced highly worked
metal and
il'reg
ul
aritie in the pcriph
ery
of the hole
that acted
a
furth
er
stre
co ncentrations.
o
IntaKe
Row
III
o
O U
o
o 3
CJ
o
o
o
o
o
Exh
aust
0
0
O .
0
O
0
0
0
0
0
0
Type A liner
0
Intake
0
0
Row
o I
0
L - J
0
0
0
0
V 0
2
0
L..:.J
0
0
0
0
0
o 0
3
o
O
-...
t: ..:::10
0 0
0
0
4
0
O
-...
0 0
t-. .JO
@
0 0
0
0
0
G
()
G
0
0
0
0
0
G
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0
0
Exhaust
Type B liner
F W l -RE 33.- CombusLion-ehamber liner con Ll'ucLion (from ref. 15)
By reaming, sanding, and
vapor
blasting the punched edges
the
resistance to th e
rmal
cracking wa
vast
ly improved.
Table V how the experimental
result
where a comparison
i' presented of the
number
of crack measured
in
even liners
in th e a -fabricated condition and seven liners in the im
proved condition. A large
red
uction OCCLli'S in
the
number
of cracks
at
the two
in
pection periods conducted
after
hours
and
20
minutes and after
16
hours
and 40 minute o
engine operation.
Stress concentr ati ons r
eSUlt
ing from operation.-
In
orne
case the st ress concentration are not built in ,
but
are pro
duced as a
result
of
operating condition. For exam
ple
surface
attack
c
an
produce discontinuities that
act
a
stre
concentrations. I n an investigation on the
th
erm al hock
resistance of nozzle blades, Bentole and Lowthian (ref. 9)
found that if the te Lblades were poli
hed and etched after
every 250 cycles in a mild chemical so
lution
, the crack re i t
ance was va tly improved. They attributed this improve
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7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
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BEHAVIOR OF MATERIALS UNDER C
ONDITIONS
OF THERMAL STRESS
23
ment largely to the removal of urface irregulariti
es
by the
mild chemical change without, how ever , an appreciable
attack by the chemical on the grain boundarie. Prior te t
in which aqua regia had been used to remove surface scale
for in pection purposes had definitely reduced thermal hock
re istance of
the
material and led to early
intercry
talline
cracking. These re tilts point to the importance of urface
n,ttack,
and in
a l
ater
section
the
po sibility of avoiding such
attack
by
the
u e of surface coating will be discu sed.
EFFECT OF CONSTRAI NTS
Thermal
stres es r es
ult
from con
traint
that
pr
eve
nt
free
expan ion of the variou ections of
the part
tmder con ider
ation. Vhile in many cases
the co
n
straint
is
inh
ere
nt in
the
phy ical continuity of the part, it fre
qu
ent ly i po ible to
incorporate some mea ure of relief by
proper
de ign . Fol
lowing are several illus
trative ca e .
Turbine wheels.- In
Lhe
turbine wheel, for example, the
u e of the fir-tree -type attachment enable th e de
ignel
Lo
provide a loose fit between the
blad
e
and
di
k. Th
e
cl
earan ce
can
then
be use d for
at
lea t partial expansion in
Lhe rim
re ion ,,-here
Lhe
tempera Lure is Lhe highest.
Ev
en in LUI -
bine disks
wiLh
we
ld
ed
attaehments
,
iL
is possible
Lo
improv
e
lhe thermal tress r e i
Lance
by providing a s
lo
L (
fig.
35)
c - Lower bend
In
louver flop
Mos t common type of crock
Second most common type of c
ro
ck
- Buckle
Uncommon crock
Lorge buckle and typi cal crock enlarged
C-22310
C-2056
FIG RE 34.- Typical
crack and buckle
at louver (from ref. IS) .
FIGL:RE 3S.- \\ elded blade
attachment
\\'ith keyhole
;;
lots (fr
om
re
f.
11
) .
bet
\\
-een the blad
e
The hot rim may then expand and
partially close the 10L . The u e of tress-relieving holes at
Lhe ba e of tbe
lo
t probably i good practice.
Turbine nozzles .- In Lurbln nozzle ane , con traint i
ometime minimized by means of the arrangement
hown
in
the righ t ide of figure 36. The left ide shows an early form
of de ign in which the nozzle vanes are welded at
both
ends
onto thick
ring.
Th e
outer
ring i at lower
temperature
and therefore doc not
ex
pand
so
much
as the blades.
Free
ex
pan
ion of the blade is thereby
pr
evenLed, which condition
indu e high
compr
cs ive plastie flow followed by residual
len ile stress; successive rep etition produce thermal fatigue
failure. f the nozzle vane i floa ted in eu t-out e tion of
ring,
th
e blade can expand fr
ee
ly and the
rin
g e
rv
e only to
po
sition the blade.
ixed
Floating
F I
GU RE
36
N ozzl
e
diaphragm.
-
7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
27/37
24
REPOR'f 117O---NATIONAL
ADVISORY
COMMITTEE FOR AERO l
AUTIC
Temperature,
C
20 0
300 .
400
500 .
60 0 - .
700
745
730
400 -
,- - Cen ter
line
F I
Gl RE
C a l c u l a t c e l tcmpc
r
atu
rc
eli
lribu
tion in
blade
aflc l'
4
second s coolin g (from ref.
J
) .
IL shou
ld
be emphasized, of
co
m
e,
Lha t thi free-floating
de ign docs
not
completely remove tre s
in
th e
rmal
hock
because the blade still do e no t cool uniformly ,,-hen subjected
Lo a blast of cold air, Figure 37 shows Lhe computed temper
a,
Lure
distribu tion in a nozzle vane invest igation by Bentele
and Lo,,-thian (re
f.
9). This temperature dist
ribution
was
compu ted for a time 4 seconds after the applicaLion of an air
blast
onto
the
blad
e initially aL
50
0
C.
The smface i , of
cour
e, at
a much lower temperature than th0 in terior of the
blade. By idealizing the geom
et
ry of the nozzle vane
and
compu ting Lhe stresses
by
an approximate m
et
hod, Bentele
and
Lowthian found an elastic tress of over
100,000
pounds
per square inch tension near the leadiflg edge. This stress
wa ,,-ell above the clastic
limit
of tbe ma terial and obviously
plastic flow
must ha
ve occulTed. The lo ca tion of ulLimatc
failure
in
thermal cycling agreed with the
pr
ediction , based
on ela Lic tress analysis.
Th
e usc of hollow nozzle vane prohfihly improves Lhennal
shock resistance by reducing thrl'mal
in
e
rtia
and
by
evening
out temperature di stribuLion. Ail' cooling Lbrough the
hollow
van
es, of comse, flith er improves the thermal hock
resistance , but even wi thou t cooling the hollow blades
should give
beller
performanc e in addition to l'rduced weight
aod traLeg ic malCl'ial cont ent c:
onjdrl'
ed , 0 important nt.
tI l('
Pl ( ,
011
t t i
W
'lIZE
EFFECT
Large i
ze
i really nothing more Lhan the fidditio n of
ron Lraint , since in a bod y of
lar
ge size Lh e portion undergoing
rapid te
mp erature
c
han
ge is ge ne
rally
preven ted from expan
ion 01' contra ction by
fi
massive , e
Lion
which do cs
not
pCl'crive the impose d tem pe
rn t1ll e
rhfinge for nn fippreciahle
period of time. A laboratory investigation co nd cted to
study
iz
e effect on
brittl
e ma terials
will
now be describ d,
and then
several
pra
ctical ca es involving size e
ff
ect will
be
discu ed.
Laboratory investigation on brittle
materials
,- FigUl'e .
how ome t
es
t resul ts to demonstrate size effect in brit tle
materials. The Le L were conducted on geomcLl'icaUy
similar specimens of steatite, cooled
in
nch a ma
nn
er th
at
they
ac t
ed es e
ntiall
y a infinite hollow cyli
nd
er
rapidly
cool ed
at
their
outer mf a
ce . Th e pecimen were fir t
heated to fl, uniform tempera
Lure and
Lhen quenched
at
Lheir sUl Iace by ail' ,
and
in
olher
tes L , by water.
The
initial tempel'atlU'e differen
ce
betw
ee
n lhe pecimen and the
coolant required Lo cause fracture in one cycle was measlU ed.
An
anal ysi
s,
imilar
Lo that
hown earlier for
th
e flat pIa
Le,
an readily be made to indicate that tbi initial
tem
pera
tu r
e difference should vary linearly
with th
e reciprocal of
diameter , which is well verified in figure
3 .
For a given
pecimen diameter the water quench, which is more severe
and
for which the
va
lue of
{3
is greater
than
for the air
quench , r equired lower initial temperatUl'e differe
nc
e to
produce failure. Bo th traight lines inter ect the vertical
axis
at
a te
mp
e
ratm
e value of approximately
250
0
F.
The
in ter cept on the vertical axis repre ent the ca e of infinite
size, or complete COD traint, and the value of this intercept
1800
1600
l
,
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7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
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BEHAVIOR
OF MATERIAL NDER CONDITIONS OF
THERMAL STRESS
25
FI G U
RE
39.- Thcl mal-shock rcsistant rocket nO)lzlo.
hould be
/
afor teatite.
Bas
ed
on
the data given
by
Bu
e em (ref.
3), the value
of 250
0
F i in good agreement
with the
theoretical
va
lue for thi
material.
Figure
3 is presented chiefly to
demonstrate
the reeip
rocal
nature
of thermal sho ck re istance to size,
and
al 0 to
point
ou t
that
there is a tempCl'atme difference below wl)ich
failure will not oecur, even for infin ite ize.
Bui
lt-up struetur
e.-
In
ome ca e
it may be
pos ible to
minimize ize effect by building up a
la r
ge
structure
from
mall units, each of which is
highly re istant
to thCl'l11al
ho
ck
because
of
it size.
Figure 39
show a conceivabl
('
arrangement
for a
rocket
nozzle liner.
The
small blocks
might
have
to be lightly cemented together, or held io elh(,L
by
a wire mesh, for mechanical
rea
ons;
thermally
the:y
CS-6162
FI G URE
40.-
Cro
ss s
cction
' of
thick,
interme
diate, and Ihin
1 laic
whecls (from ref. ]3 ) .
would act independ( ntly and
they
wOlllcl he grcnlly superio
in
thermal
bock.
Eff
eet of
massive
eores.-
Temp
e
raiure
changes
are
usually imposecl at the surface; it i prev( ntion of expanSiOlJ
or
contraction by the
inner
core that incluces thCl'mal
stre
s.
The
usc of hollow nozzle vanes in ihis connection has already
been referenced;
other examp
le
can be found in
tbe loco
motive
wheels and the turbine disks. Figure 40 how
three locomotive wheels investigat('d
by
chr
ader and
co,,-orker
in
reference ]3. All wheels
have
(.he ame huh
and
rim, hut Lhe Lhiclm(' s of Lhe plate, which connects the
lwb
to the rim, ha . h('('n varied. The reasoning here \Va
that
as the.
rim
is heaLed by the
braking action iL
free
expan ion is
prevented by the
plate. Hence, a thinner
plate might
offer less con
lraint and thereby improve
life.
Tbe
results
of
the tesl
of
frference 13
arc
shown
in .figme
41. Three condiLions of h at treatmenL are shown, and in
all cases
the H- by
%-inch wheel,
the tbinne t
of
the
t
hr
ee,
lasted by far the greaLe l
number
of LesL cycles.
Likewi
e,
figme 42 (ref.
11
) shows
lhe re
ult of ome
ana
lyLical stuelie on
tmbine
eli
Ie
profiles.
The
solid profile is
the
disk
pI' viou Iy described ,
and
tbe solid lines
represent
Lbe
1'0.
hal
and
tangenLial lre ses
in lhi
di k
ba
ed
on the
mea med temperalm
e eli tribuLion
in
lhe central plane.
The dotted
profiles repro
enl
redesign lhaL reduce
Lhe
weigh t
as well as Lhe stre .
Effeet of localized strain absorption.- In ome case
geometrical configmaLion dicLaLes
that Lhe
toLal Lhermal
elongation of a large portion of a
body
be equaled
by
the
elon
gation
of a small eclion.
1 he
unit elongaLion 0 ] s
lrain
in the
sm a
ller s('ction is thus reater
than llH' tr
fl.in in Lhe
larger ection.
Figme
43 sch('maLically indicates a simple
case of this typ('. Sections Band C arc assumed
o
be of
equa
l (emp('ratlll t', buL 1 \\
('1
lhan
thaL of ecLions A
by fl
value of
A
. I f the entire
body
i
un
tr(' sed when aL uni
form tcmperaLme,
Lhe
Lhermal elongation a.4.TAlA where
50
40
V
;no>
~ ~
O'u
30
-0 -
o
20
EO.
: : 00
z 10
r - -
f
-
r -
-
. -
f -
-
I
Rim
quenched
-
--
r -
Wheels _
-
subjected to
-
severe
drag
lesl
-
I
o
Oil
quenched
-
-
Unlreated
-
1
- -
-
I-
m
..
.
Arrow indicates
wheel
did not fracture
FH1lJ
RE
41. - EffccL of plate h i c k n c ~ i ) on numbc r of drag; Ics ts requircd
10
produc( fracl mc (from re
f.
-
7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
29/37
26
REPORT
1l7
N ATIONA L AD V
ISORY
CO
MMI
TT E E F OR AERONAUTICS
'
3
=
-
I
o
80
,00
0
60 ,
000
40,000
20
,
000
o
60
,00
0
4
0,00
0
F
-
2
j,
o
-20,00 0
-4 0
,000
I
-
60,000
-80 ,0
00
-100,0000
---
-
-
-
- - -
2
'-
r ....
--
- : -
:::.::.::-
-=
c :: ::
C-=- -=.-
~
~
,\
~
~ . . . : : - : : : :
~ ~
\
Disk
W
ei
ght
\,
ro
f ile
ra tio
I
1.
000
2
.
817
\
.673
'\
3 4 5 6
7
8
9
Disk radius,
In.
FI GI '
R}:; 42.- E las t ic
st
ress dist r ibut ion for va riou, d isk pr ofile (from
ref.
11
).
a is
th
e coefficien t of e
xpan
ion and
LI
is the length of
sect ion A, mu st be match ed by an elonga tion d ue to stl'es
in section B and
C.
I f th e cro section of B i
rn
a sive
co mpared wi th that of a ll t he
tra in
i ind uced in ect ion
C. Thu
s, if
e
c
is th e tra
in
in
C
EcL
C=
a. 1T4LA
(1 6)
or
LA T
c r aA A
(16a)
I n the elas ti.c range the tr ess indueed in C as a result of this
stra in is
(
17
)
where Ec is the elast ic modulu of seetion C.
Th e foregoing case illu tra tes the very i
mpo
r tan t fact th
at
geometrical configm a tion may impose a stre and strain
mul tiplica t ion f
ado
r . The product EaT
o
is so met ime
though t of as the maximum st r ess d uc to temp era t m e
change
To
that can b e imp osed at a poi
nt,
since th i produ
ct
repr
ese
nts the tre
l
eq
uircd
to
constrain comp letely the
thermal dilation . It, i seen, hov
;reye
r , from t
hi
examp le
th
at
the maximum tre s in the tem may be many t im
the s
tr
ess fo r complete constrain t, depending on the value
LA l
e
Th us, unu ually high stre e are f1 eC] uen tl. i
mpo
se d
on th e weake t m
em
ber of a
s.
\'stem .
I f
C
W
Cl e
, for exa
mp
l
e,
a weld of small ax ial dimension
co
mp
ared with ection A
and B , the r atio lA le would be very large, and fai lure of th e
II-eld would oCC
Ul
at low
tem
perat ure d
iO
e
l
ence in the
system . This fa ilur e would be du e not to poor tl enath of
th e weld metal, but rather to poor de ign, which require
large elongations to be ma tched b) ' high loca
li ze
d
tr
ain .
In the case of welded s
tru
c
tur
es, the high
st
resses a.
nd
s train
may also res ult if
th
e bony is at uniform temper
at
ur e if the
var ious componen t ha ve c1ifl er en t coeffi ci
ent
of therm al
oxpansion .
Thi
s illus
tr at
ion
tIm
e
mph
asize one of the
many reason weld s are so sensitive to th ermal
E FFE CT OF I N I T I AL S UR
FA
CE STR ESS
I n ome cases it i poss ible to
in
troduce init ial str esse
th
at
c
ount
eract the eHect of the
rm
al st ress a
nd
lllereb.,
impr
ove
therm al shock res i tancc . The use of hot blas tin g, for
exa
mp
le,
in
order to inLroduce c
ompr
e ive surface tre ses
h as been amply demon st
rate
d
in
th e ca e of mech anical
f
at
igue at room t e
mp
era tUl e. The arne idea can be app li ed
to par t operat ing at high te
mp
eratm e prov
id
cci the Le
mp
era
tw
e is no t so
hi
gh as to
annea
l
the
inclu ced tre ses . In
ome cases the urface stresses should
be
ten ile, in other
co
mpr
e sive; and illustraLion of each will now be presented.
Residual tension.- In the case of Lurbine wh
eel,
the
operating tr esse arc compl'es ive; hence, it i d es irable to
in troduce a re i
clu
al tensile str ess to oD r l the opera ting
s
tr
c s . This can be a h ieyed when th e wheel i co n tructed
in
two pa
rt
s, uch as s
hown in
fi
g
W
e
44.
Th
e ce
ntr
al
l
egion
where the
temp
erat
ur
e j low, i usually made
of
fe
rriti
c
material th at can eas il.\ be forged and ha good low-temp era
tUl C strength.
Th
e r im region is made of aust eni t ic
F IG URE 43.-C ross
section
of body in
which
l
arge
st ress a nd t ra i
a re
induced
in sma ll membe r as a result of temperature change in
la rge membe r .
-
7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf
30/37
BEHAVIOR OF MATERIALS
UN
DER CONDITIONS OF THERMAL STRESS
27
mat
erial which has good hi gh- tempe
ratur
e strength , nece -
sar,\- for
re
i
ting
the
high
te
mp
erature in
th
i area. The
two part are joined by providing space for weld met al,
as shown
in
the figure.
On
e
pra
ct ice tha t has bee n fo
ll
owed
i
to
heat
the rim
r egion
to
a higher tempera t ure t han the
centra
l reg
ion
befor e in
sert
ion of the we ld m etal.
When
the
r
im
cools,
it
th er efore eA
ect
ive
l.,
-
hrin
.
ks
on to Lhe
ccnter
region
and et
up a y tern of r esidual stre ses, tensile at
th e
rim and
co
mp r
e sive
at
th
e ce
nt
er.
Tn
subseque
nt
oper
ation
the incl uce cl therm al
C'o
mpres ive sLr e s
aL
t he
rim is co un teracted b.,- th e init ial Lt' nsile kess. In the lower
portion of th e figure is bown the t ress eli tribution that
would occ ur
in
thi case if
the
te
mp erature
cI ifl'er ent ia l of
400
0
F were maintained between thc
rim
and the cenLer
region
during
the welding pl'oee
dure
. T il i
stress
distribution
is
ca
lculated for the eli k
pr
eviousl.,- d i cus cd for which ,
without
this s1u'inking
practi
ce, the
compres
ive
tre at
the
center
would be about
60
,000
pound
per
quare indl
and at
the
rim
,
over]
00.000
pound
s per
quare
inch .
Tht'
only
region tha t suffers rr
om hi
gh
st
re ' is t
il t'
rt'g iO
Il ill1m
rd
i-
at
ely
adjace
nt to the ,dd. A small
amo unt
of pia.
tiC'
H
ow
may
take
plact' in
this
region,
but
lite te lllp t'ntt
uJ (
's
in
t,hilocatioll lo\\-er than at
t t
I'im
, and t Il('re are
110
geomrt ri cn l fl tr eflS ('onct'lltrnJioTlfl_
'
.
'
'
S t r c ~ d i ~ t r i b u t i o n
in weld
ed
and
s
hrunk
disk (from
ref. 11 ) .
Residual
c
ompression.
- In
some
cases the
desirabl
e initia.l
stress
is th
at
of
co
mpr ession.
Vol
e
tb
roo].;: and Wulff
(
1' f.
1
6)
ha
ve , for
rxampl
e, m ade a ve ry
exten
ive
inv
es
tigation on
the possibilit.'- of indu c
in
a
sui table initial tresses in ho ll
o
circul
ar edi lldr rs. Their project was conducted in con
n ec
tion wi t h the guided mi ssil e program a
nd
th e in ter est
wa pr i
marily
in rocket nozzles. Th e)Tther efore c
on
ider ecl
hollow c.dindCl's that were sudde
nl.
h
eate
d
in
the cent
cr
b
.,
- a Global' rod
Lo
simu la t
('
the
s
udd
en
a
ppli
ca t
ion of co
m
hu
Lion
in
( li
e rockrt
11
ozzlr .
An
ea rl.,- find ing wa t h
at
fa ilu rt'
r('
s
ul
ted