- Email: [email protected]
On the effective surface energy involved in the brittle fracture of 7030 brass
ON THE
EFFECTIVE
THE
SURFACE
BRITTLE
ENERGY
FRACTURE
INVOLVED
IN
OF 70/30 BRASS*
and W. ROSTOKERT
H. NICHOLS
A 70/30brass wetted with mercury fails at about the engineering yield stress in a brittle manner. The degree of embrittlement is temperature dependent, showing an abrupt reversion to the fully ductile state in the manner of the transition displayed by body-centered cubic metals. The effective surface energy associated with this brittle fracture has been analysed from experimental measurement of alpvs. &1’2 and a, vs. C (crack length). In both cases, the evidence is that the effective surface energy is less than 10s ergs/cm2. ENERGIE
EFFECTIVE
DE
RUPTURE
SURFACE FRAGILE
MISE D’UN
EN
OEUVRE
LAITON
LORS
DE
LA
70/30
Un laiton 70/30 imbibe de mercure se rompt d’une man&e fragile aux environs de sa limite d’8lasticit8 pratique. Le degre de fragilitb depend de la temperature et on peut montrer qu’il y a transition brusque et retour B 1’Btat ductile. Cette transition s’effectue de man&e semblable B celle observbe dans les m&aux B reseau cubique. La relation entre 1’6nergie effective de surface et la rupture fragile a BtB BtudiBe iLpartir de mesures experimentales de a, en fonction de d-1/z et bg en fonction de C (longueur des fissures). Dam les deux cas, il apparait que 1’8nergie effective de surface est infbrieure B IO3ergs/cm2. ZUR
EFFEKTIVEN
OBERFLBCHENENERGIE
BEIM
SPRiiDBRUCH
VON
70/30-MESSING
70/30-Messing, das mit Quecksilber angefeuchtet ist, bricht in spreder Weise bei ungefhhr der normalen FlieDspannung. Der Grad der VersprGdung hiingt von der Temperatur ab und zeigt einen abrupten tibergang zum vollduktilen Zustand, iihnlich dem ubergang, den kubisch-raumzentrierte Metalle aufweisen. Die effektive Oberfliichenenergie,die mit diesem Spradbruch verkniipft ist, wurde aus den Versuchsergebnissen van 0, gegen d-1/z und Us gegen C (RiDlilnge) abgeleitet. In beiden Fallen stellt sich heraus, daB die effektive Oberfitichenenergiekleiner als IO3 erg/cm2 ist.
Recrystallized Zn when amalgams
alpha brass containing
exclusively
30 per cent
bending
wetted with liquid mercury or mercury will fracture in simple tension at room
temperature
at or near its normal
engineering
intergranular of
observable
yield
the
twin
in
band
recrystallized interfaces
measure of plastic distortion.
metals,
provides
an
The micro-
structure at 250 x magnification of the cracked zone in a coarse-grained brass specimen is illustrated in
increasing temperature of testing, point ; with ductility is progressively restored. A graphic plot of
Fig. 1. Clearly any plastic distort,ion is beyond
tensile ductility against test temperature takes the form of the transition from brittle to ductile be-
resolution used, which means that if a plastically deformed zone exists at the fracture surface it is less
havior found with most body-centered
than about
The transition governed
temperature,
by the recrystallized
fashion as predicted
cubic
metals.
which is quite sharp, is
basically
originating
at the wetted
the same as encountered
1 x lop3 mm in thickness.
less than
the 3 x 10-l
worked metal discovered
mm
This is conthickness
further
interface
in brittle
is
body-
centered cubic metals and that true surface energy is a dominant factor in the process. The
structure
of
70130
brass
provides
opportunity to demonstrate the magnitude metal embrittlement on a micro-scale.
a
good
of liquid The re-
crystallized structure is populated by twin bands. In cross-section the twin interfaces are straight lines which terminate abruptly and without change of direction at grain boundaries. Since the brittle fracture
produced
by
wetting
with
mercury
is
* Received February 5, 1960. t Metals Division, Armour Research Foundation, Chicago, Illinois. ACTA METALLURGICA,
VOL. 8, NOVEMBER
1960
788
of
by Orowan@) on
cubic metals.(l)
It is the intent of this paper to demonstrate that fracture
plastically
grain size in the same
for body-centered
siderably
the
FIG. 1. Intersection of twin interfaces with an intergranular crack in TO/30 brass embrittled by wetting with mercury. Y 260
NICHOLS
SURFACE
ROSTOKER:
AND
ENERGY
.4ND
BRITTLE
FK.4CTURE
789
the fracture surface of low carbon steel broken below the transition
temperature.
siderable importance
This
point
since, according
is of con-
to Orowan, the
effective surface energy associated with common brittle fracture must be of the order of lo6 ergs/cm2 rather than the l-2
lo3 ergs/cm2 characteristic
x
of
true surface energies. Assuming for the moment that the brittle fracture of 70130 brass wetted with mercury does not involve a plastic energy
energy dissipation can
be
term, the effective
estimated
from
criterion for a ductile-brittle
the
surface
Cottrell-Petch
transition.
Rearranging
the terms of their equation of parameters,
the surface
energy, y, becomes CJ,K,d1’2 ‘=
j3G 14
where or = flow stress;
FIG. 2. Fracture stress at room temperature of 70/30 brass as a function of grain size, rl, when unwetted and when wetted with mercury.
K, = slope of the tlow stress vs. d-n2 function; d = mean grain diameter; /3 = numerical factor;
value of K, the magnitude
G = modulus of rigidity. For a mean grain diameter
of 0.062 mm, the flow
stress of 70/30 brass was determined lb/in2;
values
of
K,
and
G were
as 15.8 x lo3 determined
13.5 x lo3 and 6.03 x lo6 lb/in2, respectively.
as
Using
assumption
that brittle fracture
be
for the propagation
brittle
ergs/cm2. fracture
This signifies
that in the
is obtained
The effective surface energy associated fracture can be estimated
2.4 x lo3
to be
without
significant plastic strain energy absorption.
Petch’st3) estimate of/l as equal to 4, y is calculated to truly
of y* is computed
280 ergs/cm2. This is well below the maximum value set by the Cottrell-Petch criterion and supports the
with brittle
from the Griffith condition
of an existing crack:
of 70130 brass, the associated c’i = ~(EyIG)
surface energy should be less than this value. The surface energy associated with brittle fracture can be estimated from the relationship
where ai = stress E = Young’s
cF = u,, + Kc~--l’~
re-initiate
propagation
in an
modulus.
If the crack propagation follows the Griffith relationship, the slope of the plot of o‘i against C--1/2 yields a
where uF = fracture stress; go = an intercept value; K = the functionics]
to
existing crack of length, C;
term which is equal to (Ey)l12. This analysis
;
Y = Poisson’s ratio.
applied
to ship plate steel below its transition temperature Felbeck
and
surface
energy
Orowan(6)
to
estimate
the
to be of the order of lo6 ergs/ems,
which was in good agreement with the plastic energy associated with the plastically worked zone revealed
Stroht4) has shown that the measured values of K permit the derivation of reasonably correct values of y for Fe, Zn, Mg and MO. In these cases y refers to the
by X-ray
surface energy of the metal with respect to its own vapor. Petchf5) has shown that hydrogen embrittle-
Crack propagation studies have annealed brass sheets (0.020 in.
been made thick x 12
wide x 16 in. long)
tensile
ment of iron can be interpreted
on a model of reduced
surface energy (reduced value of K) brought about by adsorption of hydrogen to crack nuclei surfaces. The fracture stresses of recrystallized 70/30 brass
led
apparent
diffraction.t2)
under uniaxial
on in.
loading.
Susceptibility to brittle fracture was produced by wetting the sheet specimens with mercury in a broad band across the 12 in. width of the test specimen. A 5164 in. slot was located in the wetted zone at a
wetted with mercury for a range of grain sizes have been measured at room temperature and are plotted
point equidistant
in Fig. 2. It will be noted that a linear relationship exists between (TV and d-1’2. From the measured
* This should signify the surface energy of 70/30 brass with an adsorbed film of mercury.
from both edges:
It is characteristic
ACTA
790
METALLURGICA,
of brittle fracture in brass that velocities of propagation are not high. One can initiate a crack and stop its propagation
two observers
the crack length applied
“walked”
watched
on demand,
load.
across
The
1960
m. 23
I
and measured
and another
crack
the width
could
recorded
be essentially
of the specimen
and a
series of crack lengths and their associated propagation loads measured.
In all cases, the cracks remained
the wetted zone and propagated
transversely
in
to the
: 20 0 -_ t
c;t, , , , , , , ,
axis of tension.
.5
.3
Two types of curves were obtained. When the specimen was wetted with mercury only on one side, the crack propagated
across the width of the specimen
faster than through the thickness
direction,
I.1 .9 1.3 1.5 .7 Inverse Square Root Of Crock Length, in.-“2
1.7
1.9
4. Stress to propagate a crack as a function of crack length. 70/30 brass sheet wetted on both sides with mercury.
FIG.
with the
result that there was brittle fracture on one side and superficial
8,
by rapid unloading of the tensile machine.
On re-loading, the
VOL.
ductile
By wetting
both sides of the thin brass sheet, the
fracture apparent on the other. The plot of oi against C- II2 for this test is shown in Fig. 3. From the slope of the linear plot obtained, the
ductile
value of apparent surface energy was computed to be about lo6 ergs/cm2 in good agreement with the work
because the slope is obviously
of Felbeck and Orowan.
portion
eliminated. plotted
of fracture,
The
results
together
be expected
in
by all appearances, of
Fig.
several
4.
This
specimens was
approaching
was are
necessary zero as is to
if the surface energy is to decrease from
lo6 to lo3 ergs/cm2 or less. Within the scatter band of the data,
one cannot
do other
than
estimate
the
surface energy as between zero and about lo3 ergs/cm2. By all methods of evaluation, the fracture of 70130 brass
wetted
with
mercury
appears
to
be nearly
ideally brittle. ACKNOWLEDGMENT
This work was performed with
the
Pitman-Dunn
Arsenal, whose sponsorship are gratefully
under research contract
Laboratory
of
Frankford
and permission to publish
acknowledged. REFERENCES
I I
141 0 InVerSe
I 2
I
Square Root Of Cwck Length, in.-“2
FIG. 3. Stress to propagate a crack as a function of crack length. 70/30 brass sheet wetted on one side with mercury.
1. H. NICHOLS and W. ROSTOKER, paper submitted for publication in Actn Met. 2. E. OROWAN, Weld. J. 34, 1576’ (1955). 3. N. J. PETCH, Proc. Conf. on Fracture Shampscott 1959. Wiley, New York (1959). 4. A. N. STROH,Advanc. Phys. 6, 428 (1957). 5. N. J. PETCH, Phil. Mag. 1, 331 (1956). 6. D. K. FELBECKand E. OROWAN, Weld. J. 34, 570s (1955).
EFFECTIVE
THE
SURFACE
BRITTLE
ENERGY
FRACTURE
INVOLVED
IN
OF 70/30 BRASS*
and W. ROSTOKERT
H. NICHOLS
A 70/30brass wetted with mercury fails at about the engineering yield stress in a brittle manner. The degree of embrittlement is temperature dependent, showing an abrupt reversion to the fully ductile state in the manner of the transition displayed by body-centered cubic metals. The effective surface energy associated with this brittle fracture has been analysed from experimental measurement of alpvs. &1’2 and a, vs. C (crack length). In both cases, the evidence is that the effective surface energy is less than 10s ergs/cm2. ENERGIE
EFFECTIVE
DE
RUPTURE
SURFACE FRAGILE
MISE D’UN
EN
OEUVRE
LAITON
LORS
DE
LA
70/30
Un laiton 70/30 imbibe de mercure se rompt d’une man&e fragile aux environs de sa limite d’8lasticit8 pratique. Le degre de fragilitb depend de la temperature et on peut montrer qu’il y a transition brusque et retour B 1’Btat ductile. Cette transition s’effectue de man&e semblable B celle observbe dans les m&aux B reseau cubique. La relation entre 1’6nergie effective de surface et la rupture fragile a BtB BtudiBe iLpartir de mesures experimentales de a, en fonction de d-1/z et bg en fonction de C (longueur des fissures). Dam les deux cas, il apparait que 1’8nergie effective de surface est infbrieure B IO3ergs/cm2. ZUR
EFFEKTIVEN
OBERFLBCHENENERGIE
BEIM
SPRiiDBRUCH
VON
70/30-MESSING
70/30-Messing, das mit Quecksilber angefeuchtet ist, bricht in spreder Weise bei ungefhhr der normalen FlieDspannung. Der Grad der VersprGdung hiingt von der Temperatur ab und zeigt einen abrupten tibergang zum vollduktilen Zustand, iihnlich dem ubergang, den kubisch-raumzentrierte Metalle aufweisen. Die effektive Oberfliichenenergie,die mit diesem Spradbruch verkniipft ist, wurde aus den Versuchsergebnissen van 0, gegen d-1/z und Us gegen C (RiDlilnge) abgeleitet. In beiden Fallen stellt sich heraus, daB die effektive Oberfitichenenergiekleiner als IO3 erg/cm2 ist.
Recrystallized Zn when amalgams
alpha brass containing
exclusively
30 per cent
bending
wetted with liquid mercury or mercury will fracture in simple tension at room
temperature
at or near its normal
engineering
intergranular of
observable
yield
the
twin
in
band
recrystallized interfaces
measure of plastic distortion.
metals,
provides
an
The micro-
structure at 250 x magnification of the cracked zone in a coarse-grained brass specimen is illustrated in
increasing temperature of testing, point ; with ductility is progressively restored. A graphic plot of
Fig. 1. Clearly any plastic distort,ion is beyond
tensile ductility against test temperature takes the form of the transition from brittle to ductile be-
resolution used, which means that if a plastically deformed zone exists at the fracture surface it is less
havior found with most body-centered
than about
The transition governed
temperature,
by the recrystallized
fashion as predicted
cubic
metals.
which is quite sharp, is
basically
originating
at the wetted
the same as encountered
1 x lop3 mm in thickness.
less than
the 3 x 10-l
worked metal discovered
mm
This is conthickness
further
interface
in brittle
is
body-
centered cubic metals and that true surface energy is a dominant factor in the process. The
structure
of
70130
brass
provides
opportunity to demonstrate the magnitude metal embrittlement on a micro-scale.
a
good
of liquid The re-
crystallized structure is populated by twin bands. In cross-section the twin interfaces are straight lines which terminate abruptly and without change of direction at grain boundaries. Since the brittle fracture
produced
by
wetting
with
mercury
is
* Received February 5, 1960. t Metals Division, Armour Research Foundation, Chicago, Illinois. ACTA METALLURGICA,
VOL. 8, NOVEMBER
1960
788
of
by Orowan@) on
cubic metals.(l)
It is the intent of this paper to demonstrate that fracture
plastically
grain size in the same
for body-centered
siderably
the
FIG. 1. Intersection of twin interfaces with an intergranular crack in TO/30 brass embrittled by wetting with mercury. Y 260
NICHOLS
SURFACE
ROSTOKER:
AND
ENERGY
.4ND
BRITTLE
FK.4CTURE
789
the fracture surface of low carbon steel broken below the transition
temperature.
siderable importance
This
point
since, according
is of con-
to Orowan, the
effective surface energy associated with common brittle fracture must be of the order of lo6 ergs/cm2 rather than the l-2
lo3 ergs/cm2 characteristic
x
of
true surface energies. Assuming for the moment that the brittle fracture of 70130 brass wetted with mercury does not involve a plastic energy
energy dissipation can
be
term, the effective
estimated
from
criterion for a ductile-brittle
the
surface
Cottrell-Petch
transition.
Rearranging
the terms of their equation of parameters,
the surface
energy, y, becomes CJ,K,d1’2 ‘=
j3G 14
where or = flow stress;
FIG. 2. Fracture stress at room temperature of 70/30 brass as a function of grain size, rl, when unwetted and when wetted with mercury.
K, = slope of the tlow stress vs. d-n2 function; d = mean grain diameter; /3 = numerical factor;
value of K, the magnitude
G = modulus of rigidity. For a mean grain diameter
of 0.062 mm, the flow
stress of 70/30 brass was determined lb/in2;
values
of
K,
and
G were
as 15.8 x lo3 determined
13.5 x lo3 and 6.03 x lo6 lb/in2, respectively.
as
Using
assumption
that brittle fracture
be
for the propagation
brittle
ergs/cm2. fracture
This signifies
that in the
is obtained
The effective surface energy associated fracture can be estimated
2.4 x lo3
to be
without
significant plastic strain energy absorption.
Petch’st3) estimate of/l as equal to 4, y is calculated to truly
of y* is computed
280 ergs/cm2. This is well below the maximum value set by the Cottrell-Petch criterion and supports the
with brittle
from the Griffith condition
of an existing crack:
of 70130 brass, the associated c’i = ~(EyIG)
surface energy should be less than this value. The surface energy associated with brittle fracture can be estimated from the relationship
where ai = stress E = Young’s
cF = u,, + Kc~--l’~
re-initiate
propagation
in an
modulus.
If the crack propagation follows the Griffith relationship, the slope of the plot of o‘i against C--1/2 yields a
where uF = fracture stress; go = an intercept value; K = the functionics]
to
existing crack of length, C;
term which is equal to (Ey)l12. This analysis
;
Y = Poisson’s ratio.
applied
to ship plate steel below its transition temperature Felbeck
and
surface
energy
Orowan(6)
to
estimate
the
to be of the order of lo6 ergs/ems,
which was in good agreement with the plastic energy associated with the plastically worked zone revealed
Stroht4) has shown that the measured values of K permit the derivation of reasonably correct values of y for Fe, Zn, Mg and MO. In these cases y refers to the
by X-ray
surface energy of the metal with respect to its own vapor. Petchf5) has shown that hydrogen embrittle-
Crack propagation studies have annealed brass sheets (0.020 in.
been made thick x 12
wide x 16 in. long)
tensile
ment of iron can be interpreted
on a model of reduced
surface energy (reduced value of K) brought about by adsorption of hydrogen to crack nuclei surfaces. The fracture stresses of recrystallized 70/30 brass
led
apparent
diffraction.t2)
under uniaxial
on in.
loading.
Susceptibility to brittle fracture was produced by wetting the sheet specimens with mercury in a broad band across the 12 in. width of the test specimen. A 5164 in. slot was located in the wetted zone at a
wetted with mercury for a range of grain sizes have been measured at room temperature and are plotted
point equidistant
in Fig. 2. It will be noted that a linear relationship exists between (TV and d-1’2. From the measured
* This should signify the surface energy of 70/30 brass with an adsorbed film of mercury.
from both edges:
It is characteristic
ACTA
790
METALLURGICA,
of brittle fracture in brass that velocities of propagation are not high. One can initiate a crack and stop its propagation
two observers
the crack length applied
“walked”
watched
on demand,
load.
across
The
1960
m. 23
I
and measured
and another
crack
the width
could
recorded
be essentially
of the specimen
and a
series of crack lengths and their associated propagation loads measured.
In all cases, the cracks remained
the wetted zone and propagated
transversely
in
to the
: 20 0 -_ t
c;t, , , , , , , ,
axis of tension.
.5
.3
Two types of curves were obtained. When the specimen was wetted with mercury only on one side, the crack propagated
across the width of the specimen
faster than through the thickness
direction,
I.1 .9 1.3 1.5 .7 Inverse Square Root Of Crock Length, in.-“2
1.7
1.9
4. Stress to propagate a crack as a function of crack length. 70/30 brass sheet wetted on both sides with mercury.
FIG.
with the
result that there was brittle fracture on one side and superficial
8,
by rapid unloading of the tensile machine.
On re-loading, the
VOL.
ductile
By wetting
both sides of the thin brass sheet, the
fracture apparent on the other. The plot of oi against C- II2 for this test is shown in Fig. 3. From the slope of the linear plot obtained, the
ductile
value of apparent surface energy was computed to be about lo6 ergs/cm2 in good agreement with the work
because the slope is obviously
of Felbeck and Orowan.
portion
eliminated. plotted
of fracture,
The
results
together
be expected
in
by all appearances, of
Fig.
several
4.
This
specimens was
approaching
was are
necessary zero as is to
if the surface energy is to decrease from
lo6 to lo3 ergs/cm2 or less. Within the scatter band of the data,
one cannot
do other
than
estimate
the
surface energy as between zero and about lo3 ergs/cm2. By all methods of evaluation, the fracture of 70130 brass
wetted
with
mercury
appears
to
be nearly
ideally brittle. ACKNOWLEDGMENT
This work was performed with
the
Pitman-Dunn
Arsenal, whose sponsorship are gratefully
under research contract
Laboratory
of
Frankford
and permission to publish
acknowledged. REFERENCES
I I
141 0 InVerSe
I 2
I
Square Root Of Cwck Length, in.-“2
FIG. 3. Stress to propagate a crack as a function of crack length. 70/30 brass sheet wetted on one side with mercury.
1. H. NICHOLS and W. ROSTOKER, paper submitted for publication in Actn Met. 2. E. OROWAN, Weld. J. 34, 1576’ (1955). 3. N. J. PETCH, Proc. Conf. on Fracture Shampscott 1959. Wiley, New York (1959). 4. A. N. STROH,Advanc. Phys. 6, 428 (1957). 5. N. J. PETCH, Phil. Mag. 1, 331 (1956). 6. D. K. FELBECKand E. OROWAN, Weld. J. 34, 570s (1955).