Post on 30-Jun-2020
Mechanical and physical properties of ZnSe windows to be used with the FEANICS (Flow Enclosure Accommodating Novel Investigations in Combustion of Solids) experiments were measured in order to determine design allowables. In addition, the literature on crack growth properties was summarized. The average Young’s modulus, Poisson’s ratio, equibiaxial fracture strength, flaw size, grain size, Knoop hardness, Vicker’s hardness, and branching constant were 74.3 ± 0.1 GPa, 0.31, 57.8 ± 6.5 MPa, 21 ± 4 mm, 43 ± 9 um, 0.97 ± 0.02 GPa, 0.97 ± 0.02 GPa, and 1.0 ± 0.1 MPam^0.5, respectively. The properties of current ZnSe made by chemical vapor deposition are in good agreement with those measured in the 1970’s. The hardness of CVD ZnSe windows is about one twentieth of the sapphire window being replaced, and about one-sixth of that of window glass. Thus the ZnSe window must be handled with great care. The large grain size relative to the inherent crack size implies the need to use single crystal crack growth properties in the design process. In order to determine the local failure stresses in one of the test specimens, a solution for the stresses between the support ring and the edge of a circular plate load between concentric rings was derived.
https://ntrs.nasa.gov/search.jsp?R=20060051712 2020-07-20T02:56:50+00:00Z
1
Mec
hani
cal P
rope
rties
of Z
nSe
for
the
FEA
NIC
S M
odul
e
Jon
Sal
em
NA
SA
Gle
nn R
esea
rch
Cen
ter
Cle
vela
nd, O
hio
2006
Ele
ctro
mag
netic
Win
dow
s S
ympo
sium
May
1 -
4, 2
006
2
OU
TLIN
E
Bac
kgro
und;
FE
AN
ICS
Mis
sion
Gen
eral
pro
perti
es o
f ZnS
eE
stim
atio
n of
cra
ck g
row
th p
aram
eter
sG
rain
siz
e ef
fect
sTe
st re
sults
S
umm
ary
3
BA
CK
GR
OU
ND
NA
SA
mis
sion
s re
quire
the
safe
-use
of
ligh
t wei
ght b
rittle
mat
eria
ls:
-Spe
cial
ty W
indo
ws
-Sol
ar c
once
ntra
tors
-Ele
ctro
nic
subs
trate
s-C
ombu
stor
line
rs-B
earin
g ba
lls-L
eadi
ng e
dges
Sing
le C
ryst
al
Appl
icat
ions
Poly
crys
talli
ne
& C
ompo
site
Ap
plic
atio
ns
}
4
FEA
NIC
S
Mis
sion
-su
ppor
t stu
dy c
ombu
stio
n of
thic
k an
d th
in s
olid
fuel
s in
mic
rogr
avity
:
Forc
ed I
gniti
on a
nd S
prea
d Te
st
Solid
Inf
lam
mab
ility
Bou
ndar
y A t
Low
-Spe
ed
ZnS
e w
indo
w
Flow
Enc
losu
re A
ccom
mod
atin
g N
ovel
In
vest
igat
ions
in C
ombu
stio
n of
Sol
ids
ZnSe
w
indo
ws
Pres
suriz
ed
com
bust
ion
cham
ber
Win
dow
ho
lder
Win
dow
as
sem
bly G
aske
tO
-rin
gs2.
25”
5
OB
JEC
TIV
ES
Rev
iew
lite
ratu
re o
n fra
ctur
e to
ughn
ess,
stre
ngth
and
cr
ack
grow
th p
rope
rties
for C
VD
ZnS
e.Id
entif
y de
sign
val
ues
for r
oom
tem
pera
ture
, hig
h hu
mid
ity e
nviro
nmen
t: ap
plie
d st
ress
of 1
0 M
Pa
for 1
0 ye
ars.
Run
nec
essa
ry te
sts
to c
ompl
imen
t the
lite
ratu
re d
ata.
Mos
t pap
ers
did
not g
ive
full
para
met
er s
et fo
r des
ign
=> A
dditi
onal
obj
ectiv
e: re
anal
yze
exis
ting
data
set
s.
6
CV
D Z
nSe
Lite
ratu
re
Ope
n Li
tera
ture
:
1.A
.G. E
vans
and
H. J
ohns
on, “
A F
ract
ure-
Mec
hani
cs S
tudy
of Z
nSe
for L
aser
Win
dow
App
licat
ions
,”J.
Am
. Cer
am. S
oc. V
ol.
58, N
o. 5
-6, p
p. 2
44-2
49 (1
975)
2.S
.W. F
reim
an, J
.J. M
echo
lsky
, Jr.,
R.W
. Ric
e, a
nd J
.C. W
urst
, “In
fluen
ce o
f Mic
rost
ruct
ure
on C
rack
Pro
paga
tion
in Z
nSe,
”J.
Am
. Cer
am. S
oc.,
vol.
58, N
o. 9
-10,
pp.
406
–40
9 (1
975)
3.
P. M
iles,
“Hig
h Tr
ansp
aren
cy In
frare
d M
ater
ials
–A
Tec
hnol
ogy
Upd
ate,
”Opt
. Eng
., V
ol. 1
5, N
o. 5
, pp.
451
-459
(197
6).
4.K
.R. M
cKin
ney,
J.J
. Mec
hols
ky, J
r., a
nd S
.W. F
reim
an, “
Del
ayed
Fai
lure
in C
hem
ical
ly D
epos
ited
ZnS
e,”J
. Am
. Cer
amic
S
oc.,
Vol
. 62,
No.
7-8
, pp
. 336
-340
, (19
79)
5.R
.W. R
ice,
S.W
. Fre
iman
, and
J.J
. Mec
hols
ky, J
r., “T
he D
epen
denc
e of
Stre
ngth
-Con
trolli
ng F
ract
ure
Ene
rgy
on th
e Fl
aw-
Siz
e to
Gra
in-S
ize
Rat
io,”
J. A
m. C
eram
. Soc
.,V
ol. 6
3, N
o. 3
-4, p
p. 1
29-1
36 (1
980)
.6.
N. F
erne
ilus,
G, G
rave
s, a
nd W
. Kne
ct, “
Cha
ract
eriz
atio
n of
Can
dida
te L
aser
Win
dow
Mat
eria
ls,”
pp. 1
88-1
95 in
SP
IE V
ol.
297
Em
ergi
ng O
ptic
al M
ater
ials
, (19
81)
7.R
.L. T
aylo
r and
J.S
. Goe
la, “
Spe
cific
atio
n of
Infra
red
Opt
ical
Mat
eria
ls fo
r Las
er A
pplic
atio
ns,”
pp. 2
2-35
in S
PIE
Vol
. 607
O
ptic
al C
ompo
nent
Spe
cific
atio
ns fo
r Las
er B
ased
Sys
tem
s an
d O
ther
Mod
ern
Opt
ical
Sys
tem
s, (1
986)
.8.
“Est
imat
ion
of Z
nSe
Cra
ck G
row
th P
rope
rties
for D
esig
n of
the
FEA
NIC
S (F
low
Enc
losu
re A
ccom
mod
atin
g N
ovel
In
vest
igat
ions
in C
ombu
stio
n of
Sol
ids)
Win
dow
s,”J
.A. S
alem
, NA
SA
TM
213
359,
200
5.
9.“M
echa
nica
l Cha
ract
eriz
atio
n of
ZnS
e W
indo
ws
for u
se w
ith th
e Fl
ow E
nclo
sure
Acc
omm
odat
ing
Nov
el In
vest
igat
ions
in
Com
bust
ion
of S
olid
s (F
EA
NIC
S) M
odul
e,”J
.A. S
alem
, NA
SA
TM
214
100,
200
6.
Clo
sed
Lite
ratu
re:
1.J.
C. W
urst
and
T.P
Gra
ham
, “Th
erm
al, E
lect
rical
, and
Phy
sica
l Mea
sure
men
ts o
f Las
er W
indo
ws,
”Uni
vers
ity o
f Day
ton
Res
earc
h In
stitu
te, O
hio,
AFM
L-TR
-75-
28, A
pril
1975
.2.
G.A
. Gra
ves,
D.E
. McC
ullu
m, a
nd J
.M. W
imm
er, “
Inve
stig
atio
n of
the
Ther
mal
, Ele
ctric
al, M
echa
nica
l, an
d P
hysi
cal
Pro
perti
es o
f Inf
rare
d La
ser W
indo
w a
nd IT
Tra
nsm
ittin
g M
ater
ials
,”A
FML-
TR-7
7-23
, UD
RI-T
R-7
7-06
, Apr
il 19
77.
3.D
.J. I
den,
J.A
. Det
rio, J
. Fox
, “O
ptic
al W
indo
w M
echa
nica
l Stre
ngth
and
Rel
iabi
lity,
’Uni
vers
ity o
f Day
ton
Res
earc
h In
stitu
te,
Ohi
o, T
echn
ical
Rep
ort N
o. U
DR
-TR
-83-
73, J
une
1983
.
7
Mile
s: “i
ncip
ient
flaw
siz
e is
com
para
ble
to th
e gr
ains
siz
e…. T
he
effe
ctiv
e m
ater
ial s
treng
th d
epen
ds o
nly
wea
kly
on th
e vo
lum
e un
der s
tress
……
..onl
y sl
ight
ly o
n th
e de
gree
of p
erfe
ctio
n of
the
surfa
ce p
olis
h.”=
> w
eak
Wei
bull
effe
ct…
….E
ffect
for a
gra
in s
ize?
ZnS
e is
sof
t: S
crat
ches
ext
end
leng
th o
f gra
ins
caus
ing
sing
le
crys
tal,
low
ene
rgy
fract
ure.
Stre
ngth
of Z
nSe
400
100
4525
1610203040506070
Coo
rs, G
ould
, & R
ayth
eon
Mat
eria
ls [1
1]R
ayth
eon
[10]
Roh
m &
Haa
s (T
his
wor
k)
Frac
ture
St
reng
th,
MPa
Gra
in S
ize,
um
(inv
erse
root
sca
le)
8
Mic
rost
ruct
ure
of C
VD
ZnS
e
Mic
rost
ruct
ure
varie
s w
idel
y, e
xhib
its h
eavy
twin
ning
: l =
42
±2
um p
erpe
ndic
ular
and
47±
3 um
par
alle
l (95
%
conf
iden
ce).
Gra
ins
as la
rge
as 1
50 u
m a
re a
ppar
ent.
0.25
mm
21S
200x
02
7C 5
0x 0
1
0.12
5 m
m
9
Win
dow
Stre
ngth
(Rin
g-on
-Rin
g Lo
adin
g)
SU
PPO
RT P
LATE
N
LOA
D
ROD
LOA
D
ROD
LOA
D R
ING
SUPP
ORT
RIN
G
BALL
TEST
SP
ECIM
EN
COM
PLIA
NT
LAY
ER O
R
CARB
ON
FO
IL
CARB
ON
FO
IL
LOA
D F
IXTU
RE
SUPP
ORT
FIX
TURE
TAPE
2.25
”
Thin
win
dow
s:
10
Stre
ngth
of C
VD
ZnS
e
For w
ell p
olis
hed
ZnS
e, s
treng
th is
~55
MP
a.W
eibu
ll sc
alin
g no
t app
aren
t (st
udy
need
ed),
but
Nee
d si
mili
tude
of f
law
pop
ulat
ion.
Mea
nFr
actu
re
Stre
ngth
, M
Pa
Test
Met
hod
and
Envi
ronm
ent
Test
Met
hod
and
Eniro
nmen
t
4PB
BO
3BR
OR
4PB
4P
B
BO
3B
2030405060708090100
2030405060708090100
Mea
n &
Sta
ndar
d D
evia
tion
CV
D Z
nSe
Wat
erA
ir ~4
5% R
H
Dry
N2
(126
5)(4
05)
A e(mm
) =
Larg
e 4-
PB
Sm
all
4-P
BS
mal
l 4-
PB
11
Wei
bull
Dis
tribu
tions
(Bal
l-on-
3 B
all L
oadi
ng)
Wei
bull
mod
ulus
of ~
5, n
omin
al s
treng
th o
f >50
MP
a, b
ut
stre
ngth
dep
ends
on
envi
ronm
ent –
SC
G.
σ θm
#
20
30
40
50
60
70
80
90
100
0
Prob
abili
ty
of F
ailu
re
Bia
xial
Fra
ctur
e S
treng
th, M
Pa
12
Wei
bull
Dis
tribu
tions
(Rin
g-on
-Rin
g Lo
adin
g)
Wei
bull
mod
ulus
of ~
9, n
omin
al s
treng
th o
f ~60
MP
a.
Agr
ees
with
AFM
L da
ta (1
39 te
st, m
= 9.
2, σ
f= 5
4 M
Pa)
.
σ θm
#
20
30
40
50
60
70
80
90
100
Bia
xial
Fra
ctur
e St
reng
th, M
Pa
Prob
abili
ty
of F
ailu
re
13
Frac
ture
Tou
ghne
ss M
etho
ds
d nP/
2
Wg
W
d
P/2
PW
m
L
a
2h
B
P P
a
Dou
ble
Tors
ion
Dou
ble
Can
tilev
er B
eam
14
Frac
ture
Tou
ghne
ss M
etho
ds
W
B
a oa 3
a 2a 1
a 1
a
2c
α 1=
a 1/W
α o=
a o/W
α=(a
1+a 2
+a3)
/3W
hR
emov
e4.
5h to
5h
SEPB
CN
B
SCF
or IF
15
Frac
ture
Tou
ghne
ss
Frac
ture
toug
hnes
s in
crea
ses
with
cra
ck s
ize
and
low
er h
umid
ity:
0.3
M
Pa√
mfo
r sm
all c
rack
s an
d 0.
9 M
Pa√
mfo
r lar
ge c
rack
s in
dry
en
viro
nmen
ts.
AS
TM C
1421
CN
B –
0.43
MP
a√m
.
σ θm
#
Test
Met
hod
and
Env
ironm
ent
Stre
ngth
CN
BIF
DC
B SE
NB
DC
BD
T 0.
0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Mea
n &
Sta
ndar
d D
evia
tion
CV
D Z
nSE
Wat
erA
ir ~4
5% R
HD
ry N
2
Incr
easi
ng c
rack
siz
e
Sin
gle
crys
tal
Mea
nFr
actu
re
Toug
hnes
s,
MPa
√m
16
R-c
urve
Beh
avio
r
Mac
ro c
rack
frac
ture
toug
hnes
s is
sub
stan
tially
la
rger
than
sm
all c
rack
or s
ingl
e cr
ysta
l val
ues.
G
rain
sam
plin
g v
s. g
ain
brid
ging
=>R
-cur
ve…
.
Stre
ss
Inte
nsity
Fa
ctor
, K
I , M
Pa√
m
Cra
ck S
ize,
mm
0.
00.
10.
20.
30.
40.
50.
63.
84.
00.
0
0.2
0.4
0.6
0.8
1.0
Ran
ge o
f exp
ecte
d fla
w s
ize
ac
for F
EA
NIC
S:
Ran
ge o
f mac
rocr
ack
fract
ure
toug
hnes
sm
easu
rem
ents
Cra
ck w
idth
, 2c
Sta
tic L
oad,
Y =
1.2
6
Cra
ck d
epth
, a
Rep
orte
d R
ohm
& H
aas
ZnS
e gr
ain
size
Wat
er
Dry
N2
Sing
le g
rain
sD
ozen
s of g
rain
s
17
Slo
w C
rack
Gro
wth
(v =
AK
In )
Thre
e ty
pes
of S
CG
dat
a on
ZnS
e:-c
onst
ant s
tress
rate
test
ing
(Dyn
amic
Fat
igue
)-c
onst
ant s
tress
test
ing
(Sta
tic F
atig
ue)
-fra
ctur
e m
echa
nics
test
ing
(DC
B a
nd D
T)
Mai
n is
sues
with
the
data
:-s
mal
l num
ber o
f tes
ts-s
igni
fican
t sca
tter
-poo
r rep
ortin
g
Mac
ro c
rack
stre
ss in
tens
ities
are
sub
stan
tially
larg
er
than
thos
e ex
pect
ed fo
r fai
lure
s fro
m s
mal
l cra
cks
–N
eed
sim
ilitu
de b
etw
een
the
test
dat
a an
d co
mpo
nent
.
18
Slo
w C
rack
Gro
wth
(Con
stan
t stre
ss ra
te o
r dyn
amic
fatig
ue, w
ater
)
18 d
ata
poin
ts; p
oor r
egre
ssio
n co
effic
ient
an
d la
rge
stan
dard
dev
iatio
ns.
Frac
ture
St
ress
, M
Pa
Stre
ss R
ate,
MPa
/s
0.01
0.1
110
100
3035404550607080
Evan
s &
John
son
B-O
-3B
Reg
ress
ion
95%
Con
fiden
ce In
terv
al
n =
50
32
A =
1.08
x 1
025
r2 = 0
.14±
19
Slo
w C
rack
Gro
wth
(Con
stan
t stre
ss o
r sta
tic fa
tigue
, air)
29 d
ata
poin
ts; b
ette
r reg
ress
ion
coef
ficie
nt
and
stan
dard
dev
iatio
n; fi
ve ru
n ou
ts.
Failu
re
Tim
e, s
Stre
ss, M
Pa
4550
5560
100
101
102
103
104
105
106
107
Mck
inne
y et
al
Reg
ress
ion
95%
Con
fiden
ce In
terv
alFa
iled
on lo
adin
g
n =
21
6A
= 64
6r2 =
0.3
4±(5
)
20
Slo
w C
rack
Gro
wth
(DT
and
DC
B in
air)
Two
data
regi
mes
mac
ro a
nd s
mal
l or s
ingl
e cr
ysta
l.N
o m
athe
mat
ical
exp
lana
tion
of th
e sh
ift o
r the
as
sum
ptio
ns u
sed.
Crac
k Ve
loci
ty,
m/s
Stre
ss I
nten
sity
MPa√
m
0.2
0.3
0.4
0.50
.60.
80.9
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Reg
ress
ion
Frei
man
et a
lEv
ans
and
John
son
Sin
gle
crys
tal e
stim
ate
Frei
man
et a
l.n
= 25
6
A =
6.2
x 10
-3
r2 =
0.69
n =
40A
= 1.
8 x
1018
Single Crystal or Small Crack
Macro-crack
±
21
Est
imat
ion
of S
mal
l Cra
ck
Par
amet
ers
from
Mac
ro C
rack
Dat
a
Nee
d ob
serv
atio
n of
act
ual,
smal
l cra
ck g
row
th ra
tes.
n IAK
v=
Cra
ck
Vel
ocit
y, v
K Ipo
lyK I
smal
l
Stre
ss I
nte
nsi
ty,K
I
v ter
min
al
Cra
ck
Vel
ocit
y, v
K Ipo
lyK I
smal
l
v ter
min
al
Stre
ss I
nte
nsi
ty,K
I
Mor
e re
alis
tic
mod
el:
Mor
e gr
ain
s en
cou
nte
red
22
Est
imat
ion
of S
mal
l Cra
ck
Par
amet
ers
from
Mac
ro C
rack
Dat
a
Ass
ume
equi
vale
nt te
rmin
al v
eloc
ity:
Ass
ume
iden
tical
slo
pes
(n):
n IcSi
ngle
Sing
len Ic
Poly
Poly
KA
KA
v=
=
n
IcSi
ngle
IcPo
lyPo
lySi
ngle
KKA
A⎟⎟ ⎠⎞
⎜⎜ ⎝⎛=
n IAK
v=
Crac
k Ve
loci
ty,
vK I
poly
K Ism
all
Stre
ss I
nten
sity
, K I
v ter
min
al
23
Slo
w C
rack
Gro
wth
(DT,
DC
B, c
onst
ant s
tress
in a
ir)
Two
data
regi
mes
: Mac
ro a
nd s
mal
l or s
ingl
e cr
ysta
l.R
easo
nabl
e ag
reem
ent b
etw
een
smal
l cra
ck a
nd
shift
ed m
acro
cra
ck c
urve
s.
Crac
k Ve
loci
ty,
m/s
Stre
ss I
nten
sity
MPa√
m
0.2
0.3
0.4
0.5
0.6
0.8
0.9
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Reg
ress
ion
Frei
man
et a
lE
vans
and
Joh
nson
Sing
le c
ryst
al e
stim
ate
Frei
man
et a
l.n
= 25
6
A =
6.2
x 10
-3
r2 =
0.69n
= 25
A =
3.7
x 10
8
Single Crystal or Small Crack
Macro-crack
n =
21
6A
= 4.
82 x
10-6
n =
21
6A
= 6.
5 x
103
McK
inne
y, S
tatic
Loa
d 4P
B, K
Ic =
0.9
0 M
Pam
0.5
McK
inne
y, S
tatic
4P
B, K
Ic =
0.3
3 M
Pam
0.5
±
±
±
24
0.3
0.4
0.5
0.6
0.8
0.9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Reg
ress
ion
DC
BD
TDT
and
DC
BD
yn. F
at.,
KIc
= 0
.9 M
Pam
0.5
Dyn
. Fat
., K I
c =
0.33
MPa
m0.
5
Wat
er
n =
12
5A
= 5
x 10
-3
r2 = 0.
22
n =
50
32
A =
9.97
x103
n =
40
2A
= 1.
09 x
103
r2 = 0.
94
Slo
w C
rack
Gro
wth
(DT
and
DC
B in
wat
er)
Con
sist
ent D
T da
ta, s
catte
red
DC
B d
ata.
Crac
k Ve
loci
ty,
m/s
Stre
ss In
tens
ity M
Pa√
m
±
±
±
25
0.3
0.4
0.5
0.6
0.7
0.8
0
50x1
0-6
100x
10-6
150x
10-6
200x
10-6
250x
10-6
300x
10-6
DC
B, W
ater
DT
Wat
erN
onlin
ear R
egre
ssio
n
Non
linea
r Reg
ress
ion
DC
B A
ir
n =
34.1
A =
124
n =
32.8
A =
1.04
x 1
04
Slo
w C
rack
Gro
wth
(DT
and
DC
B, w
ater
)
DC
B w
ater
dat
a ha
s m
any
low
vel
ocity
, hig
h st
ress
in
tens
ity v
alue
s –
crac
k pi
nned
-tru
ncat
e.
Non
linea
r fits
giv
e sm
alle
r par
amet
ers.
Crac
k Ve
loci
ty,
m/s
Stre
ss I
nten
sity
MPa√
m
}{
26
0.2
0.3
0.4
0.5
0.6
0.8
0.9
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Reg
ress
ion
DT
Eva
ns &
Joh
nson
, DT
& D
CB
Con
st. s
tress
rate
B-O
-3B,
KIc
= 0.
9 M
Pam
0.5
Con
st. s
tess
rate
B-O
-3B
, KIc
= 0
.33
MPa
m0.
5
DC
B, t
runc
ated
dat
a
n =
40
2A
= 1.
97 x
1020
n =
24.6
A =
282
r2 = 0.
90
n =
50
32
A =
1.08
x 1
025
Single X'tal / Small Crack
Macro-crack
n =
40
2A
= 1.
09 x
103
r2 = 0
.94
n =
50
32
A =
9.98
x103
DT,
KIc
= 0
.33
MPa
m0.
5
Slo
w C
rack
Gro
wth
(DT,
DC
B, C
onst
ant S
tress
Rat
e in
Wat
er)
Mac
ro c
rack
dat
a an
d co
nsta
nt s
tress
rate
dat
a ag
ree
whe
n a
mac
o fra
ctur
e to
ughn
ess
is u
sed.
Shi
fted
mac
ro c
rack
cur
ve a
nd s
mal
l cra
ck c
urve
agr
ee.
Crac
k Ve
loci
ty,
m/s
Stre
ss In
tens
ity M
Pa√
m
±
±
±
±
27
Slo
w C
rack
Gro
wth
(Par
amet
er S
umm
ary)
Like
ly v
alue
s ar
e n
= 40
, APo
ly=1
000,
Asi
ngle
= 10
20
6.5
x 10
34.
8 x
10-6
21 ±
64-
poin
t Sta
tic (2
8)M
cKin
ney
et a
l. A
ir
3.7
x 10
86.
2 x
10-3
26 ±
6D
CB
(11)
Frei
man
et a
l.
Air
1.46
x 1
01328
225
DC
B (9
), Tr
unca
ted
““
“
8.61
x 1
025.
0 x
10-3
12 ±
5D
CB
(21)
Frei
man
et a
l.
1.97
x 1
0201.
09 x
103
40 ±
2D
T (2
5)“
““
1.08
x 1
0259.
98 x
103
50 ±
32B
-O-3
B, D
yn. (
18)
““
“
5.05
x 1
0501.
11 x
1013
86D
T an
d D
CB
, Lin
eEv
ans a
nd Jo
hnso
n
A Sm
all
m/s
(MPa√m
)-n
Am
/s (M
Pa√m
)-n
n ±
SDn
Test
Met
hod
(num
ber o
f tes
ts)
Dat
a So
urce
28
Cra
ck B
ranc
hing
Con
stan
t
Bra
nchi
ng c
onst
ant A
b=
1 ±
0.1
MP
a√m
, res
idua
l st
ress
= 9
MP
a.
r b-0.5, m
-0.5
1020
3040
5060
7080
Stress at Failure Location, MPa
1020304050607080
CV
D Z
nSe
Reg
ress
ion
2rb
σ f=
Abr
b + σ
th
29
SU
MM
AR
Y
Bas
ed o
n 19
70’s
dat
a, th
e si
ngle
cry
stal
or s
mal
l cra
ck S
CG
pa
ram
eter
s fo
r CV
D Z
nSe
in w
ater
are
n<
40, a
nd A
sing
le>
1020
, K
Ic=
0.33
MPa
√m
.Th
e m
acro
-cra
ck p
aram
eter
s ar
e m
uch
diffe
rent
: 25
< n
< 80
and
A P
oly
= 10
3 , K
Ic>
0.60
MPa
√m
.S
treng
th is
~ 5
5 M
Pa
with
a W
eibu
ll m
odul
us o
f ~ 6
to 9
.S
mal
l cra
ck p
aram
eter
s es
timat
ed fo
r mac
ro-c
rack
dat
a ag
ree
reas
onab
ly w
ith p
aram
eter
s es
timat
ed fr
om s
treng
th d
ata.
But
, we
real
ly n
eed
a S
CG
mod
el th
at in
corp
orat
es R
-cur
ve
beha
vior
, and
obs
erva
tion
of a
ctua
l sm
all c
rack
gro
wth
rate
s.M
any
of th
e ex
istin
g da
ta s
ets
cont
ain
muc
h sc
atte
r and
too
few
da
ta p
oint
s.