Fig.: 5.1 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag,

Fig.: 5.1

Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag, Munich (2013) 2. Edition

y

z

0

mode III

N

N

B

xr

z

x

y

modeI

modeI

mode II

mode II

sN

W a

F

F/2 F/2

L/2 L/2

W = 10 mmB = 2 … 10 mmL = 80 mms = 40 … 70 mma = 0.5… 7.5 mmN = 2 mm

K = fF s

B W 3/2 W

aI

W

af = 2.9 − 4.6 + 21.8 − 37.6 + 38.7

W

a12

W

a32

W

a52

W

a72

W

a92

f = W

a

2

3

W

a1.99 − 1 − 2.15 − 3.93 + 2.7 W

a

W

a

W

a

W

a2

W

a1 −

32

W

a1+2

SENB specimen (single-edge-notched bend specimen)

Fig.: 5.2a


W

a

H/2

H/2

N

s

O D

F

F

W/2W = 40 mmH = 150 mms = 120 mmD = 10 mma = 18 … 22 mmN = 3 mmB = 2 … 10 mm

K = fF a

B W

1/2

W

aI

W

af = 1.99 − 0.41 + 18.7 − 38.48 + 53.85 W

a

W

a 2

W

a 3

W

a 4

SENT specimen (single-edge-notched tension specimen)

Fig.: 5.2b


W G

a

l

H/2

H/2

N

s

O D

F

F

W = 40 mmH = 48 mmG = 50 mms = 22 mmD = 10 mma = 18 … 22 mmN = 2 mmB = 2 … 34 mml = 1.5 mm

K = fF

B W 1/2 W

aI

W

af = 29.6 − 185.5 + 655.7 − 1017 + 638.9

W

a12

W

a32

W

a52

W

a72

W

a92

CT specimen (compact tension specimen)

Fig.: 5.2c


0 2 4 6 8 10

260

B (mm)

K

; K

(MP

amm

)240

220

200

180

160

140

120

100

cIc

1/2

a

ESZ/EDZ B

EDZ

B (mm)

K

; K

(MP

amm

)c

Ic1/

2

240

210

180

150

120

90

60

0 10 20 30

b

B (mm)

Bmin

c

Ic

K

K

IcK

cK

SENT

CTBmin

Fig.: 5.3

a

B

100 µm machined notch(razor blade notch)

stable crack growth(fracture mirror length)

damage area

residual fracture area b

Fig.: 5.4


x

rpla

y

y

Fig.: 5.5


200 µm

a b

50 µm

Fig.: 5.6


s/2

/2

2

1

f max

3

W

1 hinge point2 sharp notch3 support

1 n(W

a)

Fig.: 5.7


c

s/2

/2

stable crack growth

stretch zone brittle fracture

initial crack

SZWS

ZH

SZW

SZ

HS

ZH

x

y

1

3

2

a

b

d

100 µm

5 µm

10 µm

Fig.: 5.8


b

Ty n

x

dR

21

R

F

f resp. v

AG

a1

a2

a3

f (i=1...3)i

JI

f resp. v

f3f2f1B

AGB

a

Riss

A

Ga1

a2 a3

1

I1I2

I3

I1 I2 I3

JIcc

a

d

a

crack

Fig.: 5.9


loadingparameter

J;

technical crack initiation

physical crack initiation

stable crack growth a

a = 0.2 mmaSZW

blunting Line

crack propagation

resistance againstcrack initiation

crack blunting

crack initiation

resistance againstcrack propagation

J ; 0.2 0.2

J ; i i

Fig.: 5.10


collecting lens

junction diode

rotating mirror

start

stop

laser

deflectionmirror

semiconductorprism

F

Fmotor

v

t

evaluation andgraphics

CT specimen

Fig.: 5.11


T

F

FFQ

max

F

FQ

Fmax

S S

T

type I type II

5 % 5

%

vcvc

Fig.: 5.12

v; v ; fLv; v ; fL


0 1 2 3 4 50

1

2

3

4

5

crack initiation

a

50 µm

b

c

200 µm

1 mm

f (mm)

crack propagation

crac

k bl

untin

g

F/(

B(W

−a

)

) (N

mm

)

eff

-2

Fig.: 5.13


AG

Fmax

unnotched specimen notched specimen

A0

Fmax

F (

N)

F (

N)

Fig.: 5.14

Lmax maxL0v ; f0

Lv ; f (mm) Lv ; f (mm)

v ; f


Charpy impact testerICIT-4J

support

striker

specimen

photoopticaltransducer

deflection (f) -sensor

amplifierdigital

oscilloscope

load (F) -transducer

load–deflection diagram

analysis of F–f diagram

time resp. deflection (ms; mm)

AG = Apl + AelFmax

Fgy

F1

Apl AR

tB ; fmax fgy

loa

d F

(N

)

- checking of experimental conditions

- SEM analysis of fracture surface- fracture mechanics concept- checking of geometry- independence of fracture mechanics values

F1 < Fmax AH > 3 AGtB > 3

KId ; Id ; JId

personalcomputer

Fig.: 5.15


AG = Apl + Ael

Fmax

Fmax

FmaxFmax

Fmax

Fmax

fmax fmax fmax

fmaxfmax

fgy fgy

fgyfgy

Fgy

Fgy

Fgy

Fgy

FF

FF

AG

Apl

Ael

Ael

AG

AGAG AR AR

AR

Apl

I II III

Ia IIa IIIa

f

F

fmax

Fig.: 5.16


a/W = 0.45 a/W = 0.2

F = 36 N1

F = 28 Nmax

F = 8 N1

F = 36 Nmax

F = 8 N1

F = 62 Nmax

F = 36 N1

F = 53 Nmax

v =

1 m

sI

-1v

= 2

.9 m

sI

-1

Fig.: 5.17


F

s

L

W A

a

B

0.05 < a/W < 0.15 0.1 < a/W < 0.4 0.3 < a/W < 0.7

B

B

Fig.: 5.18


0 0.2 0.4 0.6 0.80

0.5

1.0

1.5

2.0

2.5

3.0

JBL

JFEM

JMC

JFEM

JRPM

JFEM

JFEMJST

v = 1.5 mss/W = 4

RT

I-1

PVCC

a/W

J-in

tegr

al r

atio

Fig.: 5.19


10

IcK ; K (MPamm )

Id1/2

100 1000

100

10

1

0.1

I = 3466 K-1.73

Fig.: 5.20


0.1

IcJ ; J (Nmm )

Id-1

1 100

10000

1000

100

1

10

10

I = 224 J-0.94

Fig.: 5.21


0.01

Idk [mm]

0.1 1

100

10

Idk = 3.6 -0.83

Fig.: 5.22


masses

lifting device

accelerationunit

temperature chamber

controller

dropweigth

support

clamped testsheet

F

strain gauge

instrumenteddrop weigth

cross-head

spring

Fig.: 5.23


-700

5

10

15

20

25

0 wt.-% 5 wt.-%10 wt.-%20 wt.-%25 wt.-%

PA 6 + impact modifier

-50 -30 -10 10 30 50 70 90

T (°C)

J

(N

mm

-1)

dST

Fig.: 5.24


00

v

PVC/chalkPP/chalkPVC/SiO

PE/BWPE/HP

2PE/SiO2

1

2

3

4

5

6

7

0.1 0.2 0.3 0.4

J

(N

mm

-1)

dST

Fig.: 5.25


F

(N

)m

ax

v

0 0.1 0.2 0.3 0.4

50

100

150

200

250

300

350

400

450

500

v

0 0.1 0.2 0.3 0.4

PVC/chalkPP/chalkPVC/SiO

PE/BWPE/HP

2PE/SiO2

ba

f

(mm

)m

ax

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0

Fig.: 5.26


coupling agent content (wt.-%)

0 0.25 0.50 0.75 1.00 1.25 1.50

0.8

1.0

1.2

1.4

1.6

b

2 µm5 µm

a

surfactant stearic acidJ

/J

S

T

M

Id

= 0.9 = 1.5

Fig.: 5.27


(10-3

mm

) Id

123 173 223 273 323

PVC

PVC + Kreide (jv

= 0,17)

T (K)

PVC

PVC + chalk (= 0.17)v

-150 -100 -50 0 50

T (°C)

110

100

90

80

70

60

50

40

30

20

Fig.: 5.28


0 0.1 0.2 0.3

v

c

0 0.1 0.2 0.3

v

d

0 0.1 0.2 0.3

v

b

0 0.1 0.2 0.3

200

250

300

350

400

450

v

0.30

0.35

0.40

0.45

60

90

120

150

180

210eff

1

2

3

4

5

F

(N

)m

ax

a

f

(mm

)m

axJ

(N

mm

)

Id-1

K

(M

Pam

m

)

Id1/

2

K (a )ld

0K (a )ld

Fig.: 5.29


0 0.1 0.2 0.3

; experiment

model

PE/GF

PP/GF

v

J

/JId

0

0.5

1.0

1.5

2.0

2.5M Id

Fig.: 5.30


0 0.25 0.50 0.75 1.00

coupling agent content (wt.-%)

PP + glass-fiber( = 0.13)v

0.8 mm

f

F

100 µm

100 µm

F

f

0.8 mm

100

N

100

N

0.4

0.6

0.8

1.0

1.2

A

/A

G M

R

A

/A

GRM

Fig.: 5.31


J (

Nm

m-1)

a (mm)

0 0.2 0.4 0.6 0.80

1

2

3

4

E/P copolymer + 10 wt.-% GF

with 0.4 wt.-% CA

without CA

Fig.: 5.32

CA – coupling agent content


a

(k

Jm

)-2

0 20 40 60 80 1000

20

40

60

80

100

;

with coupling agent

without coupling agent

PE content (wt.-%)

experiment

model;cN

Fig.: 5.33


0 0.2 0.4 0.6 0.8

1

3

5

7

9 TPU/ABS blends

TPU/ABS 50/50

TPU/ABS 20/80

ABS

J (

Nm

m

)-1

a (mm)

amin amax

Fig.: 5.34


J (

Nm

m

)-1

a (mm)

amin

0 0.2 0.4 0.6 0.8

4

8

12

16

T = 30 °C

A (µm)

A = 2.00 µmA = 1.45 µmA = 1.40 µmA = 1.30 µmA = 1.20 µm

0

amax

A 1.4 µmc

4

3

2

11.0 1.5 2.0

J

(N

mm

)

-10.

2Fig.: 5.35


J (

Nm

m

)-1

a (mm)

amin

0

amax

10

20

30

T = 23 °C

A (µm)0.3

10

8

6

4

2

0.6 0.9 1.2

A 0.4 µmc

A = 1.00 µmA = 0.57 µmA = 0.54 µmA = 0.40 µmA = 0.39 µmA = 0.36 µm

00.2 0.4 0.6 0.8

0

J

(N

mm

)

-10.

2

Fig.: 5.36


brittle copolymer 1

tough

high impact

500

1

2

3

4

5

6

7

T (°C)

8

6

4

2

0 1 2 3 4A/D

copolymer 1 (30 °C)copolymer 2 (20 °C)

J

(N

mm

)

-10.

2

403020100-10-20-30

0

copolymer 2

(A/D

) c

Fig.: 5.37


T (°C)

(w

t.-%

)

-80

0

20

40

60

80

100

high impact

brittle

tough

energy - determined

EP

R

-60 -40 -20 0 20 40

Fig.: 5.38

J ST Id

J 0.2


t (min)

175

Id

0

K

(M

Pam

m

)

150

125

100

75

1/2

10 20 30 40 50

w

composition 2

composition 1

Fig.: 5.39


2 µm

Fig.: 5.40


dJ

(Nm

m-1)

1.0 1.5 2.0 2.50

50

100

150

200

0 10 20 30 40 50 60

carbon black

sulfur

carbon black content (phr)

sulfur content (phr)

Fig.: 5.41


material selectiondimensioning

strength verification

> zul

strain verification

demands on technologymanufacturing monitoringunrealizable realizable

realization

fracture behavior

tough undefined brittle

Charpy impact strength

sufficient unsufficient

velocity-temperature-

shifting-conceptsufficient unsufficient

fracture mechanicsconcept

K < KI I zulor

J < J

K > K

J > JI I zul

< zul > zul < zul

I I zul

I I zul

Fig.: 5.42


Documents

Fig.: 5.1 Chapter 5: Fracture Toughness Measurements in Engineering Plastics. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Verlag,