Zelation betxeen B r i m 1 1
and
Eorsk..vell 3arCiness Nu%bers.
'
Dear :sir:
In a c c o r d m c e with the requirelnents f o r
t h e d e ~ r e eo~ E a c h e l o r o f Science, a thesis enf~tizd,
f
R R e l a t i o r , 'cetaeen 3 r i n e l l and F.ocLrX::i.eliEarcdness
Numberst1, is h e r e n i t h enclozed.
Respectfully a u " b n i t t e d ,
In determining the s t r e n g t h of metals, hardness has long
been used as a basis of comparison.
in the case of
This is especially true
s t e e l s for the hardness 2s given by t h e Erinell
nachine is d i r e c t l y proportional t o t h e - t e n s i l e strength.
Usually t h e harder a metal is, t h e stronger it w i l l be.
For
this reason, hardness machines are in general u s e f o r deter-
mining the relative strength of metals.
The Brinell is considered tne standard hardness t e s t i n g
machine.
The tensile strength of all steels, whether in the
n a t u ~ a ~state
l
o r heat treated, is directly proportional t o
t h e i r Srineli n m b e r .
The. Bockwell machine is nucn lighter
and is easier t o use, since ~ i t nit, e reading can be made
in l e s s time thaa it' t a k e s t o load the specimen in the Bri/
nell.
However, it has been impossible to compsre the hard-
nees of metals unless a l l the t e s t s a r e made by the same sachine.
Since the Brinell is considered. t h e stanciard, the
3ockwell has not been i n general u s e as t h e r e was no way of
getting toe Brinell h ~ r d n e s sfrom the Rockwell tests.
In 'the s2ring of 1923, F . de la iI;iacorra made a number
of hardness t e s t s with the E r i n e l l and. Rockwell aachines in
order t o find the relation, if any, betmeen the hardness
numbers of metals as given by these two mechines.
He found
t h a t there existed a d e f i n i t e relation and in his tJhesis
gave a curve snowing this relation.
I
It Tnas suggested by P r o l e s s o r Dogdrey that =ore extensive t e s t s be made t o v e r i f y
m d to
add to t h e results
elready obtained.
It
pres
nitlrl t h i s purpose in view that
this thesis viTas unaertekcn.
Althougk t h e 3ockwell and Brinefl niachines are d i f f e r e n t
the
they
The hardnese number f o r
principle.
metal in each case is determined by
the depth a spherical surface mill penetrate under a given
lo-aa.
The Brinell method is based upon determining the resis-
tance o f f e r e d t o indentation by a heraeneii sphere, the latter
being subjected t o a given pressure.
For hard metals a
3009 kg. ?,ve-&h$. is sp.~plied.: ~ h i l eSCO kg. is t h e load u s e d
f o r s o f t metals.
In each case a- ball 10 mm. in diameter is
The prassure is applied by mesos of a hydrzulic pump
used.
which holds t h e weight suspended, thus g i v i n g ttn absolutely
uniform loading.
Brinell expressed t h e hcrdness 5y t h e
pressure in kilogrzms per square m i i i i n e t e r of spherical
area
.
Since
would
difficult
measure the depth
the impression or t o f i g u r e the area each tiine from the
width of the indentation, a chart has been prepared from
which the hardness numbers may be reaci d i r e c t l y , the width
of the impression being read through a microscope with scale
at taohed.
The Rockwell method is sizilsrr t o the B r i n d l e
The
depth is not measured from the surface of the work however.
Two impressions are
made, one superimposed upon the other.
The first i s made ~ ~ i .at hLgad of 10 kg., the second with a
l o a d of 100 kg.
The hardness number i s d i r e c t l y prhportionsl
t o the depth t o yz~hicht h e me.jor l o a d Grives t h e b+ll below
t h a t t o which t h e [dinor .load has ~revlously
I$.
This
h a r h e s s number i s r e ~ dd i r e c t l y from a diz.1 on the machine.
Four d i f f e r e n t types of points o r balls a r e used in mak--Lng
the indentations. The standard for a o s t n e t e l a is t h e
one-sixteenth icch ball.
a r e oi;ta.ize";y
F o r very hard metals, best results
using a cone s'n~pped.d i a o n d point.
Yhen this
is used the major load is changed from 1CO kg. t o 1% kg.,
t h e rninor l o a d remaining t h e sane.
an e i g-h t h i r c h
g-~ia
i
Tor the s o f i materials,
quz-rtcr inc'a b i l l e r e used alfk t h e sane
Loads as 1~1hent h e s i x t e e n t h inch b a l l is used.
Very little c o n s i d e r ~ ~ t i o'vnas g i v e r in selecting aetals
ads t o t h e i r couposition, heet trea.tment, e t c .
variety
The purpose
p o s s i b l e , and
select them so that t h e y covered t h e total raage of barb-ess
could
the
machine,
Before any t e s t s Tere imde upon t h e specimens, a f l a t
surface was ground upon therfi end t h i s surface Bas smoothed
and polished by mea.cs 31 ernery paper.
Thus a l i t h e iiapres-
s i m s were maae upon s, f l a t smooth surface s o that t h e r e
, would be as little e r r o r as p o s s i b l e in reading t h e diameter
of t h e impression made by t h e Brine11 ball and
89
that in
both t k e Zt?ckCvefl and 3 r i c e l l iizschiizes t L e b e l l would bear
at a l l p o i n t s niti? equal irtensity oi pressure.
Two Brine11 t e s t s 'yere mede on each speciaen and floe
Rookwell t e s t s ~ i t hthe sixteenth inch ball.
ahenever p o s s i -
b l e , t h a t is when t h e r e was enough space on t h e specimen,
tests were made n i t h t h e e i g h t h inch b a l l , the q-uarter inch
b a l l and t h e d i a o n d ~ o i n t ,f i v e of each being t h e usual nm-
ber.
The average of the readings of each machine was then
computed and tabulated.
-',
In t a k i n g
t h e hardness with the B r i ~ e l lmachine, care
was taken t h e t l the load in every case wzs kept on t h e speci-
men-f o r at least f o r t y f i v e seconas, as up to that time the
depth of the indentation varies ~ i t hthe time of loading.
period
seconds
depth
the impres-
sion reasins constant.
I n a,pplying the load with the E r i n e l l mzchine the
~ e i g ~ xere
t s ? w e d s l o w l y off t h e i r supports so t h a t the
.
loadd osas ' of
_
-
s l o w l y applied nature and did not he-ve the ef-
impact which might have been the
fect
.-
a,
.
load
were applied suddenly.
.
The Z o c h e l l rnachirre was zdjusted so t h a t i n , a l l cases
the time for the applicztion of t h e major l o a d was ct least
f i v e seconds.
Immediately a.fter the t o t a l mejor load had
bben imposed upoo t h e specimen, t h e handle was replaced in
-
I
its S o r s e r position, r e ~ o v i n gt h e loac, and then t h e reading
was takeo.
It
WEB
feu? that if any length of t i m e TZS
allowed t o elcgse between t h e time hen t h e h a l e loac? bad
I
been a.pplied a n d the time of this reading, t h a t there was a
slight veriatioo in t h e results.
F r o m t h e data taken the verious curves shown were pJ.otted
mil equations w r i t t e n e x p e s s i o g t h e relation s h m b ; ~these
curves.
In determining tlie squation f o r the relation between the
Brine11 hardness n u b e r s and the Eockwell hardness numbers as
given by t h e sixteenth inch, e i g h t h inch, and q u a r t e r inch
balls, it mas noted that these t h r e e curves w r e very similar
i n na.ture t o a c u v e o o pege 15C of L i k a l s flxechanical a d
Graphical- Computation" Tol. 11, f o r nhich an eqiation of the
A
form y = a+bx
+
G had been written.
It was assumed from this
-
5
ar? e q ~ s t i c nof t h e f.grz? 3 = &+3E
+ C would fit t h e Rockw e l l Z r i n e l l curve, 3 Seing t h e Rockwell harbess nuaber m d
+kqV
L
i
~
~
E, the E r i n e l l hsrdness number.
In orc?er t o verify this
assumption, a p o i n t ( 1 ? 4 , ~ kwzs
)
chosen on t h e curve.
Then
T h i s l a s t equation is of t h e first order in B so t h a t a p l o t
of (B,a
-
3k) will a ~ p r o x i r r a t ea straight l i n e depending on
s-&
how well this f o r 3 of e q ~ a t i o nrill fit this curve.
A plot
of this forn is shown rn~.~de
from ten p o i n t s taken fro12 the
g r i n e l l Ei.ockwell curve end s i n c e they a l l are on a s t r a i g h t
line it is evident that this .is the proper f orni for the equa-
t.ion of t h e curve.
-
&
Yk Since FL - &
- El
+ QE
by d i v i d i n & t h e data into two perts znd adding t h e two con-
s t a n t s 81 a d X2 zzwybe determined.
The equation obtzined
i n Chis mm2nner mzs f~un2t o fit t h e curve v i t k l e s s than 1%
error.
The method of deterrrining t h e constants is shown below.
Ek z-ni: zit 2s tzken from t h e curve e q u d l e 6 40 and -5.5
re-
spectively.
3 i v i d i n g these t e n values of x and xn4C into two parts
Y + ~ 5,
and s d d i n g up t h e veluee i n eack pert, ne g e t two equations
Tne equztions for the other curves on t h e S r i n e l l Sockv;ell p l o t were found ir a s i n i l z r macner.
ii nuilber at' t e s t s ;yere :ibde Iqon C a t t e e 1 specimens
which n e r e furnisned by Xr.
X. .4.
iibdun-llur.
'rea.dings oa t h e s e s?eci:r:ens were, i . r
eacil
specimen,
k.;t
2
The 3 r i n e l l
, the
s m e fzr
t r ;ioclro;reil readi-ngs vs-ried c o i l s i C ~ r a - b l y .
This was t o be zxpected as t h e naterial was ? l e i n l y non-
The Zrinell b e l l covered enough e r e z t o g i v e
one average i l ~ ~ r e a e s s .The r j , ~ o k x e l lc i x t e e r t h ixch S e l l , be-
aomogeneous.
A-
czuse ox its s i z e , ggve x i d e l y d i f f e r e n t results eccording t o
bne ckarzcter of t h e g z r t of m e a e t a l ;lpm : ~ h i c sit r e s t e d .
d-
in rnachi3ic.g tr.ese specimens,
AB&im-?Jur frequently broke
t h e p o i c t of the t a d xpon t r , e casting, in:ica'cing
tain p o r t i o n s w e r e very h z r C .
that cer-
k s e c t i o n tkrongh t k e n z t e i
s h m e d flams an5 air h o l e s s o that a great vE,rimce in t h e
3ocic;~eilreadings w6,s to 5 e expected.
Ect *:;her, t h e average of
t h e s e r e e & i n g s ;vere taken it vas foucd -,hat they c?:aparec very
y e l l zit2 the r e s t of ;ne
GOGS
tests whick hza bee2 rvx u y n hmoge-
rdet&ls.
One of the adve-%ages of t r e s ~ c k x e i l:asshine 3 v e r the
useless
t k e 'ms,sChess of the case a s t & e Isa,d is sa h e a t y that t h e
~ar&2ess05 t h e m e t a l belot-i %the case has es m ~ c h t odo
' t r i n e i i reading 2s t k e ectual k e r k e s s
deterrining ;ze
The 3ocLr.~elli z c c k i ~ e , :ince
case.
ijvith
the
01
a emparat i v e l y l i g h t
lclsti
the
reading
actual hzr!&iess o2 t h e case, unless the c z s e is ext-.Id e l y
- ,- 5rineI.i hardness of the case rimy be d e t e r m n e d .
.~,e
Thls
c s s e hardened s t e e l s .
Apparzntly t h e i 2 e a l relation b e t v e e r the t z o macnines
for
-
q~
,4~h-rlc
-l
2al;s
l
cr;;azs
; h , ~r e l s " , ~ ~::2 .r;ore neai.17 s p s r o a c i a
strsisht line function. The r e a s o n f o r t h i s is apparent.
iTb,a
3T2,.,,G2:
3arbess
-
is based iqon thi? area under ;3xessui.e,
y j h i l c t k e 3sck;:.el~n;rLqess
7
is -the d e p t h t o ~h"niclr_ t h e % a l l is
I T ~sixteenth
v ~ixch
zball
.
tiler ths;.il 9i;hcr
the eignt;- inch
naturally p;netrates fuz~~uartar
>all 2,ad
the a r e s t h a n x i t h t h e o t h e r tao bells.
The degth of pene-
/
t r a . t i o n of t h e 3 i a m n d poi-lt is & h o s t d i r e c t l y groportionsi
t o t h e area s o tbat we m u l d expect t h e curve f o r t h e diauond
p o i n t t o a2?roximete
30i:d
E
strsizht line.
The curve f o r t h e die-
p o i n t Las a r e & s o ~ l z ~ b lconstiznt
y
s l o p e : ~ b L l e t h e quarter
inch b a l l gives a curve vhich has a very sharp cha,nge 02
slope.
F r o n the nature of t h e curves, it c m be see2 tha* f o r
the s o f t metals the E o c k x e l l is rilore eccurate than t h e Bri-
nell, i. e . , f o ? o n l y a slight chaage i;? the S r i n e l l f i ~ r d n e s a ,
:+liere is a considera.212 variation in t h e F.oc'x:zell hardaess
number.
This indicates that for aof t s e t a l s t h e Sockxeif
rnachine would b e raore sensitive than , t h e Brine11 i n conparing
e number oi speciinens l o r r e l z t i v e h e r b e s s ,
For
2
Dockvell
hak&~essof over 1 0 C (sixteenth inch b a l l ) or a G r i m 1 1 aardjness of m3re then 220,
the sixteenth inch ball on t h e Rock-
L e l l machine is not as accurate as t h e Brine11 machine and
t h e 5i:aaond p o i n t should be usixi.
Eowever t h e r e is a consid-
erable vzriation f r m t h e cuzve d r a m f o r t h e r e l a t i o n bemesn %he dimond poi%
L
t h e Erileil s o t h a t it is n o t
xholly satisfactory.
It
can be e e s i l y seen ~ k the
y
Xoclcwell is more a.ccurate
for a o f t mat.ekj.als.
Tit11 deep ispressions of the Srinelf
b~J.1, f o r a considerablz chc-nge in the depth of t h e indenta-
t i o n , t h e r e is
2
relatively small change in t h e zrea under
the
pressure.
readings for s o f t
only
a l i t t l e T,whilet h e Roclmell machine, xhich depeads upon the
i
depth of penetration, shows a great v s . r i a t i o n ia hardness n u -
b e r s f o r t h e sai'ile s2eci:aens.
t
F o r =y
metal havil?g a hardness nrrinber of l e s s than 30
Brinell the sixteenth inch ball on the Eockxe3.l machine is
practically useless as it is at about this point that t h i s
ball is sunk into t h e speciaen untii its holder csmes t o r e s t
upon the metal.
tk ,
'
I
For materials s o f t e r than this, the eighth
inch or quarter inch ball should. be -used with the stme load..
It aas suspected t i a t the reason f o r variations i l the
E l o c h e l l readings was t h e d i f f e r e n c e i n hardness of the vari-
ous grains in t h e m~terial, This szspicion nas strengthened
sornevhat by the fact that the msterials which seemed fafrly
homogeneous usually gzve uniforra IiockiRell readings.
A nmber of t e s t s with t h e 3 ~ c k . ~ esli lx t e e n t h inch 5ali
1':
--
\.
were made upon specizens o l cast brass and heat treated aluminum b r o n z e vhich were polished and e t c b e d t o show t h e grain
s t r ? ~ o t u r e . The t a s t s oil the a l u i n u n bronze speclaen proved
very l i t t l e , since t h e g r a i n s were a l l of practically the
II
I
sane hzrdress.
Eor~ever, z i d e ver~ationswere found in the
c a s t brass speciren, and mherever t ~ s oreadings s e r e 'known t o
be on the saae grain, they checked very c l o s e l y .
This t e s t
aas somewhat unsatisfactory as it was impossible t o a s c e r t a i n
t h e exact grains upon ~ h i c ht h e tests had been mede.
The
accompanying Siue print shows that each grain gives approxi-
Cast
Four
Brass
Times A c f u ~ /S i z e
/
11%
BO///
Rochiwe// N u m b e r s
P o ; o t NO.
Po,'- t
0.
t t
Po ~ 'fn
1
3 .4
2
/9.5
10
3
4
7
//
450
42.1
2 ZO
31.2
13
45,2 2 0
26.5 Z /
28.4.
,
/z
17
18
28.0.
/7*0,
5
z8.0
29.0
6
43.5 / 4
46.8
7
z%s
5
48.6
22
23
8
43.0
/6
47.5
24
,
36.a
3 8.5,
R.S.H a m / ' / f a r ,
w J B o y % e ~ / s- Mau 1 ~ 2 4
and
the
gains
variation
hardness.
The aet'aod f o r flSri-ng
r
t h e e r r o r in using t h e plotted
curves is shown by t h e exzillple given below.
reading
ball)
taking
ress r'raifi curve is equal t o
-
45 x
T e z c e c t a g e e r r o r = 705
1~0
= 21.3%
w
The rnaximaa e r r o z f o r the various curves is given be1o.c.
1 /1611 1/81f
"Lali b a l l
1 /4"
ball
3imond
3oint
;tIasimu;-a numerical e r r o r
-
Tkas it is proba.ble thzt in
-
2-
few instances t h e r e rill
be a consider~~b.bie
e r r o r in using %hem curves unless
of readings a r e tzksn.
2.
nunber
Ir general, however, these curves
will give reshlts which a r e sufficiently accurate.
1;imufacturers generally s p e c i l y metals t o b e w i t h i n a
certain r m g e
,
\
\
3f
3rinell 'ilarrbess.
Ifa p.ockxell raachine
were used instead of a s r i x e l l , these specifications m u l d be
cr,~q
b o e dby t h e pro&~.;loer
f o 3osk:v:ruell h a r b e s a n?m'Ders.
Since
t o e a l i o ~ ? a b l erazge is considerable, e sisal1 e r r o r is ?ex-
zis:;iblz,
equations
derived
,32zae r e s u l t s z s s a e curves,
curves
-,vithinone 3er c e n t .
The equatinns for t h e four curves "re given uelow.
1"
8 ball
4
ball
S i n c e these equations f i t t h e curve very c l o s e l y , it
betmesa tce hr,rdaess z s given by t h e s e two mzcnines.
the
Z o c k ~ e l lNo.
1/16"
:ie-,te r iaL
Lead
Zoc-per
G2s.t Zinc
zrass
Copper
Bronze
tl
ball.
l a *a
1/6"/4ft
ball
ball
7
-L
/1S11
ball
Bronze
1/S1l
ball
1,411 D i a a f ~ n d
bail
~doint
1/16lf
ball
2il.d S t e e l
fl
!I
(Cast S t e e l
(Eeas P e a a t e G j
/
ball
1/41!
ball
~ / l ~ l l l/&fi
b&ll
'7 0
rtg
Steel
150
j . 5 0 C . ~--e a , t
)
(Treatad S t e e l )
Cast S t e e l
,
'15
Steel
169
84
Steel
196
86
( Cast S t e e l )
( "eet ~re e t ed)
1%
69
,. ,,&\el S t e e l
200
3G
3 r ~ yCzst iron
205
,??7
91
Steel
205
32
lr
205
ball
1 /4"
+.
1
n
Ziwaonh
20j.n-b;
97
93
Stainless s t e e l
Steel
7tainless S t e e l
1/161f
1/ ~ i i
ball
bell
117
( S t e e l , rdra-wr, a t
)340
118
( ~ e z "t e z t e e d )
( Steel
j
340
122
3tainless S t e e l
375
i23
.steel
3 $20
125
if
406
126
1I
415
127
11
415
128
11
4.30
129
if
44C
130
:,Yhits S s s t I r o n
450
1/6fl
1 /4"
Sall
ball
3iaiioni.i
?oii:t
*" L
u ~ d
7
berial
Steel
I1
II
tl
OI
Steel.
11
1/15"
1/61!
ball
ball
1 4 Dizzfiond
Taiat
ball
l / i ~ t ~l / i l f
ball
bail
T o o l 3"csei
Steel
1 /411
1
Dismond
Point
30C,Yi)Nv'~ ' n s j . 5 3 6 i n . . . V < i d U 3 3 ' f ' j V A Y V U
A ? q ~ & j <A.5''--,>
-,d n u 1 . i i 4 2 3 ~
Q
1CI
Q
-Q
0
\
1
0
Q
I
-0
.>
0
.
ry
Z
?
0
.
.
'
..