Fatigue Crack Paths 2003

S p are elastic and plastic coefficients respectively. The work [3] contains more details

S Y i I I I T N E K , , , , , and

about the determination of these coefficients

S

i

S n

M Y Y p e I I I , ~ , ,

for the general case of mixed-mode elastic-plastic

S

I , , , Q

V

p

p

n

fracture. These coefficients are different for various geometric configurations. Thus, the

radial distance r normalized by the crack length a maybe found from relation (1) to be

M p

c

a function of the angular direction T, the material properties, the stress strain state and

the mixed-mode parameter

.

When calculating the crack growth trajectory it is necessary to distinguish the

following principal moments. Firstly, proceeding from theoretical precondition one can

estimate the crack front shape as a set of successive positions of the assumed crack tip

on its propagation trajectory, as was made by Shlyannikov and Dolgorukov [4]

2 / 1 * 1

>

@

­

' ' i i 1 sin cos 2 T S

T S

'

i i a a a a a a 2 2 i

(3)

i

i

i

° ¯ ° ®

*1

1 arcsin i

E E

i

a

i

where is crack growth direction or crack deviation angle. Secondly, in fatigue life

1iT

i N '

i a '

along its growth

calculations it is necessary to connect the crack length increment

trajectory with the corresponding number of loading cycles

.

Let in Eq. 3 have the physical sense of the fracture damage zone size G . Then i a ' i

Eq.1 can be applied to the crack path prediction for the two typical geometric

configurations containing the single-edge and the central initial cracks of length and

0 E

0 a

obliqueness

as shown in Fig.2,a and b. Crack path prediction for the mixed modes I

1 E 0r and II initial crack can be carried out making use of the following scheme. This scheme

involves replacing a bent crack with a staightline crack approximation, as shown in

Fig.2. The principal feature such modeling is determination of the crack growth

direction and definition of crack length increment in this direction. Crack may be

assumed to grow in a number of discrete steps. After each increment of crack growth,

the crack angle changes from the original angle and so does the effective length of 1 a 0 E 0 a

the crack. For the next increment of crack growth, one has to consider the new crack

length and crack angle . As shown in Fig.2, O Ais the initial crack length oriented at an angle . Let = A Bbe the crack growth ncrement for the first rowth

0 E

step. It would correspond to the fracture damage zone size. Making use of Eq.1, G and

hence

0 a G can be computed. The value is then extended along A Bwith the angle 0r

0r

whose value is determined by the crack growth direction criterion. For the single 0 T

edge crack geometry (Fig.2,a) the first step of crack growth obtained as I

and

T

0

0

sin

(4)

x

0 0 r T

, c o s

o r y

T

0 0

0