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Mechanical Engineering
Mechanical behaviour of materials
LaboratoryLaboratory – – Part 1Part 1MEASUREMENT OF FRACTURE TOUGHNESS OFMEASUREMENT OF FRACTURE TOUGHNESS OF
METALLIC MATERIALS : KMETALLIC MATERIALS : K ICIC
(ASTM E399(ASTM E399--09)09)
L.L. GiudiciGiudici
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Aim of the Test
Determination of fracture toughness of a metallic material
(KIC or JIC) in mode I.
KIC Linear elastic fracture mechanics. Non-linearmaterial deformation is confined to a small regionsurrounding the crack tip. Plain strain.
(ASTM E399-09 Standard)
JIC Elastic-plastic fracture mechanics. Theplastic zone is larger, although not on large scale.
(ASTM E1820-09 Standard)
Material: steel
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Provini
SE(B) Specimen
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Crack lenght a measurement
1- OPTICAL METHOD
by means of microscope or camera
2- CRACK GAGE
by means of electrical output (R or V)
3- COMPLIANCE
by means of extensometer (clip on gage)
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COMPLIANCE
Compliance method is used to define crack lenght a.
ci coefficients are different for each type of specimens (ASTM E399-09)
P applied load [N]
B thickness [mm] E Young modulus [MPa]
V displacement [mm]
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K (Stress Intensity Factor)
For Compact Specimens:where:
]m[MPa⎟ ⎠
⎞⎜⎝
⎛ = w
a f W BW
PK P applied load [N]
B thickness [mm]
W width [mm]
f(a/w) geometry function
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡⎟ ⎠
⎞⎜⎝
⎛ +⎟
⎠
⎞⎜⎝
⎛ +⎟
⎠
⎞⎜⎝
⎛ +⎟
⎠
⎞⎜⎝
⎛ +
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
⎟ ⎠ ⎞⎜
⎝ ⎛ −
⎟ ⎠
⎞⎜⎝
⎛ +
=⎟ ⎠
⎞⎜⎝
⎛ 4
4
3
3
2
210
2
3
1
2
W
ac
W
ac
W
ac
W
acc
W a
W
a
W
a f
c coefficients are different for each type of specimen (ASTM E399-08)
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Precracking
It’s difficult to obtain a machined notch that well simulate a natural crack in orderto provide a good test result. The Precracking is the usual way for this purpose. A fatigue precrack grows from a machined notch applying an alternated load tothe specimen in force control (typically 20 Hz and R = Pmin/Pmax)
NB: crack length is measured from the load line
P
P
Pmax [N]
Pmin [N]
t [s]
aia0
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Precracking
The load P is calculated from the K value. K is usually decreasing while cracklength a increases.
K iniz max precric = 1.4 K fin max precric = 20 MPa m^0.5 ai = 23 mm a0 = 31 mm (W =51 mm)
a [mm]
K [MPa m0.5]
(K fin max precr ; a0 )
(K iniz max precr ; ai )
ai a0
W
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Precracking
If the force cycle P is maintained constant, the maximum K and ΔK will increase withcrack size according to f(a/w) value.
If K critical value is reached, the failure of specimen occurs.
If K < K threshold, the crack does not growth.
⎟ ⎠
⎞⎜⎝
⎛ =
w
a f W
BW
PK
7
7.5
8
8.5
9
9.5
10
10.5
11
11.5
12
0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58
a/W
f(a/W)
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Precracking
In precracking K has to be chosen in order to verify some requirements of thestandard.
NOTE: K Q = K IC only if all the requirements are satisfied
K IC (ASTM E399-09)K max precr < 0.8 K Q
K max fin precr < 0.6 K Q
K max fin precr / E < 0.00032 m0.5
0.45 < a0 /W < 0.55
a0 – ai > 0.025 W
a0 – ai > 1.3 mm
ai a
0W
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KIC - Test
An increasing load (typically ramp) is applied on the specimen, such that:
/s]m[MPa75.2d
d55.0 ≤≤
t
K
A curve Load Vs Displacement is recorded.
Displacement is usually measured by a Clip on Gage (COD).
Load vs. COD
0 0.125 0.25 0.375 0.5
COD (mm)
0
2000
4000
6000
8000
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KIC – Data analysis
Construct a secant line r 5, with a slope = 0.95r, where r is the slope of the tangent to theinitial portion of the data record (red line). P5 load value is the interception between r 5and test data graph.
PQ load is defined as below:
L o a d v s. C O D
0 0 .1 2 5 0 .2 5 0 .3 7 5 0 .5
C O D ( m m )
0
2 5 0 0
5 0 0 0
7 5 0 0
1 0 0 0 0
- If P P5, then P = PQ (see Type II and III)
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KIC – Data analysis
a is defined as the average value of three measurements a1 a2 e a3 made at ¼ ,
½, and ¾ of the specimen thickness.
]m[MPa⎟ ⎠
⎞
⎜⎝
⎛
= w
a
f W BW
P
K
Q
Q
QUALIFICATION
The difference between each two of the three measurements must not differ morethan 10% from the mean value.
0.85 a < as1, as2 < 1.15 a
0.025W
1.3 mm
To calculate KIC, at the end of the test the fracture surfaces have to be observed bymeans of microscope in order to measure the crack lenght after failure (a) withgood precision.
a1
a2
a3
as1
as2
as1 , as2 >
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SPECIMEN
E = 206000 MPa
R s = 2000 MPa
R m = 1800 MPa
= 0.3
W = 28 mm
B = 14 mm
ai = 12 mm
h = 2.5 mm
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KIC – Specimen and test parameters
PRECRACKING
a0 = 13.9 mm
K iniz max precr = 21 MPa m^0.5
K fin max precr = 15 MPa m^0.5
R = 0.1
f = 20 Hz
TEST
Speed test = 0.700 mm/min
Displacement control ai
a0
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KIC – Qualification Requirements
K Q is K IC only if:
Pmax / PQ < 1.10 a,B > 2.5 (K Q / Rsn)2
In addition both precracking and test have to verify the following qualificationrequirements (ASTM E399-09):
PRECRACKING
K max precr < 0.8 K Q
K max fin precr < 0.6 K Q
K max fin precr / E < 0.00032 m0.5
0.45 < a0 /W < 0.55
a0 – ai > 0.25 W
a0 – ai > 1.3 mm
TEST
|a1- a2|, |a3- a2|, |a1- a3| < 0.1 a
0.85 a < as1 , as2 < 1.15 a
as1 , as2 > 0.025W , 1.3 mm
75.2dd55.0 ≤≤
t K
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