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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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L.L. GiudiciGiudici – – FRACTURE TOUGHNESS: KIC / JICFRACTURE TOUGHNESS: KIC / JIC

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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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5

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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