部分材料的断裂韧度(包含AISI 4340)

ADVANCED MATERIALS LABORATORY

Fracture Toughness Measurement

Objectives

1. To make a valid measurement

of

the plane strain

fracture toughness of

a given material.

2. To observe and understand a typical brittle fracture process.

Background

The

phenomenon

of

brittle

fracture

deals

with

sudden

failure

of

structural

components without warning. This is attributed to presence of cracks or

crack-like

defects

in

the

material

that

appear

during

processing

or

during

fabrication and assembly of the component. The theory behind this

phenomenon,

as

it

applies

to

many

engineering

structures,

is

referred

to

as

Linear

Elastic

Fracture

Mechanics

(or

LEFM).

According

to

this

theory,

the condition for brittle failure can be expressed as

where

KI

is

called

the

stress

intensity

factor

and

is

dependent

on

loading

conditions and the flaw size in the material, and KIC is a material

property known as the plane strain fracture toughness. The stress

intensity factor is usually expressed as

where Q is a geometry correction

factor

depending on the

geometry of the

structural

component

and

the

crack

geometry,

is

the

applied

stress,

and

'a' denotes the crack size. Definitions of these quantities for many

typical

situations

are

presented

in

an

Appendix

at

the

end

of

this

handout

for your convienience. Finally note that KI and KIC have dimensions of

stress

(i.e. Mpa

or ksi

).

In order to use the above criterion for fracture two conditions have to

be met. These are

(i) small scale yielding condition. All in-plane dimensions of the

component as well as the crack size should be larger than fifteen times

the critical plastic zone size (r

IC

), which is defined as

where

is the yield strength of the material.

(ii) plane strain condition. The thickness of the sample should also be

larger than fifteen times the critical plastic zone size (r

IC

).

Experimental Procedure

The ASTM standard (E399) for plane strain fracture toughness testing

provides

a

procedure

for

calculating

values

of

K

IC

for

metallic

materials.

The test permits three different specimen shapes: a bend specimen, a

C-shaped

specimen,

and

a

compact

test

specimen

(CTS).

The

CTS

will

be

used

in this laboratory.

The procedure for measuring K

IC

with a CTS is as follows:

1.

Make

a

guess

of

the

expected

value

of

K

IC

.

This

enables

you

to

calculate

an estimated critical plastic zone size.

2. To ensure that

only small-scale

yielding occurs at

the crack tip,

the

length, a, of the crack and the remaining ligament, (

W

- a), should be

greater than or equal to 15r

IC

.

a, (W - a )

IC

.

3.

To

ensure

plane

strain,

the

thickness,

B,

of

the

CTS

should

be

greater

than or equal to 15r

IC

.

B

IC

.

4.

Once

a

CTS

is

machined,

according

to

the

dimensions

calculated

above,

a sharp crack is introduced at the root of the machined notch. This is

accomplished by fatigue pre-cracking the specimen. This procedures

involves

imposing

a

time- varying

tensile

load

on

the

CTS

to

cause

a

sharp

crack to initiate and slowly grow at the root of the machined notch. The

maximum fatigue load should be less than 0.6 times the value of the

estimated final fracture load:

P

f

max

Q

.

5. The fatigue-generated protion of the crack should be at least 1.2 mm

long.

6. Once a sharp crack exists, the actual K

IC

test can be performed. The

test consists of increasing the tensile load, P, on the specimen slowly

while

measuring

the

crack

opening

displacement,

?.

Plotting

the

P

versus

? produces a curve

similar to the one shown in Figure 1. Fast fracture

is indicated by a gross nonlinearity in the load-displacement record.

7. To calculate the K

Ic

, first calculate a conditional K

Q

using

The geometric variables a, W, and B are defined in the sample schematic

in the datasheet. Determine, a, by measuring the initial crack length

(notch

plus

fatigue

pre-crack).

P

Q

is

determined

by

projecting

a

line

whose

slope is five percent less than the original slope of the P -

? curve.

P

Q

is the load corresponding to the intersection of this line with the

P -

? curve. See Figure 1.

8. The ratio P

max

/P

Q

should be less than 1.10, where P

max

is the maximum

load encountered in the test.

P

max

/

P

Q

< 1.10.

9. If condition 8 holds, then calculate

(K

Q

/

?

y)

2

. If this quantity

is less than the specimen thickness, B, the crack length, a, and the

remaining ligament (W - a), then K

Q

is equal to K

Ic

. Otherwise the test

is not a valid K

Ic

test.

Figure 1. Schematic of the typical load-COD plot obtained in a fracture

toughness experiment.

References

W.T. Matthews, Plane Strain Fractue Toughness (K

Ic

) Data Handbook for

Metals,

AMMRC

MS73-6,

U.S.

Army

Materials

and

Mechanics

Research

Center,

Watertown, MA, 1973.

Damage

Tolerant

Design

handbook,

Metals

and

Ceramics

Information

Center,

Battele Columbus Laboratories, Columbus, Ohio, 1975.

C.M.

Hudson

and

S.K.

Seward,

of

Sources

of

Fracture

Toughness

and

Fatigue

Crack

Growth

Data

for

Metallic

Alloys,

International

journal

of Fracture, V. 14, 1978, pp. R151-R184.

C. Hudson, S.K. Seward,

and Fatigue Crack Growth Data for Metallic Materials, Part II,

Frac., V. 20, 1982, pp. R59-R117.

DATA SHEET

Material:

B =

a =

PQ =

?

y=

KQ=

mm

mm

N

MPa

MPa

mm

N

Pmax =

Pmax/PQ < 1.10 ?

B, a, (w-a) >

?

y)2 ?

Invalid Test ?

(KQ /

N

MPa

Valid Test KIC = KQ =

(KQ

/

?

y)2

Pfmax =

Representative

data

for

K

Ic

for

several

metals

are

given

in

Table

1,

along

with

the

values

of

corresponding

critical

plastic

zone

sizes.

Also

include

in Table I is the crack length L* = 2a° which in a Griffith crack

configuration would cause fracture initiation at an applied stress of

(1/2)

?

y.

Note

that

L*

is

essentially

the

characteristic

length

dimension

which

specimen

crack

length,

remaining

ligament

and

thickness

must

exceed

in

order

to

obtain

a

valid

K

Ic

value

for

material.

The

combination

of

high

K

Ic

and low

?

y leads to relatively large values of critical plastic zone

size, and rather long cracks are required before initiation will occur

at stress levels which are some fraction of the general yield stress.

Table 1. Typical values of plane strain fracture toughness, K

IC

, at room

temperature (for illustration purposes only)

MATERIALS

E

?

y

K

IC

(MPa

(GPa)

(MPa)

) r

IC

(mm) L*(mm)

Steels

Medium carbon

(AISI-1045)

Pressure Vessel

(ASTM-A5330-B)

High Strength Alloy

(AISI-4340)

Maraging Steel

(250-Grade)

Aluminum Alloys

2024-T4

7075-T651

7039-T651

Titanium Alloys

Ti-6AL-4V

Ti-4Al-4Mo-2Sn-05 Si

Ti-6Al-2Sn-4Zr-6Mo

Polymers

PS

PMMA

PC

PVC

PETP

Ceramics

Si

3

N

4

SiC

Al

2< /p>

0

3

Soda-Lime Glass

Electrical Porcelain

210

210

269

483

50

153

75

74

330

503

338

34

27

32

50

72

23

945

55

88.0

16.0

256.0

0.4

0.3

1.7

0.5

1.4

0.4

0.9

0.1

6.4

14.4

1.6

27.2

8.0

22.4

6.4

4.8

210

1,593

210

1,786

72

72

72

108

108

1,020

108

1,150

3.25

3. -

4.

2.35

2.5 -

3.

3

310

410

350

73

-

0.6 - 2.3

1.2 - 1.7

2.5 - 3.8

1.9 - 2.5

3.8 - 6.1

3.4

0.7

1.

4. - 5.

3. - 5.

16. - 18.

WC - 15 wt% Co (cermet)

570