Behavior of Materials Under Conditions of Thermal Stress2.pdf

7/21/2019 Behavior of Materials Under Conditions of Thermal Stress2.pdf

1/37

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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2/37

-

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


3/37

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


4/37

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


5/37

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.


6/37

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.


7/37

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 +


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


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

~

"-

"-

"-

~

- - ,


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 ).


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

).


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


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.


23/37

20

REPORT 1170

-

NA'I'lO

AL DVlSORY COMMIT

TEE

FOR

AERO

AUTI CS

('Huse the disk to bursL 0011


24/37


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


26/37

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.


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

,


28/37

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.


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 .


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

Behavior of Materials Under Conditions of Thermal Stress2.pdf

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Transcript of Behavior of Materials Under Conditions of Thermal Stress2.pdf