Crack Paths 2012

condition of fatigue crack growth is affected by the crack kinking angle which, in turn, is

a function of the ratio between crack length and microstructure characteristic length.

A K I N K ECDR A CIKN A S E L F - B A L A N CMEIDC R O S T R EFSISELD

Stress Field and Projected SIFs

Let us consider an infinite plate (see Figs 1 and 2, where the y-axis is a symmetry axis

)(f

)(f

along y-axis and shear stress

for the crack), submitted to remote normal stress V

W

.

Assume the existence of a self-balanced microstress field, characterized by a material

length d (for instance due to microstructural inhomogeneities, see Ref. [1]), with two

d x f V ) / (~

V

non-zero stress components: a normal stress along the y-axis

~

and a shear

a

d x f S2cos /

d x

a d x f W ) / ~(

(this

W

stress

~

. For the sake of simplicity, we assume

could be regarded as a first order approximation through Fourier series of a general periodic function), Fig. 2. Under the uniform remote stresses ) ( f V and ) ( f W , the remote

) (

f

f

l S V ) (

SIFs of the projected crack of semi-length l aligned with the x-axis are

KI

) (

l S W ) (

V~

and W~ , the micro SIFs of

and

KII

. Under the self-balanced microstresses

f f

the projected crack are shown in Ref.[12] using the Buckner’s superposition principle:

¸ ¹ · ¨ © d l J l d x x l d x x l l a l a l II a a S S S V V S 2 2 ~ 2 c ~ 2 ~ 2 ³ ³ l

K

~

(1)

S W

d x

³

³

dl

S W

S

x ldx W ~

S

~ 2

2~

l

2cos

~

¸¹·¨©§

Jl

dx

0

2

2

0

2

2

0

x l

KI

-

kII

E

KII y0

a

l

1

b

kI

2

x

KII

kII

2c

1c

kI

0 2 02

KI

Figure 1. Kinked crack in an infinite plate.

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