Fatigue Crack Paths 2003

5 illustrates the hysteresis loops of load vs. displacement and of torque vs. angle of twist

obtained under mixed-mode (I+III) loading. The crack-tip opening point was

determined from the unloading compliance method.

The mode I and mode 111 J-integral ranges, A11 and A1111, are estimated from the

loading part above the opening point by the following equations.

AKZ

r

1

A J I = T I ° f f ( l — V 2 ) - 1

[ 3 ] :P d u _ A P e f f A u _ 5 A P e f f A u e ] A ] _KIZIIeff l 3 U 9

H , - —( E+v)+27rb2 p

( )

WhereAKIeff and AKHIeff are the m o d eI and 111 effective stress intensity ranges. E is

Young's modulus, v is Poisson's ratio and b is the radius of the ligament of the

specimen. APeff, Au and Aue are also shown in Fig. 5(a), and Up is the energy

corresponding to the shaded area shown in Fig. 5(b). J-integral values for pure modeI

and III were estimated from Eqs. (8) and (9).

For the case of mixed-mode(I+III) loading, the total range AIHHI can be given as the

s u mof A11 and A1111:

AJHIII : A J I+ AJIII

(10)

In the following, w e denote AIHHIby A ]for simplicity.

Fatigue CrackPropagation

Mixed-mod featigue tests were conducted under NIH/A11: 0.5, 1, and 2 at about A ]

_5

S U S 3 1 6 N G

1 O E|||||

|

| | | | | | | | |

1 1 1 1 1 1 1 5

0)

I

-13

1.57

I

'3

- da/dN =4.25x10 A J I .

—

>I

_ _

_ _

o \

J

a 10‘6 —

I

—

2 E

’

E

"Q s - :

, I

I -

/

6“

I’

_

8 1O‘7 :—

' /

—:

g

: : _

l/

: :

.2

l

1:,

I \ _ — 0 Model

g0

-

_]3

L41 --——— I ModeIII

@- l _8 _

da/dN =7.70xl0 AJIII _ Mixedmode

@- O 5

5 A AIIH/AJ,=0.5

‘M

_ I

_

g

I U Ajlll/Ajlzl

U _

_ V AJIII/AJI=2

l 0 ‘ 6 l l é l l 3 2|

I A I I I é I é2| I Il 4z l ‘ l é 5l é l

l0

l0

l0

J-integral range, A] N / m

Figure 6. Relation between crack propagation rate and A].