prof. niguse tebedge msc paper

7/21/2019 Prof. Niguse Tebedge MSC Paper

1/115

L HIGH UNIV RSITY

Residual Stresses

in

Thick

Welded

Pla

ME SUREMENT OF

RESIDU L

STRESSE

A

TU Y OF M E T H O

RITZ

ENGINEER

l SOR TORY

LIBRARY

Negussie Tebed

Coran A

lpst

Lambert T

Februa

ry 9

Fritz Engineering Laboratory

Report

No 337


2/115

Residual

s t r e s s e s in Thick Welded Pla tes

ME SUREMENT

OF

RESIDUAL STRESSES

A STUDY OF METHODS

by

Negussie

Tebedge

~ r a n

A. Alpsten

Lambert

Tal l

Fr i t z Engineer ing Laboratory

Department

of

iv i l

Engineer ing

Lehigh

Univers i ty

Bethlehem Pennsylvania

February 1971

~ r i t z

Engineering

Laboratory Report

No. 337.8


3/115

337.8

TABLE OF CONTENTS

ABSTRACT

1 . INTRODUCTION

2.

THE

METHOD OF

SECTIONING

2.1 In t roduc t ion

2.2

Prepara t ion

o f

Tes t

Specimen

2.3

Measuring Technique

2.4 Evalua t ion

o f

Data

3. THE HOLE DRILLING METHOD


3.2 Mathar s Method

3.3 S o e t e s

Hole D r i l l i n g

Method

4. OTHER METHODS

A BRIEF

SURVEY

4.1

Grooving-Out

Methods

4.2

Gunner t s

Method

4.3

Schw aighofer s Method

4.4 Def lec t ion Methods

4.5 The Trepanning Method

4.6

The

X-Ray

Method

4.7 The Ult rason ics Method

4.8 The

B r i t t l e

Lacquer Method

4.9

Indenta t ion Methods

5.

SUMMARY AND

CONCLUSIONS

6. ACKNOWLEDGEMENTS

7.

TABLES

AND

FIGURES

8.

REFERENCES

i

5

5

6

10

15

18

18

32

4

4

43

43

44

46

47

49

50

52

53

56

57

104


4/115

337.8 i

BSTR CT

ne

of

the major

problems associated

with the use

of

metals a t present i s

tha t created

by the presence

of

residual s t resses .

In general , residual

s t resses

tend to

reduce strength; in some

s i tua t ions

however, the i r

presence

may

improve

the

st rength.

The various phases of the

manufacturing processes

causing

residual s t resses are too

involved

general ly

to permit even

an approximate

prediction

of the magnitude

and

dis t r ibu t ion of them based on theoret ical

considerat ions.

I t

i s

natural therefore , to resor t also to

experimental means

for

the i r determination.

Unfortunately,

residual

s t resses cannot be

measured

di rec t ly

in

the

manner

tha t applied

s t resses

are measured.

Thus, the measurement of res idual s t resses i s ra ther del ica te

requir ing

much time, patience,

and expense.

In

th i s

paper,

some

of

the

di f fe ren t

techniques

of

residual s t ress

measurements

are investigated.

Special

at tent ion i s given to the measurement

of

residual s t resses

in s t ruc tura l

members where

the appl icab i l i ty

simplici ty,

accuracy and

saving

in time each

method

can

offer are

discussed.

For a specif ic comparison of a number of methods,

actua l

comparisons were made under

laboratory

condit ions.

Measurements

of

residual

s t resses

were made using

the method

of sectioning, a destruc t ive method, and two different hole

dr i l l ing

methods both

semi-destruct ive.

For comparison,

the


5/115

337.8

ii

methods

w r ~

app l ied to one

specimen

having

uniform

r es idua l

s t r e s s d i s t r i bu t ion along i t s l eng th .

The procedure

of t e s t i ng prepa ra t ion

o f specimen

and requ i red

t o o l s and

measur ing dev ices

working

cond i t ions

and

s imi la r re l evan t in fo rmat ion are descr ibed . The record ing

o f

data as wel l as i t s i n t e rp re t a t i o n

i s

discussed

including

both

manual and

automated procedures using the

computer;

the

necessary t h e o re t i c a l background i s supplemented in br i e f .

The poss ib l e causes of e r ro r s during the record ing and

i n t e rp re t a t i o n of

da ta

and

t he i r minimizat ion are discussed .

othe r

methods

of r es idua l s t r e s s

measurement

which

may

be of genera l i n t e r e s t a re mentioned and

list

of

re fe rences

i s

presen ted .


6/115

337.8 -1

1.

INTRODUCTION

One

of

the major

problems

a t presen t assoc ia ted

with the t e chn ica l use

o f

meta l s

i s

t ha t o f

r es idua l s t r e s se s .

Many schemes

and

methods have been dev ised over the p as t

e igh ty years for measuring r es idua l

s t r e s s e s

s ince

Kalakoutsky

performed such measurements in 1888. h i s t o r i c a l survey on

methods

o f

measuring re s idua l

s t r e s s e s

can be found in Refs .

1 2 3 and 4.

Severa l

papers

deal ing

with

the var ious

methods o f r es idua l

s t r e s s

measurement have

appeared during

the

l a s t

few yea rs . The

v a r i e ty

o f proposed

methods shows

t h a t r e s id u a l s t r e s s measurement still arouses cons iderab le

i n t e r e s t in t e chn ica l c i r c l e s .

The var ious

phases of the

manufactur ing processes

caus ing

re s idua l s t r e s se s

in

s t ru c t u ra l m e ~ e r s are

too

i nvo lved g en e ra l l y

to permi t

more

than an approximate

p re d i c t i o n o f

the

magnitude and d i s t r i b u t i o n

o f

r es idua l

s t r e s se s

based

on

t h e o re t i c a l

cons idera t ions .

t

i s

n a tu r a l

the re fo re

to

r e so r t

a l so

to exper imenta l

means fo r t h e i r

determinat ion.

Unfor tunate ly

re s idua l s t r e s se s cannot be

measured

mechanica l ly in

the

manner t h a t

app l ied

s t r e s se s are

measured.

Thus the

measurement

o f

r es idua l s t r e s se s

i s

o f g r ea t

i n t r i n s i c

i n t e r e s t

but r a th e r

d e l i c a t e

requ i r ing

much t ime

and expense.

Laboratory specimens may not reproduce

the

e f f e c t s

o f

r es idua l s t r e s se s

in big

s t r u c tu r e s .

Hence s imple


7/115

337.8

-2

sys temat ic , and

p r a c t i c a l methods with s u f f i c i e n t accuracy

and

not excess ive s e n s i t i v i t y ,

app l icab le to

the measurement

o f

re s idua l s t r e s s e s in

f u l l - s c a l e members

o f

var ious c ross

s ec t i o n s are

of

g re a t i n t e r e s t . Ways o f

improving the

s e ns i t i v i t y and

the

p re c i s i o n

of the measuring devices

should

be s tud ied so long as t h i s aim does not c o n f l i c t with the

p ra c t i c a l cond i t ions o f the measurements .

The a v a i l a b l e methods of exp lo ra t ion f a l l i n t o two

ca tegor i e s : mechanical methods and phys ica l

methods. The

former r eq u i r e

d i s tu rbance

o f

the

s t r e s s e s

and

the l a t t e r

do

not .

The

bas i c

concept

adopted

by the mechanical methods

fo r the de termina t ion o f re s idua l s t r e s s s s i s to re l ea se the

r e s i d u a l

s t r e s s

on

the

sur face

by

appropr ia te

removal o f

mate r i a l . Since r e s i d u a l s t r e s se s form an i n t e rn a l l y

balanced sys tem

o f s t r e s s and

are

produced by

mutual i n t e r ac t i o n

o f

var ious elements o f the s t r a ined body, removal of

mate r i a l

such

as

by

cu t t i n g ,

d r i l l i n g , and

grooving,

w i l l

cause

unbalanced

and p a r t i a l r e l a x a t i o n

o f s t r e s s in

each

p a r t .

Thus, the mechanical methods do not measure the

ac tua l

s t r a i n

produced by the ex i s t i n g re s idua l s t r e s s , what they do

measure

i s

the r e l x ~ d

s t r a i n in one p a r t

of the body when

the re s idua l

s t r e s s sys tem i s

di s tu rbed .

The mechanical methods, sometimes known as

r e l a x a t i o n

methods ,

a re

e i t h e r

d e s t ru c t i v e

o r semi

d e s t ru c t i v e

in na tu re .

The d e s t ru c t i v e methods, as the name

impl ies , requ i re t o t a l des t ruc t ion beyond any

hope o f

repa i r ,

before r e s id u a l s t r e s se s can

be

evalua ted . The semi -des t ruc t ive


8/115

337.8

-3

methods, on the othe r hand, produce

only

l oca l damage which

gene ra l ly can be

r epa i red

for

example, by

welding.

The

d es t r u c t i v e

charac te r i s t i c s

o f t he

mechanical

methods

have

been

one of the major incent ives

for

using

physica l

methods.

Such

methods

may be

used to .measure

the

ex is t ing r es idua l s t r e s s

d i r e c t l y

without

requi r ing any

des t ruc t ion of the t e s t specimen. Among these methods, the

X-ray

d i f f r a c t i on technique and

t he .u l t ra son ic methods

a re

the

most impor tan t

s ince

they

measure s t r a ins d i r e c t l y

on

the

s t r a in ed metal . Unlike the

mechanical methods,

they

may not deal wi th the average s i t ua t ion but

sample only

a

pa r t i c u l a r

c las s

o f the gra in aggregate . I f the sampling i s

not

r ep r e s en t a t i v e

the

phys ica l methods

and

the mechanical

methods may not measure the same

th ing .

In gene ra l the

mechanical

methods

measure only

macros t resses

the X-ray

methods may superimpose the micros t r e s s to the macros t ress

and

the

u l t rason ic methods provide i ~ f o r m t i o n

only on

the

d i f fe rence between t he pr inc ipa l r es idua l s t r e s s e s and not

on

the abso lu te

magnitude

of these

s t re sses .

This leads

to a s i t ua t ion

seeking

the

answer to the

fami l ia r ques t ion

What i s ac tua l ly

being

measured ?

The

purpose

o f t h i s s tudy

i s to i nves t iga te

d i f f e r e n t

t echn iques

of

r es idua l s t r e s s measurement

taking

in to

cons idera t ion the a pp l i c a b i l i t y

s impl i c i ty economy,

accuracy

and saving in

t ime each

method

can of f e r .

For

the

purpose of

comparison,

the

methods cons idered

a re

app l ied

on one specimen,

with

a uniform r es idua l s t r e s s d i s t r i b u t i o n

along the

l ength .

A l4H202*, STM A36

s t ee l

b u i l t up from

*The des igna t ion H r e f e r s to a

wide f lange

sec t ion bu i l t up

by welding component p la t e s as opposed to the des igna t ion

W for i o l l e d wide-f lange

sec t ions .


9/115

337.8

4

flame cu t p la tes

with

fill t welds was the se lec ted

work

piece .

Residual s t r e s s measurements using the method o f

sec t ion ing

and

two

d i f f e r e n t

ho le d r i l l i ng methods were

conducted.

The procedure o f t e s t i ng used as wel l as the

r e s u l t s are discussed

in

de t a i l .


10/115

337.8

-5

2. THE

METHO OF SE TIONING


In

t he

y ea r

1888,

Kalakoutsky(5}

repor ted on a

method o f determining l ong i tud ina l

s t r e s s e s

in

bars

by

s l i t t i n g l ong i tud ina l s t r i p s from the bar and

measur ing

t h e i r

change

in length . his method known

as

the sec t ion ing

method (6 ,7)

i s based on the

p r i n c i p l e t ha t i n t e rna l

s t r e s s e s

in a mater i a l

are r e l i eved

by

sec t ion ing

a

specimen i n t o

many

s t r i p s

o f

,small

cross

sec t ion .

t

i s

bes t

appl ied to

members

when the l ong i tud ina l

s t r e s s e s a lone

are

impor tan t .

The s t r e s s

d i s t r i b u t i o n

over a cross sec t i on can

be determined with reasonab le accuracy from

the

measurement

o f

change in

length o f

each s t r i p t aken befo re and

a f t e r

the

sec t ion ing and by

applying

Hooke's Law. The ana lys i s i s

s i m p l i f i e d

by assuming t ha t the

t r ansver se

s t r e s s e s are

n e g l i g i b l e ,

and t h a t

t he

method

o f cu t t ing produces

no

apprec iable

s t r a i n s .

(2) In pra c t i c e ,

h o w v r ~

t r ansver se

s t r e s s e s

may e x i s t , but

the lower the t r n s v e ~ s e

s t r e s s es ,

the more accura te the

r e s u l t s

w i l l

be. Residual s t re sses

formed

due

to

sawing

alone depend, among

many

other

f ac to r s ,

on the spac ing o f the saw cu t s ,

the th ickness

o f p l a t e , the

speed o f c u t t i ng , and

coo l ing c ha ra c t e r i s t i c s {cool ing

l i qu i ds , e t c . } . In genera l , t he r e s idua l s t r e s s a t the very

edge

o f the

cu t

may

approach

the l oca l y i e l d s t r e n g t h of the

mate r i a l .

The

ac tua l


o f

r e s idua l

s t r e s s e s

c lose

to the su r f ace wi l l depend on the mechanica l and thermal

e f f ec t s . (8) The s t r e s s decreases very r ap id ly toward the


11/115

337.8

6

i n t e r i o r where

the sec t ion ing

measurement

normal ly i s t aken .

This s t r e s s has been obse rved to be of the o rd e r

o f

0.5

to

1 5 k ,

f

d

9)

S l

1n

compress1on o r

o r 1nary

cases .

The s e c t i o n i n g method ~ s been

used

fo r years for

r e s i d u a l

s t r e s s measurements in s t ruc t u r a l s t e e l members. t

has

proved

to be

adequate , accu ra t e

and

economical

if

proper

care

i s

t aken i n the p r epa ra t ion

o f

the specimen

and the

procedure o f

measurement .

2.2

Prepa ra t ion

of

Tes t

Specimen

Se lec t ion

and

Locat ion

o f Specimen

Locat ion of the t e s t p iece a long the l eng th o f the

m ate r i a l

must first be de te rmined . The

t e s t

sec t ion

must

be

comple te ly c l e a r o f co ld -bend

y i e l d

l i n e s if

r es idua l

s t r e s s e s

due

to thermal e f f e c t s a lone are to be

measured.

To avo id

end

e f f e c t s on the

magni tude

and


of

r e s i d u a l

s t r e s s e s ,

a

d i s t ance

o f

1.5

to

2.0 t imes the maximum l i ne a r dimension

has

been recommended,

though

t h e o r e t i c a l l y a

r a t i o o f 1.0

i s

s u f f i c i e n t . 7,10)

An

edge d i s t ance

o f 2 f t .

was taken

s u f f i c i e n t

to

o f f s e t any

edge

e f f e c t s fo r the 14H202 t e s t specimen. Figure

1

shows

t he

l o c a t io n o f s e c t i o n s fo r sec t ion ing and Fig .

2

the i de n t i f i c a t i o

of var ious e lement s . Two se t s

o f measurements

were t aken fo r

the specimen used, to check

whether t he

v a r i a t i o n o f r es idua l

s t r e s s e s

a long

t he l en g th

o f

a column i s

n e g l i g i b l e .

Since

it i s i n t ended

to

s tudy d i f f e r e n t

methods o f r e s i d u a l

s t r e s s

measurement

on

the same

specimen,

conf i rmat ion o f the

un i fo rmi ty

of the s t r e s s e s a long the l eng th i s

impor tan t .

This

i s

shown

in

a

l a t e r s e c t i o n .


12/115

337.8

-7

Prepara t ion

o f Gage Holes

Figure

3

shows

the

d e t a i l o f gage hole l oca t ion fo r

the sec t ioning

of

the 14H202 specimen. Since t r ansve rse

sawing d is tu rbs

the

pa t t e rn o f r es idua l

s t r e s s d i s t r i bu t ion ,

the

gage

hole

l i n e

must be a t some dis tance from the saw cu t

l i ne

to

avoid th is .

e f fec t .

This dis tance

depends

on the

th ickness

o f

the component p la tes of the

shape

and on the

cu t t ing procedure .

(11) A dis tance of 1

inch

from

both ends

i s s u f f i c i e n t fo r t h i s pa r t i c u l a r specimen.

St ra in

measurements

are

taken over

a

10

inch

gage

l eng th by

a

1/10,000

inch Whittemore s t r a i n gage.* The

s t r a i n

readings

are ~ r o m

both top and

bottom

faces

o f the

component

pla te s .

The accuracy in

reading

depends mainly

on the gage

holes . Following the i n s t ruc t ions of the

manufacturer , gage holes were prepared using

a

No.

56

tw i s t

d r i l l (0.0465 inch diameter) to

a

depth o f 0.2

inch. Al l

holes

were reamed

using

an angle

of 60

and depth

o f

0.005

to 0.01

inch. An

i l l u s t r a t i o n i s

shown in Fig.

4

A

drill

b i t q p b l ~ o f

making

such

a

hole

in

a

s ing le

opera t ion

i s

commercia l ly av a i l ab l e .

The gage holes

were cen t ra l ly

loca ted

using

a

s tandard 10 inch punch and the resu l t ing

measured dis tance

between

the gage holes showed

a

var i a t ion

of

0.01

inch.

Prepa ra t ion o f gage holes a t welds and

f l ame-cu t

areas i s

d i f f i c u l t ,

because the mater ia l

has a higher

y ie ld

s t r eng th

a t

such

l o ca l i z ed

areas

due

to meta l lu rg ica l

changes

from

the

high

hea t

inpu t . Unrel iable readings may r e s u l t if

*U.S. Pa ten t No. 1638425-2177605.


13/115

337.8

-8

the

gage

holes a re not p rope r ly prepared.

Gage holes

a t

edges o r a t

corne rs ,

though

not

d i f f i c u l t to prepare , may

give unre l i ab l e read ings s ince

the

holes may

have

d i f f e r e n t

al ignments , and the extensometer cannot usua l ly be

made

s t ab l e

while

t ak ing measurements .

Deta i l

fo r

Sect ion ing

The number o f l ong i tud ina l s t r i p s to be cu t depends

on

the an t ic ipa ted r es idua l

s t r e s s

d i s t r i b u t i o n .

This

in

tu rn depends upon many

f ac to r s ,

such as edge prepa ra t ion

(universa l

mi l l ,

welded,

flame

c u t ) ,

grade

o f

s t e e l ,

dimension 6 f the

specimen

and

so

fo r th .

For

the 14H202

sec t ion , a in . spac ing was used a t reg ions o f an t i c ipa t ed

s teep s t r e s s grad ien t , and a t in .

spacing

a t regions o f low

s t r e s s

grad ien t as

shown

in Fig. 3.

To determine the overa l l

p a t t e r n o f

re s idua l s t r e s s


with

a l e s se r

number

o f

l ong i tud ina l cu t s

a

pa r t i a l sec t ion ing

10,12)

can be made. The re s idua l s t r e s s

d i s t r i b u t i o n through the th ickness of

the

p la t e s

can be

determined

from changes on s t r a i n readings

a f t e r

s l i c ing

o f sawed s t r i p s .

Method o f

P a r t i a l

Sect ion ing

The

number o f l ong i tud ina l s t r i p s to be cu t can

be

reduced s i g n i f i c a n t l y

i

the method o f pa r t i a l sec t ioning

i s

u t i l i z e d . This

method, however,

requ i re s

a p r i o r

knowledge

o f the pa t t e rn o f r es idua l s t r e s s d i s t r i b u t i o n . reasonab le

es t ima te

on

the

pa t t e rn

o f re s idua l s t r e s s d i s t r i b u t i o n r a th e r

than i t s magnitude,

i s

o f more importance for an

e f f ec t i v e

use


14/115

337.8

-9

o f t h i s

method. The

approximate

var i a t ion in r es idua l

s t r e s s d i s t r i bu t ion can

be

pred ic t ed from the

geometry

o f the

p l a t e

o r

shape, manufactur ing

process , hea t

t reatment

(such

as

flame

cu t t ing ,

welding ,

e t c . , and the

mechanical

proper t i e s o f the mater ia l .

Locat ions

for

p a r t i a l

sec t ioning

are so

determined

t h a t they l i e near o r a t

l oca t ions of t r a ns i t i ons

of r es idua l

s t r e s s grad ien t s .

Locat ions

B a n d C shown in Fig.

5,

for

example,

would be

the approp r ia te loca t ions for the case o f

the edge welded

p la t e .

t i s

apparent , t ha t

complete

sec t ioning

of the p l a t e from

Locat ion

B to

Locat ion

C i n to smal ler s t r i p s

would

con t r ibu te no s ign i f i c a n t

accuracy

in

r es idua l

s t r e s s

measurement to those obta ined

a f t e r p a r t i a l sec t ion ing i s

made

a t

B a n d

C.

This

i s t rue , provided the r es idua l

s t r e s s

d i s t r i bu t ion

i s l i ne a r in the region. This a l so

holds

t rue

fo r

the

regions

A to B a n d C to D

where

the r es idua l s t r e s s

va r i e s l i ne a r ly , s ince

the e r ro r

caused

by bending

a f t e r

p a r t i a l sec t ion ing i s o f a secondary order . The sequence

o f

p a r t i a l

sec t ioning

has

no

in f luence

on

the

f ina l

r e s u l t s ,

s ince unloading of the

f ibe r s

w i l l

always

be

l i n e a r l y e l a s t i c .

Figure

shows

the

layout o f

cu t t ing

pos i t ions for

p a r t i a l

sec t ioning used

on

the

shape 14H202. The lower

por t ion o f

the f igure

shows the d e t a i l for complete

sec t ioning

to

be performed

on

t ~ p a r t i a l l y sec t ioned

specimen. The

t o t a l

number

of cu t s requ i red

for

p a r t i a l

sec t ion ing i s

only

12

compared to

104 requi red fo r the complete sec t ion ing .

Figure

7 shows one f lange a f t e r

complete

sec t ioning has been

performed. The number o f

cuts

could have been

reduced

to

only four

to obta in a very

s imi la r r e s u l t .


15/115

337.8

-10

Figure compares

the r e s u l t s

obta ined

for the

inner and

oute r surfaces of

the f lange

of

the l4H202

sec t ion

a f t e r p a r t i a l

and complete

sec t ioning

i s

performed.

t

i s

observed t ha t the r e s u l t s

obta ined from p a r t i a l

sec t ioning

readings are

not

very much d i f f e r e n t from those

obtained

a f t e r

complete sec t ion ing . The cu t t ing pos i t ions

determined from

a s tudy o f previous t e s t s 13)

compare very

c lose ly to the

es t imated

l oca t ion fo r

changes

in the s t r e s s

gradient .

2.3

Measuring Technique

The

obta in ing of r e l i a b l e r e s u l t s from measured

values

depends

on f ac to r s such as

the type of

s t ra in-measuring

dev ice and

the procedure o f measurement. Mechanical s t r a i n

gages

have been found

to

be p a r t i c u l a r l y su i t a b l e for

s t r a i n

measurement

because

the s t ra in -measur ing device

w i l l

not be

damaged during sec t ion ing

and

the. same device can

be

used

to

measure

repea tedly . The procedure

followed in

the Fr i t z

Engineering Laboratory w i l l be discussed t oge the r with some

add i t iona l suggest ions l a t e r .

The

Whittemore Extensometer

The Whittemore gage i s a se l f - con ta ined

ins t rument

cons i s t ing e s s e n t i a l l y o f two

coaxia l

tubes connected

with

a

p a i r

o f e l a s t i c hinges .

See

Figs .

9

and 10. Since the

gage

i s

in tended

for

repea ted measurement a t a se r i e s o f s t a t ions

r a th e r

than fo r f ixed mounting

a t

one s t a t i on

cons idera t ion

has

been given to con t ro l l ing acc iden ta l l ong i tud ina l

fo rces

which might be

appl ied by the opera tor .


16/115

337.8

-11

For s t r a i n measurements, the contac t poin ts are

i n s e r t ed i n to

the d r i l l e d holes

which are 10

0.02

inches

apar t .

Motion

between

the

two frame

members

i s

measured

d i r e c t ly

with

a d i a l i nd ica to r . A

handle,

serv ing

doubly

as

a

sh ie ld aga ins t t empera tu re change and

as

an a id to

uniform sea t ing of the

p o in t s

i s

a t tached to

the gage by

means

o f

two e l a s t i c hinges .

These hinges

preven t app l ica t ion

o f

excess ive. long i tud ina l

forces . A

force

of 5

lb . i s

recommended

for proper ly

sea t ing the points

in

the dr i l l ed

holes .

14)

sea t ing the gage i s

one o f

the ch ie f sources

o f

e r ro r . t

i s

suggested

t ha t a pos i t ion ing

angle

be used

Figs .

10 and 11) to

main ta in

the Whittemore gage in a

perpend icu la r

p o s i t i o n

to the su r face o f

the

specimen being

measured. Other sources of

er ro r

a r i se

from

the

d i a l

ind ica to r measurement of

a

chord r a t h e r

than an

arc l eng th

when

the axis of the dr i l l ed hole and the axis

of

the conical

extensometer po in t do not

co inc ide

and

temperature changes.

However,

the

e f f e c t

o f

temperature

change

on

the

ins t rument

i t s e l f i s pra c t i c a l l y e l imina ted by

the

use o f an invar

tube.

Accuracy

o f Measurements

t i s

ev iden t

t ha t changes in temperature w i l l

a f f e c t s t r a i n

readings

thus leading to wrong da ta for the

eva lua t ion

o f r e s id u a l s t r e s s

d i s t r i bu t ion unless these

e f fec t s are taken

i n to

cons idera t ion . Temperature changes

during readings

may

pra c t i c a l l y

be

e l imina ted

by

using

a

re fe rences

bar o f the same mate r i a l

as

the t e s t specimen.

The

bar should

be

put

on

the

specimen to be t e s t ed

for

a t


17/115

337.8 -12

l eas t one hour lS) ahead of t ime. This

i s

to s tab i l ize the

temperature

of the reference bar to

the

environment of the

t e s t

specimen.

I t

has been

reported l6}

tha t

the response

of

the reference

bar

and the specimen are

not

the same for

the same var ia t ion of room temperature. The reference bar

responds fa i r ly closely

to

the

room

temperature variat ions,

while the

specimen

responds with less fluctuat ion and with

considerable

time lag.

The response of

the specimen

therefore , is dependent on i t s

own size.

Measurement should

be

avoided

in direc t

sunl ight

or draf t or any other source which would cause dras t ic

temperature

var ia t ion

and

should

be

made where the

temperature

is

kept

fa i r ly uniform. This wil l

assure

readings with

minimum

effects

of

temperature changes. with such

care

taken

and under

normal

condit ions, temperature

changes may

cause

an error

corresponding

to a

s tress

of approximately 1 ks i

Note tha t a change in temperature of

SO

causes

a difference

of

1 ksi

in

the

s t ress

evaluat ion i f compensation

for

temperature

change i s

not

taken

into

account.

The effects

of

different

invest igators on

the

same readings

~ n

the

personal

effects

on

the readings have

been studied.

16) For both

cases,

no

important difference

was observed to prove these factori .al elements to have a

s ignif icant influence upon the

accuracy.

Further experimental errors may be at t r ibuted to

inaccuracies

in

the

mechanism of

the

extensometer, the dia l

indicator system, and effects

of

los t motion when the motion

i s in the

opposite

direct ion.

Such iriaccuracy

may

not be


18/115

337.8

-13

improved s ignif icant ly

by increasing the number

of

measurements on a

gage length. For example

for the

Whittemore

s t ra in

gage

t

was

found

tha t

the

accuracy

would be

imporved

by about 0.2 ksi

by

increasing the

number of measurements from

5

to 15.

16)

For

three

measurements

an accuracy

of

about

1

ksi

with

a

confidence

level of

99

could be obtained.

Procedure of Measurement

Attention should be given to

the importance of

obtaining

a

good

se t

of

i n i t i a l

readings

since

they cannot

be duplicated af ter the

specimen

has been cut . Better

accuracy could

also be obtained

by

estimating

precisely

the l a s t f igure of the reading whenever

the

dia l indicator

l ies between

the smallest

division.

The following i s a recommended

procedure

which has

successfully been followed in the past

in

Fri tz

Laboratory:

1.

Clean a l l

gage

holes using

carbon

te trachloride

or any other cleaning solut ion and

ai r

blas t

2. Take the

reading

on

the reference

bar.

3. Take

readings on the specimen.

I t is suggested

to

take

an intermediate

reference

bar reading

i f the

number

of gage hole readings exceed 15.

4.

Read

the reference

bar again.

5. Repeat

steps

2 3

and

4

unt i l

a l l gage

points

are read.

6. Do step

5

for at leas t three

times

on

the

whole

piece.

7.

I f

three

readings on

the

same

se t

of

holes di f fer

by

0.0001

inch

or more

the

gage holes

should

be


19/115

337.8

-14

checked careful ly and

additional

se ts .o f

readings usually two

more) should

be taken

on

the

reference

bar

and

on

the

specimen.

Addit ional

readings up to five more times

may

sometimes

be necessary to get

bet te r

resul ts .

I f

a great variat ion pers is ts t

suggested

to

make a new se t of holes very

near to the discarded ones,

since

badly

dr i l l ed or reamed holes

cause

large deviat ions

in reading.

After the i n i t i a l readings are taken and recorded

on

the data

sheets,

the specimen

i s

par t ia l ly or

completely

sectioned. I t

i s

suggested

to cover

a l l

gage points with

tape

to keep out

d i r t

and to avoid

damage

which

may

occur

in

the process

of

moving, handling,

sawing,

e tc .

The

measuring procedure af te r the par t ia l

or

complete sect ioning

i s proceeded

in

the same manner as

the

i n i t i a l

readings.

An example of

data sheets of

recorded

values for a

por t ion of a

flange i s

shown in Tables

1-5.

Table shows

a

data sheet

for the recording of

in i t i a l

readings,

Table

2

af ter

par t i a l sect ioning,

and

readings af ter complete

sectioning

are

shown in Table 3. Note tha t f ive readings

were taken for gage points 8 and 75

in Table

2 since the

. (

variat ion

in

reading was greater

than

0;0001 in.

Computations

for

res idual

s t resses

af ter

par t ia l and complete sect ioning

are shown in Table 4

and

Table 5,

respectively.

The

formats

used

in

Tables 1-5 have been

found very

convenient for the

recording of data and manual computations

of residual

s t resses .


20/115

337.8 -15

2.4 Evaluation of Data

The

computations of the

relaxed

s t ress from ,the

measured s t ra in i s based on the assumption

that

the

dimensional changes caused by the

relaxation

are purely

l inear elas ' t ic .

By

vi r tue of

the

l inear s t ra in dis t r ibu t ion

postulated in

the

beam

theory, the

average axia l

s t ress

cr

in

terms of

top and bottom

strains

e t

and

e

b

read'

from the

cut element

i s :

1)

where

E

i s Young's

ModuluSl

Since s tra ins are read

a t top and

bottom

'surfaces,

evaluat ion

of res idual s t resses a t

the

respective,surfaces

are

made

using the experimental data.

Let

A

be the average valiue of i n i t i a l readings on

one gage length. For each gage . l ~ n g t h

A

i s evaluated

using

1 n

A I:

n

i=l

A.

1

where n =

number

of

readings

on one

gage

l ength usua l ly three.

A = r ~ a d i n g value a t each

~ y ~ l e .

1

The average vlaue

of

i n i t i a l readings on the reference bar

(Ref.

A

i s evaluated for

every

in terval

of

reference bar

reading.

I n a

s imilar

manner, average values

of

f inal


21/115

337.8

-16

readings af ter par t i a l or complete

sectioning) for gage

lengths and the

reference bar

wil l be computed as Band

(Ref.

B),

respectively.

Using Hooke's

Law,

the

residual

s t ress a t

the

measured surface i s then,

E

= -E =

L

x

AL

r r

where At i s the recorded

change

in

length.

3

For

manual computation,

use

the data

sheets

(Table 4 or 5), to calculate the

res idual

s t resses as

follows:

1.

Compute

A -

B

(Col.

2.

Compute Ref.

A -

Ref. B

(Col.

3.

Compute

AL

=

(A-B)-(Ref.A-Ref.B)

(Col.

4.

compute

residual

s tress

AL

(Col.

r

=

x E

L

where

L

=

gage

length

(10 in.

for

Whittemore gage) .

5)

6

7

8

Step 3

gives

tens i le

s t resses

as posi t ive and

compressive

s t resses negat ive,

which

i s the usual

convention.

Figure

12 shows

the res idual

s t ress

dis t r ibut ion

measured a t locat ion A.

Comparison

of

residual

s t ress

measurement a t the

two

ends i s

shown in

Fig.

13. Using

the

evaluated

res idual

s t resses , the equilibrium condition for

the

whole

section

was

checked.

Theoretically,

since

no

external

forces exist equil ibr ium

requires tha t

the

sum

of

the s t r esses

over

the

whole

cross sect ion must be zero. For


22/115

337.8

-17

th is

par t icu la r

case a

difference of 0.7

ksi was

o m p u t e d ~

This difference may be

at t r ibuted

to the effec t of saw

cutt ing

and

accumulated

experimental

er rors

9)

Use of the computer wil l

great ly reduce the amount

of

numerical

work

involved; i f a large number

of

residual

s tress

measurements

i s

to be

encountered. Computer

programs

for general evaluat ion

of residual

s t resses have been prepared

and

have been found

very

versa t i le 17) These programs

are:

PLOTRS

-

reduces

data

obtained

from

measurements

before

and

af t e r sect ioning

and

s l ic ing to obtain

average readings.

RSN

-

computes

residual s t resses

- plots resul t ing residual s t resses

-

uses reduced data

from

PLOTRS to compute

the

two-dimensional residual s tress dis t r ibut ion

- checks

equilibrium of

residual s t resses

-

provides

input

for

PLOTIS

PLOTIS - plots

i sos t ress

diagram of

residual

s tress

dis tr ibut ion

Using

the computer program

PLOTRS

the residual s tress

dis t r ibut ion for the section 14H202 was

evaluated and

the

resul t ing plo t i s shown in Fig. 14.

The poss ib i l i ty of

automatic

recording of the

original

gage readings

into a tape or cards by means of

l inear

transducers is under

study. 18)

After th i s

s tage

manua

recording computation and plot t ing wil l no longer be required.


23/115

337.8

-18

3. THE HOLE-DRILLING METHOD

3.1

Introduction

Principle

The hole-dr i l l ing method,

sometimes referred to as

the

hole-relaxat ion

method,

i s based on

the

fact

that

dr i l l ing

a

hole in

a

s tress f ie ld disturbs the equilibrium

of

the

s tresses thus resul t ing in

measurable

deformations on the

surface

of

the

pa r t

adjacent to

the

hole.

From a

knowledge

of the

magnitude and

direct ion

of

relaxation s t ra ins

size

of

hole,

property

of materia l ,

and

geometry of

the

body being

examined, the

magnitude

of residual s t resses may

be calculated.

Histor ical Review

The hole dr i l l i ng method probably was f i r s t proposed

and

applied

by J . Mathar 19) of the

University

of Aachen

Germany)

in

1932. Mathar

used

mechanical

and

opt ical

extensometers

to

measure the changes

in displacement between

two points across the hole. y

dr i l l ing

a hole,

he observed

a par t i a l e l as t i c recovery in the immediate vic in i ty of

the

hole. From measurement

of th is e las t i c recovery, t

was

possible

to determine

the

residual

s t resses in the specimen.

In

his experiment,

Mathar used a dia l

extensometer,

placed

in

a radia l direct ion

with one

gage point

very near

to the hole.

His experiments were l imited

to

pure

tensi le

and

pure

compressive

s t resses .

The cal ibrat ion of the measuring

gage was accomplished

by

tes t ing a specimen

of

about the same


24/115

337.8

-19

s ize as the

work

piece in

a

machine for tension t e s t s

dr i l l ing

the

specimen and a t

the same

time carrying

out

measurements. e then establ ished experimental curves

for the

determination

of the actual

s t resses .

These curves

give the t rue

s t resses

direct ly as

a function of the

dia l

readings. His

apparatus

and resul ts

have been

subject to

cr i t ic ism

because

vibrat ions

during dr i l l ing operations

make

the

reading unsteady

and i r regular .

Replacing the mechanial extensometer with

elec t r ica l

resis tance

wire

s t ra in

gages, Soete

and

vancrombrugge(20)

of the University of

Gent

(Belgium),

eliminated the di f f i cu l t i e s of

measurement

and

improved

the pre,cision. At

the

same time

they were-

able to

determine

the plane

s tress d is tr ibut ion by

measuring

the elas t ic

recovery in three

radia l

directions. On the

basis

of

Airy s

s tress

function, Soete formulated an

equation

for

the

determination

of

s t resses occurring

in

a region

of the

same

size as

the dr i l led hole, and

plotted a

diagram, showing

the

re la t ion between s tresses

and

s ta ins . with the aid

of

empirically

prepared

diagrams,

and by measuring

the s tra ins

produced

during

dr i l l i ng to different depths, Soete

and

Vancombrugge(20)

were able to

determine the

s t resses

occurring

a t different depths

under the surface of

the

work

piece.

Further work on

measuring

non-uniform residual

s t resses

by the hole dr i l l ing method was performed by

Kelsey.

22)

e

developed

a

procedure

to

determine

the

re la t ionship between surface s t ra in and

hole depth for

a

known

uniform s t ress f ie ld ; and

then

to corre la te these

data with those obtained by dr i l l ing a hole

in

a known


25/115

337.8 -20

non-uniform s t r e s s f i e ld .

His

approach i s

based

on

the

assumption

t ha t the incremental

su r face r e laxa t ion s t r a in

for

corresponding

hole-dep th

inc rease

i s

propor t iona l

to the

magnitude of the

s t r e s s a t t ha t

depth . The method

i s

empi r i ca l

and

depends on

experimental

ca l ib ra t ion .

Recent

re f inements

in

s t ra in-gage-manufactur ing

techniques have

made t poss ib le to obta in s t r a i n gages

o f very smal l dimensions. Rendler and vigness 23)

repor ted

successful

r e s u l t s o f res idual s t r e s s measurements

using dimensions as smal l as 1/16 in .

diameter holes

and

1/16

i n .

s t r a i n

gages . Cardiano and

sa le rno 24)

repor ted

t ha t

the

exper imenta l data

confirm

with the assumed theory

for measurement o f

r e s id u a l

s t r e s s on p l a t e with

l i n e a r l y varying s t r e s s

f i e ld using the toe

o f t e e -

f i l l e t

welds) .

Recent ly ,

Ber t

e t . a l . 21) repor ted

on the

a p p l i c a b i l i t y

of

the

ho le -d r i l l i ng

technique for experimental

determinat ion of

r e s id u a l

s t resses

in

rec t angu la r o r tho t rop ic

mater ia l s .

Though cons iderab le work has been done i n recen t

years to

e s t a b l i sh

the

method t h e o re t i c a l l y t

would

st ll

seem t ha t

the

so lu t ion o f

the

problem must be

of

an empi r i ca l

na ture .

St ra in

Measurements

The

purpose of

measuring

the

r e l i eved

s t r a i n by

dr i l l i ng i s

to eva lua te

the

r e lease in

s t r e s s .

This

seems

to be the only

manner

o f determining i n t e rn a l s t resses . s ince

the

forces ac t ing w i th in m a te r i a l usua l ly a re unknown,

in


26/115

337.8

-21

both magnitude and

d i r ec t i o n .

In

b r i e f

measurement o f

s t r a i n

i s

bas ica l ly the only manner

in

which s t r e s s can

be

determined

s ince

s t r e s s

i s

not

fundamental

phys ica l

quan t i ty

l i k e

s t r a i n

but

only

der ived quan t i ty . These

arguments however

requ i re

two fundamental

assumptions

fo r

the

determinat ion

o f

r es idua l s t r e s se s : the

equ i l ib r ium

o f the

s t r e s se s

i ns ide

body

and the con t inu i ty of the

deformed mate r i a l .

The

s t r a ins

a re

measured

as an

e l a s t i c recovery

a f t e r re l ea se

o f

the p rev ious ly

ex i s t i n g sys tem

o f i n t e rn a l

s t r e s se s . The amount o f recovery i s smal l . For accl i ra te

ev a l u a t i o n

o f

s t r e s s a t

poin t

the gage

l eng th

must be

shor tened .

To

provide care fu l cons idera t ion for these

two f ac to r s

measuring device with

very

s h o r t gage

l eng th

and

high

prec i s ion should be used .

Three types o f measur ing dev ices

are unive rsa l ly

used

namely e l e c t r i c a l op t i ca l and mechanical

gages.

The

bonded e l e c t r i c a l

s t r a i n

gages

o f f e r

the

most

accura te

and

convenien t

means o f measur ing s t r a i n s espec ia l ly

i

re s idua l

s t r e s se s could be

complete ly f reed.

Opt ica l gages can give

accura te read ings because o f the f ac t t h a t beam

o f

l i g h t

can ac t

as an i n f i n i t e l y r i g i d w ei g h t l e s s and i n e r t i a l e s s

p o in t e r

o f

fa r

g re a t e r

l eng th

than would

be p ra c t i c a l

for

mechanical po in te r s . In sp i t e o f the advantages o f

e l e c t r i c a l

and o p t i c a l

methods however pure ly

mechanica l

devices

are

still in widespread

use and

fo r many purposes are much more

convenient .


27/115

337.8 -22

Features o f

the

Hole -Dr i l l ing Method

The hole

d r i l l i n g

methodhas the advantage of

removing

a

minimum

amount o f mate r i a l which

makes

it

the

l e a s t des t ruc t ive o f

the

mechanical

methods

for measuring

r es idua l s t r e s s e s . The method can

be termed

as s imi

destr .uct ive

i

holes of very small

d iameters

are

used.

I f des i red , the hole can be f i l l e d

by

welding o r

e l se , a

b o l t

o r plug can

be in se r ted in

the hole .

Unlike o the r

mechanical

methods the hole

d r i l l i n g

method

permi t s

the eva lua t ion

of

r es idua l

s t r e s se s

a t what

i s

e s se n t i a l l y

a

p o in t ,

a

spec ia l app l ica t ion o f

which

i s

the

measurement

of t r ansve rse

r es idua l s t r e s s .

Appl ica t ion

as

a f i e ld

t e s t

i s r e l a t i v e l y

simple and

r e s u l t s

can be

obta ined r ead i ly and economica l ly .

This

method

however

has a l imi t a t ion of depth and i s

used

to measure s t re sses

very near to

the su r face .

3.2

Mathar s

Method

In orde r t o exp la in the

p r in c ip l e

of the method

consider a

specimen

subje6ted to a

un iax ia l s t r e s s which i s

uniform

through

the

th ickness . measuring gage i s

mounted

on

t h i s t e s t piece to measure the

s t r a i n

in the same

d i r ec t i o n

as the

app l i ed s t r e s s .

I f

a c i r c u l a r

hole i s d r i l l e d between

po in t s a

and

b

in Fig .

15

t h i s hole w i l l become e l l i p t i c a l and the

d i s t ance between

a

and

b

wi l l be changed: increased i the

s t r e s s was t ens ion , decreased i the s t r e s s was

compression.

I f the r e l a t i o n s h ip between

the change in

t h i s

dis tance

and


28/115

337.8

-23

the s t r e s s i s determined by ca lcu la t ion

o r

ca l ib ra t ion

t e s t ,

then the s t r e s s

in the

t e s t

piece

in

the

d i r ec t i o n

ab

can

be

c lacu la t ed

from

the

change

in

the

dis tance

between

a

and

b .

19

For the case o f b iax ia l s t a t e of s t r e s s , one

measurement w i l l

not

be enough,

and the

deformat ion o f the

hole must be measured in a t l e a s t

three

d i rec t ions in order

to determine the magnitude and d i r e t i o ~ of the

p r in c ip a l

s t r e s se s . In t h i s sec t ion , the case wi th

a uniax ia l

s t a t e

o f

s t r e s s

only

w i l l

be

cons idered .

Cal ib ra t ion Tes t

c a l i b ra t i o n t e s t i s requ i red in order to determine

the r e l a t i o n s h ip between the s t r a i n

of

the t e s t

dis tance

produced due to d r i l l i n g ,

and

the s t r e s s

in

the t e s t piece .

Cal ib ra t ion can

be done

e i the r

by ca lcu la t ion o r by exper iment .

Cal ib ra t ion by ca lcu la t ion

was

f i r s t repor ted by

Kirsch, 25) who ca lcu la ted

the

deformat ion of a

hole in

a

member o f i n f i n i t e width in

terms

of the uniax ia l app l ied

s t r e s s . Willheim

and Leon 26)

extended t h i s

method

approximate l

to

members

o f f i n i t e width . Mesmer 27) genera l i zed the formula

fo r the

case

of plane s t r e s s

d i s t r i b u t i o n ,

under the assumption

t h a t the d i r ec t i o n of the p r in c ip a l s t r e s se s were

known.

fu r the r genera l i za t ion

was

given

by

Campus,

28)

expanding the

formulas

to

the case in which the p r in c ip a l axes d i rec t ions

are

unknown.

Extensive

work

has been done in

recent

years to

e s t a b l i sh c a l i b ra t i o n by

ca lcu la t ion fo r

the

case

of


29/115

337.8 -24

uniform 20,29,30,3l,32) and

non_uniform 2l,22,23,33) res idual

s tress dis t r ibut ion over the thickness of

the

pla te

Experimental cal ibrat ion

can

be made

by mounting

a t e s t specimen in a tens i le machine

and

dr i l l ing on the

s tressed

t e s t

piece a hole s imilar to

tha t

to

be used

for

the

residual s tress

determination. The f l a t plate i s loaded

a t various s t ress levels

and

the changes

in distance between

the gage

points

are

determined as dr i l l ing

progresses.

From

th is must be

subtracted the dis tance

increase which

would

have

occurred

i f

the hole

did not

exis t

n

experimental

cal ibrat ion was conducted for a

uniaxial

s t ress s t a t e A known

s t ress

was applied

in the

direct ion of

the

gage lengths on a t e s t specimen,

with

the

hole

and

gage system al igned

as shown

in Fig. 15. The

t e s t specimen

was

designed to sa t i s fy cer ta in design

requirements using available equipment, which are

discussed

in

the

following sections.

The

Calibrat ion Test

Specimen

In

designing

the cal ibrat ion t e s t

specimen

t was

necessary to consider and sa t i s fy

the

following

points :

a)

the

applied t ens i le s tress

must

be uniform

throughout

the

cross-sect ional

area

of

the

specimen.

b a measurable

change

in s t ra in in

the

material

should be

produced.


30/115

337.8

-25

c) the hole

must

be

small compared with

the

specimen dimensions

and

must be far

enough

from

a l l

boundaries.

d) the applied

load

must be of a magnitude

not

to produce

plas t ic flow

of

the

mater ia l

near

the hole due to

high

s t ress

concentrat ion.

The specimen, It by 4 in. cross sect ion

and

5 f t .

in

length,

mounted in

an 800,000

lb. mechanical

type

tes t ing

machine may indicate the presence of unwanted f lexural

s t resses .

Requirement

a)

was

sa t i s f ied

by

reducing the

f lexural s t resses in the

t e s t

sect ion

to negl ig ible

values

less than two

percent

of the applied s t ress by proper

alignment.

Alignment was carr ied out

by

mounting s t ra in

gages on a l l four sides of the

specimen

a t a distance of 6

inches from

each grip

end

Fig.

16).

This dis tance i s

suff ic ien t

to make

the

section

of

in teres t

remote from

the

boundary

and

thus

not influenced

by the

St. Venant end effect .

Any change in machine-specimen

alignment

during

t e s t could

be detected from the readings of

the

gages

mounted

on opposite

sides of

the specimen.

I t i s cer ta in tha t

residual

s t resses in

the

s p e i ~ e n

wil l af fect the uniformity

of

the s t ress d i s t r ibu t ion .

To

eliminate the

res idual s tresses ,

the

t e s t specimen was heat

t reated

a t

a

temperature

of l200

0

F

for

one and one-half

hours

1 hour

per

inch of

thickness).

The

specimen

was then l e f t

ins ide

the

furnace

where

t

was

allowed

to

cool

uniformly

a t

a very

slow

ra te . This temperature-time combination wil l

reduce res idual

s t resses

to a negl ig ible value

without

introducing

metal lurgical

changes.


31/115

337.8

-26

Requirement

b) was

for

a measurable

s t ra in

output

from

the

gage

lengths. In general ,

the

s t ra in

relaxations

due

to

hole

dr i l l ing

are

very

small

in

value.

This

dif f icu l ty

could be rel ieved by

increasing the magnitude

of the

applied

s t ress

and also

by

increasing the

gage length.

A

Huggenberger

extensometer with 20 and 100 gage

lengths

and nominal

s t ra in

sens i t iv i ty of 0.001 0.0000394

in .

was used for

s t ra in measurement. In

Fig. 17

the extensometer with i t s

accessories i s

shown.

Requirement

c),

tha t

the

boundary must be

a t

such

a distance from

the hole

without affect ing the measurements

may be sa t i s f ied i f a minimum width

of ten

times 20) the

diameter of the

hole i s used. The change

in s tress

dis t r ibu t ion caused

by the unsymmetrical

reduction

of cross

sect ional

area

due to

the

dr i l l ing could be

reduced

s ignif icant ly i f the

cross-sect ional

area of the specimen i s

large compared to tha t of the

hole.

Use of a in.

diameter on

the Ii

by 4

in. specimen

i s

within these

requirements.

This dimension combination

of

hole diameter

ana gage

length

provides suff ic ien t e,dge distance

so

as to

give an

appreciable change

in

s t ra in outside the region

where

plas t ic deformation may be

encountered.

Calculations

based on

equations

given by Timoshenko 34) for a small hole

in a wide plate subjected to a uniaxial tension showed that

the

longitudinal and

the t ransverse s t resses

four diameters

from the

hole axis

in the longitudinal direct ion

deviate

less

than four

and one

percent , respectively

from

the longitudinal

s tress

remote

from the

hole.

Accordingly, the minimum pi tch

i s 2 in.

for

in. diameter holes.


32/115

337.8 -27

Requirement (d) was

for

an applied s t ress

of

such

magnitude

tha t

no plas t ic

flow

of

the

mater ia l should occur

in

the

region

of

the

hole.

So

long

as

the

s t resses

are

less

than 4

p e r c e n ~ 1 9 ) of the

proport ional l imi t ,

no plas t ic

deformation due to high.

s t re s s concentrat ion wil l

occur

near

the hole. To improve th is

s i tua t ion ,

a t e s t material

may

be

selected

having

a high yie ld point.

But

for

the

purpose

of

comparison,

the

choice of the

t e s t mater ia l was

res t r ic ted

to A36stee l ,

and

th i s permitted

an

applied

s t ress

of

about

14 ksi .

Preparat ion of Gage Points

Gage lengths

of

20

and

100

rn were

used

simultaneously for the same hole for the purpose of

comparison

(Fig.

15). The gage points

for the

2

gage

length were each located a t 10 rn from

the

center of the

hoie.

The gage

points

for the 100 gage

length were

located a t 10 and 110

rn

from

the

center of the

hole.

The region to be measured was made smooth

and

careful ly prepared. Coating the surface with lay-out dye

was of

help for

smooth scribing. The

gage points

were

marked

f i r s t

with a

l ight

hammer

blow

using a standard

punch

(Fig. 17). The gage

points were.s tee l

bal ls of 1/16

in.

diameter. The gage point fur thest from the hole was

imbedded

using a special punch

(Fig.

17) af ter dr i l l ing a hole smaller

in diameter than

the s tee l

bal l , using

d r i l l

No. 56 (Fig. l8a) .

Since

imbedding

using

a

punch

i t s e l f

may

introduce

undesirable

res idual s t resses ,

those gage points

in

the vicini ty

of the

main hole to be dr i l led were

fixed

using Armstrong A 6 Epoxy

adhesive,

as

shown

in Fig. l8 b) .

In

both cases, care

was


33/115

337.8

-28

taken to make sure tha t the holes were imbedded not

too

deeply, to

prevent the measuring gage

from

s i t t i ng properly;

th is

i s done

by

sinking the

ba l l s

equator

s l igh t ly

below

the surface. In

general ,

gage points imbedded using

the

standard

p unch seem to be

more preferable ,

since

they

are

easier to perform, and can be

fixed strongly

in to posi t ion.

Dri l l ing

Technique

The location and alignment of

the

hole was controlled

by means of a hole milling f ixture as shown in Fig.

19. The

hole

was

dr i l led

using

a

i

in .

high

speed

center-cut t ing

end

mill .

The bottom

of the

hole i s to be

f l a t

to permit

meaningful measurements

of

the hole depth.

Hole

depth

increments are read

using

the allowed tolerance of 0.0002

in.

depth gage micrometer. Care was taken to keep the end mil ls

sharp to avoid

blemishes

or tears , and th is was

checked

by

closely

observing

the

condi t ion

of the

cut t ing

edges a t

appropriate operat ion in te rva ls .

At the

ea r l i e r

stage of th is study a boring uni t ,

which included the

end mill., Versamatic

(to reduce speed

of rota t ion) ,

and

e lec t r i c

dr i l l

centered

on

the specimen

by the mill ing f ixture

was

used. Clearance

was provided

beneath

the

milling f ixture for chip removal and for gage

.

point protections. . Both ends of the f ix ture carr ied index

marks for

center ing the uni t

over

the gage assembly

in

the longitudirial direct ion.

With

the uni t held

to

the

specimen

in

the

indexed

posi t ion, a

cross bar

was

placed

against the end of. the f ixture and

clamped

to

the

specimen.

The

cross bar remained

on

the specimen throughout

the t e s t

and provided a posi t ive index stop for the f ix ture . To


34/115

337.8

-29

reduce effects tha t may be caused by a high ra te of

dr i l l ing

.

the

1100 rpm speed

of

the

elec t r ic

motor was

reduced

to a

desirable speed of 180 rpm using a speed

reducing

device.

This device ( Versamatic ) also served

s i m u l t n ~ o u s l y

the

purpose

of

acting as

a f lexible coupling.

Figure 2 shows

the equipment

used

in an assembled view. In Fig. 21 a l l

equipment used and the

cal ibrat ion specimen

in

the tes t ing

machine

i s shown.

At a

l a te r

stage of th is

study

a

portable

magnetic

base

press

(Fig.

22 was

available

and

was

used

with

greater

ease

and eff ic iency.

The t ime required

to

complete the

dr i l l i ng

for

one

hole

using th is equipment has reduced to

about f i f teen minutes

compared

to about four hours when

using

the original se t . A speed of 190 rpm was considered suff ic ient

to

minimize

the

residual

s t resses

tha t

may

be

induced

due to

machining.

Test

Results

A i - i n . diameter hole was dr i l led on the cal ibrat ion

specimen to

determine

the re la t ionship

between

the

measured

s t ra in and

the

corresponding hole depth.

The specimen was

st ressed to 13

ksi

in tension

and

the milling was stopped

a t average

increments

of

0.04

inch in depth af te r which

measurements were taken. The

character is t ic curve of

the

measured s t ra in

re laxat ion as

a function

of

non-dimensional

hole-depth is shown in Fig.

23.

The

plot

shown

in Fig. 23

indicates

tha t

the surface

s tra ins increase rapidly up to a depth-diameter

ra t io

of

about


35/115

337.8

-30

0.8 and do not change appreciably for

g r ea t e r hole

depths .

Thus, c a l i b ra t i o n

based on a hole depth

o f one diameter

makes

use

of the

maximum re leased

s t r a i n and

was

used as a

s tandard depth to e s t a b l i sh the ca l ib ra t ion

curve.

Cal ib ra t ion

requi red

conduct ing severa l s imi la r

t e s t s on the

same

specimen

while

the

specimen

i s sub jec ted

to d i f f e r e n t

l eve l s

o f loading.

To

obta in

t e s t

points the

r e lease in

s t r a i n

due

to

d r i l l i n g

and

the

corresponding

s t r e s s

o f

the specimen need to be known. o apprec ia te a

be t t e r

unders tanding

o f

the changes in s t r a ins during

the

whole

opera t ion ,

t would

be adv isab le to take

s t r a i n

readings before and a f t e r

changes

in s t r e s se s have occurred .

The following

s t eps

in

s t r a i n

measurements

are recommended:

Take readings:

1)

before the

specimen i s

loaded

2) a f t e r the specimen i s loaded

3) a f t e r d r i l l i n g

i s per formed

4)

a f t e r

the specimen i s

unloaded.

Figure

24

shows

schemat ica l ly the

h is to ry

o f s t r a i n

changes

fo r

an i dea l

case

t ha t

would occur

during

the

whole opera t ion

o f ca l ib ra t ion .

Cal ib ra t ion t e s t s were conducted

for

uniform

s t r e s se s o f

13.3

ks i ,

16.7

ks i

and

20.0 ks i .

The

h is to ry o f

s t r a i n changes i s p lo t t ed for each

t e s t as shown in

Fig.

25.

I n i t i a l

and

f ina l

readings

were

taken while the

specimen

was

under a nominal ly

smal l load 10

kips equiva lent to

1.6

ksi )

in

order

to

maintain the

gr ip

which

was o r i g i n a l l y es tab l i shed

for

the al ignment o f the specimen.


36/115

337.8

-31

All

t e s t

resu l ts Fig.

25 show

tha t the unloading

l ines do

not pass through

the origin.

This

discrepancy

may

be due

to the sum

of

the

residual s tress

original ly

exist ing

in the specimen

and

the residual

st resaes induced due

to the

,mil l ing operat ion.

Since

the specimen has been heat- t reated,

the

major

par t of the difference

may

be due

to

the mil l ing

operat ion.

To determine the to ta l change in s t ra in readings

tha t might

have occurred

during the milling operations,

a

t e s t

was

conducted

on

the

unloaded

cal ibra t ion

t e s t

specimen.

Two holes were

dr i l led on

the specimen

using

the same

end

mil l and milling procedure as used previously.

A

to ta l

number of four measurements,

two

longitudinal and

two

t ransverse

readings were taken Fig.

18 before

and

af te r the dr i l l ings .

~ h

resul t ing readings are

given in Table

9. I t

is noted

that

a l l

four

readings are almost ident ical even

for

the

two

different

directions.

Based on

these

four

measurements the

average

residual

s t r a in

due

to the

milling

operations

alone

was

determined as

38 x

10-

4

ro

Table

9). This

value

was

taken in to account,

and separated

from

the

to ta l s tra ins

in

order

to

establ ish the f inal form of the cal ibra t ion

curve.

In

general ,

t

is

necessary to measure such i n i t i a l s tra ins ;

, i t is expected tha t

lower

values

should

yield

be t te r resu l ts .

Figure 6 shows

a

sca t te r band of

t e s t

points

obtained from

f ive

cal ibrat ion tes ts . , The cal ibrat ion curve

shown in

Fig.

7

is

obtained as the

ari thmetic

mean

of

the

t e s t

points .

Using th i s re la t ionship,

the residual

s tress

dis t r ibu t ion

in the

l4H202

section

can

be

determined.


37/115

337.8

-32

A t o t a l number

o f

28

holes were

dr i l l ed on the

oute r surfaces of the two f langes of the

14H202

shape using

the

same

procedure

o f

hole

dr i l l i ng

as

appl ied

to

the

ca l ib ra t ion t e s t specimen. Figure 28 shows the layou t of

holes used

on one

f lange o f the shape. A

r a d i a l

d r i l l

press (Fig.

29) was used to

d r i l l

holes

on

the

shape but

a t

a

l a t e r

s tage the por tab le magnetic base d r i l l (Fig.

30)

was

found to

be more

conven ien t .

The s t eps in

s t r a i n

measurements followed were

s imi la r to

those

used

in

the

sec t ioning

method

(Sect ion

3 .3 ) .

Tables 6 to 8

show

the da ta shee ts for recording s t r a ins

and

eva lua t ing

the r e s id u a l

s t r e s se s where hole numbers to 10

are used as an

example.

The d i f fe rence in s t r a i n

readings

obtained from the 28

hole

dri11ings are shown

in

Fig. 31.

Using

the

c a l i b ra t i o n curve

(Fig.

27) and the

d i f fe rence

in

s t r a i n

readings ,

the r es idua l s t r e s se s a t

the

28 loca t ions were determined.

The

average

r es idua l

s t r e s s

d i s t r i bu t ion across

the

surface

of the f lange was

eva1uated

r

and

the

r e su l t

i s shown in Fig. 32.

3.3 Soe te ' s Hole Dri l l ing Method

?r inciple

s oe t e ' s method o f

hole

d r i l l i n g i s based on

the

same

fundamental

p r i n c i p l e

as t ha t of

Mathar s (Sec t ion 3 .2 ) ,

excep t

t ha t in

Soe te ' s

method, measurements are taken using

e l e c t r i c a l r e s i s t an ce wire s t r a i n gages in s tead o f mechanical

extensometers .


38/115

337.8 -33

The

s t ra in

gages Soete and

vancrombrugge(20)

used, t h o ~ h

the smallest

available

a t the time,

were

long

compared

to

the

s ize

of

the

hole.

I f

t

is

desired

to

make

residual

s t ress measurements near weldments or flame

cut edges,

t

i s

apparent tha t s t ra in gages having shor t

gage lengths

should

be

used because of the sharp

s t ress

gradients

tha t

exis t in

such

neighborhoods.

Recent

refinements

in strain-gage

manufacturing techniques have

made t possible to obtain

s t ra in gages of

very small

dimensions.

Thus,

a hole of a very

small

diameter and depth

may suff ice

for

a res idual

s t ress

measurement.

Use

of

such

small dimensions cause

only

a to lerable amount of destruction

of

the mater ia l

and

have

a specia l advantage when used in

regions

with

steep s t ress gradients .

In th i s

method too,

the

experimental

approach

requir ing the determination of empirical cal ibrat ion constants ,

was used

to

evaluate

res idual

s t resses .

Calibrat ion

Test

The reasons

for

the cal ibrat ion t e s t and

the

method

of appl icat ion has been

explained

in

Section

3.2. Calibrat ion

was made on the same t e s t

piece

as used for Mathar s method.

The

hole-gage

assembly used

i s

shown

in

Fig. 33. Foil s t ra in

gage rose t te

type EA 09 125RE with a

gage length

of

0.125

inch were

used.

The

main reason

for

using

th is assembly is

because

t was the

only

type

specia l ly

prepared for

residual

s t ress

measurements

avai lable

commercially

a t

the t ime.

With

preassembled

gages,

the necessary

operat ional

sk i l l i s

reduced

to tha t of locating the cut te r in the center

of

the roset te .


39/115

337.8

-34

The

radia l

orientat ion

of the gages has

the

advantage

of

obtaining a

sa t i s fac tory

sens i t iv i ty especially a t high

s t ress

levels . 30)

Theoret ical Consideration

The procedure for

obtaining the

cal ibrat ion constants

was simplif ied by

making

the minimum

principal

s t ress

zero

and

by applying a known s t ress in the longitudinal direct ion of the

t e s t

piece.

Under such a uniaxial

condit ion, Rendler and

vigness 23)

have shown tha t cal ibrat ion constants A and B may

be

determined

from

the

formulas:

A

=

5 )

6)

where

~ l

=

radia l

s t ra in

in the direct ion of the

appl ied

load

longitudinal

st.rain) ,

~

=

radia l

s t ra in

in

the

direct ion

perpendicular

t.o

the

appl ied

load

transverse

s t ra in ,

and

a

=

applied

s t ress .

After

the cal ibrat ion

constants

A and B for the

hole-gage

assembly are determined,

the principal

s t resses

can then be

evaluated

using the formulas:

E:I A+B

Sin

.Y)

-

2

A-B Cos ,Y)

max

=

2AB Sin Y

+

Cos

.y)

7

)

E

2

A+B

Cos.y)

-

E

A-B in y)

a

=

8)

mln

2AB Siny

+

Cos

y)


40/115

337.8

-35

I

1 -

22

3

where y =

tan

-

I ]

1-3

1 .2

and.

3

=

s t ra ins

measured

by

s t ra in

gages G

l

G

2

and G

3

respect ively

(see

Fig.

33).

The

direct ion of the maximum

principal s t ress

f

measured counterclockwise from the t ransverse direct ion s

given by

3 = iy

9)

To

use the cal ibrat ion constants obtained

from

the

t e s t piece n actual res idual s tress

measurements

on any

specimen, the

following variables

must be considered:

1.

Material -

grade

of s tee l

2. Stress

t ens i le or

compressive (uniform);

bending

(non-uniform)

3.

Geometry

- thickness , width,

length

4.

Hole-gage assembly

5.

Method

of

hole

dr i l l ing

The

cal ibrat ion constants

A and B

contain

the

material constants E and (Young s Modulus and Poisson s

ra t io) , which

are

constant for a l l e las t i c and i sotropic

mater ia ls .

Since

a l l grades

of s t ruc tura l

s tee l have

essen t ia l ly

the same values of E and the. variq.ble caused

by a difference n

mater ia l

may be neglected.

I t

has

been

reported

(22) that cal ibra t ion constants

obtained

under

uniform

tens i le s t ress give resu l t s of less

than

f ive

percent dif ference

than those

obtained under

uniform


41/115

337.8

-36

compression

st ress .

This may be at t r ibuted to the exact

s imilar i ty of the s t r ess s t r a in

curves

in tension and

compression.

Assurance must

be provided tha t the

cal ibra t ion

constants

are

independent of

the specimen s ize .

I t

has

been reported 23)

tha t

val id

cal ibra t ion

constants

are

assured for plates whose

boundaries

are

a t a

distance

equal

to

or

greater

than

eight

hole

diameters from the

hole center

l ine and for plates

of

four or more hole diameters in

thickness.

The hole ;gage assembly

is

the predominant variable

tha t changes the

values

of

cal ibrat ion

constants .

The constants

may

be

made

independent of

the assembly

dimensioning

i f a l l

of

the

important dimensions of

the

hole

gage assembly are

made

proportional to

the dimension of the cal ibra t ion model.

s long as th is principle of simili tude is maintained, a l l

the different hole-gage assemblies wil l be represented by a

single

non-dimensionalized specif ica t ion of

the cal ibra t ion

model. This wil l be t rue

provided

the

res t r ic t ions pertaining

to

the

material boundaries

are

observed.

Although the

dr i l l ing technique

affects the

accuracy of the

method,

t should be

pointed out

that

for

a

specified hole diameter

the

method

wil l

be

independent

of

machining s t resses as long as a standardized dr i l l ing

procedure

i s

used

throughout the

whole

operation,

including

the cal ibrat ion t e

prof. niguse tebedge msc paper

Documents