Characterization technics in fracture mechanicsincluding
K1c test, J1c test and da/dN-K curve measurement
1
Jianqiang [email protected]
Safety factor and damage tolerance design
Conventional turbine runner design
approach: max <
YS or
UTS
Fracture mechanics damage
tolerance approach: K < K1c, af < ac
[ALSTOM HYDRO]
Fracture toughness K1c and fatigue crack growth rates da/dN-K should be known. 2
CT specimen(compact tension)
( )( )
2 2 3 3 4 4
3/ 21/ 2
(2 a w) 0.886 4.64a w 13.32a w 14.72a w 5.6a wPKBW 1 a w
+ + + =
B = 0.5W In general
Fracture toughness K1c test (ASTM E399)
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USERText BoxK=f() est fonction du stress P et une caracteristique du defaut (B ou a ou W)
Fatigue pre-cracking is often used to obtain a sharp crack with small plastic deformation;
Chevron notch is necessary to initiate a straight crack;
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Fatigue pre-cracking (ASTM E399)
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5Crack mouth opening displacement
Load
CMOD
PQ
( )WafWB
PQ /KQ =
(c)
USERText BoxCrack Mouth Opening Displacement
Small scale yielding and plane strain conditions:
YS
Q
YS
Q0
K2.5B and
2
K2.5a
6
If not, increase specimen thickness B () or fatigue pre-cracking length a0 ()
KQ = K1c ?
7KQ = K1c ?
Even the two previous conditions are met, the recording of force-displacment
curve could include some non-linarity for two reasons:
plasticity near the crack tip;
beginning of stable crack extension.
if Pmax/PQ < 1.10 and the two previous conditions are met, then KQ = K1C
8Material studied CA6NM steel
K1c testing - small scale plasticity and plane strain condition
a = initialcracklength
B = specimenthickness
a, B 258 mm !, if a/W = 0.5, W= 516 mm !!
2
K2.5Bet 2
K2.5aYS
1c
YS
1c
C Mn Si S P Cr Ni Mo
CA6NM 0.03 0.57 0.37 0.02 0.02 12.68 4.03 0.67
Chemical composition of the tested material CA6NM (wt. %)
E (GPa) YS (MPa) UTS (MPa) A (%)
CA6NM 207 763 837 27.0
Tensile properties of the tested material
Fracture toughness
K1c test is not appropriate for CA6NM steel
The Rices J Integral Going back to Griffith ?
=S
dSx
uTwdyJ with = ijijdw
crack
[Rice, J Appl Mech 35, p.379, 1968]
9
)1( 2=EJK
)1( 22
vE
KGJ ==(plan strain)
Linear Elastic Fracture Mechanics (LEFM)
Stress singularity near a crack tip
o(r1/2) is higher order stress terms
)o(r)f(r 2
K 1/2ij +=
S
S
r
ax
K-controlled zone
Small-scale yielding
)m(MPa aY K =
10
Going back to Griffith ?
)f(r 2
Kij =
Elastic-Plastic Fracture Mechanics (EPFM)
Generalisation of the approach with the HRR field near a crack tip
)(frI
J ij
1)1/(n
nyyij
+
=
S
S
a
J-controlled zone
Large Scale Yielding
J represents the elastic-plastic stress fields intensity near a crack tip
As fo K and Kc, when J reaches a criticalvalue Jc, the crack will propagate stably
n
yyy
+=Ramberg-Osgood
[Hutchinson, J Mech Phys Solids 16, p.13, 1968] [Rice & Rosengren, J Mech Phys Solids 16, p.1, 1968] 11
Hutchinson + Rice & Rosengren
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Measure of J at begining of a R-curve (initiation of crack extension) Test on SENB and CT specimens; W= 2 inch and B= 1 inch usually; B can be reduced to 0.25 W; Modified geometry for that the extensometer can measure the load-
line displacement (work)
Fracture toughness J1c test (ASTM E1820)
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Procedure: Fatigue pre-cracking of n specimens (n5) to the same a0 Stop the tests at different af Marking of final crack length
Break the specimen
Measurement of af Fitting of J-a curve
JQ = (BL)(J-a)
13
Multi-specimen method
P-v curve J-a curve
Long and expensive
Procedure:
Fatigue precracking of one specimen,
Ductile tearing of specimen with partial unloading to get the elastic compliance,
After the final unloading, heat tinting to measure a0 and af , and break the
specimen,
Results analysis.
P-v curve J-a curve
Single-specimen method
0.0 0.5 1.0 1.5 2.0 2.5 3.00
5
10
15
20
25
30
35
40
45
L
o
a
d
(
k
N
)
Load line displacement (mm)0.0 0.5 1.0 1.5 2.0 2.5 3.0
0
100
200
300
400
500
600
700
data points regression line
J
(
k
J
/
m
2
)
crack extension - a (mm)
1/C
Load-unload slope compliance crack length a
Plastic area under P-v curve + elastic part J integral
0.0 0.5 1.0 1.5 2.0 2.5 3.00
100
200
300
400
500
600
700
J
(
k
J
/
m
2
)
crack extension - a (mm)
J0.2
0,2mm offset line
14
)(1E
KJ 22
el =
)a(WBA
J0n
plpl
=
plel JJJ +=
Force
Load-line displacement
15
Calculation of J and a
Apl
depends on specimens geometry
[ ]5432 677.650355.464106.335u-11.242u4.06319u-1.000196 / uuWai ++=a= ai -a0
Calculation of J
Calculation of a
For the candidate JQ value is a valid measurement of J1c, several conditions should be met, including:
B and W-a0 > 10 JQ/Y Straightness of a0 et af, a - aavg < 0.05B a (marking) - a (predicted) < 15%
e.g. CA6NM steel, K1c = 245 MPa ,YS = 763 MPa, UTS =837 MPa
B 3.31 mm ! 16
J-a curve and validation
Initial procedure 12.7 mm thick smooth CT specimen
Problems :
Significant lateral contraction is observed.
There are nearly no crack growth at the side surfaces of the specimen while the crack
front at the center advanced by more than 2 mm.
KJ1c measured = 452MPa !!! (valid test, K1c = 245 MPa ).
10 mm
crack extension direction
Fracture surfaceSpecimen
2 mm
17
New procedure 12.7 mm thick side-grooved CT specimen
Fracture surface
The crack tunneling is less pronounced by the introduction of side-grooves.
The crack still grows faster at the center of the specimen compared to the side surfaces.
The test is not valid according to ASTM E1820 (straightness of af).
crack extension direction
BN = 0.8 B
2 mm
18
12.7 mm smooth specimen
Side-grooves effect
Smooth specimen: invalid test KJ1c = 452 MPa !!!
Side-grooved specimen: invalid test K1c = 241 MPa .
12.7 mm side-grooved specimen
10 mm 10 mm
19
New procedure 25.4 mm thick side-grooved CT specimen
crack propagation direction
Fracture surfaceBN = 0.8 B
The crack extension front is nearly straight, the specimen is in plane strain condition
(little lateral contraction).
The test is valid according to ASTM E1820.
5 mm
20
J-a curve
0.0 0.5 1.0 1.5 2.0 2.5 3.00
100
200
300
400
500
600
700
B = 0.5 inch B = 1.0 inch
J
(
k
J
/
m
2
)
crack extension - a (mm)
0.2 mm offset line
Thickness effect 12.7 mm vs 25.4 mm
Similar fracture initiation toughness J0.2
values can be obtained on both thin and thick
specimens even though the test done on thin specimen was not valid according to ASTM
standard E1820.
The tearing modulus dJ/da is much higher for thin specimens than thick specimens.
thickness
(mm)
J0.2(kJ/m2)
KJIc(MPa )
dJ/da
(MPa)
12.7 256 241 215
25.4 266 245 128
Measured values
21
12.7 mm thick specimen 25.4 mm thick specimencrack propagation direction
5 mm 5 mm
Thickness effect 12.7 mm vs. 25.4 mm
J1c 12.7 mm: significant crack front curvature and lateral contraction.
J1c 25.4 mm: straight crack extension front and little lateral contraction
However, the measured fracture initiation toughness J0.2
values are approximately
equal.
22
fatigue
precracking
Microscopic fracture surface SEM observation
transgranular
fracture
intergranular
fracture
500 m
stable crack extension
dimple ductile
fracture surface50 m
23
Fracture mechanism in ductile material
d
=
23
exp21
RdR
VM
H
=
Growing crack in a ductile material1Stage 1: Void nucleation
Stage 2: Void growth
Stage 3: Void coalescence
where, R: current void radius, and stress triaxiality
For the stage 2: Rice and Tracey2 established the following law:
1[Gullerud et al., Eng Fract Mech 66, p.65, 2000] 2[Rice & Tracey., J Mech Phys Solids 17, p.201, 1969]
24
FEM model
Mesh of CT specimen
12.7 mm thick smooth specimen
12.7 mm thick side-grooved specimen
Voce nonlinear isotropic hardening law:
where, R0, Q, b, material constants,
p, accumulated plastic strain
CA6NM: YS = 763 MPa, R0 = 2665 MPa,
Q = 42.7 MPa, b = 3000
quarter of specimen: 41599 nodes, 22940 elements
(20-node elements + 10-node elements)
[ ])exp(10 ppYSeq bQR ++=
25
FEM Results
-0.50 -0.25 0.00 0.25 0.500.0
0.5
1.0
1.5
2.0
12.7 mm thick smooth specimen 12.7 mm thick side-grooved specimen 25.4 mm thick side-grooved specimen
S
t
r
e
s
s
t
r
i
a
x
i
a
l
i
t
y
(
)
Normalized distance to midsection (Z/B)
Variation of stress triaxiality across
the specimen thickness
-0.50 -0.25 0.00 0.25 0.500.000
0.005
0.010
0.015 12.7 mm smooth specimen 12.7 mm side-grooved specimen 25.4 mm side-grooved specimen
P
l
a
s
t
i
c
s
t
r
a
i
n
i
n
t
h
i
c
k
n
e
s
s
d
i
r
e
c
t
i
o
n
(
Z
)
Normalized distance to midsection (Z/B)
Variation of plastic strain across the
specimen thickness
For 12.7 mm thick smooth specimen, the stress triaxiality falls rapidly for |Z/B| >
0.25.
For 25.4 mm thick side-grooved specimen, the plane strain condition is maintained
over the entire specimen thickness.
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Main differences between K1c and J1c tests
K1c J1c
Concept Linear Elastic Fracture Mechanics
(LEFM)
Elastic-Plastic Fracture Mechanics
(EPFM)
Loading condition Small-Scale Yielding
(Elastic)
Large-Scale Yielding
(Elasto-Plastic)
Extensometers poistion
(CT specimen)
Crack Mouth Load-Line
Testing Procedure P-v curve KQ K1C P-v curve J-a curve JQ J1C
Application field Brittle materials
(high strength & low toughness)
Ductile materials
(low strength & high toughness)
27
Charpy test
ASTM E23: Standard test methods for notched bar impact testing of metallic materials
28
Charpy test on Titanics steel
Can we estimate fracture toughness K1c from Charpy test ?
=
2051 YSYSYS
c CVNK
Rolfe-Novak-Barsom correlation:
29
Titanics steel at 0oC
Actual A36 steel at 0oC Energy absorbed as function of temperature
Fatigue crack growth da/dN - K curve
[Paris et al. The Trend in Engineering 13, p.9-14, 1961]30
Measure of da/dN-K curve Test on CT and MT specimens; W= 2 inch and B= 0.5 inch usually; B can be reduced to 0.05 W; Modified geometry for that a longer ligament can be used for crack
growth measurement
Fatigue crack growth rates measurement (ASTM E647)
31
( )( )
2 2 3 3 4 4
3/ 21/ 2
(2 a w) 0.886 4.64a w 13.32a w 14.72a w 5.6a wPKBW 1 a w
+ + + =
da/dN K curve
Where to start the measurement (test) ?32
start of test
K decreases
until the threshold
K increases
end of test
da/dN K test
33
2max,
1
=
YSmy
Kr
pi
2
, 21
=
YScy
Kr
pi
(Monotonic)
(Cyclic)
108.01 >
= mm
dadK
KC
K decreasing phase K-gradient limit (ASTM E647)
Monotonic and cyclic plastic zones
34
K decreasing at R = 0.1 and R = 0.7
[Bui-Quoc T. et al. Final report of project CDT P3768, 2009]35
da/dN-K curve of CA6NM steel at R = 0.1 and R = 0.7
[Bui-Quoc T. et al. Final report of project CDT P3768, 2009]36
Main fatigue crack closure mechanisms in metals
(a) Plasticity-induced closure
(b) Roughness-induced crack closure
(c) Oxide-induced closure
(d)Closure induced by a viscous fluid
(e) Phase transformation-induced closure
[Suresh & Ritchie, Int metall Rev 29, p.445, 1984]37
vv
LoadP-v curve P-v curve
Pv
=
compliance of
opening crack
Pv ='v
Fatigue crack closure measurement
opeff KKK = max
Effective stress intensity range keff :
38
( )meffKCdN
da =
Pariss equation:
[Trudel A. et al. Int J Fatigue 66, p. 39-46, 2014]
Master curve
39
Thank you for your attention!
Questions ?
40
Relation entre G et K
-Dplacement impos
-plaque dpaisseur unitaire
-Contrainte plane
La propagation de la fissure de a a+ se traduit par une dcroissance de lnergie lastique: dU= - G On peut retourner ltat initial en refermant la fissure avec les forces qui agissaient entre a et a+ . Lnergie G est gale au travail de ces forces de fermeture :
2I I
I I I0
K K1 8 xG K dx d 'o : G2 E 2 E2 x
= = pipi
22 I
IKG (1 ) en dformation planeE
=